A PRECISION OPTICAL TRAPPING ASSAY:
MEASURING THE CONFORMATIONAL
DYNAMICS OF SINGLE E. COLI RECBCDHELICASES
byAshley R. Carter
B.S. & B.S.E., University of Michigan, 2002
M.S., University of Colorado, 2007

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Department of Physics
2008This thesis entitled:
A PRECISION OPTICAL TRAPPING ASSAY: MEASURING THE
CONFORMATIONAL DYNAMICS OF SINGLE E. COLI RECBCD HELICASES
written by Ashley R. Carterhas been approved for the Department of Physics

Thomas Perkins, Department of Molecular, Cellular, and Developmental Biology andDepartment of Physics (Lecturer)

Konrad Lehnert, Department of Physics

Date

The final copy of this thesis has been examined by the signatories, and we find thatboth the content and the form meet acceptable presentation standards of scholarly
work in the above mentioned discipline.

Carter, Ashley R. (Ph.D., Physics)
A PRECISION OPTICAL TRAPPING ASSAY: MEASURING THE CONFORMATIONAL DYNAMICS OF SINGLE E. COLI RECBCD HELICASES
Thesis directed by Professor Thomas Perkins, Department of Molecular, Cellular, andDevelopmental Biology and Department of Physics (Lecturer)

Helicases are enzymes that unwind double-stranded nucleic acids [e.g., deoxyribonucleic acid (DNA)]. Unwinding occurs by converting chemical energy [e.g., adenosine
triphosphate (ATP) hydrolysis] into a translocation-induced unwinding event, although
the exact mechanism of how ATP is coupled to unwinding along DNA is unknown. The
first step in understanding this mechanism is to determine the step size of movement.
Structural data suggests that the mechanical step size of unwinding is one base-pair (bp)for each ATP molecule hydrolyzed, while biochemical data suggests that the rate-limited
kinetic step size for unwinding is multiple base-pairs (∼4 bp). To address this question,
we directly measured the translocation step size of a helicase, the E. coli RecBCD helicase, using a single molecule assay. Previous single-molecule measurements of RecBCD
failed to resolve steps due to limited resolution (∼6 bp). We increased resolution to 1 bp
in a precision optical trapping assay by actively stabilizing the microscope and reducing
multiple types of trap laser noise. With this precision assay, we observed both forwards
and backwards steps that were variable in size and had an average step size of 4.4 bp.
The variability and multiple base-pair step size are in part due to ATP-independent, ±3
bp conformational dynamics in the RecBCD-DNA complex. Thus, our results support amechanism in which the RecBCD helicase has a variable step size; the average of whichquantitatively agrees with the previously determined kinetic step size.

Dedication

I would like to dedicate this thesis to my husband Greg. Only he knows the blood,
sweat, and tears that have gone into this colossal undertaking.

Acknowledgements

This work was supported by an Optical Science and Engineering Program Fellowship (a part of the National Science Foundation Interdisciplinary Graduate Education Research Traineeship), a National Physical Science Consortium Fellowship, aPhysik Instrumente NanoInnovation Grant, the National Science Foundation (Phy0404286 and Phy-1551010), a Burrows Wellcome Fund Career Award in the Biomedical
Sciences (TTP), a W.M. Keck Initiative in the RNA Sciences, and NIST.
I would like to acknowledge several parties for their support in building the
instruments. Gavin King was the chief designer and builder of the AFM experimentand was crucial in the building of the back-scattered detection experiment. In addition, Allison Churnside worked extensively on the AFM FPGA control electronics.
Early design and building of the optical tweezers instrument was carried out by Lora
Nugent-Glandorf and Amanda Carpenter. Design of the photodiode and servo electronics circuits was the work of Jan Hall and Terry Brown. Carl Sauer designed andbuilt custom electronics for detection by the quadrant photodiodes, servo systems formaintaining laser intensity, anti-aliasing filters, break-out boxes for voltage signals, andoffset amplifiers. Mike Whitmore built custom electronics for laser diode temperatureand current controllers. Dave Tegart built our power supply bin. James Fung-A-Fat
and Paul Beckingham provided advice on filtering and detection of electronic signals.
Blaine Horner, Kim Hagen, and Tracy Keep were responsible for building custom microscope parts and Hans Green machined our very intricate optical tweezers detection

vi
arm and AFM assembly. Alan Patee and Gavin King did an excellent job designing the
AFM assembly.
I would like to thank several people for support in nanofabrication of the fiducial marks. Early nanofabrication advice was given by Dan Schmidt and David Alchenberger. In addition, Theresa Ulrich and Wayne Halsey were responsible for patterning
holes on microscope cover glass and were aided by Amanda Carpenter. David Alchenberger was responsible for early fabrication of low-index glass posts, while Gavin King
helped determine protocols for fabricating low-index glass posts and was chiefly responsible for fabricating silicon disks with a shadow mask. Hern Paik aided shadow mask
development. Yeonee Seol helped make a repository of silicon disk slides.
I would like to acknowledge several people for their help in software design.
Allison Churnside designed software for FPGA control and AFM imaging along withLouisa Eberle. Gavin King helped write the AFM software, as well as software forstabilizing the sample using back-scattered detection. Yeonee Seol, Amanda Carpenter,and Lora Glandorf helped design many of the optical tweezers calibration programs.
Specific thanks to Yeonee Seol for the DNA hairpin experiment software and Amanda
Carpenter for the PZT mirror calibration software.
There are many people that helped with the biological assays. Martha Hosotani
helped perform all of the RecBCD assays and was instrumental in running the experiment. RecBCD assays on chi sites were aided by Jessica Rouge. Wayne Halsey prepared
all of the DNA and gave advice on assay preparation. Yeonee Seol prepared the DNA
hairpin assay. Hung-Wen Li and Hsiu-Fang Fan purified the biotinylated RecBCD
enzyme. Lora Nugent-Glandorf, Yeonee Seol, Amanda Carpenter, Martha Hosotani,
Justin Kuczynski, and Theresa Ulrich helped to make buffers and reagents, determine
lab protocols on surface preparation, bead preparation, bead-DNA binding, and otherassay preparations.
I would like to thank several people for their efforts on analyzing the experi-

vii
mental data. Many thanks go to Marileen Dogterom, Koen Visscher, and Ben Kalafut
for providing step finding algorithms. In addition, Martha Hosotani was very helpful inanalyzing the RecBCD data, and Betsy Siewert aided in providing early programs toanalyze DNA elasticity and length data. Andy Leifer was also helpful in programminga scaled power spectral density function. Thanks also go to the computing staff, especially James Raith and Mike Paige for keeping my computer running and Jim McKown
and Peter Ruprecht for maintaining perknas.
I would like to thank my committee members: Konrad Lehnert, Henry Kapteyn,
Margaret Murnane, and Art Pardi for reading my thesis and guiding my graduate
career. I would also like to thank other mentors who guided my research or advised
me: Meredith Betterton, David Wilson, Peter Rosenthal, Jeff Orszak, Dana Anderson,
Myron Campbell, Young-Kee Kim, Hung-Wen Li, Keith Schwab, and Mark Manheimer.
I would like to also thank my friends and family for encouragement over theyears: Lily, Nikita, Dad, Mom, Nic, Bub, Ryan, Marme, Papaw, Grandma, Grandpa,
Mum, Pop, Susan, Jimbag, Mike H., Betty, Jessica, Owen, Evan, Bill, Patricia, Meredith, Mike P., Laura, Mark, Emily, Kevin, Amanda, Marty, Martha, Allison, Keith, Juan,
Kirk, Carl, Christine, Ariel, Allison, Hern, Justin, Yeonee, Wayne, Lora, Gavin, Andy,
Julie, Vasilly, Stephanie, Adam, Jen, Janet, and of course my husband Greg.
Finally, I would like to thank the most important person in my graduate career,
my advisor Thomas Perkins. If I were to mention everything that he has done it
would probably fill my entire thesis. He has been involved in the conception, funding,
instrumental design and building, software design, biological assay development, datataking, analysis, and publication for all of my experimental results. He has mentored me
through six years of graduate school with Tuesday night experimental sessions, dinners
at the Sunflower and the Med, beer at the Sink and Catacombs, Biophysical Society
Annual Meetings, and countless hours spent rewriting all of my manuscripts. I am
grateful for his support, friendship, and understanding. Thank you Tom.

Contents

Chapter
1 Introduction

1

2 Experimental technique

13

2.1

2.2

2.3

Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.1.1

Optical trapping microscope . . . . . . . . . . . . . . . . . . . . .

13

2.1.2

Modified microscope for the AFM application . . . . . . . . . . .

18

2.1.3

Detection electronics . . . . . . . . . . . . . . . . . . . . . . . . .

23

2.1.4

Laser stabilization . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.1.5

Microscope stabilization . . . . . . . . . . . . . . . . . . . . . . .

28

2.1.6

AFM tip stabilization . . . . . . . . . . . . . . . . . . . . . . . .

31

Biological assays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.2.1

Fiducial mark fabrication . . . . . . . . . . . . . . . . . . . . . .

31

2.2.2

Sample preparation. . . . . . . . . . . . . . . . . . . . . . . . .

34

2.2.3

DNA preparation . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

2.2.4

DNA tethered particle assay. . . . . . . . . . . . . . . . . . . .

37

2.2.5

RecBCD assay . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

2.3.1

Positional calibration . . . . . . . . . . . . . . . . . . . . . . . . .

39

2.3.2

Mirror calibration . . . . . . . . . . . . . . . . . . . . . . . . . .

41

ix

2.4

2.3.3

Trap calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

2.3.4

Positional measurement . . . . . . . . . . . . . . . . . . . . . . .

45

2.3.5

DNA elasticity measurement . . . . . . . . . . . . . . . . . . . .

48

2.3.6

DNA length measurement . . . . . . . . . . . . . . . . . . . . . .

48

Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.4.1

Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.4.2

Noise determination . . . . . . . . . . . . . . . . . . . . . . . . .

50

2.4.3

Step detection . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

3 Microscope stabilization to 1 Å

53

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.2

Decreasing low-frequency laser noise . . . . . . . . . . . . . . . . . . . .

56

3.3

Increasing the sensitivity of laser-based detection . . . . . . . . . . . . .

57

3.4

Firmly coupling fiducial marks to the sample . . . . . . . . . . . . . . .

60

3.5

Active microscope stabilization . . . . . . . . . . . . . . . . . . . . . . .

62

3.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

4 Modified microscope stabilization for AFM

66

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

4.2

Increasing the sensitivity of back-scattered detection . . . . . . . . . . .

70

4.3

Active microscope stabilization using back-scattered detection . . . . . .

74

4.4

Ultrastable scanning and registration . . . . . . . . . . . . . . . . . . . .

77

4.5

Application to AFM . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

4.5.1

Measuring tip position to 0.2 Å . . . . . . . . . . . . . . . . . . .

79

4.5.2

Active stabilization achieves 0.3-Å tip stability . . . . . . . . . .

81

4.5.3

Stable AFM scanning and registration . . . . . . . . . . . . . . .

83

4.5.4

Stable AFM imaging . . . . . . . . . . . . . . . . . . . . . . . . .

85

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

4.6

x
5 Precision optical trapping assay sensitive to Ångstrom-scale motion

90

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

5.2

Noise in optical trapping assays . . . . . . . . . . . . . . . . . . . . . . .

92

5.2.1

Thermal noise. . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

5.2.2

Surface noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

5.2.3

Laser noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

5.3

Stabilizing trap laser noise . . . . . . . . . . . . . . . . . . . . . . . . . .

96

5.4

Ångstrom-scale tracking of trapped bead motion . . . . . . . . . . . . .

97

5.5

Stability and resolution of 1-bp along DNA . . . . . . . . . . . . . . . .

99

5.6

Precision force control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.7

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6 Conformational dynamics of the RecBCD-DNA complex

107

6.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6.2

Discrete motion along DNA . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.3

Conformational dynamics in the RecBCD-DNA complex . . . . . . . . . 110

6.4

Conformational dynamics were ATP-independent . . . . . . . . . . . . . 117

6.5

Conformational dynamics were DNA sequence-dependent . . . . . . . . 120

6.6

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7 Conclusions

126

Bibliography

128

Appendix
A Acronym Index

139

B Variable Index

142

xi
C Software Index

148

C.1 Optical trapping experiment . . . . . . . . . . . . . . . . . . . . . . . . . 148
C.2 AFM experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
D Hardware Index

160

E Protocol Index

209

E.1 Potassium hydroxide-clean cover slips . . . . . . . . . . . . . . . . . . . 209
E.2 Piranha-clean cover slips . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
E.3 Affix stuck beads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
E.4 Fabricate HSQ fiducial marks . . . . . . . . . . . . . . . . . . . . . . . . 212
E.5 Fabricate silicon fiducial marks . . . . . . . . . . . . . . . . . . . . . . . 213
E.6 Fabricate etched holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
E.7 Prepare DNA tethered particle assays . . . . . . . . . . . . . . . . . . . 216
E.8 Prepare RecBCD assays . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
E.9 How to guide: thermal evaporator . . . . . . . . . . . . . . . . . . . . . 220
E.10 How to guide: scanning electron microscope . . . . . . . . . . . . . . . . 221
E.11 How to guide: fiber alignment . . . . . . . . . . . . . . . . . . . . . . . . 224
E.12 How to guide: intensity servo tuning . . . . . . . . . . . . . . . . . . . . 229

xii

FiguresFigure1.1

DNA structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.2

Models of DNA unwinding . . . . . . . . . . . . . . . . . . . . . . . . . .

7

1.3

RecBCD structure and function . . . . . . . . . . . . . . . . . . . . . . .

9

1.4

Precision optical trapping assay to measure RecBCD motion . . . . . .

11

2.1

Diagram of the optical trapping microscope . . . . . . . . . . . . . . . .

15

2.2

Pictures of the optical trapping microscope . . . . . . . . . . . . . . . .

16

2.3

Diagram of the atomic force microscope . . . . . . . . . . . . . . . . . .

20

2.4

Pictures of the atomic force microscope . . . . . . . . . . . . . . . . . .

21

2.5

Quadrant photodiode circuit. . . . . . . . . . . . . . . . . . . . . . . .

24

2.6

Diagram of laser stabilization and performance . . . . . . . . . . . . . .

26

2.7

Picture of the laser stabilization . . . . . . . . . . . . . . . . . . . . . . .

26

2.8

Diagram of microscope stabilization . . . . . . . . . . . . . . . . . . . .

29

2.9

Fiducial mark fabrication . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2.10 DNA constructs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

2.11 Position calibration curves . . . . . . . . . . . . . . . . . . . . . . . . . .

40

2.12 Trap calibration is sensitive to polarization . . . . . . . . . . . . . . . .

44

2.13 Trap calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

2.14 Window type affects data smoothing. . . . . . . . . . . . . . . . . . . . .

51

xiii
3.1

Basic principle of microscope stabilization. . . . . . . . . . . . . . . . . .

55

3.2

Sensitivity of vertical signals . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.3

Fiducial mark movement . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

3.4

Fabricated fiducial mark signals . . . . . . . . . . . . . . . . . . . . . . .

63

3.5

Microscope stabilization to 1 Å . . . . . . . . . . . . . . . . . . . . . . .

64

4.1

One motivation for an ultrastable AFM . . . . . . . . . . . . . . . . . .

68

4.2

Basic principle of AFM stabilization . . . . . . . . . . . . . . . . . . . .

69

4.3

Back-scattered signals . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

4.4

Ångstrom-scale microscope stabilization using BSD . . . . . . . . . . . .

75

4.5

Stabilized microscope scanning using BSD . . . . . . . . . . . . . . . . .

78

4.6

Ångstrom-scale microscope registration using BSD . . . . . . . . . . . .

80

4.7

AFM tip signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

4.8

Ångstrom-scale AFM tip control . . . . . . . . . . . . . . . . . . . . . .

84

4.9

AFM scanning and registration . . . . . . . . . . . . . . . . . . . . . . .

86

4.10 Ultrastable AFM imaging . . . . . . . . . . . . . . . . . . . . . . . . . .

87

5.1

Intensity noise affects optical trapping . . . . . . . . . . . . . . . . . . .

95

5.2

Reduction of intensity noise . . . . . . . . . . . . . . . . . . . . . . . . .

98

5.3

Precise tracking of trapped bead position . . . . . . . . . . . . . . . . . 100

5.4

Positional stability of 1 bp along DNA . . . . . . . . . . . . . . . . . . . 102

5.5

Resolution of 1 bp steps along DNA . . . . . . . . . . . . . . . . . . . . 103

5.6

DNA hairpin unfolding dynamics show need for force precision . . . . . 105

6.1

RecBCD motion shows forward, backward, and variably sized steps . . . 111

6.2

RecBCD motion shows ±3 bp fluctuations . . . . . . . . . . . . . . . . . 113

6.3

Fluctuations are conformational dynamics in the RecBCD-DNA complex 114

xiv
6.4

Conformational dynamics were ATP-independent and occur when RecD
is engaged . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

6.5

Conformational dynamics were force-dependent . . . . . . . . . . . . . . 118

6.6

Conformational dynamics are independent of changes in the ATP-bindingsite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.7

Type II conformational dynamics were dependent on ATP but were notstudied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.8

Conformational dynamics are dependent on the upstream double-stranded
DNA sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

D.1 Building the microscope part 1. . . . . . . . . . . . . . . . . . . . . . . . 161
D.2 Building the microscope part 2. . . . . . . . . . . . . . . . . . . . . . . . 162
D.3 Building the microscope part 3. . . . . . . . . . . . . . . . . . . . . . . . 163
D.4 Building the microscope part 4. . . . . . . . . . . . . . . . . . . . . . . . 164
D.5 Building the microscope part 5. . . . . . . . . . . . . . . . . . . . . . . . 165
D.6 Building the diode laser system part 1. . . . . . . . . . . . . . . . . . . . 166
D.7 Building the diode laser system part 2. . . . . . . . . . . . . . . . . . . . 167
D.8 Building the diode laser system part 3. . . . . . . . . . . . . . . . . . . . 168
D.9 Microscope base plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
D.10 Condenser arm focusing plate adapter. . . . . . . . . . . . . . . . . . . . 170
D.11 Condenser arm focusing plate spacer. . . . . . . . . . . . . . . . . . . . . 171
D.12 Detection mount off condenser arm. . . . . . . . . . . . . . . . . . . . . 172
D.13 Detection mount off condenser arm picture. . . . . . . . . . . . . . . . . 173
D.14 Upside down lens adaptor plate part 1. . . . . . . . . . . . . . . . . . . . 174
D.15 Upside down lens adaptor plate part 2. . . . . . . . . . . . . . . . . . . . 175
D.16 Upside down lens adaptor plate part 3. . . . . . . . . . . . . . . . . . . . 176
D.17 Microscope bridge plate part 1. . . . . . . . . . . . . . . . . . . . . . . . 177

xv
D.18 Microscope bridge plate part 2. . . . . . . . . . . . . . . . . . . . . . . . 178
D.19 Microscope bridge plate part 3. . . . . . . . . . . . . . . . . . . . . . . . 179
D.20 Microscope bridge plate part 4. . . . . . . . . . . . . . . . . . . . . . . . 180
D.21 Microscope bridge plate part 5. . . . . . . . . . . . . . . . . . . . . . . . 181
D.22 Objective holder part 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
D.23 Objective holder part 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
D.24 Riser for 733.3D Physik Instrumente stage. . . . . . . . . . . . . . . . . 184
D.25 Microscope dichroic holder part 1. . . . . . . . . . . . . . . . . . . . . . 185
D.26 Microscope dichroic holder part 2. . . . . . . . . . . . . . . . . . . . . . 186
D.27 Microscope dichroic holder part 3. . . . . . . . . . . . . . . . . . . . . . 187
D.28 Microscope camera mount.

. . . . . . . . . . . . . . . . . . . . . . . . . 188

D.29 Color filter holder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
D.30 Lens mount. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
D.31 Mercury lamp to liquid light guide mount part 1. . . . . . . . . . . . . . 191
D.32 Mercury lamp to liquid light guide mount part 2. . . . . . . . . . . . . . 192
D.33 Mercury lamp to liquid light guide mount part 3. . . . . . . . . . . . . . 193
D.34 Mercury lamp to liquid light guide mount part 4. . . . . . . . . . . . . . 194
D.35 Mercury lamp to liquid light guide mount part 5. . . . . . . . . . . . . . 195
D.36 Mercury lamp to liquid light guide mount part 6. . . . . . . . . . . . . . 196
D.37 Mercury lamp to liquid light guide mount picture. . . . . . . . . . . . . 197
D.38 Gimbal mirror mount part 1. . . . . . . . . . . . . . . . . . . . . . . . . 198
D.39 Gimbal mirror mount part 2. . . . . . . . . . . . . . . . . . . . . . . . . 199
D.40 Fiber launch to 3D translation stage adaptor. . . . . . . . . . . . . . . . 200
D.41 Double dichroic mount part 1. . . . . . . . . . . . . . . . . . . . . . . . . 201
D.42 Double dichroic mount part 2. . . . . . . . . . . . . . . . . . . . . . . . . 202
D.43 Double dichroic mount part 3. . . . . . . . . . . . . . . . . . . . . . . . . 203
D.44 Double dichroic mount part 4. . . . . . . . . . . . . . . . . . . . . . . . . 204

xvi
D.45 Double dichroic mount part 5. . . . . . . . . . . . . . . . . . . . . . . . . 205
D.46 Double dichroic mount part 6. . . . . . . . . . . . . . . . . . . . . . . . . 206
D.47 Intensity servo electronic diagram. . . . . . . . . . . . . . . . . . . . . . 207
D.48 Intensity servo picture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
E.1 Scanning electron microscope display and controls . . . . . . . . . . . . 225
E.2 Scanning electron microscope column . . . . . . . . . . . . . . . . . . . . 226
E.3 Scanning electron microscope auxiliary control panel . . . . . . . . . . . 227
E.4 Scanning electron microscope primary control panel . . . . . . . . . . . 228

Chapter 1

Introduction

Helicases are ubiquitous enzymes that are present in almost every cellular process
involving nucleic acids, either DNA (deoxyribonucleic acid) or RNA (ribonucleic acid)[65, 93, 111]. As an initial step in nucleic acid metabolism, helicases must unwind
double-stranded nucleic acids into their constituent single strands by translocating along
the nucleic acid template and disrupting the bonds between the two strands. Helicase
research has focused on answering the basic scientific question of how these enzymes
are able to convert chemical energy into the mechanical work of movement and strand
separation [65, 66, 93, 111]. This is often difficult due to the exquisitely small movementsof helicases, Ångstroms to nanometers [3, 19, 24, 28, 30, 61, 68, 67, 83, 109, 125, 142],
and the monumental task of synchronizing an ensemble of helicases to measure the timedependent process of chemical energy conversion to movement [12]. With the adventof single-molecule studies in the last fifteen years, the dynamics of unwinding can betracked in individual helicase molecules [19, 28, 83], removing the need for synchronicity.
Plus, in the last three years, the tracking of single molecules has reached the Ångstromscale [1, 76, 83], making it the right time to answer this basic scientific question. Our
research focuses on directly measuring the unwinding of DNA by the RecBCD helicase
found in E. coli using a precision optical trapping assay. These measurements offer
insight into the mechanism of helicase unwinding and shed light on the first steps ofmany DNA processes.

2
While the double helix structure of DNA allows for stable packaging of the
genome, this double helix must be unwound into its two complementary strands for
any DNA metabolism to occur [65, 93, 111]. DNA structure has four bases (cytosine,
C; guanine, G; adenine, A; and thymine, T) that are linked into strands via a backboneof alternating deoxyribose sugars and phosphate groups (Fig. 1.1). This backbone isantisymmetric such that the 3’ end of DNA has a terminal hydroxyl group from a deoxyribose sugar ring while the 5’ end terminates with a phosphate group. The strands
are joined through multiple hydrogen bonds in Watson-Crick, complementary base-pairs(A with T, 2 hydrogen bonds; G with C, 3 hydrogen bonds) to form the double helix.
The sequence of bases forms a genetic “code” that gives instructions on how to build
proteins. The code is “read” when (i) DNA is copied into RNA in transcription and (ii)the RNA is translated into a sequence of amino acids, the building blocks of proteins,during translation. To pass along the genetic code, DNA undergoes replication, where
the double-stranded DNA molecule is copied to form two double-stranded molecules.
Processing also occurs during repair or in recombination, a pathway that allows for the
breakage and rejoining of two double-stranded DNA molecules such that genetic information can be swapped or double-stranded breaks can be repaired. During all of theseprocesses the double helix of DNA must be unwound to expose the underlying bases.
Helicases are enzymes that unwind either DNA or RNA by translocating along thenucleic acid and disrupting the hydrogen-bonding of the base-pairs [41, 65, 66, 93, 111];
as such, helicases are employed in almost every process in the cell that involves nucleic acids, from transcription and translation to DNA recombination [65]. This highly
diverse functionality leads to a number of mechanistic and structural differences between helicases. Helicases bind to various substrates (single- or double-stranded, RNA
or DNA), move along the nucleic acid in different directions (3’ to 5’ or 5’ to 3’), andbelong to one of six structural super families (SF1-SF6) [38, 111]. SF1 and SF2 helicases
are structurally similar and contain two “RecA-like” folds, while SF3-SF6 helicases are

3

Figure 1.1: DNA structure. Two DNA strands are twisted together to form a double
helix. Each strand contains nitrogenous bases and a backbone of repeating sugar andphosphate groups. Strands are held together through weak hydrogen bonding of thebases that must be disrupted for unwinding to occur. Figure credit: adapted from theU. S. National Library of Medicine.

4composed of six “RecA-” or “AAA+ -like” folds that form a hexameric ring. Additionally, within each super family there are further structural motifs that subdivide them.
However, in all cases helicases are motor proteins that convert chemical energy fromthe hydrolysis of a nucleoside triphosphate, generally adenine triphosphate (ATP), intomechanical work, which both translocates the helicase and unwinds the nucleic acid duplex. This leads to several structural similarities among the super families, termed core
domains [111]. These core domains consist of a pocket for the binding and hydrolysis of
the nucleoside triphosphate and an “arginine finger” for coupling of chemical energy intoa physical conformational movement of the enzyme. The differences between helicases
support the diverse functionality needed for nucleic acid metabolism, while the helicase
similarities allow for the coupling of chemical energy into the unwinding of the nucleic
acid duplex.
An important and basic question in helicase research is how helicases convert
chemical energy from ATP hydrolysis into a translocation along the nucleic acid [65,66, 93, 111]. Since we are interested in this question as it applies to the SF1 helicase,
RecBCD, we will focus on SF1 or SF2 helicases moving along DNA. Previously, x-ray
crystallography has been used to observe helicase-DNA complexes in different stagesof ATP hydrolysis. In this way these structural studies have postulated a 1 basepair (bp, 3.4 Å) movement of the helicase along the DNA given the hydrolysis of one
ATP molecule [13, 61, 125, 141]. This movement per ATP is the mechanical step
size. Additionally, biochemical assays have been used to measure the kinetically ratelimited translocation step by synchronizing an ensemble of helicase molecules moving
along DNA. This rate-limited translocation is the kinetic step size. Under conditions
where ATP is rate-limiting one would expect that the rate-limited translocation and thetranslocation per ATP would be the same; that is to say the kinetic step size would equal
the mechanical step size of 1 bp. However, measurements of the kinetic step size in these
conditions have yielded multiple base-pair steps, typically ∼4 bp [24, 28, 68, 67, 124].

5
Thus, there is a conundrum in the field as to why the ATP-limited kinetic step size does
not correspond to the mechanical step size.
Currently, there are two leading models to explain the observed data [66]: theinchworm model [124] and the Brownian ratchet model [62]. In the inchworm model,
there are multiple ATP hydrolysis events that rapidly occur before a slower, rate-limited
process moves the helicase by the same multiple of base-pairs, allowing for a mechanicalstep size of 1 bp and a multiple base-pair kinetic step size. The model is termed
inchworm because it assumes that the rapid ATP hydrolysis events move one section of
the helicase along the DNA by 1 bp until the tension in the helicase allows for a large
conformational change that moves the rest of the molecule. There is some evidence forthis model. The SF1 helicase, UvrD, has a kinetic step size of 4 bp with 4 ATP hydrolysis
events per step [124], and the SF2 helicase, NS3, has a 3 bp rate-limited translocation
step with 3 faster kinetic steps per rate-limited step [83]. In the other leading model,
the Brownian ratchet model, the helicase weakly binds the DNA when bound to ATP
and moves forward when thermal fluctuations disrupt the hydrogen bonds between the
DNA bases. Once forward, ATP is hydrolyzed and the helicase tightly binds the DNA
preventing the rebonding of the bases. In this model the energy from ATP hydrolysis
and the thermal bath are used to affect movement, allowing for a multiple base-pairkinetic step size. This model was proposed after the SF2 helicase, NS3h, was shownto unwind several base-pairs without ATP [62]. While other models are conceivable toexplain the observations, these two models are the most popular.
All of the models that explain helicase unwinding can be classified as either activeor passive [66]. Generally, one might think that an active helicase is an enzyme thatuses ATP, while a passive helicase does not require an energy source, but since allhelicases require a nucleoside triphosphate for unwinding to occur, active and passive
have taken on different meanings. An active helicase uses a mechanism to actively
melt the bonds between base-pairs while a passive helicase is an enzyme that waits for6thermal fluctuations to open the bonds (Fig. 1.2). In this terminology, the inchworm
model is an example of an active helicase model, and the Brownian ratchet model is an
example of a passive helicase model.
Our goal was to measure DNA unwinding by a particular helicase, RecBCD, anddetermine which model, if any, best describe RecBCD unwinding. More specifically,
we measured the translocation step at rate-limiting ATP concentrations using a singlemolecule technique [15]. By observing translocation at rate-limiting ATP we hoped
to confirm or refute previous data showing multiple base-pair steps. By using a singlemolecule technique we could directly measure RecBCD movement without synchronizing
an ensemble of helicases and without measuring an average translocation. Both theprevious structural and biochemical studies measure an ensemble of molecules and arelimited to an average measurement. Averages in populations are sometimes misleading
because they smear out dynamic fluctuations, obscure multimodal behavior, and maskrare but interesting events [12]. A direct measurement of RecBCD motion revealed theactual kinetic step size and suggested a model to reconcile the structurally determinedmechanical step size with biochemical measurements.
In addition, measurements of RecBCD gave us insight into how a complex protein
processes DNA. RecBCD is a multifunctional enzyme in E. coli responsible for bothexcising foreign DNA and repairing double-stranded DNA breaks through the DNA
recombination pathway [56, 59, 112]. When RecBCD binds blunt end DNA, it uses its
helicase function to unwind the DNA while digesting the double-strands with a nuclease
until it recognizes a specific sequence only present in E. coli DNA, the chi site (Fig. 1.3
A). During chi site recognition the enzyme pauses [114], then after chi recognition it
switches tasks from that of foreign DNA excision to DNA repair. The helicase slows
down, the nuclease cleaves only one strand, and the enzyme begins to load the protein
RecA to form a filament that is targeted for DNA recombination [110, 114]. This
complex function leads to a complex structure (Fig. 1.3 B). RecBCD is a heterotrimer

7

Figure 1.2: Models of DNA unwinding. In an active unwinding model the helicase opens
the DNA bonds, while in a passive unwinding model thermal energy disrupts bonding
between the two strands.

8with two motor domains, RecB and RecD, that translocate along opposite polarity
DNA strands and are each SF1 helicases [110]. Unlike other motor protein domains
which generally work together to move the enzyme, RecB and RecD are decoupled fromone another and move at different rates [25, 26, 122]. Before chi recognition RecD isfaster, and thus the lead helicase, whereas after chi recognition RecB is faster [122]. The
RecC subunit is intimately coupled to RecB and contains the domain for chi recognition
along with a “pin” structure that contacts the double-stranded DNA [110]. The nucleasedomain is found in the RecB subunit [110]. This complex structure allows for one of thehighest unwinding rates, 1 kbp/s, and processivities (number of base-pairs unwound ina single binding event), 36–48 kbp, though the reason for both are unknown [66]. Future
direct measurements of RecBCD movement may elucidate this functional behavior of
the enzyme.
To directly measure single-molecule RecBCD motion, we used a precision opticaltrapping assay (Fig. 1.4) [18]. Previous measurements of individual RecBCD molecules
using optical trapping techniques were limited by a 20-Å resolution [96]. In the previous
experiment, a DNA molecule (∼2.4 µm) was stretched between two points: a RecBCD
helicase biochemically linked to the surface and a micron-sized polystyrene bead. Beadposition relative to the trap center was measured by a detection laser. As RecBCD
unwound the DNA, the bead was pulled toward the helicase and the corresponding
bead motion was used to calculate the change in DNA length. Since step sizes in DNA
length could be as small as 1 bp or 3.4 Å, we needed to reduce the 20-Å noise in theassay. There were three main sources of noise. The first source of noise was Brownian
motion of the bead, which has a zero-mean, and therefore, can be averaged away given
enough time [18, 94]. The second source of noise was microscope drift between thesurface (where RecBCD is attached) and the objective (which controls movement of
the optical trap, and thus, the bead) [89]. To reduce this surface-based noise, we
actively stabilized the microscope to 1 Å in 3D (bandwidth, ∆f = 1–25 Hz) [17] by9Figure 1.3: RecBCD structure and function. (A) RecBCD is a complex helicase built forprocessing double-stranded DNA breaks in E. coli . When RecBCD binds a blunt DNA
end, it unwinds and digests the double-stranded DNA until it reaches a specific sequence
only present in E. coli DNA, a chi site (χ). After chi site recognition, RecBCD slows
down, deregulates DNA digestion, and loads RecA. (B) To perform these complicatedtasks RecBCD has two helicase motor domains, one in the RecB subunit and the otherin RecD that bind the DNA with opposite polarity and move at different speeds. The
RecC subunit contains a ”pin” structure which contacts the double-stranded DNA andacts as the separation point for the duplex. RecC also has the amino acids that recognize
the chi site. RecB contains the nuclease domain that digests the DNA. Figure adaptedfrom Singleton et al. [110].

10measuring the position of a fiducial mark on the surface (fabricated post) and using
this position in a feedback loop to the stage controller to keep fiducial mark position(and hence surface position) constant [17, 16]. Finally, the last source of noise was thelasers. Pointing instability causes a movement of the trapped bead with respect to thedetection laser and intensity noise in the trap causes both movement of the trapped
bead, if under load, and fluctuations in the force on the bead [18]. To counteract laser
noise, we also used an active stabilization technique that reduced pointing instability to
0.5 Å (rms, ∆f = 0.03–100 Hz) and intensity noise to ∼0.01% (rms, ∆f = 0.2– 2000
Hz) [18]. The resulting optical trapping assay with both surface and laser stabilization
was capable of resolving 1 bp motions along DNA [18]. In comparison with other highresolution techniques [1, 76], this method is surface-coupled for easier assay development,
reduces fluctuations in force, and allows for high-resolution positional data after force
perturbations.
Using this precision optical trapping assay we were able to measure RecBCD
motility with sub-nanometer resolution. We observed that RecBCD moved both forward and backward at low ATP concentrations. Steps were variably sized with anaverage step of 4.4 bp, agreeing with the previously measured biochemical kinetic step
size of 4 bp [68, 67]. In addition, there were large (±3 bp) fluctuations that occurred at
higher frequencies than RecBCD stepping. These fluctuations were ATP-independent
and were only present when single-stranded DNA engaged the RecD helicase, indicating that the fluctuations were actually conformational dynamics of the RecBCD-DNA
complex. RecBCD-DNA conformational dynamics were not affected by the presence ofan ATP-analog or mutations in the ATP-binding pocket, suggesting that the conformational dynamics are not movements within the enzyme of the ATP-binding pocket.
However, the conformational dynamics were dependent on the sequence of the upstream
base-pairs, indicating that RecBCD is interacting with the upstream double-stranded
DNA in the absence of ATP and unwinding it. The different conformations are then11

Figure 1.4: Precision optical trapping assay to measure RecBCD motion. A DNA
molecule is stretched between the RecBCD helicase and an optically trapped bead.
One detection laser (pink) measures the bead position (xbd ), which is used to calculate
DNA length. The other detection laser (green) measures the position of a fiducial mark(xfid ), which is used to stabilize the surface. The trap laser (not shown) is also stabilized
to reduce multiple types of laser noise.

12translocations of RecBCD along the DNA template even in the absence of ATP. These
data suggest a model for helicase movement where the enzyme is able to move in multiple base-pair steps without ATP and uses the chemical energy of ATP to drive forward
motion. Thus, our findings are consistent with helicase models with large multi-basepair steps [66], but not with models that require an ATP-rate-limited, translocational
step size of 1 bp [13, 61, 125].
Further explanation for these findings can be found in the remaining pages of the
document. The general experimental technique for building the instrument, preparing
the biological assay, taking the data, and analyzing the output traces can be found in
Ch. 2. In Ch. 3, active stabilization of the microscope to 1 Å is discussed and closely
follows the publication in Applied Optics by Carter et al. [17]. A modified version of thisstabilization technique can be used to stabilize an atomic force microscope (AFM). This
diversion from the main topic is dealt with in Ch. 4 and closely follows the publication
in Optics Express by Carter et al. [16] and the submitted work by King, Carter et al.
[51]. In Ch. 5, we discuss active stabilization of the trap laser to ∼0.01% and theapplication of both trap and microscope stabilization to an optical trapping assay. The
result is a precision optical trapping assay sensitive to 1 bp motion along DNA. This
chapter closely mimics the submitted work by Carter et al. [18]. The last topic coveredin Ch. 6 is measurements of RecBCD movement and conformational dynamics, whichdraws from information in the prepared work by Carter et al. [15].

Chapter 2

Experimental technique

One of the most important themes in this work is that by actively stabilizing boththe microscope and the lasers we can achieve Ångstrom-scale sensitivity in an opticaltrapping experiment. Moreover, it is this active stabilization that allows for precision
studies of the RecBCD helicase and gives rise to an ultrastable AFM. In this chapter wedetail the experimental techniques of these stabilized assays: the optics and electronics
that make up the instruments (Section 2.1), the preparation of the biological samples(Section 2.2), the software routines for data collection (Section 2.3), and the methods
to analyze the data (Section 2.4).

2.1

Instruments

2.1.1

Optical trapping microscope

Our highly stable optical-trapping system, based on earlier work [17, 89], consistedof a high-powered, neodymium-doped yttrium orthovanadate crystal laser (SpectraPhysics, Millennia IR, 10 W, λ = 1064 nm) for trapping and two diode lasers (Blue Sky
Research, VPSL, 50 mW, λ = 785 nm and 850 nm, line width = ∼0.5 nm FWHM) for
detecting bead motion and stage drift (Fig. 2.1 and Fig. 2.2). All three lasers were
coupled into the microscope (Nikon, TE-2000) using dichroic mirrors (Chroma) andfocused by a high numerical aperture objective (Nikon, PlanAPO-100X-IR, numericalaperture = 1.4). In the image plane, the two diode lasers were positioned so as to scatter14
light off either a fiducial mark or an optically trapped bead. Both the forward-scattered
light and the incident beams were collected by the condenser and were imaged onto
a quadrant photodiode (QPD, PerkinElmer Optoelectronics, YAG-444-4A) to detect
position [100, 128]. The lasers were separately translated in the image plane by piezoelectric, lead zirconate titanate (PZT) mirrors (Physik Instrumente, S-330.2SL) thatwere placed in a conjugate plane to the back-focal-plane of the objective. Pure rotationsin this plane lead to pure translations in the image plane. We translated the sample
using a 3D, closed-loop PZT stage (Physik Instrumente, P517.3CD). This instrument
was also used to stabilize a microscope to 1 Å (see Ch. 3). In this incarnation, both ofthe diode lasers measured stage drift, while the trap laser was not used.
The apparatus was designed to both passively and actively minimize mechanical,
thermal, and laser noise. The trap laser head was mounted on a research-grade optical
table (TMC), while the diode pump lasers were housed in a different room to minimize
acoustical and thermal noise. The fan in the trap laser head unit was disabled andreplaced with an always-on, ducted, 18.6-L/s fan to reduce 0.4-Hz intensity noise causedby transient heating of the neodymium-doped yttrium orthovanadate crystal. The diodelasers were both current and temperature stabilized. The current controller electronics
consisted of a proportional-integral servo controller capable of 25 ppm/ ◦ C at 137 mA,
5 VDC (similar to 505B, Newport). Diode laser temperature controller electronics
consisted of a proportional-integral-differential servo controller capable of ±1 millidegree
at ±2 A, 6 VDC (similar to 350B, Newport). The temperature controller variables wereset by the Ziegler-Nichols closed-loop tuning method [143]. All three lasers were actively
stabilized (see Section 2.1.4) to reduce pointing, mode, polarization, and intensity noise.
We passed each laser through an acousto-optic modulator (AOM; Isomet, 1205C-2,
lead molybdate crystal) to modulate intensity; a single-mode, polarization-maintaining
fiber (OZ optics, SMJ-A3A4P-3S-1064-6/125-3AS-3-1) and a polarizing beam splitter(Newport, 10FC16PB) to convert pointing, mode, and polarization noise into intensity

15

Figure 2.1: Diagram of the optical trapping microscope. The trap laser (TL) andtwo diode lasers (DL, λ = 785 nm and 850 nm) were actively stabilized (see Section
2.1.4) by a feedback loop using an acousto-optic modulator (AOM). All three lasers
were then coupled into the microscope via dichroic mirrors and were focused by theobjective (Obj). In the image plane (black box), the two diode lasers scattered off eithera fiducial mark or an optically trapped bead, and the forward scattered light was imaged
onto a quadrant photodiode (QPD). Each laser was independently translated in theimaging plane by mirrors in a plane conjugate to the back-focal-plane of the objective.
Acronyms represent the following: polarizing beam splitter (PBS), optical isolator (OI),
photodiode (PD), piezo-electric (PZT, lead zirconate titanate), half-wave plate (λ/2)
and beam sampler (BS). Blue-shaded components and green-shaded components are in
optically conjugate planes.

16

Figure 2.2: Pictures of the optical trapping microscope. Top. Optical trapping instrument. Middle. Zoom-in of the microscope and detector arm. Bottom. Zoom-in of thelaser optics before the microscope.

17
noise; a beam sampler (Newport, 20B10NC) and photodiode to measure the intensity;and an electronic feedback loop to the AOM to minimize the resulting intensity noise.
We improved the mechanical stability of the microscope by stiffening the condenser
pillar with an aluminum trapezoid (12.5-mm thick). Also, the objective and stage were
mounted with custom-built monolithic parts, and the whole apparatus was mounted
on a research-grade optical table, separate from the trap laser. Cables to and fromthe microscope were stress-relieved using monolithic mounts, and multiple cables weretied together to increase stiffness. We supported the detection optics directly off thevertical condenser pillar with a 0.15-m cage assembly. Thermal noise was reduced bycoupling the lamp to the microscope with a liquid light guide (Roffin, 3-mm diameter).
To minimize laser noise, optics external to the microscope were mounted on 38-mmdiameter monolithic posts (where possible), enclosed in a box, and the beam path was
further enclosed in 25-mm-diameter tubing (where possible). We also reduced the beam
path length before the microscope to ∼1 m. Measurements were made in an acousticallyquiet (NC30), temperature-regulated room (±0.2 ◦ C). For a detailed list of custom parts
see Appendix D.
Vibrational testing suggested that the current limitations in the mechanical stability of our system are the fiber launches and the QPDs. In vibrational testing, theposition of a fiducial mark was measured (see Section 2.3.4) as different optical or mechanical components were tapped lightly by hand. In general, the system was passively
reducing enough noise if tapping did not create more than 2-nm spikes at 100 Hz. For
this test, a normal noise level was 0.2 nm peak-to-peak at 100 Hz for the lateral directions and 0.5 nm peak-to-peak at 100 Hz for the axial direction. Components that show
larger noise levels than 2 nm needed to be mechanically tightened or stress-relieved.
After vibrational testing, the system needed to mechanically settle (usually over a dayor so) before actual measurements could be made. For the optical trapping microscope,
the main sources of noise were the fiber launches and the QPDs. The fiber launch sta-

18
bility directly couples into the pointing stability of the laser, and the QPD is held by along attachment to the condenser lens (see Appendix D) creating unwanted motion. To
improve the optical design of these components in the AFM application, we switched toa back-scattered detection (BSD) scheme with the QPDs firmly mounted to the optical
table, removing the need for optics attached to the condenser lens. We also launchedboth lasers from the same fiber (see Section 2.1.2), increasing the differential pointing
stability.

2.1.2

Modified microscope for the AFM application

We modified our general microscope design for the AFM application (Fig. 2.3
and Fig. 2.4). In the optical trapping microscope we detected forward-scattered light,
however this detection scheme is not compatible with AFM due to limited or poor
quality optical access opposite of the imaging objective. BSD, initially demonstrated
over 10 years ago for optically trapped beads [33], is a viable alternative. In our BSD
setup, two stabilized diode lasers (see Section 2.1.4; Lumics, ∼100 mW, λ = 810 nm
and 845 nm) were focused at the image plane and the back-scattered light was collectedusing a single, high numerical aperture objective. BSD often suffers from inefficientuse of light (0.02-0.1%) [44], with prior work separating BSD signals from the incident
light via partially reflective mirrors that decreased the power of both the incident andback-scattered light [44, 50, 49]. While increasing the laser power would increase theamount of back-scattered light, a low laser power minimizes potential perturbation in
future applications. For instance, in an application involving AFM where we want tomeasure the position of a metal-coated cantilever in vacuum, deflection due to laser
heating can be substantial ( 1 nm/µW) [4, 6]. Thus, we sought to minimize laser noise
while maximizing the efficiency of photon collection. To do so, both lasers were directed
into the back of the microscope objective using a dichroic mirror [17]. Efficient collectionof the back-scattered signal was achieved using an optical isolator, which consisted of a

19polarizing beam splitter and a quarter-wave plate. We further increased this efficiency
by under-filling our 10-mm-diameter QPD with a 6-mm back-scattered beam, in contrast
to previous experiments that used an overfilled QPD [33] or BSD in combination witha reflective element [50, 49] to deduce vertical position. As a result, with only 1.3 mW
incident upon the objective (and 60% of that at the sample [88]), we achieved a highcollection efficiency (5%) of the input light at the QPD. This efficiency enabled us to
use low laser power (800 µW at the laser focus) while achieving high sensitivity (seeCh. 4). Independent control of both lasers in the sample plane was achieved with two
separate mirrors in a conjugate plane to the back-focal-plane of the objective.
In verifying microscope stabilization, we used one laser to detect sample position(810 nm) and the other laser as an independent verification (845 nm). However, in
the AFM application, we stabilized the sample with respect to the AFM tip, where
both the sample and the tip were detected by lasers. We therefore introduced twolasers that by design share a largely collinear beam path. Common-mode noise (e.g.,mechanical motion of the fiber tip) was suppressed in this differential measurement
scheme. Thus, the differential stability between the lasers will be the ultimate limitation[19 pm laterally, 73 pm vertically, ∆f = 0.1–50 Hz, see Ch. 4].
For the AFM application, we custom-built an AFM assembly that mounted directly onto the optical microscope frame. Detailed drawings of the AFM assembly that
contain the AFM tip are presented elsewhere [20]. In the AFM application, we separately measured the position of the AFM tip and a fiducial mark on the sample withtwo diode lasers and back-scattered detection, as discussed above. Sample and tip position were controlled with a pair of 3D, closed-loop PZT stages (Physik Instrumente,
P363.3CD and P733.3DD), which were both mounted on coarse-positioning stages. The
six axes of motion (i.e., x, y, z on both stages) were controlled with custom software (National Instruments, LabVIEW 8.5) and a field programmable gate array card (National
Instruments, PCI-7833R). Commercial silicon and silicon-nitride tips were used [Mikro-

20

Figure 2.3: Diagram of the atomic force microscope (AFM). (A) Detailed view of theimage plane where the AFM tip and sample positions were detected by focused lasers
scattering off a fiducial mark on the sample and the apex of the tip. (B) Two diodelasers (DL) were actively stabilized by the combination of optics shown in the gray box.
The stabilized diode lasers (SDL) were coupled into the microscope similar to Figure
2.1. Because the AFM tip is in the forward-scattered direction, the back-scattered light
was imaged onto the QPD. The combination of the polarizing beam splitter (PBS) andquarter-wave plate (λ/4) led to highly efficient back-scattered detection. Each laser
was independently translated in the imaging plane by mirrors in a plane conjugate
to the back-focal-plane of the objective. Acronyms represent the following: opticalisolator (OI), acousto-optic modulator (AOM), photodiode (PD), piezo-electric (PZT,
lead zirconate titanate), half-wave plate (λ/2) and beam sampler (BS). Blue-shaded
components are in optically conjugate planes.

21

Figure 2.4: Pictures of the AFM. Top. AFM instrument. Bottom. Inside the acoustically isolated box is the microscope and laser optics.

22
Mash, CSC38/noAl (stiffness = 0.08 N/m); Veeco, DNP-S (stiffness = 0.06 N/m)]. For
AFM imaging, we deduced cantilever deflection via a third diode laser (λ = 785 nm)
in a standard optical-lever geometry [75]. More specifically, we reflected the 785-nm
laser off the back side of the AFM cantilever and detected its deflection with a QPD.
We calibrated each cantilever by contacting the AFM tip to the cover slip, yielding atypical sensitivity of ∼30 mV/nm. To minimize thermally induced cantilever deflection[6], we used cantilevers without a metallic coating (or removed the metallic coatingchemically). Nonetheless, we maintained a deflection sensitivity of <20 pm (rms, ∆f= 0.1–1000 Hz). We deduced the mechanical response time (∼100 µs) of the silicon
nitride cantilever by measuring the resonance width (FWHM) of the thermally driven
fundamental resonance peak in air.
As in the optical trapping microscope, the AFM apparatus was constructed suchthat passive and active stabilization reduced mechanical, thermal, and laser noise. There
were a few instrumental differences. To further reduce mechanical vibrations, an opticalbreadboard (TMC, 77-113, 91.6-mm-tall with adapter) was mounted on the optical table
as a riser to shorten mount height. In addition, the microscope pillar was replaced by a
0.4 m X 0.18 m X 0.09 m monolithic aluminum column. We also placed lead bricks instrategic locations on the optical table to more equally distribute the table weight; we
did not see an appreciable difference in stability by doing this. The whole assembly was
enclosed by a custom-built, acoustically isolated box. To image the sample, the mercury
lamp was replaced by a gooseneck light-emitting diode (McMaster-Carr, 6799T1). The
room was not temperature-regulated, but during experiments the air-handling system
was turned off, all of the doors were closed, and the room temperature was allowed toequilibrate.

23
2.1.3

Detection electronics

The position of the fiducial mark or trapped bead was detected by a QPD (250
kHz bandwidth with custom electronics; ∼40 µW laser power at detector). Lateralmotion was deduced from the normalized intensity difference on the QPD while verticalmotion was deduced by the sum signal – the total light falling upon the four quadrantsof the QPD. The normalized differences, as well as the offset-amplified sum signal, weredigitized using 16 bits at either 4 or 10 kHz, and the resulting voltages were converted
to positions (see Section 2.3.1). More specifically, the four currents from each QPD
were converted into voltages using a transimpedance amplifer with a resistance of 100
kΩ. Then a summing and subtraction circuit using operational amplifiers (similar to thecircuit in the UDT application note “Quadrant/Bi Cell Photodiode”, Fig. 2.5) generated
the x (left quadrants - right quadrants), y (top quadrants - bottom quadrants), and z(sum of all quadrants) voltage signals. The x and y signals were normalized by division
to reduce the effect of amplitude changes on the QPD. The voltages were then filteredwith an 8th-order, low-pass, elliptic filter (Frequency Devices), and digitized with a
16-bit, 20-V-range data acquisition card (National Instruments, PCI-6052E). In themodified microscope for AFM, the data acquisition card was upgraded to an 18-bit
data card (National Instruments, M-series High Accuracy) and a field-programmablegate array card (National Instruments, PCI-7833R). Prior to digitization the z signal
undergoes a further amplification stage (50–1000X) using a differential amplifier with
an offset. After digitization, we used software calibration curves to convert the voltages
into position records (see Section 2.3.1). Customized software was written in LabVIEW(National Instruments, version 7.1 or 8.5) on a computer (Dell Dimension 9200) with afast processor (Intel Core2-Duo, 2.66 GHz).

24

Figure 2.5: Quadrant photodiode circuit. Figure credit: UDT application note “Quadrant/Bi Cell Photodiode”.

25
2.1.4

Laser stabilization

To reduce laser noise, we used active stabilization (Fig. 2.6 A). Specifically, we
passed the laser sequentially through an AOM, a single-mode, polarization-maintaining
fiber, and a polarizing beam splitter. The AOM diffracted the laser and we selected thefirst order beam using an iris and beam blocks. The combination of the single-mode,polarization-maintaining fiber and the polarizing beam splitter transformed pointing,mode, and polarization noise into intensity noise. We then sampled 10% of the lightonto a large-area (10-mm-diameter) photodiode (PerkinElmer Optoelectronics, YAG444-A). The photodiode signal was analyzed using custom-built feedback electronics
that output a voltage signal to the AOM to modulate the power in the diffracted beam
so as to stabilize the output laser intensity. The photodiode current was converted
to voltage using an analog transimpedance amplifier with a resistance of 10 kΩ. The
custom-built feedback electronics consisted of a low-delay, proportional-integral analog
servo controller operating at a bandwidth of 200 kHz. The circuit diagram for the
feedback electronics is listed in Appendix D.
Simple application of this active stabilization method to the trap laser resulted
in a gain inversion when the output intensity of the AOM was changed substantially.
The gain inversion was caused by transient heating of the AOM crystal, resulting inindex changes that shifted the diffraction angle (∆θ) of the beam. Previous measurements of pointing instability after large intensity changes (almost the full range) in adifferent AOM crystal (germanium) have been as large as 4 mrad in just 2 s [53]. In
our experimental geometry, the transient pointing error was converted into a time- andhistory-dependent intensity error. In other systems, this AOM-induced error would leadto translations of the trap laser focus — uncorrected this could correspond to an 8 µm
lateral motion [∆θfobj , where fobj is the effective focal length of the objective (2 mm)].
To minimize the effects of the AOM pointing instability, we imaged the AOM crystal

26

Figure 2.6: Diagram of laser stabilization and performance. (A) Optical layout for
laser stabilization. Acronyms represent the following: optical isolator (OI), photodiode(PD), beam sampler (BS), polarizing beam splitter (PBS), and acousto-optic modulator(AOM). (B) Diode laser intensity prior to stabilization (gray) and after stabilization(black). Traces were smoothed with a box-car window and decimated to 100 Hz.

Figure 2.7: Picture of the laser stabilization implemented on the 785-nm diode laser.

27(Fig. 2.1) on to the fiber mount coupling lens, eliminating lateral translation of thelaser beam on the coupling lens that would otherwise accompany a changing diffraction
angle.
To verify the performance of the intensity stabilization, we sampled 10% of theintensity onto a second photodiode (Fig. 2.6 A, PD2). Voltages from this second photodiode were digitized, filtered, smoothed with a box-car window and decimated to
100 Hz, and normalized. Without stabilization, the intensity fluctuated 2.5% peak-topeak for the 785-nm diode laser, greater than the manufacturers specification of 0.5%
peak-to-peak (Fig. 2.6 B). Measurements of intensity before the AOM were within
specification, thus the excess noise probably arose from the other laser noise sources(pointing, mode, or polarization). With stabilization, we decreased the intensity noiseby 580-fold to achieve a normalized stability of 1.7x10−5 rms at 100 Hz. Similar stabilization of 5x10−5 and 4.0x10−6 was achieved for the 850-nm laser and trap laser,
respectively. This result demonstrates the effectiveness of our scheme whereby a variety of noise sources can be systematically minimized without directly measuring andindividually addressing each one.
To maximize the performance of the feedback loop, we tuned the parametersof the AOM, fiber, photodiode, and servo electronics. The AOM diffraction efficiency
was maximized at the expense of the loop closure time by passing a collimated, 2mm-diameter beam through the AOM. At near-infrared wavelengths and this beam
diameter, the diffraction efficiency was measured to be ∼70% while the AOM rise time
was nominally ∼1 µs. The AOM driver was set so that the “bias adjust” knob was
turned all of the way down and the “power adjust” knob was turned such that diffraction
efficiency was maximized (all of the way up and then backed off a quarter of a turn).
The power efficiency through the fiber was tuned when the AOM output was at 60%,
see Appendix E. The photodiode resistance (R, 10 kΩ) was selected so that the incident
power (∼1 mW) matched the voltage range (0–10 V) of the servo electronics. Incident

28
power is related to voltage through the responsivity of the photodiode, which was 0.45–
0.5 W/A for our wavelength lasers. In addition, the photodiode resistance was selected
to maximize the bandwidth of the photodiode (∼1 MHz), i.e.,s∆f =∆fgain
,
2πCR

(2.1)

where ∆fgain is the gain bandwidth (45 MHz) and C is the total capacitance of thecircuit (40 pF). We tuned the servo electronics to minimize the noise and maximize theloop closure time, see Appendix E. The feedback loop closure time was limited by the
response of the silicon photodiode to infrared light [7, 97]. Increasing the amount ofincident light on the photodiode decreased this problem, but limited the output power.
We selected a 10% beam sampler as a compromise between bandwidth and output
power. Hence, we maximized the performance of the feedback loop by compromising
between power efficiency and bandwidth.

2.1.5

Microscope stabilization

Drift between the objective and sample is a long-standing problem in microscopy.
However, the introduction of a fiducial mark, or a reference point, into the systemprovides a means to measure and minimize objective-sample drift. Historically, thefiducial mark has been a micron-sized bead affixed to the microscope cover slip [14,115]. However, these beads tend to exhibit >1 Å motion relative to the sample (seeSection 3.4), so we fabricated micron-sized posts on the cover slip to provide stablefiducial marks (see Section 2.2.1). We measured the position of the fiducial mark using
laser-based detection to directly measure the objective-sample distance (the laser focal
position is subject to objective drift, while the fiducial mark position is subject tosample drift). Since we have a measure of objective-sample drift we now have a means of
reducing it. Previously, our group sought to passively subtract drift [89], however, as the
microscope drifts farther out of alignment simple subtraction is not possible. Here, we29
actively stabilized the objective-sample position to minimize instrumental drift. Active
microscope stabilization was achieved by (i) measuring the position of a fiducial markon the sample, and (ii) using this position in a feedback loop to a PZT stage to keep
sample position constant (Fig. 2.8).

Figure 2.8: Diagram of microscope stabilization. We first detect sample position by
scattering a laser beam off a fiducial mark. The light from the scattered beam iscollected by a quadrant photodiode detector that outputs a voltage, which is calibrated
into position (xfid ). A feedback loop compares xfid to a reference position, xref , andoutputs a signal to the piezo stage to keep the sample at the reference position.

To test the performance of the microscope stabilization we used a second laser tomonitor the position of a second fiducial mark on the surface. Using this method, we
report a microscope stability of 1 Å rms in 3D over 1–25 Hz using forward scattered
light (see Ch. 3). We also achieve similar stability using back-scattered light: <1 Å rms
in 3D over an order of magnitude larger bandwidth, 0.1–50 Hz (see Ch. 4). The slightly
better stability using back-scattered detection is probably due to the more compact
optical design and the decreased pointing noise of the lasers, which have been launchedout of a single fiber.
To maximize the performance of the microscope stabilization we tuned the parameters of the detection electronics and the feedback loop. The detection electronics

30
measure the voltage of the incident light on the QPD (see Section 2.1.3), which is thencalibrated into a position of the fiducial mark using a calibration curve (see Section
2.3.1). We set the gain on the detection electronics such that the fiducial mark position had a 0.2-nm peak-to-peak noise level, laterally, and a 0.5-nm peak-to-peak noiselevel, vertically, over a bandwidth of 1–100 Hz (for a micron-sized glass post, x-y gain
= 4.5, differential gain = 1, post gain = 1, and vertical gain = 50). Too much gain
led to amplification of noise, while bit noise persisted at low gain levels. In addition,
we maximized the software feedback loop by tuning the gain and bandwidth parameters. The inputs to the feedback loop were the current position of the fiducial mark(e.g. xfid ), the desired position of the fiducial mark (e.g. xref ), the gain (g), and thethreshold for loop output. The algorithm calculated the difference between the desired
position and the current position. If the difference was above the input threshold value,
it was multiplied by the gain, and output as a relative movement of the PZT stage(Fig. 2.8). We set the desired position to zero in 3D, the gain to 0.05 in all dimensions,and the threshold values to 0.05 nm, laterally, and 0.1 nm, vertically, though the gain
and threshold values vary with the bandwidth of the feedback loop. To tune the gain
values, we increased the gain until oscillation and backed off until the noise decreased
to a plateau. The threshold value was set to about a quarter of the peak-to-peak noiselevel for fiducial mark position over the desired bandwidth; for example, at 100 Hz, thepeak-to-peak noise level is 0.2 nm, laterally, so the threshold value is 0.05 nm, laterally.
In the optical trapping microscope, the feedback loop was software-based (LabVIEW)
with a maximum bandwidth of 100 Hz that was limited by the computer processor anddata collection algorithms (see Section 2.3). In the AFM application, the feedback was
upgraded to field-programmable gate array control that ran at a 500 Hz bandwidth[21], the resonance frequency of the loaded PZT stage. The larger bandwidth increased
performance three-fold.

31
2.1.6

AFM tip stabilization

AFM tip stabilization was similar to microscope stabilization except for a few key
differences. We measured AFM tip position at 300 nm above the surface (see Section
2.3.4), instead of fiducial mark position. Focusing of the lasers and alignment of thebeams was done with the aid of micrometer stages to move the fiber tip relative to acollimating lens and to move the fiber tip-lens assembly relative to the piezo mirror.
AFM tip position measurements required compensating for crosstalk, which we didwith a linear compensation algorithm. The software-based feedback loop was run in
LabVIEW 8.5 to accommodate the M-Series data acquisition card, instead of LabVIEW
7.1, though the bandwidth was still 100 Hz. Finally, the gain of each axis of the tip
PZT stage had to be individually set. Setting of the PZT stage gain followed publishedprotocols by Physik Instrumente.
In the actual AFM experiment this software-based tip stabilization was upgradedfor field-programmable gate array control [21, 51] with an increased bandwidth. In thisscheme, the PZT stage position was updated every 1 ms.

2.2

Biological assays

2.2.1

Fiducial mark fabrication

Melted polystyrene beads. The easiest fiducial marks to produce were melted
polystyrene beads. We first cleaned microscope cover slips in ethanolic 6 M potassiumhydroxide (see Appendix E) and constructed sample chambers (see Section 2.2.2). Second, we flowed in 0.1–1 pM polystyrene beads (Interfacial Dynamics, surfactant-free) in
10 mM Tris buffer. After 5 min, the flow chamber was rinsed with 100 mM magnesium
acetate and allowed to sit for 10–20 min. Then, we rinsed with ethanol and removed theexcess liquid. When the flow chamber was dry, we heated it in the oven at 100 ◦ C for 15
min, and then filled the chamber with water. Unfortunately, these melted beads were32
not firmly affixed to the cover slip and demonstrated significant (>1 Å) motion (seeSection 3.4). To address some of this concern the above procedure for melting beads
was changed with varying success. The current best procedure for melting polystyrene
beads is listed in Appendix E.
Low-index glass posts. Symmetric nano-scale low-index glass posts were fabricatedon cover slips using hydrogen silsesquioxane (HSQ, Dow Corning, FOx-16) and e-beamlithography (Fig. 2.9 A,B). First, we cleaned the cover slips in a 10 min piranha etch(100 mL sulfuric acid and 15 drops hydrogen peroxide at 80 ◦ C, see Appendix E). The
cleaned cover slips were spin coated at speeds of 1–5 krpm with HSQ to produce posts
with heights ranging from ∼400–1000 nm. Then, thin aluminum films (nominally 15 nm)
were vapor deposited to prevent charging during the next step, e-beam lithography (38keV, 450 µC/cm2 dose). When exposed to electron irradiation, HSQ cross-links to form
glasslike features as small as 20 nm [85]. This fine control allows for highly symmetric,
circular structures to be fabricated. Asymmetric structures lead to crosstalk between
the x and y motions on the QPD. After e-beam exposure, the aluminum was etched(10 s in 16:1:1:2 phosphoric acid to nitric acid to acetic acid to distilled water), and the
HSQ was developed (10 min) by using tetramethylammonium hydroxide. Finally, toensure the HSQ was fully cross-linked, samples were thermally cured at 400 ◦ C for one
hour. A more detailed protocol is listed in Appendix E.
Silicon disks. We fabricated 1 mm2 arrays of silicon disks in a 6-µm grid (Fig.
2.9 C,D) on cover slips via physical vapor deposition of silicon through a silicon-nitride
shadow mask [54]. Mask fabrication began by spinning e-beam resist (Zeon, ZEP-520)
onto 200-nm thick, 2 X 2 mm silicon-nitride membrane windows (Silson). The resist
was then exposed via e-beam lithography (38 keV, 15 pA, 50 µC/cm2 ) and developed.
Holes were then etched through the window in a reactive ion etcher (tetrafluoromethane,
16 sccm, 20 Pa, 100 W, 90 s). Next, 3-µm-tall standoffs were fabricated around theperimeter of the patterned window via optical lithography with SU-8 (Microchem).

33

Figure 2.9: Fiducial mark fabrication. (A) Atomic force microscope image showing anarray of hydrogen silsesquioxane (HSQ) posts (radius, r = 500 nm; height, h = 600
nm). Inset: zoom-in of post. (B) Protocol for making HSQ posts. (C) Atomic force
microscope image showing three silicon disks (r = 250 nm; h = 56 nm). Inset: line
scan across a disk. (D) Cartoon of shadow mask procedure to make silicon disks. (E)Atomic force microscope image showing an array of etched holes (patterned r = 50–300nm). Inset: zoom-in of hole. Image credit: Theresa Ulrich. (F) Protocol for making
etched holes.

34
Prior to depositing silicon, the glass cover slips were cleaned in ethanolic 6 M potassiumhydroxide, see Appendix E. Finally, silicon was deposited through the shadow mask inan evaporation chamber (0.1 nm/s, 1x10−4 Pa). The diameter and height of the silicondisks were measured by AFM with a high aspect ratio tip (MikroMasch, STING tip).
One general advantage of physical vapor deposition through a shadow mask is that thematerial composition (and thus the index of refraction) of the disks is highly tunable.
Additionally, by using four shadow masks in parallel, four cover slips were made per 30min cycle, where cycle time was limited by evaporator pumping time. A more detailed
protocol is listed in Appendix E.
Etched holes. We etched holes (Fig. 2.9 E,F) by spin coating cleaned (ethanolic
6 M potassium hydroxide, see Appendix E) cover slips with polymethyl methacrylate
resist (300-nm thick) and then vapor depositing a thin layer of aluminum (nominally
15 nm). Next, a chromium layer was deposited to the back side of the cover slip, toprevent etching. Then, we exposed a grid of filled circles with varying radii using e-beamlithography (38 keV, 350 µC/cm2 dose). After removing the aluminum and developing
the resist, we etched the underlying cover slip with buffered hydrofluoric acid to obtainisotropic holes. Finally, the cover slips were cleaned in methyl isobutyl ketone to remove
the resist.

2.2.2

Sample preparation

We fabricated fiducial marks (see Section 2.2.1) onto cover slips for use in active
stabilization. To enhance usability in single-molecule assays, the cover slips were cleaned
with a 10-min piranha etch (100 mL sulfuric acid and 15 drops hydrogen peroxide at
80 ◦ C, see Appendix E) after nanofabrication. We constructed epoxy-rigidified flowchambers (internal volume 15 µL) for enhanced stability using double-stick tape (3M)
as a spacer and 5-min epoxy (Devcon) for rigidity. Cover slips were recovered (>20
times) and cleaned after use by soaking the flow chamber in boiling water for 1 hour (to35remove the cover slip) and piranha cleaning the cover slip for 10 min. Surface chemistry
after such cleaning was compatible with single-molecule biophysics experiments.
For experiments with only a trapped bead, we used 10-fM polystyrene beads(Interfacial Dynamics, 330-nm-diameter) in WB [25 mM Tris acetate (pH = 7.5), 1
mM magnesium acetate, 1 mM sodium chloride, 1 mM dithiothreitol, 0.4% Tween20 (BioRad), and 3 mg/ml bovine serum albumin (concentration cited is that before
filtration through a 0.2-µm filter)].

2.2.3

DNA preparation

For experiments with a DNA molecule, we prepared double-stranded DNA bypolymerase chain reaction (PCR; Applied Biosystems, GeneAmp XL PCR Kit) using
one digoxigenin-labeled and one biotin-labeled primer (Integrated DNA Technologies).
Labelling the DNA permitted biochemical linkage. We bought M13mp18 plasmid andused this as a template for PCR. To make different lengths (L = 556 nm, 1007 nm,
2413 nm), we used different primers and gel purified the final product. Concentrations
cited were spectrally determined (1 absorbance unit at 260 nm = 50 µg/mL of doublestranded DNA) using an ultraviolet-visible absorption spectrometer (Jenway, Genova).
Another analytical gel verified the single DNA band of the appropriate size.
Preparation of the 20TS06/T4 DNA hairpin (Fig. 2.10 A) followed publishedprotocols [136, 135]. Specifically, we prepared two DNA handles using PCR. Handle A
was made using M13mp18 template DNA, a biotin-labeled primer for the top strand,
and a bottom-strand primer with an abasic site (deoxyribose spacer) followed by ∼10
nucleotides to create a 5’ overhang. Handle B used the same template DNA. The
top-strand primer had ∼10 nucleotides that were complementary to the 5’ overhang in
Handle A, followed by the 20TS06/T4 hairpin, an abasic site, and a complementary
region of DNA to the M13mp18 plasmid. The bottom-strand primer was digoxigeninlabeled. After PCR, each handle was gel purified, concentrations were determined, and36a diagnostic gel verified the appropriate lengths. Ligation of the two handles was doneby T4 DNA ligase (Invitrogen, 16 ◦ C for 16 hours, 1:1 molar ratio of Handle A to Handle
B) resulting in two double-stranded labeled regions flanking the single-stranded hairpin.
The final DNA product was gel purified, concentrations were determined, and a final
diagnostic gel was run, as above.
For experiments with RecBCD, we prepared DNA by PCR with M13mp18 plasmid template and with one biotin-labeled primer and one unlabeled primer (Fig. 2.10
A). This created a blunt-end DNA molecule (L = 2413 nm, 993 nm) void of chi-sites
and with only one biochemical linkage for attachment to the optically trapped bead. Wethen purified the DNA and verified the concentration and length, as above. To maketailed DNA we cut the 993-nm-length blunt-end DNA with BsmBI restriction endonuclease (New England Biolabs) at a restriction site such that the purified product had an
L = 901 nm. We purchased two DNA oligos to make a tailed substrate: one with a 3’
poly-T tail (dT = 5 or 6) and a 5’ end that is complementary to the BsmBI overhang,the other with a 5’ poly-T tail (dT = 10) and a sequence that is complementary to thefirst oligo up until the 5’ end (Fig. 2.10 B). The two oligos were annealed at 70 ◦ C,
slowly cooled (4 ◦ C increments held for 30 s) to room temperature, and ligated using T4
DNA ligase to the cut DNA (16 ◦ C for 16 hours, 50:1 molar ratio of tailed substrate to
cut DNA). The final double-stranded DNA length of the tailed substrates was 908 nm.
We gel purified the product and concentrations were determined, as above. To verify
that the final product was a tailed DNA we further cut an aliquot of the product with a
DrdI restriction endonuclease (New England Biolabs) at a site upstream of the BsmBI
site. This produced a 829-nm-length DNA molecule containing the biotin label, and a
78-nm-length DNA molecule with the tailed substrate. If the digestion or ligation werefaulty then bands would appear at other lengths (a 164-nm length indicated the bluntend DNA molecule and a 72-nm length indicated the DNA molecule with the BsmBI
cut end and no ligation). There were three different tailed substrates that were created:

37
a GC-rich substrate, an AT-rich substrate, and a substrate with a mixed sequence (Fig.
2.10 B).

2.2.4

DNA tethered particle assay

Tethering DNA to the surface required biochemical linkage. DNA was prepared
as above with one biotin-labeled primer and one digoxigenin-labeled primer. These labels enabled us to attach a DNA molecule at one end to a streptavidin-coated bead
(Spherotech, 320 nm diameter) and at the other end to an antidigoxigenin-coated coverslip (Fig. 2.1). Coated cover slips were made by incubating 20 µg/ml antidigoxigenin
antibody (Roche) suspended in 0.1 M sodium phosphate buffer for 1 hour in flow chambers. Bead-DNA complexes were made by incubating streptavidin-coated beads (900pM) at a 9:1 molar ratio with labeled DNA at room temperature. After washing theflow chamber with WB, the bead-DNA mixture was flowed into the chamber and allowed to incubate for 1 hour before washing again. A more detailed protocol is listed
in Appendix E.

2.2.5

RecBCD assay

RecBCD preparation protocols were adapted from those in earlier studies [27, 96]
based on the biotinylated RecBCD derivative, RecBCD-bio. RecBCD-bio unwinding
rates agree, within experimental uncertainty, to the wild type unwinding rates in bothbulk and single molecule experiments [8, 27, 114]. Both RecBCD-bio and RecBCDbio with a knockout RecD helicase were expressed and purified by our collaborators(Hung-Wen Li and Hsiu-Fang Fan). Streptavidin beads were sonicated, then incubatedfor 1 hour with DNA (9:1 mol ratio, 900 pM beads) in WB. Concurrently, biotinylated
bovine serum albumin (Vector) at 10–100 mg/ml in 100 mM sodium phosphate buffer(pH = 7) was incubated within a flow chamber for 30 min at room temperature topromote adsorption. After washing with WB, the chamber was incubated with 5 mg/ml

38

Figure 2.10: DNA constructs. (A) We used four DNA constructs. We made DNA
tethers using DNA labeled with a biotin (bio) and digoxigenin (dig). For DNA hairpin constructs, we prepared two DNA handles, one with a hairpin, and ligated them
together. The abasic sites in the two handles were used to stop the PCR extension
reaction. For RecBCD DNA constructs, we made DNA with a blunt-end for RecBCD
binding, the other end was biotin labeled for bead linkage. There are two endonucleasesites within this DNA construct for preparation of the last construct, the tailed DNA.
The BsmBI site was used to cut the DNA so that tails could be attached, the DrdI site
was used to cut the DNA to check ligation. (B) DNA tailed substrates had 6 T’s on the
3’ end and 10 T’s on the 5’ end, GC-rich constructs contained 3 G-C base-pairs before
the tail, while AT-rich constructs contained 4 A-T base-pairs before the tail (yellow
boxes).

39
streptavidin (Molecular Probes) for 30 min. After further washing, RecBCD-bio at 15nM was introduced and incubated for 2 hours. After washing again, the bead-DNA
mixture was introduced and incubated for 40 min and then washed with WB. A moredetailed protocol is listed in Appendix E. Enzymatic reaction was initiated by flowing
in WB supplemented with 2 µM ATP, 1.1 mM E. coli single-stranded binding protein(Promega), and an oxygen-scavenging system (6 mg/ml glucose (MP Biomedicals), 0.2
mg/ml glucose oxidase (Roche Applied Sciences), 30 units/ml catalase), unless otherwise
stated. Where indicated, 2 µM ATP was substituted for 2 mM AMP-PNP (adenylyl
imidodiphosphate, Sigma-Aldrich) or 2 mM ADP (adenine diphosphate, Sigma-Aldrich)in the above solution.

2.3

Data collection
Data collection relied on data cards (National Instruments, PCI-6052E, PCI-

6703, and M-series) and a software suite in LabVIEW (see Appendix C). The methods
outlined below were automated for reproducibility and ease of use.

2.3.1

Positional calibration

Data collection requires calibrating the voltage from the QPD into position. To
do this, we sequentially scanned the fiducial mark through the detection laser focus in
all three axes using the PZT stage and recorded the resulting QPD signals (Fig. 2.11).
We fit the QPD lateral response to a 7th-order polynomial over a ±180 nm monotonic
range, and the vertical response to a 1st-order polynomial over a ±50 nm linear range.
The fit coefficients were then used to calibrate voltage from the QPD into a position in
nanometers. Since fiducial marks and conditions vary, this calibration is repeated foreach experimental trace. To determine sensitivity, or the slope of the curve, we fit boththe lateral and vertical response to a 1st-order polynomial over a ±50 nm range.
Motion in one axis that leads to an optical signal on an orthogonal axis (Fig. 2.11)

40

Figure 2.11: Position calibration curves. Calibrations were measured by moving thestage in one axis, while monitoring the on-axis (thick line) and off-axis response (thinline). Signals in x, y, and z are represented by green, red, and blue, respectively.
Centering the fiducial mark in the laser beam required fitting the derivative of a Gaussian
to the lateral response (dashed line).

41
complicates detection. Thus, we sought to minimize such optical crosstalk between axes.
To remove most of the crosstalk, we precisely centered the fiducial mark relative to thelaser beam using an automated routine. Centering was achieved by fitting the lateral
response along the horizontal axes to the derivative of a Gaussian and then translating
the PZT stage to the Gaussian center point. Further crosstalk removal required carefulmechanical adjustments of the fiber tip (translations in x, y, and z) to align the laser
focus axially in the microscope. Axial alignment consisted of (i ) measuring the crosstalkin one axis and determining the slope, (ii) translating the fiber in that axis until the slope
was minimized, and (iii) repeating this minimization for the other axes. Additionally,
the back-scattered signals required rotating the quarter-wave plate and the QPD and
fixing the mounting angle of the quarter-wave plate such that back reflections off it did
not enter the QPD. Using these techniques we obtained ∼2% crosstalk between axes
over a 200-nm region. For raster-scanning applications, increased accuracy, or for large
displacements, we parameterized the residual crosstalk [24].

2.3.2

Mirror calibration

In the optical trapping microscope we use PZT mirrors to translate the 850-nm
and 1064-nm lasers in the image plane. While the PZT mirror input is in voltage, werequest these translational movements in nanometers, requiring a mirror calibration.
This mirror calibration was done once and was valid unless mirror position on the
optical table changed. We calibrated the PZT mirror by scanning a fiducial mark in agrid using the calibrated PZT stage and determined the PZT mirror voltages associatedwith the center of the fiducial mark at each stage position. We plotted the 2D grid ofvoltage coordinates, and checked for linearity; a tilted grid means that mirror movement
in one axis will generate significant crosstalk on the other axis. The mirror position in
the mount was rotated to minimize this crosstalk and create a linear grid. We thendetermined the calibration for nanometers into volts by linearly fitting the data and42using the slope in each axis along with a linear crosstalk term. To check this calibration,
we scanned both the fiducial mark and laser in a grid using the PZT stage and PZT
mirror, respectively. The distance of the laser from the fiducial mark center was recorded
and verified to be within 5%.

2.3.3

Trap calibration

In the optical trapping experiment we can change the force on the bead (FT ) either
by changing the bead position (xbd ) or the trap stiffness (kT ), as FT = kT xbd . To change
the trap stiffness, we adjust the intensity of the trap (I). This is because the potential of
the trapped bead (U ) is both proportional to trap stiffness, |U | =R

F = 12 kT < xbd >2 ,and given by the potential of a dipole in an electric field (E), |U | = αE 2 = αI, where
α is the polarizability. The trap calibration converts trap stiffness (in pN/nm) to a
voltage for the trap intensity servo.
There are three methods to calibrate trap stiffness: the equipartition method, thepower spectrum method, and the drag method. These three methods have been reviewed
extensively [87, 94, 118]. Briefly, the equipartition method draws on the equipartition
theorem that allows 21 kB T of energy per degree of freedom, kB is Boltzmann’s constantand T is temperature. Applying this theorem to our trapped bead yields
kT =

kB T
,
< x2bd >(2.2)

where kT is trap stiffness and xbd is the bead position. The power spectrum method
relies on the fact that the responsivity of a trapped bead, as measured by a power
spectrum, will roll-off at a particular frequency (f0 ) given a particular trap stiffness.
The full equation iskT = 2πβf0 ,(2.3)

where β is the drag coefficient of the trapped bead (β = 6πηrbd far from a surface, η isthe viscosity of the liquid and rbd is the bead radius). Finally, in the drag method, the43stage is moved at a particular velocity (v) so as to create a drag force on the trapped
bead. By calculating the drag force and measuring the bead position we can determine
the trap stiffness,
kT =

βv
.
xbd

(2.4)

By calibrating trap stiffness using all three of these methods, we can easily check ourstiffness calibration for inconsistencies. The equipartition method does not depend on
the drag coefficient (and therefore the bead size or the viscosity of the liquid), the power
spectrum method does not depend on the positional calibration, and the drag method
will measure the linearity of the trap and so this does not have to be assumed.
We first calibrated the trap stiffness by measuring bead position at ten different
voltages of the trap intensity servo. Using this bead position and the resulting power
spectrum, we calculated the stiffness given by both the equipartition method and thepower spectrum method. For stiffness measurements that were not within 10%, wefollowed a series of steps to correct the inconsistencies. First, we checked to make surethe measurement axes were aligned with the trapping axes (Fig. 2.12). This is importantin the equipartition method where one degree of freedom is measured along the trapping
axis. Rotating a half-wave plate moved the trapping axes into alignment. Second, weused all new buffer and sample chambers, since the power spectrum method is sensitive
to the viscosity of the liquid. In addition, the power spectrum method is very sensitive
to the height above the surface, so we selected the height before every measurement toremove drift or we used a fiducial mark to stabilize the stage in z. Finally, if the trap
calibration still did not agree, we rechecked the mirror and positional calibrations, as
the equipartition method is sensitive to these calibrations.
We then measured the linearity of the trap and the trap stiffness with the dragmethod. We measured the bead position at multiple velocities of the stage, plotting dragforce vs. bead position. By fitting a line to this curve and measuring the residuals we44

Figure 2.12: Trap calibration is sensitive to polarization. Left panels. Trapped beadposition (ybd vs. xbd ) fit to a line to show polarization orientation. Right panels. For
the trapped bead in the left panels, the stiffness vs. trap power is shown for both theequipartition method (orange) and the power spectrum method (red). Polarization
orientation must be aligned with the measurement axes for the equipartition method
and power spectrum method to agree.

45
assessed the linearity of the trap; within 5% for ±100 nm. The slope of the line (fit over
±50 nm) was the trap stiffness. It is important when taking this data to account for theslope of the stage and to set the height appropriately. We repeated this measurementof trap stiffness using the drag method at the same ten different intensity servo voltage
levels used above.
Finally, using the equipartition, power spectrum, and drag data, we determined
the trap calibration. We plotted the trap stiffness measured by each of the three methods
against the trap voltage (Fig. 2.13) and verified the stiffness at each value. The data
was within 10%. A line was fit to the data (in voltage vs. stiffness) and the linear
coefficients were written out as the trap calibration. This calibration was repeatedfor each bead size and buffer condition, though once taken the calibration is valid aslong as the instrument does not change. We checked the calibration by uploading thecalibration file and using it to send a voltage to the trap intensity servo. We measured
the difference between the desired and measured trap stiffnesses and verified that thedifference was ±5%. We also verified that the stiffness of the trap was not sensitive
to the position above the surface by measuring trap stiffness at various heights. From
100–1000 nm above the surface the stiffness decreased by ∼2

2.3.4

Positional measurement

We want to measure the position of a fiducial mark over time to both characterize
the sample drift and to actively stabilize the sample. In Section 2.3.1 we calibrated theposition of a fiducial mark, here we want to use that calibration to take positional
measurements over time. To measure fiducial mark position, we first coarsely centered
the fiducial mark in the laser focus using a camera. Second, we scanned the sample
laterally and fit the resulting QPD voltage curve with a Gaussian to find the fiducial
center; we then moved the stage or laser so as to laterally align the fiducial and laser.
Next, we scanned the sample in z and selected the center position. We repeated the46

Figure 2.13: Trap calibration. Stiffness is calculated by the equipartition method (redcross), the power spectrum method (green circle) and the drag method (blue triangle).
All data points are simultaneously fit with a line (black) and the residuals are plottedat the top of the graph (black diamonds).

47
lateral centering and then took positional calibration curves in 3D, see Section 2.3.1.
Finally, we used the calibrations to measure the position vs. time. For monitoring thefiducial mark position detected by two laser beams, one beam was aligned using the PZTstage (785-nm laser) and the other was aligned using the PZT mirror (850-nm laser).
Note: In the modified microscope for the AFM experiment there were no PZT mirrors soboth lasers were aligned using the PZT stage and movement between the lasers was doneby turning a mirror knob by hand. A differential measurement was taken by subtracting
the positional data recorded by the lasers (e.g. xdif = xmonitor − xin−loop ). Active
stabilization was achieved by inputting the in-loop positional data into the software
feedback loop and using the monitor positional data as the definitive measure of stability.
In the ultrastable AFM experiment we also want to measure and stabilize tip
position. To measure tip position, we first coarsely centered the AFM tip on the 810nm laser focus using a camera. Second, we touched the tip to the surface and retracted
it 300 nm with the AFM PZT translation stage. We then aligned the tip with respect
to its laser to minimize crosstalk accompanying lateral motion. This alignment wasachieved by dithering the AFM tip along each axis sequentially and changing the center
position of the dither. This procedure collapsed the majority of the crosstalk (which
was deterministic and reproducible) onto the vertical axis. Next, we translated the tip
about its optimum alignment point on each axis sequentially and fit the center portion(±50 nm) of the resulting curves to first-order polynomials. The linearity of the signal
and the crosstalk within this restricted region allowed us to use a linear parametrization.
This calibration was then used to convert voltage from the 810-nm QPD into position.
Finally, we measured position over time and used this measurement as the in-loop
signal to stabilize the tip. When monitoring the stability of the technique, we aligned
a second laser, the monitor laser, to the tip to measure position as well. For imaging,
we calibrated while in contact with the surface.

48
2.3.5

DNA elasticity measurement

A DNA elasticity measurement stretches the DNA while recording the force on
the DNA at each extension value. This measurement is used to laterally align the tether
point to the laser, as well as determine the DNA contour length and persistence length.
First, we trapped a DNA-tethered bead. We then determined the vertical location of thesurface by monitoring the z voltage on the QPD as the tethered bead was brought into
contact with the surface [87], and we lowered the stage 300 nm. Next, bead position wascalibrated. Finally, the program laterally moved the stage to stretch the tether, whilemeasuring bead position to determine both force and extension [131]. The resulting
elasticity curve was fit with the modified Marko-Siggia formula [71] to determine thetether point, DNA contour length, and DNA persistence length. The tether point, whichis the position of the tether anchor relative to the laser focus, was used to align the tether
to the laser. We stretched the DNA twice in both lateral directions to center the tether
and a third stretching curve was used to determine DNA contour length and persistence
length. The error in the tether point and persistence length measurement was ∼2 nm,
while the error in the DNA contour length was 7 nm rms due to the uncertainty inthe bead radius. If the elasticity measurement showed a larger error we rechecked thepositional, mirror, and trap calibrations.

2.3.6

DNA length measurement

To measure DNA contour length, we first determined the vertical location of thesurface by monitoring the sum signal as a tethered bead was brought into contact withthe surface [87]. We calibrated the trapped bead position and then lowered the stage 300
nm. We found the lateral tether point position by performing a 2D elasticity-centering
procedure, which also returned the persistence length. Bead-DNA complexes anchoredby multiple DNA molecules (determined by a low persistence length) were not studied.

49
We next centered the 850-nm laser on a nearby fiducial mark by moving the laser with
the PZT mirror and calibrated fiducial mark position. Finally, we stretched the DNA
along the y-axis using the PZT stage to a specified force (with a corresponding move of
the fiducial-tracking laser). After recalibrating the fiducial mark, we actively stabilized
the sample using a simple software-based feedback loop with a 100 Hz update rate anda proportional gain of 0.05. Concurrent with measuring fiducial mark position, thesoftware also measured the trapped bead position to determine DNA length [131].
For measuring DNA hairpin dynamics under constant force, we implemented aforce clamp in parallel with the above stage stabilization. We modulated kT at 100 Hz
such that the force (FT = kT xbd ) was maintained to ∼0.01%. Modulations in kT wereabout ∼20% to maintain constant FT .
For measuring RecBCD movement, we implemented a pseudo force clamp inparallel with the above stage stabilization. RecBCD movement causes motion of thebead relative to the trap center, which changes the force. To keep the force within 15%of the initial value we allowed movement of the trapped bead to ±10 nm from the clamp
position (70 nm). Bead motion larger than this triggered the stage to reset the beadposition back to the clamp value, with a corresponding movement of the PZT mirrorthat controls the fiducial-tracking laser.

2.4

Data analysis

2.4.1

Data processing

Raw data was collected at 4 or 10 kHz and filtered using an 8th-order, low-pass,
elliptic filter. The data was digitized with a 16-bit, 20-V-range data card in the opticaltrapping experiment and an 18-bit, 20-V-range data card in the AFM application. We
then used a software filtering algorithm in IGOR. We smoothed the data with either amoving box-car window or a moving Savitzky-Golay window [101]. The box-car window

50smooths out higher frequency signals and introduces a bias into the data if the signal has
a nonzero second derivative, as compared to the Savitzky-Golay window [101]. For an
illustration of how the two windows smooth differently see Figure 2.14. Where indicated,
we also decimated the smoothed data so that each point was independent, that is weremoved all of the overlapping windows from the smooth function.

2.4.2

Noise determination

To determine the noise level of the data, we used three different metrics. The
first metric was to take the standard deviation (σ) of the data smoothed with a box-car
window; the upper limit in the bandwidth is the smoothing frequency while the lower
limit in the bandwidth is the inverse time interval. The second metric was to calculate
the integrated noise over a particular bandwidth. We first calculated the power spectrumof the raw data using a scaled power spectrum function (Power Spectral Density.ipf in
IGOR), a Hann window, and the largest window size possible. Then, the square rootof the integral of the power spectrum over the specified bandwidth was calculated togive the integrated noise. Theoretically, the standard deviation and the integrated noise
should be equal given Parseval’s theorem; experimentally, they were within 5%. The
final metric was to plot the histogram of the data and measure the HWHM. For a
Gaussian peak the HWHM is related to the standard deviation by a factor (HWHM =√2 ln 2σ).

2.4.3

Step detection

To determine steps within the data, we used three different metrics. The first
metric was to plot the histogram of the data. Step size was the distance between peaks
and the noise level was the HWHM. The second metric we used was a pair-wise distancedifference of the data. The pair-wise distance difference is a measure of the distance
between pairs of points in the data. By plotting a histogram of the pair-wise distance

51

Figure 2.14: Window type affects data smoothing. We simulated 100-Hz, raw, positional
data (black, top) by adding Gaussian noise to an ideal 1-nm stepping signal. At first,
steps occur every 10 s, then 5 s, then 2 s, and finally 1 s, as separated by the orange
dashed lines. The raw data is smoothed to 10 Hz (pink), 1 Hz (gray), and 0.1 Hz (red)using a box-car window (middle top), a Savitzky-Golay window (middle bottom), anda binomial window (bottom). Data is presented as back-and-forth steps for clarity. If
we instead plot linearly increasing steps (data not shown) and fit these steps with astep fitting algorithm [48], we can quantitatively compare the smoothing algorithms.
We define the parameter rbest as the ratio of the smoothing frequency at which we fit
90% of the steps with the correct height and the dwell time, divided by the stepping
frequency of the simulated data. For the box-car window rbest = 2.7; for the SavitzkyGolay window rbest = 1.0; and for the binomial window rbest = 0.2.

52difference there will be peaks at intervals of the step size; the noise is defined as the
HWHM of the peak. In addition, we took the power spectral density of the pair-wise
distance difference histogram; a peak in the power spectrum will occur at the most likely
distance-difference, the step size. Finally, we fit the data using a step finding algorithm
based on a maximum likelihood parameter [48]. The data was assumed to be either
increasing or decreasing. One step was fit to the data and the likelihood parameter was
found. Then two steps and so on until the algorithm reached the user defined stopping
point (300 steps) and output the plot of likelihood vs. number of steps, which contained
a peak. The user then input the number of steps just to the left of the peak and theprogram output the fit steps, the mean and standard deviation of which was the step
size and the accompanying noise level, respectively.

Chapter 3

Microscope stabilization to 1 Å

3.1

Introduction
Mechanical drift between the objective and sample is a long-standing problem in

microscopy that occurs in all three dimensions. Typical drift rates, around ∼1 nm/s
[52, 89], can be caused by mechanical settling of the objective or stage, thermal heatingof the objective or sample, or acoustic vibrations. Such large drift increasingly limits
the localization precision of the microscope. Localization of a single object is not limitedby the Rayleigh criterion and has been widely used in single molecule experiments toresolve nanometer-scale motion of beads [119], fluorophores [138], and organelles [58].
Localization in vivo can also resolve features down to 16 nm [133], well below the diffraction limit (∼200 nm). In addition, there is a strong desire to increase the localization
precision to 1 Å for a myriad of biophysical applications [77], including measuring [1]enzymatic motion along DNA. As researchers increase localization precision to measuresmaller and smaller distances, the mechanical drift between the microscope objective
and the sample becomes increasingly problematic.
Moreover, in surface-coupled optical trapping assays this unwanted mechanicaldrift is the dominant source of instrumental noise [89]. The goal of our research is
to use surface-coupled optical trapping experiments to measure the discrete motion ofa helicase as it unwinds the DNA duplex. Motion can be as small as 1 bp (3.4 Å)[61, 125], while mechanical drift limits localization precision to ∼6 bp (20 Å) [89, 96].

54
In a surface-coupled optical trapping assay (Fig. 2.1), the enzyme is typically anchoredto the surface, while an optically trapped bead, indirectly coupled to the enzyme bya protein or a DNA molecule, detects the enzymatic motion [5, 11, 45, 48, 64, 120,
132, 140]. Drift is then coupled into the bead-enzyme distance measurement, obscuring
the underlying motion. Ideally, such unwanted drift would be eliminated in all three
dimensions, since many experimental geometries are sensitive to both horizontal andvertical drift [96, 130, 131].
The introduction of a fiducial mark, or a reference point, into the system provides a means to measure and minimize objective-sample drift. Commonly, the fiducial
mark is a micron-sized bead affixed to the microscope cover slip, the position of which
is deduced using video-imaging analysis [14, 115]. Such measurement has been used
in a feedback loop to stabilize an optical microscope in three dimensions [14, 115],
achieving 0.8-nm stabilization at 25 Hz [14], though without independent verification.
Compared to video-based techniques, laser-based detection [33, 37, 128] offers significantly enhanced bandwidth and potentially sub-picometer resolution [23]. Laser-based
detection also depends on the relative position of the laser (set by the objective) to afiducial mark (attached to the cover slip) in three dimensions [100] and is, therefore, apromising candidate for 3D stabilization of the objective-sample position. The problem
is that, historically, instrumental noise particularly at low frequencies (0.1–100 Hz) has
limited laser-based detection measurements [37, 49, 128].
We overcame this instrumental noise and used laser-based detection to achieveÅngstrom-scale stabilization of an optical microscope in 3D. We first measured theposition of a fiducial mark coupled to the microscope sample with a detection laser (λ =785 nm), the in-loop laser. Then, we used a software-based feedback loop to a PZT stage
to compensate for drift in the fiducial mark position (Fig. 3.1). Hence, we effectively
stabilized the microscope sample position to the in-loop laser focus, which is coupled tothe objective, stabilizing the sample-objective distance. Several factors contributed to55

Figure 3.1: Basic principle of microscope stabilization. We measured the position of thesample (e.g. xin−loop ) by detecting the scattering of a focused laser beam (λ = 785 nm)
off a fiducial mark. This position is then used in a feedback loop to a piezo-actuatedstage to keep sample position constant. To monitor stability, we measured the positionof a second fiducial mark (xmonitor ) using another focused laser (λ = 850 nm).

56
this experimental realization: decreasing the low-frequency instrumental noise apparent
in laser-based detection, increasing the sensitivity of laser-based detection to verticalmotion, and fabricating a fiducial mark that was firmly coupled to the sample (andthus, an accurate representation of sample position). Using this technique, we achieveda stability of 1.1 Å, 1.0 Å, and 0.9 Å (rms, ∆f = 1–25 Hz) in x, y, and z, respectively.
The stabilities reported here are independently verified with a second detection
laser (λ = 850 nm), the monitor laser, which monitors fiducial mark position (Fig.
3.1). The simple application of feedback loops, without independent verification of theirperformance, can lead to erroneous conclusions of stability. Let us consider one sourceof instrumental noise: laser-pointing instability. Such pointing noise causes apparent
motion between the objective and the sample that is erroneously compensated for by
the feedback loop. Without independent verification, we have no knowledge about thiserroneous compensation. We note that the use of a monitor laser is not always a truly
independent verification since the monitor laser is immune to common-mode fluctuations
that both lasers share, such as air currents and vibrations of optical mounts. However,in our system a large fraction (40%) of the optical path is not common-mode, andthe common-mode optical elements (excluding the objective) are rigidly attached tothe microscope frame or the optical table by custom-made, large-diameter (38-mm)
aluminum posts. Vibrational testing suggests that the limits in the mechanical stabilityof our system are the fiber launches and the QPDs, which are independent for each laser.
Therefore, in our system, the monitor laser did represent an independent measurementof microscope stability.

3.2

Decreasing low-frequency laser noise
More than a decade ago it was shown theoretically that laser-based measurements

could achieve subpicometer localization of micron-sized beads [23]. However, instrumental drift, particularly at low frequencies (.01–100 Hz), limited such measurements [128].

57
To overcome this instrumental drift, we significantly increased the low-frequency stability of laser-based detection by addressing multiple sources of laser noise.
Previously, our group addressed one source of low frequency noise, laser pointing
noise, by using fiber-coupled lasers and holding the fiber end in a stable, mechanicalmount [89]. However, fiber coupling a laser translates pointing instability into intensity
noise. Additionally, coupling a laser into a single-mode polarization-maintaining fibertranslates mode and polarization fluctuations into intensity noise. This added intensity
noise adversely affects position measurements, particularly in z, where measurements
are proportional to intensity.
To minimize the effects of various laser noise sources, we used an AOM-based laser
intensity stabilization (see Section 2.1.4). The active stabilization method consisted ofpassing the laser sequentially through an AOM, a single-mode, polarization-maintaining
fiber, and a polarizing beam splitter (Fig. 2.6). Then we sampled 10% of the light ontoa photodiode to measure intensity, which was stabilized by a feedback loop to the AOM.
This method decreased the intensity noise of both detection lasers to 0.002–0.005% overthe low-frequency bandwidth of 0.02–100 Hz. In this manner, a number of noise sources(pointing, mode, and polarization) were minimized by translating them into intensity
noise that was also minimized, in turn, by the intensity feedback loop. In addition, we
have stabilized the low-frequency laser noise responsible for limiting previous positional
measurements.

3.3

Increasing the sensitivity of laser-based detection
Previously, our group showed that laser-based detection is sensitive enough totrack the position of a fiducial mark in the lateral directions (x and y) with 1 Å precisionat 1 kHz [89]. We now needed to increase the sensitivity of the signal in the verticaldirection, z. The z positional signal is deduced from the sum voltage of the QPD (seeSection 2.1.3), which is proportional to intensity. More specifically, this vertical signal

58
arises because laser intensity is phase-shifted by the Guoy phase shift at the focus of
the laser [100]. This phase-shifted intensity scatters off the fiducial mark and interfereswith the incident beam in the back-focal-plane of the condenser. The interference leads
to a small modulation on top of a comparatively large signal that is proportional tointensity. Hence, fluctuations in intensity appear as fluctuations in z.
The inherent sensitivity (in volts per nanometer, see Section 2.3.1) in z was small(0.2 mV/nm), as deduced by moving the fiducial mark vertically through the laser
focus (Fig. 3.2 A, purple). To increase this sensitivity, we used an offset amplifier
to optimally match the variable portion of the sum signal to the 20-V dynamic rangeof the 16-bit data acquisition card. This amplification led to an enhanced sensitivityof 27 mV/nm, sufficient to resolve 1 Å motion (with a digitization of 0.3 mV/bit).
Finally, the combination of offset amplification with intensity stabilization yielded an
additional benefit: small, periodic oscillations in the sum signal were eliminated. Since
intensity was stabilized before the laser entered the microscope, these oscillations are
not cavity effects between the bead and the cover slip that are forward-scattered [86].
We speculate that these oscillations result from a small amount of reflected light that
feeds back into the diode laser cavity (making it through both the AOM and the opticalisolation system) and cause mode-hopping of the laser.
After increasing the sensitivity of the signal in z, we measured the noise levelof the signal using differential detection, as was done previously for x and y [89]. In
this technique, the position of one fiducial mark is measured with two detection lasers.
The difference in the position records is calculated (e.g., zdif = zin−loop − zmonitor ),which computationally removes any mechanical drift and leaves residual laser noise[89]. Even after removing mechanical drift, the original z signal was shown to be too
noisy to achieve 1 Å stability in zdif (Fig. 3.2 B). This excess noise was primarily
intensity noise. Thus, in the intensity-stabilized zdif measurement there was marked
improvement. However, only by coupling intensity stabilization with offset amplification

59

Figure 3.2: Vertical sensitivity enhancement. (A) Height calibration signals for anaffixed bead that was scanned vertically through the detection laser. The traces represent the inherent signal (purple), offset-amplified signal (black), offset-amplified signal
with intensity servo active (blue). (B) Differential measurements of vertical motion(zdif = zin−loop − zmonitor ) using two lasers and a 400-nm-diameter affixed bead as afiducial mark. Traces represent the inherent signal (purple), the intensity-stabilized
signal (gray), and the offset-amplified signal with intensity servo active (blue). Traces
displaced vertically for clarity.

60
did we achieve a 1 Å differential stability. More quantitatively, the average short term
(1–25 Hz) differential stability was 1 Å, determined from the average standard deviationof a non-overlapping series of one-hundred 1-s intervals (σ̄z ). Long-term differential
stability was ≤3.3 Å as measured by the standard deviation over a 100-s interval (σz ,∆f = 0.01–25 Hz). We note that, as before [89], lateral differential stability was excellent(Fig. 3.3), achieving sub-Ångstrom precision (σ̄x = 0.4 Å, σ̄y = 0.4 Å). Since differential
stability is a measure of the residual laser noise in the system, it represents an ultimate
limit for microscope stability using this technique.

3.4

Firmly coupling fiducial marks to the sample
The enhancements in laser stabilization and sensitivity can only improve mea-

surements of sample position if the fiducial marks are firmly coupled to the cover slip.
Previously [89] and in Figure 3.2, 400-nm-diameter polystyrene beads, melted to thecover slip, were used as fiducial marks. Unfortunately, our melted beads still demonstrated significant motion. When differential detection or video-based detection wasused to detect the position of one fiducial mark, fiducial movement relative to the surface was undetected (Fig. 3.3 A). However, if differential detection was used to detect
two fiducial marks, then fiducial movement relative to the cover slip was visible. In
fact, in ∼80% of our traces, beads moved ≥1 Å relative to the cover slip (Fig. 3.3 B).
Such motion limited our ability to stabilize the microscope and presumably limited thestability of the work of others as well, though in such cases this added motion would
have been unseen without an independent measurement.
To surmount these challenges, we fabricated an array of fiducial marks that werean integral part of the cover slip. Low-index glass posts (see Section 2.2.1) yielded
excellent optical signals with sensitivities in x, y, and z sufficient for sub-Ångstrom
resolution and were, as expected, stable relative to the cover slip (Fig. 3.3 C). To
elucidate how these sensitivities scaled with volume, we constructed a range of posts

61

Figure 3.3: Fiducial mark movement as displayed by a differential measurement in x
(xdif = xin−loop − xmonitor , green) and y (ydif = yin−loop − ymonitor , red). (A) Bothlasers measure the position of one affixed bead (inset), masking the underlying bead
movement. (B) Each laser measures the position of different affixed beads (inset) sothat bead motion is apparent. The displayed trace is truly an average response with anoise level that is the median value for ten trials. (C) Each laser measures the position ofa fabricated post (inset), which does not display movement. Traces displaced verticallyfor clarity.

62
with varying w (350-725 nm). Interestingly, the sensitivity was proportional to thevolume of the post (Figure 3.4 A), agreeing with a model of the post as a point with apolarizability proportional to its volume [37, 100], even though the dimensions for larger
posts were comparable to the wavelength of the laser (λ = 785 nm).
As an alternative fiducial mark, we also investigated etched holes (see Section
2.2.1). Holes with different openings, w, gave different signals (Fig. 3.4 B). For thesmallest openings investigated, 100 nm, we measured an approximately linear signal
over an extended range. However, for larger openings, the response was nonlinear in
the middle of the hole. We conclude that hemispherical holes yielded high quality
signals, but flat-bottom holes did not. Additionally, holes have their optical center ∼1µm below the plane of the trapped bead, which requires detector beam foci to be indifferent planes, an added complication.

3.5

Active microscope stabilization
To actively stabilize the microscope, we first measured post position with thein-loop laser. Then the stage position was updated at 100 Hz to keep the position
constant in all three axes. The monitor laser, recording the same post, independently
determined microscope stability (Fig. 3.5 A). We note that this independent verificationof microscope stability, once performed, is not necessary in day-to-day stabilization
applications. Using the monitor laser, we achieve short-term microscope stabilities, as
described in Section 3.3, of σ̄x = 1.1 Å, σ̄y = 1.0 Å, and σ̄z = 0.9 Å (∆f = 1–25 Hz);and long-term stabilities of σx = 1.7 Å, σy = 1.2 Å, and σz = 3.5 Å (∆f = 0.01–25 Hz).
We note that the bandwidth of our feedback loop (100 Hz) is limited by the resonancefrequency of the stage (unloaded: 450 Hz horizontal and 1100 Hz vertical) and thesoftware-based processing speed. Stiffer PZT stages with higher resonances should leadto lower noise and higher bandwidth stabilization.
The robustness of this 3D stabilization was demonstrated by introducing a large,

63

Figure 3.4: Fabricated fiducial mark signals. (A) Horizontal response for low-index
glass posts of varying size. Posts were a constant height, h = 600 nm, with widths (w)of 350 nm (blue), 550 nm (green), or 725 nm (red). Inset, geometry of a post. (B)Horizontal response for etched holes of varying size. Holes had a constant radial depth(r = 500 nm) with initial openings, w, of 100 nm (blue), 200 nm (green), or 300 nm(red). Inset, geometry of a hole.

64

Figure 3.5: Active microscope stabilization to 1 Å. (A) Sample positional stability
measured by the independent monitor laser, xmonitor (green), ymonitor (red), and zmonitor(blue). (B) As in A, independent position records with active stabilization before andduring heating. At 40 s, the objective was heated, leading to significant vertical driftthat was compensated for by moving the PZT stage (e.g., zst , purple, vertical stage
position). Traces displaced vertically for clarity.

65
temporally controllable drift. We heated the objective with the trap laser (λ = 1064nm), which had a transmission of 59% [88]. This type of perturbation is often foundin optical-trapping assays [87, 96, 130], and a similar motion arises from the common
problem of objective settling. Specifically, we actively stabilized the microscope at aconstant low laser power of 50 mW (Fig. 3.5 B), then the laser power was increased bya factor of three to 150 mW at 40 s. During the following 50 s, the active stabilizationcompensated for the thermal expansion of the objective by moving the PZT stage 44
nm to keep the vertical position of the post constant. We note that active stabilizationin the presence of substantial drift yielded excellent long term stabilities of 1.5 Å, 1.4
Å, and 2.6 Å (∆f = 0.02–25 Hz) for σx , σy , and σz , respectively. Short-term stability(1–25 Hz) was essentially unchanged at 1.1 Å, 1.0 Å, and 1.0 Å for σ̄x , σ̄y , and σ̄z ,respectively.

3.6

Conclusions
The experimental advances presented here allow for 1 Å stabilization of an optical

microscope in three dimensions. The keys to achieving this stabilization were decreasing
low-frequency laser noise, increasing the sensitivity of the measurement in z, and firmly
coupling a fiducial mark to the surface to measure microscope drift. We anticipate
that this technique will be useful in precision particle tracking [138] and surface-based
fluorescence measurements [11]. More importantly, active microscope stabilization sets
the foundation for a precision optical trapping assay. Typically, surface-coupled opticaltrapping assays have a ∼20-Å noise level [96] that is dominated by mechanical drift [89].
By stabilizing this mechanical drift we reduce the noise so that precision measurements
are possible. In particular, measurements of enzymatic motion along DNA (helicase
unwinding, polymerase extension, translocase movement), which could be as small as 1
bp (3.4 Å), are especially motivating.

Chapter 4

Modified microscope stabilization for AFM

4.1

Introduction
Drift is a long-standing problem in microscopy. In an AFM, lateral drift between

the sample and the AFM tip at ambient conditions is on the order of 5 Å/s [52, 123]. To
circumvent drift and achieve Ångstrom-scale resolution, fast, lateral scanning of the tip
is necessary, though this reduces the signal-to-noise (S/N) ratio (Fig. 4.1). However,drift must be addressed for long time-scale scanning, for accurate registration of the
tip over the sample, for stationary “hovering” of the tip above a point of interest, orfor imaging 1D objects (nanotubes) and zero-point objects such as complex protein
structures, nanopores, or quantum dots. Thus, there is a clear need for tip-sample
control with Ångstrom-scale positional precision, registration, and stability. While sucha combination has been achieved passively in scanning probe microscopes at cryogenic
temperatures [29] and in ultrahigh vacuum [117], there is no routine method to achieve
this triumvirate of requirements in air or fluid at room temperature.
Several existing methods address active tip-sample control with varying success.
Commercial, closed-loop PZT stages provide for Ångstrom-scale stability using capacitive sensors to maintain stage position with respect to the frame. However, these sensors
are often located many centimeters away from the measurement position, allowing for
unseen sample drift. Tracking techniques [2, 99, 116] can yield atomic precision in
ultra-high vacuum, but they forfeit scanning or assume unvarying drift rates. Software-

67
based techniques [43] can reduce drift rates to ∼5 Å/min in ambient conditions [78], but
require predictions of future drift or compensate for drift only once per AFM image.
External optical techniques, applied in one [102, 113] or more dimensions [81, 79], havenot achieved Ångstrom-scale tip-sample stability or image registration (<10-nm overlay
precision [79]).
Previously, we demonstrated Ångstrom-scale sample control in 3D for a microscope with an optical-trapping application [17]. Stability was achieved by first detecting
the position of a fiducial mark on the sample with a focused laser, then implementing
a feedback loop to a PZT stage to keep the position constant. However, since thatwork used forward-scattered light [128], it is not compatible with AFM applications
due to limited or poor quality optical access opposite the imaging objective. Yet, BSD,
initially demonstrated over 10 years ago for optically trapped beads [33], is a viable
alternative. In this implementation, the sample and tip would be stabilized using the
BSD position of each in a feedback loop (Fig. 4.2), though we see three critical criteria
to demonstrate before BSD is adopted for tip or sample control in AFM (or in optical trapping applications). These criteria are: (i) Ångstrom-scale sensitivity in 3D, (ii)similar-scale stability, and (iii) low optical crosstalk between detection axes for scanningand registration purposes.
We overcame these limitations and used BSD to actively stabilize a microscope.
We first enhanced the BSD signals from the fiducial mark, and minimized the crosstalk
between axes (x-y coupling of 3% and x-z coupling of 1%). After establishing thesehigh quality BSD signals (Section 4.2), we then demonstrated active stabilization ofa microscope (Section 4.3) to <1 Å rms (∆f = 0.1–50 Hz). This active stabilization
allows for stabilized scans (Section 4.4), composed of orthogonal steps, and registrationthat is maintained to <0.5 Å rms, even after many 100-nm displacements (N = 14).
More importantly, this microscope stabilization represents the enabling technology for
an ultrastable AFM.

68

Figure 4.1: One motivation for an ultrastable AFM: fast scans overcome drift but
sacrifice S/N ratio. (A) AFM image of two gold nano-spheres on the surface taken witha fast scan speed (150 µs/pixel) relative to the cantilever response time (250 µs). (B)Same as in A with a slower scan speed (10 ms/pixel). Tip-sample drift during imaging
distorts the image. (C) Scan speeds that have a time per pixel that is shorter thanthe cantilever response time sacrifice S/N ratio. The force on the cantilever (Ftotal ),which is the sum of an ideal force (FR ) plus thermal noise (Fth ), changes when a surface
feature (Z) is encountered. If the time per pixel is shorter than the cantilever responsetime (red shaded region), the signal (red data point) is lower and the noise (error bars)
is higher than if the time per pixel is several cantilever response times (green shaded
region, green data point). Figure credit: Gavin King and Allison Churnside.

69

Figure 4.2: Basic principle of AFM stabilization. A focused laser scattered off a fiducial
mark on the surface and the back-scattered signal was detected by a QPD to measurefiducial position (yfid ). This position was then used in a feedback loop to the sample
PZT stage to keep fiducial position constant. Similarly, a second focused laser and QPD
measured the position of the apex of the AFM tip (ytip ), and a feedback loop to thetip PZT stage stabilized that position. Overall AFM stability relied on the differential
pointing stability between the lasers (ylasers ), which was 0.2 Å over 0.1–50 Hz. Normal
AFM imaging (zAFM ) with an optical lever arm detection was not affected.

70
The application of this active stabilization system in AFM is discussed in Section
4.5. We show that using these BSD signals we can stabilize tip position to ¡1 Å (rms,∆f = 0.01–10 Hz), which allows ”hovering” over a region of interest. In addition, bystabilizing both the tip and the sample, we achieved stable scanning and registration of
2.4 Å for one hour. Two-dimensional images taken in this way showed 4-5 pm/min ofresidual drift, similar to results achieved in cryogenic conditions of 1 pm/min [116].

4.2

Increasing the sensitivity of back-scattered detection
Previously, BSD sensitivity was reported as ∼0.2 mV/nm, which is too small tomeasure Ångstrom-scale motion (digitization at 0.1 mV/bit). We increased the sensitivity of BSD by both increasing the BSD efficiency so that more light was incident on
the detector (see Section 2.1.2) and amplifying the resulting signals (see Section 2.1.3).
To check the resulting sensitivity, we sequentially scanned the silicon disk fiducial markthrough the laser focus in all three axes using the PZT stage and recorded the resulting
detector signals (Fig. 2.11). This yielded sensitivities of 38 mV/nm, 40 mV/nm, and
20 mV/nm in x, y, and z, respectively. Thus, BSD has the sensitivity to detect singlepicometer motion, though our differential stability (19 pm) is currently limited by otherlaser noise sources (see Section 4.3). Additionally, we achieved a low level of crosstalk:
3% between x and y signals and 1% between lateral and z signals over a 200-nm region,similar to the results achieved using forward-scattered light [60]. For raster-scanning applications, increased accuracy, or for large displacements, we parameterized the residualcrosstalk [60].
The high sensitivity of BSD is not limited to silicon disks (Fig. 4.3). We directlycompared these disks to polystyrene beads (r = 300 nm) at equal amplification andwithout vertical offset amplification. The resulting records showed comparable BSD
signals. The comparable lateral sensitivity (SSi /Sps = −0.8; where SSi is the sensitivityof the silicon disk and Sps is the sensitivity of the polystyrene bead) was achieved even71
though the beads were ten-fold larger by volume than the disks; the sign change in Sps
for polystyrene beads has previously been reported [44].
Qualitatively, we would expect a larger sensitivity per unit volume to arise fromthe higher index of refraction of silicon. To test this hypothesis, we compared thesensitivity of silicon disks and polystyrene beads to the calculated value we might expect
given the index of refraction of each. Calculations by Gittes and Schmidt [37] using a firstorder interference model in the Rayleigh approximation have successfully been applied toquantitatively predict the sensitivity for forward-scattered detection by spherical beads.
These authors and others [100] have shown that the magnitude of the sensitivity scaleswith the polarizability α of the scattering particle. We applied this approximation tothe observed lateral back-scattered signals. The polarizability of a spherical scattering
particle is:αsphere = 3V [m2 − 1]/4π[m2 + 2],(4.1)

where V is the volume, and m is the index of refraction ratio (m = nobject /nsolvent ) [37].
This equation holds for the general case of complex m. By approximating the silicondisk as a sphere and using an index of 3.9 + 0.15i (amorphous silicon at λ = 810 nm)[91], we calculated the ratio of the polarizability between silicon and polystyrene to be:[αSi /αps ] = VSi ([m2Si − 1]/[m2Si + 2])/Vps ([m2ps − 1]/[m2ps + 2]) = 7.1VSi /Vps .

(4.2)

The measured ratio of polarizabilities and thus, within our approximation, the ratio ofsensitivities is 0.8. After division by 7.1, this yields a predicted volume ratio of 0.11
in agreement with the actual volume ratio of 0.10. Thus, within this approximation,
the increased lateral sensitivity of silicon relative to polystyrene was consistent with thehigher index of refraction of silicon. As a consequence, by using silicon, we could use
substantially smaller fiducial marks while retaining suitable sensitivity.
We note that the success of this first-order approximation does not prove thelateral sensitivity is linear in α nor that an interference model is the correct description

72

Figure 4.3: BSD signals vary with index of refraction of the medium and fiducial mark.
Comparison between silicon disks in water (green) and air (yellow), with polystyrene
beads (r = 300 nm) in water (red) for both lateral and vertical signals.

73
of BSD. However, like the interference model for forward-scattered detection [37], ourlateral response is quantitatively described by the derivative of a Gaussian (Fig. 4.3),
and our 500-nm-diameter, 56-nm-high disks are neither large nor small compared to
the wavelength of light and, therefore, the Rayleigh (or Mie) approximation [118] is
not strictly correct. Future work, based upon a detailed study of the response for bothsilicon disks and polystyrene beads as a function of their size and surrounding medium,coupled with improved modeling, should lead to a complete description of BSD.
Vertical response of BSD is distinctly different than that of forward-scattereddetection (Fig. 4.3). As the disk was vertically scanned through the beam waist, theback-scattered signal dramatically increased 200% from a low-level baseline to a maximum, and then monotonically decreased towards the baseline over ∼1500 nm (maximal
lateral sensitivity occurs at z = 0). In contrast, vertical motion in forward scattered detection leads to a small modulation (∼10%) on top of a comparatively large static signal[100]. We also note that the origin of our BSD vertical sensitivity was different thanprior BSD reports; we under-filled our 10-mm-diameter QPD with a 6-mm-diameterbeam (see Section 2.1.2), whereas prior vertical sensitivity was based on overfilling the
QPD [33] or using BSD in combination with a reflective element [50, 49].
One application of this work is in scanning and stabilizing a sample for AFM;
many AFM applications occur in air or vacuum. To demonstrate BSD in air (Fig. 4.3,gold), we scanned the silicon disk through the detector beam in the flow chamber, prior
to measuring the same disks in water. The sensitivities were two-fold higher in air thanin water, allowing stabilization in non-aqueous environments.
Overall, BSD detection provides excellent optical signals for both polystyrene
beads and silicon disks, and is capable of sensing very small motions with minimal
crosstalk. Lateral response was well fit by the derivative of a Gaussian and is similar inshape to the forward-scattered response. Vertical response was distinctly different andinherently more sensitive than the forward-scattered response.

74

4.3

Active microscope stabilization using back-scattered detection
To demonstrate the stability of BSD, we next actively stabilized the sample (Fig.

4.4) with the in-loop laser (λ = 810 nm), while measuring the residual motion with themonitor laser (λ = 810 nm). We achieved average short-term (1–25 Hz) stabilities (aspreviously calculated in Section 3.3) of σ̄x = 48 pm, σ̄y = 48 pm, and σ̄z = 49 pm. We
also achieved a long-term (0.01–25 Hz) stability of σx = 50 pm, σy = 49 pm, and σz =57 pm.
While previous experiments using BSD do not report real-space stabilities, they
do report power spectral densities for their electronic noise floor [33, 44]. In Figure
4.4 B, we plot the power spectral density of our actual stabilization records. At higher
frequencies (>20 Hz), our achieved stabilities were equal to or better than these previous
electronic noise floors. At low frequencies (<20 Hz), our achieved stabilities stayed low;
previous BSD work, in contrast, showed a rapidly increasing electronic noise floor aswell as a two-fold increase in the power spectral density of an optically trapped bead
between 20 and 2 Hz, suggesting significant low frequency noise [44]. Our low broadband
noise (∼10 pm/Hz between 0.1 Hz and 1 kHz) demonstrates the significant reduction
in instrumental noise achievable with BSD coupled with active reduction in optical andmechanical noise.
An excellent alternative metric for calculating stabilities is to integrate the power
spectral density within a specified bandwidth to calculate the integrated noise. We
computed the integrated noise from 0.1 to 50 Hz, a broad bandwidth useful for a rangeof AFM and optical trapping experiments. The resulting stabilities were 88, 79, and 98
pm, in x, y, and z respectively. Calculating the equivalent metric on real-space data
yields similar results as required by Parseval’s Theorem [101], verifying the appropriatescaling of the power spectral density. Thus, our stability over this real-world usefulbandwidth (0.1–50 Hz) is below 1 Å on all three axes.

75

Figure 4.4: BSD active stabilization. (A) Sample positional stability as measured
by the monitor laser: xmonitor (green), ymonitor (red), and zmonitor (blue). (b) Power
spectral densities (PSD) of the stabilized data shown in A. The lateral localization
precision limit, deduced by measuring the same unstabilized disk with two lasers [89],was substantially lower (light green).

76
The excellent stability achieved here is partially due to the optical conciseness of
BSD (see Section 2.1.1 and 2.1.2, which increases the mechanical stability and is one
potential advantage over forward-scattered techniques. Mechanical stability enables thesubstantial, yet zero mean, Brownian motion inherent in many assays to be averaged
down to atomic dimensions. Though mechanical stability is an engineering challenge inforward-scattered detection since optics are required at two different vertical levels: thatof the input light coupled into the objective and that of the output light on the back sideof the condenser incident upon the QPD. For inverted microscopes, this second verticallevel is the more technically challenging one; it requires a lightweight, mechanicallyrigid set of lenses, filters, and QPDs that is often bolted onto the condenser arm of acommercial research microscope (see Section 2.1.1 and Appendix D). In contrast, BSD
optics external to the microscope are in a single horizontal plane.
Achieved stabilities do not reflect the ultimate localization precision of BSD. A
better metric is the differential measurement (see Section 3.3) between the two lasers[89], which records the residual laser noise and is not dependent on the positional resolution of the PZT stage. We plot the power spectral density of the lateral differential
measurement (Fig. 4.4 B, light green) so that the amplitude of the residual laser noisefor different frequencies is easily visible. The integrated noise on the differential signal
from 0.1 to 50 Hz was 19 pm in both x and y, and 73 pm in z. Hence, microscope
stability using BSD will be ultimately limited by this localization precision.
Improvements in instrumentation to extend sample stabilization to this ultimate
localization precision might include better mechanical and optical design as well as
enhanced isolation from vibrations (Fig. 4.4 B, 23-27 Hz peak]. Low frequency performance can be limited by a number of factors, including non-common-mode opticalmechanical noise (e.g., differential motion between the QPDs or mirrors), variationsin index of refraction [1], and thermal stability. We speculate that our low frequency
performance is currently limited by the temperature (>1 ◦ C) and pressure fluctuations

77
in the room, which could be alleviated by moving the apparatus to a temperature regulated (±0.2 ◦ C), acoustically quiet (NC30) room, as in the optical trapping experiment.
High frequency performance is currently limited by our software-based feedback loop(100 Hz). Real-time embedded control (e.g. field programmable gate array) provides ameans for deterministic timing and increased bandwidth up to and limited by the PZTstage resonance [21]. For anticipated AFM applications, the loop closure time will limit
the scan-rate for stabilized scans, while low frequency noise will limit registration andthe ability to “hover” a tip over a specified point on the sample.

4.4

Ultrastable scanning and registration
Ultra-stable scanning of a sample requires precise steps. Ideally, such scanning

would occur without drift on any axis. Atom tracking [99], the most popular method
for sample stabilization in scanning probe microscopy [121, 123], is fundamentally incompatible with simultaneous scanning and stabilization. In this work, we demonstratesimultaneous scanning and stabilization using BSD to locally measure and thereby control sample location. The basis of scanning is a series of uniform steps. To demonstrateuniformity in the step size, we made a staircase of 0.5-nm steps sequentially in all
three axes. The sample position was actively controlled in 3D at all times with thein-loop laser. Changes in the feedback set point led to scanning. The reported results
were determined with the monitor laser, which provides an independent verificationof feedback-performance. The resulting records show linear motion in one axis withnegligible motion on the stationary axes [Fig. 4.5 A].
Individual steps were clearly resolved and repeatable in size (Fig. 4.5 B). To
provide an unbiased measurement of step size and an estimate of the S/N ratio, we
computed the histogram of the pair-wise distance difference (Fig. 4.5 C), which shows
the distance between each pair of points [35]. Ideally, every such difference would be amultiple of 0.5 nm. A Fourier transform of the pair-wise distance difference histogram

78

Figure 4.5: Stabilized microscope scanning using BSD. (A) The sample was moved in
0.5-nm steps sequentially along each axis under active stabilization. Sample position,
independent of the servo-loop, was measured with the monitor laser (xmonitor , green;ymonitor , red; zmonitor , blue). Traces displaced for clarity. (B) Individual steps smoothedwith a box-car window and decimated to 100 Hz show uniform 0.5-nm motion. Traces
displaced for clarity. (C) A histogram of pair-wise distance differences (PDD) alongeach axis shows peaks every 0.5 nm. (D) Fourier transform of the PDD histograms in(C) reveals the power spectral density (PSD) of the data as it varies with the spatial
frequency (k). The peak of the PSD is at 2 nm−1 , as expected.

79
determines the spatial frequency components present in the data (Fig. 4.5 D). Peaks
occurred at 2.0 ± 0.1 nm−1 , 1.9 ± 0.1 nm−1 , and 1.9 ± 0.1 nm−1 (peak ± FWHM)
in x, y, and z, respectively. The S/N ratio for these 0.5-nm steps is 30, 28, and 32,
for motion along x, y, and z, respectively, based on the next largest peak. Thus, ourimplementation of BSD enables both precise and accurate steps as well as scanningconcurrent with active stabilization on all axes.
Precision is fundamental to registration — the ability to repeatedly return to aparticular sample position. Sample drift limits registration, and therefore, the ability
to return to a particular location for subsequent detailed study. To demonstrate registration, we repeatedly moved the sample back and forth in 100-nm steps individuallyon all three axes for a total of fifteen 6-s cycles (Fig. 4.6 A). The average step position(xN
monitor ) after each movement back to the starting location was compared to the initial
0
step value (∆xN = xN
monitor − xmonitor ) and plotted versus the step number to show the

spread in the relative registration (Fig. 4.6 B). The standard deviations of the relative
position of these steps were 25 pm, 21 pm, and 58 pm in x, y, and z, respectively.
The experiment was repeated with 1-nm steps and yielded essentially identical results.
Thus, the registration is near to and limited by our long-term, low-frequency stability(σx = 11 pm, σy = 16 pm, σz = 40 pm, in 100 s of data filtered to 0.3 Hz).

4.5

Application to AFM

4.5.1

Measuring tip position to 0.2 Å

Before applying the Ångstrom-scale sample control afforded by BSD to stabilize
an AFM tip, we needed to establish that BSD could localize an AFM tip — a highly
asymmetric object in comparison to beads and thin silicon disks. Ideally, such a signal
would be sensitive to Ångstrom-scale motion in 3D with low cross-talk between axes.
To demonstrate these signals, we first positioned a silicon tip 300 nm above a glass

80

Figure 4.6: Registration with BSD. (A). The sample was moved in a series of fifteen
back-and-forth 100-nm steps sequentially on each axis. The steps were actively stabilized with the in-loop laser while the resulting motion was verified with the monitor
laser [xmonitor (green), ymonitor (red), and zmonitor (blue)]. (B) Mean values of the step
position subtracted from the initial value are plotted as a function of step number anddemonstrates the excellent registration of our technique.

81
surface in air and then sequentially translated it through the 810-nm laser focus alongeach axis, yielding a voltage-versus-distance curve (Fig. 4.7). The QPD signal during
on-axis motion was approximately linear, whereas the off-axis traces were nearly flat(<10% cross talk over a 50-nm range). A two-fold increase in the laser power used for
BSD (from 400 W to 800 W at the tip) did not alter the shape or the magnitude of
the BSD signals, but did introduce a slight z offset (<1 nm) on the cantilever. Such
BSD signals formed the basis for subsequent tip voltage-to-position calibration (seeSection 2.3.1). With active reduction in laser noise (see Section 2.1.4) and electronic
amplification (see Section 2.1.3), the resulting sensitivities (>6 mV/nm) were sufficient
to detect picometer-scale motion (digitization at 0.1 mV/bit).
In the current implementation, we used transparent substrates in air, but wehave also achieved proof-of-principle, tip-based BSD signals in several conditions including in liquid and through both birefringent and thin metallic substrates [51]. In
addition, nanometer-scale metallic particles (5-nm height, gold) scanned through the
tip-stabilization laser did not degrade the optical signal. Thus, BSD-based tip detection is robust to small optical changes in the local detection volume and, in principle,compatible with several different environments and non-opaque substrates.

4.5.2

Active stabilization achieves 0.3-Å tip stability

We used BSD signals to measure and actively stabilize the position of an AFM
tip in 3D. For this demonstration, both detection lasers were focused onto a silicon tip
that was 300 nm above the glass surface. We employed the 810-nm signal as the in-loop
laser and the 845-nm signal as the independent monitor laser. Long-term stabilities
detected by the monitor laser (Fig. 4.8 A) were 26 pm, 39 pm, and 25 pm in x, y, andz respectively (σ, ∆f = 0.01–10 Hz). Histograms of this data (Fig. 4.8 B) provided acomplementary analysis and were well fit by Gaussian curves, with standard deviationsof 28 pm and 26 pm in x and z, respectively. These reported stabilities represent

82

Figure 4.7: AFM tip signals in air. Records of the QPD signal versus tip position
are shown for x (green), y (red) and z (blue) on the moving axis (solid lines) and thestationary axes (dashed lines) from light scattered off a commercial silicon tip. Figure
credit: Gavin King and Allison Churnside.

83
a metric for the ultimate positional control between the tip and sample that can beachieved with our current apparatus and include the uncertainty due to pointing noise
between the detection lasers.
With this Ångstrom-scale stabilization, we also show similar-scale tip control (Fig.
4.8 C). We scanned the tip in a pattern by updating the feedback set point which changes
the position of the tip relative to the lasers while maintaining stability. Measurementsof tip position by the in-loop laser show movements on the scale of Ångstroms, an orderof magnitude better than previous tip control techniques [81].

4.5.3

Stable AFM scanning and registration

To demonstrate an ultrastable AFM, we stabilized the tip while in contact withthe surface and stably scanned (see Section 4.4) a 5-nm gold particle attached to thesample through the tip (Fig. 4.9 A). These particles are known to be robust and incompressible in ambient conditions [126] and are often used as AFM calibration standards.
To demonstrate tip-sample registration and stability, we located an individual particle
on the surface and repeatedly scanned in x, yielding a series of line scans z(x) (Fig.
4.9 B). We took a set of three line scans over 60 s and then held the tip stationary(“hovered”) 10 nm outside of the scan range for 20 s; this cycle was iterated eight times
for a total duration of 640 s. Each scan contained a peak in z corresponding to theparticle center point. The peak locations for each set of line scans were averaged. The
average peak location (xpeak ) was stable to 160 pm over eight iterations of hovering and
10 min of time (Fig. 4.9 C). Thus, the ability to stably scan and repeatedly returnthe tip to the same feature demonstrates an ultrastable AFM with both atomic-scalestability and registration.
One succinct visual representation of both registration and stability is to forma kymograph. In this presentation, successive line scans, one every 20 seconds, form
the rows of an image. A stationary object maps out a vertical path. We formed such

84

Figure 4.8: Ångstrom-scale AFM tip control in 3D at ambient conditions. (A) Tip
position records versus time were low-pass filtered to 10 Hz and offset vertically forclarity [x (green), y (red), z (blue)]. Positions were determined by a monitor laser
while the tip was actively stabilized with the in-loop laser. (B) A scatter plot of thetip position (purple) in the x-z plane from the 100-s record in A. Histograms of thedata projected onto the x and z axes were well fit by Gaussian curves with standard
deviations of 28 pm and 26 pm, respectively. (C) To demonstrate tip control, the tip
position in x and y was recorded as the tip was scanned in a pattern. The in-loop tip
position is plotted. Figure credit: Gavin King and Allison Churnside.

85
kymographs from the above data (Fig. 4.9 D) and from an hour of data where thetip was alternatively stabilized at two positions separated by 12 nm (Fig. 4.9 E). The
stability of the peak location over this hour was 2.4 Å in x.

4.5.4

Stable AFM imaging

To further demonstrate an ultrastable AFM, we show precise, independent controlof the tip and sample. We imaged a particle with a silicon-nitride tip while stabilizing the
3D position of the sample (Section 4.3) and the lateral position of the tip (Section 4.5.2).
The z position of the tip PZT stage was adjusted to maintain a constant tip-sample
interaction force (F ∼ 200 pN) which was determined via the cantilever-deflectionsensing laser. We acquired seven sequential images. Representative images at the
beginning, middle and end of the time course are displayed in Figure 4.10 A. Line scansthrough these images showed no significant lateral motion (Fig. 4.10 B).
To demonstrate atomic-scale stability and registration, we performed a 2D crosscorrelation analysis [51]. This analysis precisely tracked the location of the particle
during the 82 min of continuous imaging (Fig. 4.10 C). Over this time scale the stability and registration of our technique was <5 Å. Linear fits to the particle position
revealed residual lateral drift rates of 4 and 5 pm/min in x and y, representing a 250-fold
reduction of the inherent instrumental drift rate [51]. These residual rates, achieved in
air at room temperature, are close to those found in cryogenic conditions (∼1 pm/min,
8 K) [116]. The precision of this control (and analysis technique) are further verified bysmall average deviations — 23 and 40 pm in x and y, respectively — from the linear
fits. While we refer to the time evolution of the correlation-peak position as “residual
drift”, this apparent motion could also arise from instability of the particle relative tothe cover slip [17] or from tip-sample degradation.

86

Figure 4.9: AFM scanning and registration. (A) Cartoon of AFM scanning over a gold
particle. (B) Line scans of a gold particle taken every 20 s. Sets of three lines scans
were separated by hovering the tip 55 nm away from the particle for 20 s, forming
one iteration. The sets of line scans shown represent the first (purple), middle (green),
and final (gray) iterations of a 640 s record. Traces are displaced vertically for clarity.
(C) Atomic-scale stabilization and registration is demonstrated by plotting average peak
position (xpeak ) from the set of scans in B vs. iteration number. The standard deviationin xpeak was 160 pm over 10 min. (D) A kymograph of the above data, where rows in
the image are successive line scans. The line in the kymograph associated with hovering
is set to uniform color. (E) A kymograph of line scans formed from one hour of data
where the sample position was alternated between two positions offset by 12 nm, shows
both long-term stabilization and registration. The vertical scale bar for both C and D
is shown. Figure credit: Gavin King.

87

Figure 4.10: Ultrastable AFM imaging. (A) Images of a 5-nm gold particle taken attimes 0, 41 and 82 minutes, respectively. (B) Line scans through the center of each
image. (C) Relative lateral position of the particle plotted vs. time as determined bya cross-correlation analysis (x, green; y, red). From linear fits to the data, we deduced
residual lateral drift rates of 4 and 5 pm/min in x and y, respectively. Figure credit:
Gavin King and Allison Churnside.

88

4.6

Conclusions
With BSD, we achieved Ångstrom-scale sample localization precision, stability,

and registration in all three axes. In addition, we demonstrated that BSD can meet or
exceed the best stabilities achieved with forward-scattered detection in all dimensions.
In contrast to prior BSD work, we achieved this enhanced sensitivity when underfilling
the QPD. Fundamental to this set of state-of-the art metrics, unprecedented in aqueousor ambient conditions, is active stabilization based on a local optical measurement ofsample position. Thus, we could scan while actively stabilizing the sample on all threeaxes.
Moreover, we demonstrate that back-scattered light off the apex of a commercially available AFM tip provides a means to an ultrastable AFM without resorting
to low temperatures or ultra-high vacuum environments. Ångstrom-scale stability andregistration enable returning to a particular feature in an image, such as a domain of aprotein, and hovering the tip over this feature for extended periods — allowing detailed
study of vertical motion with high temporal resolution. Feedback is performed at relatively low frequency, so this stabilization technique should be compatible with tapping
mode and frequency-modulated cantilever detection methods. The scanning range canbe easily extended to several microns by sequential moves of the laser with a PZT mirror. We anticipate that the shape and material properties of the tip and fiducial mark,as well as the wavelength of the laser, can be varied to suit different applications. Morespecifically, silicon wafers, in lieu of cover glass, can be accommodated by shifting to alonger wavelength detector laser below the silicon band-gap. In cases where changing
the wavelength of the laser is not an option a fiducial mark could be engineered into the
cantilever that spatially separates the tip from the laser. Such separation would enable
strongly scattering, optically opaque, or time-varying specimens [98] to be studied withsimilar Ångstrom-scale stability and registration.

89
The optical and mechanical conciseness of BSD makes this technique amenable toa wide variety of applications and underlies its superior stability and optical efficiency.
We foresee integration of BSD into many applications seeking ultrastable 3D detection
and control, especially those with poor quality or limited optical access opposite of
the microscope objective, such as scanning probe microscopy and magnetic tweezers.
Though, BSD can be used in optical trapping assays as well. Such detection is more
optically compact, and in our experiments, more robust. While we do not apply thistechnique to our optical trap or use it to measure RecBCD motion, its discussion here
represents an interesting side-track and perhaps a future direction to take.

Chapter 5

Precision optical trapping assay sensitive to Ångstrom-scale motion

5.1

Introduction
Detection of single-molecule motion at or near the Ångstrom-scale reveals previ-

ously inaccessible details about biomolecular dynamics [77]. Surface-coupled trapping
assays have measured the 1-codon step of the ribosome that, with mechanical amplification, corresponds to a 2.7-nm displacement [132]. To resolve smaller motions, suchas the 1-base-pair (3.4-Å) step of RNA polymerase [1], researchers decoupled their experiments from the surface using dual-beam optical-trapping assays [1, 76] to reducesurface-induced noise. Yet, the vast majority of single-molecule optical-trapping assays
are coupled to surfaces [5, 11, 45, 48, 64, 120, 132, 140]. What is needed is a general method that permits surface-coupled optical-trapping assays to achieve positional
precision at the Ångstrom-scale.
Measurements of biological motion by optical-trapping experiments are corrupted
by various noise sources (thermal, mechanical, laser, etc). Thermally driven Brownian
motion is dominant on short time scales (<0.01–0.1 s). Such motion, which has a zeromean, can be averaged to atomic-scale dimensions at the expense of temporal resolution
and sets a theoretical limit for positional precision (i.e. the thermal limit, see Section
5.2). To achieve this thermal limit, other noise sources must be reduced to maintainÅngstrom-scale instrumental stability over the same (or ideally longer) time period.
Current surface-coupled optical-trapping assays lack such Ångstrom-scale instru-

91
mental stability. A surface-coupled assay is physically connected to its local environment(e.g., cover slip or micropipette) and thus sensitive to mechanical perturbations throughthis connection. One common application of this class of assays has a DNA molecule
attached to a surface at one end while attached to an optically trapped bead at theother (Fig. 2.1). As a first step towards a surface-coupled optical-trapping instrumentwith atomic-scale sensitivity, we stabilized an optical microscope to 1 Å in 3D [17].
In applying this technique to optical traps, two detection lasers (one monitoring thetrapped bead, the other measuring fiducial position) establish a local, differential measurement reference frame. Local detection suppresses motion (e.g., thermal expansion)
unmeasured by sensors in closed-loop stages. Differential measurement suppresses noise(e.g., air currents and objective drift) common to both lasers [89]. The ultimate limit on
instrumental stability is set by the differential pointing stability between the detection
lasers (<0.065 nm laterally, ∆f = 0.1–50 Hz).
Mechanical stabilization of the surface alone was insufficient to achieve Ångstromscale resolution in our optical trapping apparatus. The trapping laser was also a significant source of instrumental noise. To achieve base-pair resolution, dual beam experiments not only decoupled the assay from the surface, but also reduced laser pointing
instability by either encasing the optics in a helium enclosure [1] or by using a differential measurement [76]. In contrast with these passive methods, we adopted an active
method to not only reduce pointing noise but also other types of laser noise (intensity,mode, and polarization noise) that affect instrumental stability. We were motivated, inpart, by our analysis which shows that trap laser intensity fluctuations of 1% induce
apparent motion of 1 bp for a 1 µm long DNA molecule (see Section 5.2).
For studying the dynamics of molecular motors and nucleic acid structures, wesought to achieve atomic-scale stability immediately after changes in applied force. Previous work has only reported base-pair stability at constant force, presumably after any
thermal perturbations caused by changes in the trap laser power have subsided. We

92demonstrated sensitivity to 1-bp steps along DNA at moderate force and 1-bp stability
immediately following a substantial change in force (3.4 pN) as well as sensitivity to
0.1-pN force-induced changes in DNA hairpin unfolding dynamics.
In summary, prior work [1, 76] has removed the surface from the assay and has emphasized the importance of minimizing pointing noise. We stabilized a surface-coupledassay and reduced various laser noise sources, including intensity noise. Calculations
show that controlling intensity noise is important when the bead is offset from the trap
center.

5.2

Noise in optical trapping assays

5.2.1

Thermal noise

Thermally driven Brownian motion has a zero mean, so time averaging bead position, xbd , reduces the uncertainty in position as long as instrumental drift is negligible
over the time span averaged, τavg . On short time scales (<1/f0 ; f0 is the roll-off frequency of trapped bead motion), bead motion is correlated and thus not statisticallyindependent. However, by averaging N independent data points spaced at the correlap

tion time (1/f0 ), the standard deviation of the data (σD = kB T /kT ; kB T is thermal√energy and kT is the trap stiffness [118]) decreases by N . The uncertainty in xbd after
averaging a specific time (τavg ) is given by the standard error of the mean (σSEM ),σDσSEM = √ =NskB T 1=kT τavg f0s

kB T 12π 2 ηrbd,(kT )2 τavg

(5.1)

using the relationship kT = 12π 2 ηrbd f0 ; where η is the viscosity of the liquid and rbd
is the radius of the bead. (Note: This formula assumes that there is not a correction
due to proximity to a surface.) Thus, theoretically, in an optical trap with a high trap
stiffness of kT = 0.53 pN/nm and rbd = 165 nm, this uncertainty reduces to 3.4 Å (1bp) in 2.5 ms. At a moderate kT of 0.086 pN/nm, the time to average to σSEM = 3.4
Å increases to 95 ms.

93
To achieve a noise level that is at the thermal noise limit, other noise sources (i.e.
surface or laser noise) must be reduced to maintain instrumental stability over the same(or ideally longer) time period. (Note: Experimentally, our results for the trapped beadexample quantitatively matched the predictions above. We achieved 1 bp resolution,
σSEM = 3.4 Å, in 2.5 ms and 103 ms, at the respective trap stiffnesses. Thus our ability
to measure trapped bead position in an optical trapping assay is close to the thermal
noise limit.)

5.2.2

Surface noise

Current surface-coupled optical-trapping assays lack Ångstrom-scale instrumental
stability over long time-scales (100 s) [77] because of surface noise [89]. While dualbeam assays have removed the surface from optical trapping experiments to increase
resolution, we have stabilized the surface to 1 Å over 1–25 Hz in 3D [17], reducing thisnoise source.

5.2.3

Laser noise

In assays where lasers are used, multiple types of laser noise degrade instrumental
stability. For example, in an optical trapping assay, the trap and detection lasers areprone to mode, polarization, pointing, or intensity noise. Mode and polarization noise
generally appear as pointing or intensity noise after the optical element that couples thelasers into the microscope, the dichroic mirror. Thus, we will only discuss pointing andintensity noise.
Pointing noise moves the trap laser relative to the detection laser, which appears
as an erroneous trapped bead movement, δxbd . The coupling between the pointing
movement and the trapped bead movement is 1:1; so if pointing noise is on the scale ofnanometers then this source of laser noise typically dominates over atomic-scale measurements. To reduce pointing noise to the Ångstrom-scale, researchers have enclosed

94
the laser optics in a Helium-filled box [1], or have mechanically held a fiber-coupled laser
in a rigid mount [89]. In addition, researchers have used a differential measurement between two lasers to remove non-common pointing noise [76, 89].
Intensity noise, while important, has not been addressed. Intensity noise appears
as a change in trap stiffness, δkT , which causes a change in the potential energy and an
erroneous trapped bead movement, δxbd , when the bead is offset from the trap centerby a load (Fig. 5.1 A). Here we calculate the effect intensity fluctuations have on both
xbd and the contour length (L) in a DNA tethered particle assay (Fig. 5.1 B).
We used a simplified one-dimensional model where the forces on the bead werebalanced. The force exerted by the DNA (FDNA ) was equal to the force exerted by thetrap (FT ) i.e.,
FDNA = FT = kT xbd .

(5.2)

0
0 x0 , where F 00Initially, FDNA was equal to FDNA
= kT
DNA is the initial force, xbd is thebd
0 is the initial trap stiffness. If the intensity of the trap (I)initial bead position, and kT

fluctuated by δI, this caused a fluctuation in the trap stiffness (δkT = δI
I kT ), which
moved the bead (δxbd ) and changed FDNA . To calculate the current FDNA , we used a
Taylor series to expand around the initial extension of the DNA, x0DNA ,00
FDNA = FDNA
− kDNAδxbd ,

(5.3)

0
DNA
where we defined the initial DNA stiffness as kDNA
= ∂F
∂xDNA |xDNA =x0

DNA. Thus, after

the intensity fluctuation, the balance of forces in Eq. 5.2 was now rewritten as000− kDNAδxbd = (kT+ δkT )(x0bd + δxbd ).
FDNA

(5.4)

Solving for δxbd gave
00
δxbd = −x0bd δkT /(kDNA+ kT+ δkT ).

(5.5)

After calculating δxbd , we calculated the apparent change in the contour length,
δL. We determined the fractional extension of the DNA (f = xDNA /L), which is the

95

Figure 5.1: Intensity noise affects trapped bead position (xbd ) and measurements of
DNA contour length (L). (A) Unwanted bead motion (δxbd ) occurs under constantload (F ) when an intensity fluctuation (δI) decreases the trapping potential. (B) A one
dimensional diagram of the experiment and its mechanical analog. Variables represent
the following: kDNA is the nonlinear stiffness of the DNA molecule, kT is the trap
stiffness, xstage is the distance between the tether point and the trap center, xDNA isthe end-to-end extension of the DNA, and rbd is the bead radius. (C–E) Based on afirst order calculation (Eq. 5.8), the uncertainty in DNA contour length (δL) is linear
in intensity fluctuation (D) and DNA length (C), but independent of kT at constantforce (E). Calculations were performed with a constant trap force of 6 pN and rbd of
165 nm. When parameters were not varied they were held fixed at the following values:
δI = 1%, kT = 0.086 pN/nm, kDNA = 0.187 pN/nm, xbd = 70 nm, and L = 1000 nm.

96
ratio of the DNA extension to the contour length. To determine f , we used an inverse
formula valid at forces >1 pN [71],qf = 1 − (1/ 4kT xbd p/kB T ).

(5.6)

Here kB T is thermal energy (4.1 pN-nm) and p is the persistence length of the DNA(40 nm) at our ionic conditions and contour length (1000 nm) [108]. Then, we used f
to find L,
L = xDNA /f = (xstage − xbd − rbd )/f,

(5.7)

where xstage is the distance between the trap center and the tether point of the DNA.
Given Eq. 5.6 and Eq. 5.7, δL was found by calculating the initial contour length andsubtracting it from the current contour length,δL =(xstage − x0bd − δxbd − rbd )q(1 − 1/ 4pkT (x0bd + δxbd )/kB T )−(xstage − x0bd − rbd )q(1 − 1/ 4pkT x0bd /kB T )

.

(5.8)

As expected in a first order approximation, we found that δL ∝ δI (Fig. 5.1 C) andδL ∝ L (Fig. 5.1 D). We note that at constant force, δL was independent of kT (Fig.
0
0 = 0.086 pN/nm, L = 1000 nm, k 0
5.1 E). Given the parameters (FDNA= 6 pN, kT
DNA =0.187 pN/nm, rbd = 165 nm), we calculated that a 1% fluctuation in intensity createda |δxbd | of 2.2 Å and a |δL| of 3.4 Å. Thus, this calculation motivated us to address
intensity noise (which has a typical specification of ±1%) and other types of laser noisein combination with pointing noise to improve long-term instrumental stability.

5.3

Stabilizing trap laser noise
To reduce trap laser noise, we used active stabilization. Specifically, we firstminimized multiple types of laser noise by transforming pointing, mode, and polarization noise into intensity noise using the combination of a single-mode, polarizationmaintaining fiber and a polarizing beam splitter (see Section 2.1.4). We then sampled
10% of the light onto a photodiode to measure laser intensity. Finally, the intensity

97
measurement was used in a feedback loop to an AOM (placed before the fiber) thatmodulated intensity to keep the output intensity constant. Also, to minimize effects of
AOM pointing instability, we imaged the AOM crystal on to the fiber coupling lens,eliminating lateral translation of the laser beam on the coupling lens that would otherwise accompany a pointing instability.
With this stabilization, we decreased the steady state trap intensity noise to 0.01%
rms at moderate laser powers (200 mW, ∆f = 0.03–100 Hz, Fig. 5.2 A). Importantly,
similar trap intensity control of 0.01% rms was achieved immediately after dynamicchanges in intensity (Fig. 5.2, B–D). Without feedback, there was a substantial, timedependent AOM-induced error (see Section 2.1.4) between the requested and actual laser
intensity that was not present with feedback (Fig. 5.2, B,C). This long-term systematic
error could take from tens of seconds (Fig. 5.2 B) to ∼10 min (at the highest change
in laser power in Fig. 5.2 C) to stabilize. In addition to this long-term error, there
was also a short-term (∆f = 0.2–2000 Hz) AOM-induced error of ∼10% (rms) after an
intensity change that was reduced by three orders of magnitude to 0.01% (rms) withactive intensity stability (Fig. 5.2 D).
In summary, prior work [1, 76] has emphasized the importance of minimizing
pointing noise. Our calculations showed the importance of controlling intensity noise
when the bead is offset from the trap center. Moreover, we found that dynamic changes
in laser intensity using an AOM introduced significant errors. Our feedback system
successfully minimized both pointing and intensity noise (as well as other sources) during
dynamic changes in laser power.

5.4

Ångstrom-scale tracking of trapped bead motion
After reducing both surface perturbations and trap laser noise, we first demon-

strated the excellent positional stability of the trap laser relative to the detection laser.
One useful metric is to plot the power spectral density of a trapped bead (Fig. 5.3

98

Figure 5.2: Reduction of intensity noise. (A) Steady state normalized power of thetrap laser with (green) and without (red) stabilization. Data was taken after 1 hourof equilibration time. (B) A step increase in laser power from 150 to 300 mW withand without feedback. Such steps led to a slow (>10 s), substantial (>3%) systematic
error. Intensity stabilization effectively minimized this error. Traces offset for clarity.
Inset is a zoom-in of the transient noise where the data was normalized. (C) Records ofpower versus time during rapid (5 s) changes in power with and without stabilization.
Without stabilization, the final measured power was only 55% of the intended value (750mW). Only after ∼10 min at the desired power did the unstabilized trace equilibrate towithin 1% of the requested power (data not shown). (D) The short-term (5 s) fractional
standard deviation (σ) as a function of each power in C. The intensity-stabilized traceshows about three orders of magnitude improvement over the unstabilized trace and is<0.1% (black dashed line) over the full range. Traces in A–C are at 2 kHz and color in
B–D is the same as in A.

99
A, inset), which shows the noise as a function of frequency. Another useful metric for
calculating noise is to integrate the power spectral density within a specified bandwidth
to produce the integrated noise. This integrated noise (1.7 Å) was a fraction of a basepair over a broadly useful bandwidth (∆f = 0.02–100 Hz) for a 330-nm-diameter beadtrapped at a stiffness of 0.53 pN/nm (Fig. 5.3 A). The noise level was within 0.5 Å ofthe thermal noise limit and was maintained over a wide range of trap stiffness (Fig.
5.3 B). Interestingly, our integrated trap noise was only ∼0.5 Å higher than the bestreported trap stability [1], though our method used a four-fold lower stiffness and did
not require the encasement of optics in helium.
Second, we achieved atomic-scale sensitivity to bead motion. Using a PZT mirror,
we generated 0.4-nm trap motion (limited by 1 bit changes in a control voltage). The
resulting steps were well resolved [0.43 ± 0.08 nm (peak ± HWHM)] with a signal-tonoise ratio of 5 in a trace filtered to 5 Hz using a Savitzky-Golay window (Fig. 5.3 C).
Thus, by reducing mechanical perturbations and excess trapped-bead noise, we achieved
sufficient stability and precision to measure Ångstrom-scale bead motion.

5.5

Stability and resolution of 1-bp along DNA
We next achieved 1-bp stability in a surface-coupled DNA assay (Fig. 2.1) overtens of seconds. Measurements of DNA contour length (L = 556 nm) were taken at amoderate force of 6 pN with and without active stabilization of both the surface and trap
(Fig. 5.4 A). Active stabilization resulted in a four-fold decrease in the integrated noise
to 1.5 Å at 0.1 Hz (Fig. 5.4 B). Additionally, we maintained a 1-bp (3.4-Å) positional
precision over a useful frequency range (∆f = 0.03–2 Hz). The stability for a ten-foldlonger time period (Fig. 5.4 C) was slightly larger at 4.8 Å (∆f = 0.003–2 Hz). Suchlong-term traces contain some noise level changes of ≥1 bp. For analyzing steps of amolecular motor, this noise would only lead to ∼10% erroneous steps when measuring
an enzyme movement with a 0.2-Hz stepping rate. As expected, the spatial precision

100

Figure 5.3: Precise tracking of trapped bead position. (A) Inset: the power spectral
density in xbd for an isolated trapped bead (kT = 0.53 pN/nm). The integrated noise in
xbd (gray) of the power spectral density was within 0.5 Å of the thermal limit (black).
(B) Likewise, the integrated noise (gray circles) over a bandwidth of 0.02–100 Hz at
different trap-stiffness values followed the thermal noise limit (black line). (C) Stepsin xbd as the trapping laser was moved back-and-forth relative to the detection laser.
Data was filtered with a Savitzky-Golay window to 100 Hz (gray) and 5 Hz (black). A
histogram of the 5 Hz data showed distinct peaks.

101
increased with increasing force (Fig. 5.4 D) for ∆f = 0.1–10 Hz, but is currently limitedby the residual error in stage stabilization.
Ideally, we seek to perform high resolution studies of force-sensitive states. For
example, the E. coli RecBCD helicase experiences a force-induced backwards slip at a
variable time (∼1–10 s) if exposed to F > 6 pN [96]. For such states, there is only alimited amount of time to take the measurements and that time may be short comparedto the thermal equilibration time (10–1000 s). With active stabilization of the lasers andthe microscope, we attained 1-bp stability following dynamic force changes. Specifically,
the spatial precision in the 60 s after a force change of 3.4 pN (Fig. 5.4 E) yielded astability of 3.1 Å (rms) for ∆f = 0.1–10 Hz, in quantitative agreement with steady statemeasurements (Fig. 5.4 D). A small (∼2 nm), systematic offset in L accompanied thechange in force. Such offsets have been seen previously [96] and are most likely due tothe difficulty in correctly modeling the elasticity of short DNA molecules [108].
Finally, we demonstrated sensitivity to steps along DNA by moving the stage ina series of 0.34-nm increments every 5 s (Fig. 5.5 A). Conceptually, this stage motionis the signal input (Fig. 5.5 A, blue). The deduced contour length, calculated without
incorporating the stage motion, is the signal corrupted by thermal and mechanicalnoise. Quantification of steps in single-molecule experiments can be done by a stepfitting algorithm [48]. Such fitting of our data recapitulated the input motion over botha few [0.33 ± 0.08 nm (mean ± SD; N = 6)] and many steps [0.38 ± 0.13 nm (mean± SD; N = 52)]. Another metric to demonstrate step detection is a pairwise-distancedifference histogram, which revealed a peak at 0.31 ± 0.09 nm (peak ± HWHM) (Fig.
5.5 B). Experimentally, the signal-to-noise ratio of the data is ∼4, within the signal-tonoise threshold for accurate determination of steps [129]. Thus, we resolved the smallest
known biological step in the widely used surface-coupled assay.

102

Figure 5.4: Positional stability of 1 bp along DNA. (A) DNA contour length (L) measurement with (green) and without (red) active stabilization of both the trap and surface.
Data taken at F = 6 pN and xbd = 70 nm, and filtered using a Savitzky-Golay window(light = 5 Hz, dark = 0.2 Hz). (B) The integrated noise for traces in A. With active
stabilization (green), the positional stability of the system increases four-fold at 0.1 Hz
and is 1 bp (3.4 Å) over 0.03–2 Hz. (C) Record of L vs. time over 5 min, with thesame conditions and trace color as in A. (D) The integrated noise in L (∆f = 0.1–10
Hz) as a function of force at two different lengths [556 nm (black triangles), 1007 nm(blue circles)]. (E) Record of length versus time during a 3.4 pN step increase in force(purple). Trace color and conditions same as in A. Traces offset vertically for clarity in
A, C, and E.

103

Figure 5.5: Resolution of 1 bp steps along DNA. (A) To demonstrate the resolution of
the system, the stage was moved in 0.34-nm increments (blue) such that the apparent
DNA contour length changes (∆L). A step-fitting algorithm found steps (black) at 0.33
± 0.08 nm (mean ± SD, N = 6). Data taken at F = 6 pN and xbd = 70 nm, and filteredusing a Savitzky-Golay window (light green = 5 Hz, dark green = 0.2 Hz). Traces offset
for clarity. (B) A pair-wise distance difference histogram of the 0.2 Hz data from A
shows a peak at 0.31 ± 0.09 nm (peak ± HWHM).

104

5.6

Precision force control
The precise control of force developed here is beneficial to experiments beyond

resolving steps of molecular motors. Biological structures are highly sensitive to changes
in the applied force [64, 135, 136]. To illustrate the importance of steady-state force
control, we studied a previously characterized DNA hairpin, 20TS06/T4 [135], andmeasured its unfolding dynamics (Fig. 5.6). We obtained an unfolding distance (∆x)
of 19.7 nm and a force at which the hairpin has a 50% probability of being unfolded(F1/2 ) of 12.3 pN, in quantitative agreement with previous results [135]. Small forcechanges (∆F ) of 0.1 pN in either direction substantially shifted the probability of being
unfolded (Fig. 5.6). More quantitatively, a force change of <1% (∆F/F1/2 ) shifted
the probability of being folded by ∼20%. In such cases where the biological molecule
under study is exquisitely sensitive to the applied force, precise force control must be
maintained. Yet, commercial lasers rarely specify intensity stability to better than 1%.
Hence, our reduction in intensity noise to ∼0.01% rms provides a biologically usefulincrease in precision for force measurements.

5.7

Conclusions
We used active stabilization of both the surface and trap to achieve 1 bp positional

precision in a surface-coupled optical-trapping assay. By actively stabilizing multiple
forms of laser noise, we tracked bead position to within 0.5 Å of the thermal limit
and measured 0.1-pN force-induced changes in DNA hairpin unfolding dynamics. Ourcurrent short-term (∼1 s) positional precision is limited by the residual error (1 Å) in
surface stabilization. We expect that it is this noise that prevents us from reaching thetheoretical limit under these conditions [129]. Further improvements to increase surface
stabilization could include a feedback loop with a field-programmable gate array coupledwith a stiffer stage to increase the loop closure time [21]. To improve long-term stability,

105

Figure 5.6: DNA hairpin unfolding dynamics show need for force precision. DNA hairpin
dynamics under a constant load of (A) 12.2 pN, (B) 12.3 pN, and (C) 12.4 pN. Datafiltered using a Savitzky-Golay window (2 kHz, gray; 100 Hz, black). Histogram of thedata shows probability of being unfolded increases from 29% (12.2 pN) to 52% (12.3
pN) and then to 68% (12.4 pN).

106
differential laser motion could be minimized with a more compact optical design and bylaunching all three lasers from one fiber. This improved the differential laser stability
for two lasers, in a different application, from <65 pm laterally (∆f = 0.1–50 Hz) to 19
pm [16].
In comparison with existing high-resolution dual-beam methods [1, 76], we achieved
1-bp positional precision at a factor of 1.2–3 lower force with a surface-coupled assay
and without the encasement of optics in helium. Dual-beam assays enable enhanced
measurements using passive force clamps [39]. Dual-beam assays with differential de√tection offer a small ( 2), but significant, increase in time resolution [77]. In contrast,
our active stabilization method increases force sensitivity, stabilizes the geometry in all
three dimensions, and is surface coupled for rapid adoption to a wide variety of existing
assays [5, 11, 45, 48, 120, 132, 140]. Dual beam assays would also benefit from increased
force precision. Future assays could combine single-molecule force and fluorescence assays using total internal reflection fluorescence, a surface-based technique [11], with theenhancements presented here.

Chapter 6

Conformational dynamics of the RecBCD-DNA complex

6.1

Introduction
Helicases are enzymes that unwind double-stranded nucleic acid in the first stepsof nucleic acid processing [111]. One particularly complex helicase, RecBCD, is mechanistically capable of DNA unwinding and digestion, DNA recognition, and protein
recruitment [57, 92]. Functionally, it is involved in DNA repair, homologous recombination, and excision of foreign DNA in E. coli [57]. This unusual variety of mechanismand function, coupled with a high processivity (36–48 kbp) and speed (∼1 kbp/s) [66],allows for an extraordinary helicase. We are interested in determining how this complex
helicase uses the chemical energy of ATP to mechanically unwind the DNA duplex.
The first step in understanding the physical mechanism of any helicase is to determine the step size of movement. Previously, two different methods (crystallography andpre-steady state unwinding assays) yielded two proposed step sizes for SFI helicases (thestructural super family that contains RecBCD). Crystallographic studies of the enzymeDNA complex with and without ATP infer a 1 bp “mechanical step size”, which is thetranslocation per ATP hydrolysis event [61, 125]. Pre-steady state unwinding assays,on the other hand, measure the number of base-pairs per rate-limiting translocationor the “kinetic step size”. At rate-limiting ATP concentrations we would expect themechanical and kinetic step size to be equal. However, for RecBCD unwinding assays
at rate-limiting ATP concentrations, the kinetic step size is 4 bp [68, 69, 67]. Thus,

108
there is a conflict in the field over what the actual step size is for RecBCD and otherhelicases.
To resolve this conflict, we sought to directly measure the step size of RecBCD
using a single molecule optical trapping assay. Single molecule assays measure the dynamics of individual molecules, and therefore, do not require synchronization (as inpre-steady state unwinding assays) or rely on an average behavior (as in both crystallographic studies and unwinding assays). Optical trapping assays can probe theforce-dependence of unwinding and allow for measurements of the energy landscape.
However, previous measurements of RecBCD movement using this type of assay werelimited to a 6-bp resolution [96], which masked the underling 1 or 4 bp steps.
To improve resolution, we built a precision optical trapping assay that was sensitive to 1 bp movements along DNA (see Ch. 5 and Fig. 1.4). In the previous
measurement [96], a biotinylated form of RecBCD was attached to a streptavidin surface. The RecBCD then bound a DNA molecule (2.4 µm), which was biochemicallylinked to a polystyrene bead and stretched using the optical trap. Bead position (xbd )was used to calculate double-stranded DNA contour length (L) [131] and determine
RecBCD translocation. Drift in either the position of the sample [89] or trapped bead[18] obscured enzymatic motion. Here in the precision optical trapping assay (Fig. 1.4),
we actively stabilized the sample position by detecting the position of a fiducial markon the sample (xfid ) with a detector laser and using this position in a feedback loop tominimize sample drift [17]. We also actively stabilized the trapping laser to decrease
multiple sources of laser noise that affected trapped bead position [18]. In samples
where the DNA was directly attached to the surface without RecBCD, DNA length
measurements were stable to 1 bp (rms, ∆f = 0.03–2 Hz) and the precision opticaltrapping assay was capable of resolving 1-bp movements [18].
Using this precision optical trapping assay, we measured the conformational dynamics of single RecBCD-DNA complexes. RecBCD movement along DNA showed109
discrete steps that were variably sized with the average step size of 4.4 bp agreeing withpre-steady state unwinding assays [67, 68, 69]. We also observed backwards motion of
the enzyme at low ATP concentrations (2 µM) that were similar to forwards steps inboth their variability and average step size (4.3 bp). Additionally, RecBCD exhibited±3 bp fluctuations at frequencies above the stepping rate (∼0.1–10 Hz). These ATPindependent, force-dependent fluctuations were only present when the RecD helicase wasengaged on the DNA template. Moreover, the different conformations were dependent
on the upstream double-stranded DNA sequence, suggesting that they were translocations of RecBCD along the DNA template. These observations imply that RecBCD
unwinding does not occur through a series of 1 bp translocations, each of which is dependent on ATP hydrolysis, as hypothesized by crystallographic studies [13, 61, 125].
Instead, our data agrees with models of helicase unwinding that have multiple base-pairstep sizes [66].

6.2

Discrete motion along DNA
Using our precision optical trapping assay, we measured L as RecBCD unwound

the double-stranded DNA (Fig. 6.1). Data was taken at 6 pN of force, unless otherwise
noted, and in WB buffer (1 mM magnesium acetate, 1 mM sodium chloride) with 2 µM
ATP, 1 mM E. coli single-stranded binding protein, and an oxygen scavenging system
to prevent free oxygen radicals. Forward movement caused a decrease in L. RecBCD
motion (N = 20) at this low ATP concentration displayed pauses and changes in velocity(Fig. 6.1 A), as in previous experiments [96]. Traces also displayed discrete steps, whichappeared as fast translocations of the enzyme separated by pauses in movement (Fig.
6.1 B). To identify steps we used a step-finding algorithm that fit the 1-Hz data based ona maximum-likelihood parameter [48]. Each molecule displayed steps that were variable
in size from about 2-6 bp, occasionally larger. A histogram of the forward steps (Fig.
6.1 C) was fit by a Gaussian curve with a peak at 4.4 ± 1.8 bp (mean ± σ); the peak

110
step size agreed with pre-steady state unwinding assays that measure an average step
size of 3.9 ± 0.5 bp [67]. Interestingly, a two-fold increase in the ATP concentration to
4 µM did not change the average step size, which also agreed with previous results [67].
In addition to forwards motion, we noticed that all of the RecBCD molecules
studied took occasional backwards steps at the low ATP concentration used (Fig. 6.1).
While backwards steps were similar to forwards steps in both variability (2-6 bp) andaverage step size (4.3 ± 2.7 bp as determined by a Gaussian fit to a histogram of
backwards steps), the probability for a backwards step was 30%, allowing for forward
motion of RecBCD. As ATP concentration was increased two-fold, the probability of a
backwards step decreased two-fold to 14%, suggesting that backwards motion does notoccur at higher ATP concentrations, and therefore, would not have been measured inprevious assays [68, 69, 67, 96]. Forward motion after a backwards step was identicalin both size and dwell time to regular forward movement. Given this data, we interpretbackwards movement as a backwards step of the enzyme coupled with a reannealing of
the double-stranded DNA.

6.3

Conformational dynamics in the RecBCD-DNA complex
Unexpectedly, in between steps, measurements of RecBCD motion fluctuated by±3 bp at 1 Hz, well above the instrumental noise floor of ∼1 bp (Fig. 6.2). A recordof DNA length as measured by a digoxigenin-labeled DNA molecule attached to ananti-digoxigenin surface demonstrated the instrumental noise present in the assay. We
compared this record to a record of RecBCD motion where the time in between steps
was long enough so that comparison was possible (Fig. 6.2 A). A histogram of the
RecBCD motion at 1 Hz had a HWHM of 1.09 nm (3.2 bp), which was three-fold higher
than the instrumental noise (HWHM = 0.29 nm). The power spectral density of therecords (Fig. 6.2 B) showed that the fluctuations occur over the bandwidth 0.1–10 Hz,
just above the above the stepping frequency of 0.1–0.2 Hz. Comparison of the integrated

111

Figure 6.1: RecBCD motion shows forward, backward, and variably sized steps. (A)DNA contour length (L) decreases as RecBCD moves forward. Traces taken at 6 pN offorce, 2 µM ATP, and smoothed with a Savitzky-Golay window to 10 Hz (light green)and 1 Hz (dark green). (B) Closer view of RecBCD movement shows discrete steps.
Zoom-in of traces in A in red boxes. Motion was fit with a step-fitting algorithm [48](black line), which determines placement of steps (black arrows). Trace color same asin A. (C) Histograms of the steps show variably sized forward and backward motion.
Gaussian fits to the data reveal a peak at 4.4 bp ± 1.8 bp (mean ± σ) for forward
motion and 4.3 bp ± 2.7 bp for backward motion. The number of backwards steps are
30% of the total.

112
noise under the power spectral density was similar to measurements of histogram width.
RecBCD fluctuations had an integrated noise level of 0.94 nm (2.8 bp) at 1 Hz, while theintegrated noise present in the instrument was 0.28 nm. This same measurement overthe entire frequency range of the fluctuations (0.1–10 Hz) gave an integrated noise levelof 1.41 nm (4.1 bp) for RecBCD movement in between steps, above the instrumental
noise of 0.55 nm (1.6 bp). We posit that the ±3 bp fluctuations are real and enzymedependent since measurements of instrumental noise are much lower.
There are four sources of enzyme-dependent movements in our assay that could
be causing the fluctuations (Fig. 6.3). We measure the movement of RecBCD along
the DNA template through the surface-RecD-DNA attachment point, which has four
possible sources of movements: translocations of RecBCD along the DNA template(α), enzymatic movements within RecBCD (β), movements between RecBCD and thebiotin tag (γ), and movements within the biotin-streptavidin surface-attachment (δ).
We can rule out movements in the biotin-streptavidin surface-attachment, δ, because
measurements of a DNA molecule with a biotin linkage attached to a streptavidin surface
produced identical noise characteristics as that of a digoxigenin-labeled DNA molecule
attached to an anti-digoxigenin surface (i.e. there were no fluctuations). In addition,measurements of DNA contour length for RecBCD bound to a blunt-end DNA molecule
did not show fluctuations (Fig. 6.4), eliminating movement between RecBCD and thebiotin tag, γ. The integrated noise at 10 Hz for ≥5 traces was on average 0.83 ± 0.04 nm(mean ± σerror ), below the measurement for fluctuations, although slightly higher thanthe measured instrumental noise (integrated noise at 10 Hz was 0.53 ± 0.03 nm, mean
± σerror ). Thus, we hypothesize that the fluctuations are conformational dynamics inthe RecBCD-DNA complex: either translocations of RecBCD along the DNA templateor motion within RecBCD.
By measuring the conformational dynamics for different RecBCD-DNA binding
conditions, we found that the conformational changes were ATP-independent and only

113

Figure 6.2: RecBCD motion shows ±3 bp fluctuations between stepping events. (A)RecBCD motion (green), as measured by a RecBCD enzyme attached to the surface(right bottom cartoon), shows fluctuations in between steps. Measurement of L (black)for a DNA molecule attached to the surface (right top cartoon) shows the level of noisepresent in the instrument. Red box is a zoom-in. Traces smoothed with a SavitzkyGolay window to 10 Hz (light) and 1 Hz (dark). Histograms of the 1 Hz data have a
HWHM of 0.29 nm for instrumental noise and 1.09 nm (3.2 bp) for RecBCD fluctuations.
(B) Power spectral density (PSD) of the position data in the red box in A. RecBCD
motion (green) shows fluctuations at 0.1–10 Hz that are above the instrumental noise(black). (C) Integrated noise of the PSD in B. Instrumental noise (black) is at 0.28
nm at 1 Hz, while RecBCD fluctuations (green) are at 0.94 nm (2.8 bp). Over the
10 Hz bandwidth that fluctuations occur, the integrated noise for the RecBCD motion
between stepping events is 1.41 nm (4.1 bp), above the instrumental noise of 0.55 nm(1.6 bp).

114

Figure 6.3: Fluctuations are conformational dynamics in the RecBCD-DNA complex.
Conformational dynamics in the RecBCD-DNA complex are either translocations of
RecBCD along the DNA (α) or movements within the RecBCD enzyme (β) or both.
The fluctuations are not movements in the biotin attachment to enzyme (γ) or motionof the attachment to the surface (δ).

115
occurred when RecD engaged the DNA template (Fig. 6.4). To measure the effects ofATP, we stalled RecBCD in the middle of the DNA template after it had translated ∼1µm by washing WB buffer without ATP through the sample. Measurements of L did
not display RecBCD forward motion, but did display different conformations (Fig. 6.4
A). The integrated noise of the conformational changes (Fig. 6.4 B,C) for ∼5 traces at
10 Hz was 1.40 ± 0.04 nm (mean ± σerror ), similar to the integrated noise for RecBCD
conformational dynamics in between steps (1.39 ± 0.02 nm, mean ± σerror ). Since theconformational changes were ATP-independent, we then hypothesized that engaging the
RecD subunit might cause these dynamics. To check this hypothesis, we used a DNA
substrate that engaged the RecD subunit upon RecBCD binding. This DNA substrate
has an end possessing a pre-existing single-stranded (dT)N tail, where N represents
the number of T’s in the tail (see Section 2.2.3). A substrate with a 5’-(dT)10 tailcontacts the RecD subunit [105] and eliminates the initial RecBCD unwinding steps[137], whereas a 5’-(dT)6 tail does not. We measured DNA length for RecBCD boundto a substrate with a 5’-(dT)10 and 3’-(dT)5 tail and for RecBCD bound to a DNA end
with a 5’-(dT)6 and 3’-(dT)6 tail. The RecBCD bound to the 5’-(dT)10 tail exhibited
conformational dynamics (integrated noise at 10 Hz was 1.40 ± 0.05 nm, mean ± σerror ),whereas the RecBCD bound to the 5’-(dT)6 tail did not (integrated noise at 10 Hz
was 0.84 ± 0.04 nm, mean ± σerror ). This is consistent with previous measurementsthat show substrates with both a 5’-(dT)6 and 3’-(dT)6 tail act like blunt-end DNA,
whereas substrates with a 5’-(dT)10 tail act like threaded DNA [105, 137]. Thus, theconformational dynamics occur when the DNA template engages RecD.
We expect that conformational dynamics in the RecBCD-DNA complex would
be force-dependent, with increasing force showing less conformations. Experimentally,
this was the case. We measured the conformational dynamics for RecBCD stalledin the middle of the DNA template without ATP as a function of force (Fig. 6.5).
Conformational changes at 4 pN decreased from an integrated noise level at 10 Hz of

116

Figure 6.4: Conformational dynamics were ATP-independent and occur when RecD
is engaged. (A) Measurement of L for different RecBCD-DNA complexes: RecBCD
bound to blunt-end DNA (blue), RecBCD bound to a DNA end possessing pre-existing
single-stranded (dT)6 tails [134] (orange), RecBCD bound to a DNA end with a 3’-(dT)5
and 5’-(dT)10 tail (brown) that engages the RecD subunit [105], and RecBCD stalledin the middle of the DNA molecule (red) after translocation and RecD engagement.
All conditions without ATP. Traces smoothed with a Savitzky-Golay window to 10 Hz(light) and 1 Hz (dark). Histograms of the 1 Hz data show the noise level of eachcase. (B) Integrated noise for the traces in A (trace color same as in previous) showsthat fluctuations occur when RecD is engaged (brown, red). Traces from Fig. 6.2 forreference. (C) Bar graph of the integrated noise at 10 Hz for the conditions in A and in
Fig. 6.2 with N ∼ 5. Trace color same as in A and Fig. 6.2. Points that are statisticallysignificant (95117
1.69 ± 0.17 nm to 0.84 ± 0.05 nm at 10 pN. This decrease was 2.6-fold higher than thedecrease in instrumental noise that also accompanies a force change. Measurements atforces higher than 10 pN were not available due to RecBCD backsliding along the DNA
template [96].

6.4

Conformational dynamics were ATP-independent
RecBCD-DNA conformational dynamics were independent of changes in the ATP-binding site. In Figure 6.4 we observed that conformational changes occurred even
without ATP. We checked these results by measuring RecBCD conformational dynamics (Fig. 6.6) with 2 mM AMP-PNP (an ATP analog) and 2 mM ADP (the hydrolyzed
product of ATP) on DNA substrates where RecD was engaged. Conformational dynamics in both cases had a similar integrated noise level at 10 Hz of 1.4 ± 0.07 nm
and 1.36 ± 0.15 nm, respectively. We note that ADP may not be binding the enzyme
and would therefore represent the same state as without ATP. We also tested a mutant
RecBCD enzyme (RecBCDK177Q ) where the RecD ATP-binding pocket [25] had a lysine
to glutamine substitution at position 177 in the Walker A box (helicase motif I) [38].
This well established mutation decreases ATP hydrolysis and helicase activity [25]. We
did not measure a change in the level of conformations in the mutated RecBCDK177Q
enzyme; the integrated noise at 10 Hz was 1.29 ± 0.06 nm. Likewise, a four-fold increasein the magnesium acetate concentration to 4 mM did not change the conformational
dynamics either (integrated noise at 10 Hz was 1.38 ± 0.06 nm). This evidence suggeststhat the conformational dynamics are not due to changes in the RecD ATP-binding site.
We note that sometimes the measured conformational dynamics did show an
ATP-dependence. Up until this point we have only discussed one type of conformational dynamics, type I conformational dynamics. These dynamics have an integrated
noise level of 1.40 nm at 10 Hz and appeared 85% of the time. In addition, type I
conformational dynamics were always ATP-independent and only occurred when the

118

Figure 6.5: Conformational dynamics were force-dependent. (A) Measurement of L
for RecBCD stalled in the middle of the DNA molecule (red) after translocation and
RecD engagement at three different forces (top = 4 pN, middle = 6 pN, bottom =10 pN). Traces smoothed with a Savitzky-Golay window to 10 Hz (light) and 1 Hz
(dark). Histograms of the 1 Hz data show the conformational changes of each case. (B)Integrated noise at 10 Hz as it varies with force for the condition in A (red) and forthe condition of a digoxigenin-labeled DNA molecule attached to an anti-digoxigenin
surface (black). Data collected for N ∼ 5, center point is mean, error bars are thestandard deviation.

119

Figure 6.6: Conformational dynamics are independent of changes in the ATP-bindingsite. (A) Measurement of L for different conditions of RecBCD bound to DNA: RecBCD
bound to 5’-dT10 tail DNA with a four-fold increase in Mg+2 to 4 mM (gray), RecBCD
bound to 5’-dT10 tail DNA with 2 mM AMP-PNP (yellow), RecBCD stalled in the
middle of the DNA with 2 mM ADP (cyan), and RecBCDK177Q (RecBCD with amutation in the RecD ATP-binding site) bound to 5’-dT10 tail DNA. Traces smoothedwith a Savitzky-Golay window to 10 Hz (light) and 1 Hz (dark). Histograms of the 1 Hzdata show the width of the conformational dynamics. (B) Bar graph of the integrated
noise at 10 Hz for the conditions in A with N ∼ 5 shows that the conformation dynamics
do not change in each condition. Plus, the two conditions from Fig. 6.4 C are shown
for reference (RecBCD moving along DNA in between steps, green, and DNA bound to
the surface, black) and the condition for Fig. 6.4, RecBCD bound to blunt-end DNA,
blue. Otherwise, color same as in A. Points that are statistically significant (95120RecD subunit was engaged. We also observed type II conformational dynamics, which
occurred without ATP and when the RecD subunit was engaged (Fig. 6.7 A). However,type II conformational dynamics were much larger (the integrated noise at 10 Hz was
3.30 ± 0.83 nm, Fig. 6.7 B), only occurred 15% of the time, and were suppressed byadding 2 mM AMP-PNP (Fig. 6.7). Likewise, we do not observe type II conformationalchanges in the RecBCD movement assay, probably because ATP suppresses these conformations as well. While these ATP-dependent type II conformational dynamics arepotentially interesting, they are not relevant in the RecBCD movement assay and were
not studied further.

6.5

Conformational dynamics were DNA sequence-dependent
RecBCD-DNA conformational dynamics were dependent on the upstream double-

stranded DNA sequence. We measured the conformations of RecBCD bound to twotailed DNA substrates with differing double-stranded G-C content. The DNA substrates both contained a single-stranded 5’-(dT)10 tail to engage the RecD subunit
and create conformational changes, yet on one substrate the first four double-strandedbase-pairs after the tail were A-T (AT-rich), while in the other, the first three doublestranded base-pairs after the tail were G-C (GC-rich, see Section 2.2.3 and Fig. 6.8
A–C). We prepared samples with RecBCD bound to each substrate and measured L(Fig. 6.8) to see if the conformational dynamics depended on the double-stranded G-C
content. RecBCD bound to the AT-rich tailed substrate exhibited larger conformational
dynamics (integrated noise at 10 Hz was 1.75 ± 0.07 nm) than RecBCD bound to the
GC-rich tailed substrate (integrated noise at 10 Hz was 1.10 ± 0.06 nm). Thus, theconformations depend on the sequence of the upstream double-stranded base-pairs.
This result implies that RecBCD is interacting with the upstream double-strandedbase-pairs to unwind them and that the conformational dynamics that we measured arereally translocations of RecBCD along the template. The difference between an A-T

121

Figure 6.7: Type II conformational dynamics were dependent on ATP but were not studied. (A) Measurements of L for RecBCD bound to DNA with RecD engaged (RecBCD
bound to 5’-(dT)10 tailed DNA) and without ATP (brown) showed two different typesof conformations. Type I conformational dynamics (top) occur 85% of the time andare smaller than type II conformational dynamics (middle). Type II conformational
dynamics stopped when 2 mM AMP-PNP was added to the molecules that displayed
the behavior (yellow). Measurement of L for digoxigenin-labeled DNA bound to ananti-digoxigenin surface (black) for reference.Traces smoothed with a Savitzky-Golay
window to 10 Hz (light) and 1 Hz (dark). Histograms of the 1 Hz data show the widthof the conformational changes. (B) The integrated noise for the conditions in A andthe two conditions from Fig. 6.2 (RecBCD moving along DNA in between steps, green,
and DNA bound to the surface, black). Type II conformational dynamics are four-foldhigher at 1 Hz than type I conformational dynamics and are not present in conditions
with AMP-PNP (yellow) or ATP (green). Since type II conformational dynamics are
not present during RecBCD motion these conformations were not studied. Color sameas in A and Fig. 6.2.

122

Figure 6.8: Conformational dynamics are dependent on the upstream double-stranded
DNA sequence. (A) Measurement of L for RecBCD bound to 5’-(dT)10 tailed DNA
substrates with either the first three upstream base-pairs as A-T (teal) or G-C (pink).
Traces smoothed with a Savitzky-Golay window to 10 Hz (light) and 1 Hz (dark). Histograms of the 1 Hz data have a HWHM of 1.23 nm and 0.83 nm for the A-T and
G-C rich cases, respectively. (B) PSD of the position data in A, plus the instrumental
noise trace from Fig. 6.2 B (black). (C) Integrated noise for the traces in A, plus two
traces from Fig. 6.2 C for reference (RecBCD moving along DNA in between steps,
green, and DNA bound to the surface, black). Trace from Fig. 6.4 B, RecBCD boundto blunt-end DNA (blue), added for reference as well. At 1 Hz the integrated noise is0.98 nm and 0.67 nm for the A-T and G-C rich cases, respectively. This increases to
1.61 nm and 1.09 nm at 10Hz, respectively. Color in B,C same as in A. (D) Bar graphof integrated noise at 10 Hz for the conditions in A (color the same, N ∼ 5). Plus, thethree conditions from Fig. 6.4 C are shown for reference (RecBCD moving along DNA
in between steps, green, RecBCD bound to blunt-end DNA, blue, and DNA bound to
the surface, black). Points that are statistically significant (95123base-pair and a G-C base-pair is the addition of an extra hydrogen bond in the G-Ccase so that the energy needed to open an A-T base-pair is less than the energy needed
to open a G-C base-pair. This difference in energy creates a difference in the amountof base-pairs that can be unwound given a particular energy. Thus, the conformations
would be dependent on DNA sequence if they were actually unwinding events without ATP. To check this hypothesis, we compared this data to RecBCD conformational
dynamics while in between steps (Fig. 6.8 D), which should see an average G-C content of 50%. The integrated noise at 10 Hz was 1.39 ± 0.02 nm, revealing that theconformational dynamics on the AT-rich tailed substrate are slightly higher, while conformational changes on the GC-rich tailed substrate are slightly lower, as expected.
In addition, the conformational dynamics in each case are force dependent (Fig. 6.8
E), with smaller conformational dynamics occurring as the force was increased andthe AT-rich tailed substrate having the largest conformational dynamics at each force
level, as expected. These observations, taken together, indicate that the conformational
dynamics are translocations of RecBCD along the DNA template without ATP.
We note that we could not rule out the possibility that RecBCD was both translocating along the DNA template and movement within RecBCD was occurring. When
we compared the integrated noise at 10 Hz for conformational dynamics with RecBCD
bound to the AT-rich tailed substrate, the GC-rich substrate, and blunt-end DNA (1.75
nm, 1.10 nm, and 0.84 nm, respectively), we noticed that we could not account for allof the conformational dynamics as translocations. The difference between the AT-richtailed substrate and the GC-rich tailed substrate of 0.65 nm was due to translocations
that are more energetically favorable for the AT-rich tailed substrate. However, thedifference of 0.26 nm between blunt-end DNA and the GC-rich tailed substrate could
be due to movement within RecBCD or translocations. In the former case, the GC-richtailed substrate prevents translocation, whereas in the latter case the GC-rich tailed
substrate allows for some translocation. Future studies with tailed substrates that pre-

124vent translocation (i.e. cross-linked substrates) will resolve this issue.

6.6

Conclusions
Using a precision optical trapping assay, we measured the motion of RecBCD

along the DNA template. Forward motion consisted of a series of steps, with an average
step size of 4 bp, agreeing with previous pre-steady state unwinding assays that alsomeasure a kinetic step size of 4 bp [67]. These findings are consistent with multi-basepair stepping models [61, 62, 66], but not with models that require an ATP-rate-limited,
1-bp translocation step size [13, 61, 125].
We also observed backwards steps of the enzyme at 6 pN and a low ATP concentration that were variably sized and had an average step size of 4 bp, similar to forwards
motion. Since forwards motion after a backwards step was identical to typical forward
unwinding, we posit that backwards motion is movement of the enzyme in the backwards
direction along the DNA template coupled with a reannealing of the double-stranded
DNA. Structural studies indicate that backwards motion may be possible because the
RecD subunit lacks the helicase 1a motif, which is thought to control directionality ofthe motor [110]. We also observed that backwards motion decreased at higher ATP
concentrations, suggesting that backwards movement probably does not occur during
regular unwinding in vivo, because the predicted probability from our data at such highconcentrations of ATP would be vanishingly small. However, backward motion may
occur at a barrier (a bound protein, etc.) or when the enzyme pauses at a chi site, sinceforward motion would be decreased. We note that we currently can not distinguishbackward motion from conformational fluctuations in the backward direction. Future
assays that determine the force dependence of backward motion might elucidate thedifference since we might expect the amount of backward steps to increase under load
and the amount of conformational fluctuations to decrease.
In between RecBCD steps, we observed ±3 bp fluctuations that were conforma-

125
tional dynamics in the RecBCD-DNA complex. The conformational dynamics were
ATP-independent, required engaging the RecD subunit, and were dependent on the upstream double-stranded DNA sequence. These findings suggest that the conformational
dynamics are translocations of RecBCD along the DNA template by the RecD subunit.
Thus, RecBCD is able to move substantially along the DNA without ATP, indicating
the mechanism for a multi-base-pair step may be ATP-independent. Future work will
determine whether the amount of base-pairs unwound is an active or passive mechanism
by comparing the theoretical number of base-pairs unwound given thermal energy tothe experimentally determined value. We anticipate that the mechanism will be active,
given the high velocities of the enzyme (∼1 kbp), though previous helicases have beenshown to be passive [62].
Hence, we have shown that RecBCD, a structurally complex helicase [110], is alsomechanistically diverse. With ATP, it is able to move both forwards and backwards in
multi-base-pair steps, and without ATP, RecBCD is capable of translocational conformational dynamics along the DNA template. This diverse mechanism may be usefulduring processes which require high processivity, pausing, DNA recognition, and velocity changes. In addition, the larger step size may be mechanistically why RecBCD has
one of the highest helicase velocities known [66].

Chapter 7

Conclusions

In summary, we have used single molecule assays to elucidate how helicases convert the chemical energy from ATP hydrolysis into a translocation along DNA. To measure these Ångstrom-scale translocations, we first developed a precision surface-coupled
optical trapping assay that actively stabilized the sample to 1 Å [17] and removed multiple sources of trap laser noise [18]. Using this stabilized assay, we directly measured
the conformational dynamics of the E. coli helicase, RecBCD, bound to DNA with andwithout ATP. With ATP, RecBCD moved both forward and backward in variably sized
steps. The peak step size, 4.4 bp, agrees with the previously measured kinetic step sizeof 3.9 ± 0.5 bp [68, 67]. Without ATP, RecBCD showed ±3 bp conformational dynamics
that occurred when RecD was engaged. These conformations were ATP-independent,
indicating that they were not conformational dynamics of the helicase ATP-binding site.
However, the conformational dynamics were dependent on the sequence of the upstream
double-stranded DNA, suggesting that they were RecBCD translocations along the DNA
template, without ATP. These observations imply that RecBCD movement occurs inlarge steps without ATP, while ATP addition biases forwards movement. As such, ourfindings are consistent with multi-base-pair models of helicase movement [61, 62, 66],
but not models that assume an ATP-rate-limited, 1-bp translocation [13, 61, 125].
Future work will be needed to determine an exact model. Single molecule assays
could be performed with different mutations or attachment points of the enzyme to127change the conformational dynamics. In addition, single molecule measurements of
RecBCD motion after chi site recognition will be particularly illuminating because thelead helicase in the heterotrimeric complex changes from RecD to RecB. Bulk structural
studies of RecBCD crystallized with different ATP analogs will also be important in
defining the different possible states of the helicase. Thus, we anticipate that the data
we have presented is only the beginning of a multitude of measurements on RecBCD
and helicases in general. These new measurements will be aided by single molecule
techniques with 1 bp resolution [1, 76, 18], and by coupling optical trapping assays withfluorescent-based measurements [11].

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Appendix A

Acronym Index

2D two dimensional.
3D three dimensional.
A adenine, DNA base.
ADP adenosine diphosphate.
AFM atomic force microscope.
AMP-PNP adenylyl imidodiphosphate
AOM acousto-optic modulator.
ATP adenosine triphosphate.
bp base-pair.
BS beam sampler.
BSD back-scattered detection.
C cytosine, DNA base.
CCD charged-coupled device.
DL diode laser.

140
DNA deoxyribonucleic acid.
FSD forward-scattered detection.
FWHM full width at half maximum.
G guanine, DNA base.
HWHM half width at half maximum.
HSQ hydrogen silsesquioxane, spin-on glass.
Obj objective.
OI optical isolator.
PBS polarizing beam splitter.
PCR polymerase chain reaction.
PD photodiode.
PDD pair-wise distance difference.
pH power of hydrogen.
PSD power spectral density.
PZT piezo-electric lead zirconate titanate.
QPD quadrant photodiode.
RNA ribonucleic acid.
rms root mean square.
SD standard deviation.
SDL stabilized diode laser.

141
SEM scanning electron microscope.
SF super family.
S/N signal to noise ratio.
STL stabilized trap laser.
T thymine, DNA base.
TL trap laser.
VDC direct current voltage.
WB wash buffer.
λ/2 half-wave plate.
λ/4 quarter-wave plate.

Appendix B

Variable Index

C capacitance.
d diameter.
F force.
F0 initial force on the bead.
F1/2 force at which a hairpin has a 50% chance of being in the unfolded state.
FDNA force on bead from the DNA.
FR ideal force response of cantilever.
FT force on bead from the trap.
Ftotal total force response of cantilever.
Fth force response of cantilever due to thermal motion.
∆F change in force.
f fractional extension.
f0 roll-off frequency.
fobj focal length of the objective.

143∆f bandwidth.
∆fgain gain bandwidth.
g gain.
h height.
k spatial frequency.
kB Boltzmann constant.
kDNA nonlinear stiffness of the DNA.
0kDNA
initial nonlinear stiffness of the DNA.

kT trap stiffness.
0 initial trap stiffness.
kT

δkT change in trap stiffness.
L DNA contour length.
δL change in DNA contour length.
∆L the difference between the current DNA contour length and the initial DNA contour
length.
m ratio of the object refractive index to the solvent refractive index.
mps index of refraction ratio for the polystyrene fiducial mark.
mSi index of refraction ratio for the silicon fiducial mark.
N number.
n index of refraction.

144
nobject index of refraction of the object.
nsolvent index of refraction of the solvent.
p persistence length of DNA.
R resistance.
r radius.
rbd bead radius.
rbest ratio of the highest smoothing frequency that allows for accurate fitting of thedata to the actual signal frequency of the data.
S positional sensitivity.
T temperature.
V volume.
V0 reference voltage.
VSi volume of the silicon fiducial mark.
Vps volume of the polystyrene fiducial mark.
VQPD QPD voltage.
Vz the QPD sum signal voltage, which measures position in z.
v velocity.
w width.
x one of the three dimensional coordinates, lateral motion.
xbd bead position.

145
x0bd initial bead position.
xC clamp position for the trapped bead.
xDNA DNA extension.
x0DNA initial DNA extension.
xdif differential position in x.
xfid fiducial mark position in x.
xin−loop position in x as measured by the in-loop laser.
xmonitor position in x as measured by the monitor laser.
x0monitor the average initial position in x as measured by the monitor laser.
xN
monitor the average position in x at step number N as measured by the monitor laser.
xpeak position of correlation peak in x in AFM image analysis.
xref reference position in x inside of the feedback loop.
xstage distance between tether point and trap center.
xtether tether point position .
xtip AFM tip position in x.
∆x unfolding distance.
∆xN the difference between the average position in x at step number N and the initialvalue as measured by the monitor laser.
δxbd change in trapped bead position.
y one of the three dimensional coordinates, lateral motion.

146
ydif differential position in y.
yin−loop position in y as measured by the in-loop laser.
ylasers lateral distance between the laser foci in the image plane.
ymonitor position in y as measured by the monitor laser.
ytip AFM tip position in y.
Z height of surface.
z one of the three dimensional coordinates, axial motion.
zAFM position in z of AFM cantilever as measured by a standard optical lever arm.
zdif differential position in z.
zin−loop position in z as measured by the in-loop laser.
zmonitor position in z as measured by the monitor laser.
zst movement of the stage in z.
ztip AFM tip position in z.
αps polarizability of the polystyrene fiducial mark.
αSi polarizability of the silicon fiducial mark.
αsphere polarizability of a sphere.
β drag coefficient.
η viscosity.
λ wavelength.
π pi.

147
σ standard deviation.
σD standard deviation of the trapped bead data.
σerror standard error.
σSEM standard error of the mean for the trapped bead data.
σx standard deviation in x.
σy standard deviation in y.
σz standard deviation in z.
σ̄ average standard deviation.
σ̄x average standard deviation in x.
σ̄y average standard deviation in y.
σ̄z average standard deviation in z.
τavg time interval to average over.
∆θ change in angle of laser beam due to AOM pointing instability.

Appendix C

Software Index

This is an index of the top level LabVIEW programs used to collect data for thisthesis. Programs are located on the optical trapping experiment computer in B1B42 or
the AFM experiment computer in B2B17. The top level directory of all LabVIEW programs is C:\users\perkins\labview\; programs list the further location address. Some
programs were used in both experiments with minor differences between the two versions(initialize instrument.vi, BeamAlignment.vi, and StageDrift 1 Beam Multi.vi), and thus,
only described once. In the AFM experiment these programs are located in .\Gavin\ andare called Gavin initialize instrument.vi, Gavin BeamAlignment lv8.vi, and Gavin StageDrift 1 Beam Multi.vi, respectively. The software programs listed in this index do
not represent my original work and were updated by many other people, please see the
Acknowledgements. They are included for completeness.

C.1

Optical trapping experimentinitialize instrument.vi
Location: .\JILA\
Description: Initializes the PZT stage, PZT mirrors, and intensity servos. First
writes zero to the mirrors, then uploads mirror positions from file (DeltaV780.dat,
DeltaV850.dat, Delta1064.dat in location C:\users\perkins\trap\data\), and149
updates the position. The stage is initialized to the middle of the range. The
intensity servos are initialized with the values in TrapInitialize.vi.
Typical parameters: The mirrors are generally set to (5 V, 5 V), which is the
middle of the range. The intensity set points are -3 V, -9.5 V, and -2.54 V, forthe 785 nm, 850 nm, and 1064 nm lasers.
BeamAlignment.vi
Location: .\JILA\
Description: Centers the PZT mirror on a fiducial mark or trapped bead.
Sweeps the “beam PZT” mirror in x and y over the range given by plus orminus “Sen cal amplitude” nanometers, while simultaneously measuring theoutput voltage of the “beamdetect” x and y channels. Fits the voltage vs.
nanometer curve and determines the center point in x and y. Moves the PZT
mirror to the center point and updates the mirror position file (DeltaV780.dat,
DeltaV850.dat, Delta1064.dat in location C:\users\perkins\trap\data\).
Typical parameters: “beam PZT” is either 1064 or 850, while “beamdetect” is785 or 850, for centering the trapped bead or fiducial mark, respectively. “Sencal amplitude” is usually 200-800 nm.
2DHistogram.vi
Location: .\JILA\Yeonee\
Description: Plots the 2D histogram, y vs. x, of the trapped bead position.
Reads the binary data output file with extension “.eqp” from StiffnessCalbyPF&EQP.vi. Plots the 2D graph and fits a line to determine the slope ofthe data, which should be <0.01.
Typical parameters: Input the binary “.eqp” file from StiffnessCalbyPF&EQP.vi.
pow vs Stiff Optional z-PositionLock.vi
Location: ..\JILA\Yeonee\150
Description: Takes the trap calibration data. Measures stiffness of the trap
using both the power spectrum and equipartition methods over a series of intensity servo voltages. Fits a line to the stiffness vs. voltage curve. These
coefficients then need to be input by hand into a stiffness calibration file located in C:\users\perkins\trap\data\Powercal\. Naming of the file is usually“rXXXstiff-to-volt.dat” where XXX is the bead radius in nanometers. For different buffer conditions or other special situations the name can be extended
after “volt”. The user sets a height for the measurement, the parameters fortaking the power spectrum, the number of data points to be taken, the voltage
range to take data over, and whether to pick the height each time or use afiducial mark on the surface to maintain height.
Typical parameters: “Measurement Height” is usually 0.3 or 1.0 µm. “Lowpower”, “High Power”, and “Num steps” set the voltage range and are typically 1.0 V, 7.0 V, 9 steps. “bead r” is the bead radius, 0.165 µm. Parameters
to set the power spectrum settings are in yellow; “Frame Size”, “Samp Rate”,“Num avg”, “Num pts skip at beg”, “Num pts skip end”, “Num pts avg”, and“Aq rate” are 131072, 100 kHz, 15, 5, 5000, 200, and 8 kHz, respectively. To
select using the fiducial mark click “Position Clamp?” as true, otherwise click“Height?” as true to select the height each time; usually we select the height.
“Detector beam”, “Trapped bead BeamControl”, “Marker beam control” areset to 785, 1064, and 850, respectively.
StiffnessCalbyPF&EQP.vi
Location: .\JILA\Yeonee\
Description: Measures the stiffness using both the power spectrum and equipartition methods at the particular height selected and the current intensity servo
voltage. You can optionally choose to use only the equipartition method by151changing the “POWER SPECTRUM” button to false, or to use the current
height by changing the “Height” button to false. Data for the equipartition calculation continues to compile until the “stop Equipartition” button is pressed.
Typical parameters: The parameters “Bead Height”, “Bead radius”, “Beamdetect”, “beam PZT”, “Height Detect”, “Sampling Rate”, and “Frame Size”
are set to 0.3 µm or 1.0 µm, 0.165 µm, 785, 1064, 785, 100 kHz, and 131072,
respectively.
StiffnessCalCheck.vi
Location: .\JILA\Calibration Routines\
Description: Checks the stiffness calibration. First, uploads the stiffness calibration file from C:\users\perkins\trap\data\Powercal\ and converts the desired
stiffness values to intensity servo voltages. Then measures the stiffness value
using the equipartition and power spectrum methods at each desired stiffness.
Finally, compares the measured stiffness to the desired stiffness and outputs a
percentage. Data should be within 5% to check as normal. Data analyzed byprogram is sometimes wrong. It is better to do analysis in IGOR using AnalyzeStiffCheck.ipf.
Typical parameters: Parameters are set the same as in pow vs Stiff Optionalz-PositionLock.vi. The stiffness range can be set to mimic the voltage range
values by using the calibration file conversions.
CalibratePZTMirrorUsingStageAndStuckBead.vi
Location: .\JILA\Calibration Routines\
Description: This routine calibrates the PZT mirror using the calibrated PZTstage and a fiducial mark. First, the program opens up the PZT mirror calibration file PZTCalMulti.dat in C:\users\perkins\trap\data\ and reads thecalibration. If this file does not exist or the values are wrong you can estimate

152
the calibration, more on this later. Second, the laser is centered on a fiducial
mark using the PZT mirror. Then both the PZT stage and the PZT mirror
are incrementally moved the same amount in a series of positions outlining agrid. At each position the laser is recentered on the fiducial mark and the centervoltage is output. Finally, the program outputs the mirror center voltages as a
2D grid. The data is read by either MirrorCalResult.vi or pztCalibration Analysis.ipf, which calculates the movement in x of the laser in nanometers divided
by the voltage change on the mirror in x, the same thing in y, and the crosstalkterms. These numbers then need to be input by hand into PZTCalMulti.dat in
the order of movement x divided by voltage x, movement y divided by voltage
y, movement x divided by voltage y, movement y divided by voltage x; for the
785 nm PZT mirror, then the 850 nm PZT mirror, and finally, the 1064 nm
PZT mirror. To make an estimate of this calibration, you can simply move thestage and mirror by hand and follow the program’s protocol. Programs to movethe stage or laser by hand can be found in initialize instrument.vi. Usually, themirror calibration is run for a small grid to make sure everything is working andthen a larger grid is used to calibrate the mirror.
Typical parameters: “NumIterationsPerSide” is 1 for the small grid and 5 forthe larger grid. “VoltageRangePerSide” is either 1 or 2 V. “BeamControl” isthe beam for the corresponding PZT mirror that needs to be calibrated, 850 or
1064.
CheckPZTCalibrateMirrorUsingStageAndStuckBead.vi
Location: .\JILA\Calibration Routines\
Description: This program checks the PZT mirror calibration. First, it uploads the calibration file PZTCalMulti.dat from C:\users\perkins\trap\data\
and reads in the calibration. Next, the laser is centered on a fiducial mark on

153
the sample. Both the PZT stage and PZT mirror are moved the same amountin a series of positions outlining a grid. At each position the fiducial mark is
swept through the laser to determine the fiducial center position and calculate
the difference between the fiducial center position and the actual laser position.
Hence, we are checking the laser movement against the stage movement to tell if
the calibration is correct. The program outputs the difference between the stage
and laser positions and the desired laser movement in a table. If the differenceis within 5% of the desired movement the PZT calibration is working.
Typical parameters: To define the grid the user specifies “Range” and “Stepsize”, which are generally 500 nm and 50 nm. “BeamControl” is the beam forthe corresponding PZT mirror that needs to be checked, 850 or 1064.
MirrorCalResult.vi
Location: .\JILA\Calibration Routines\
Description: Plots the 2D voltage grid from CalibratePZTMirrorUsingStageAndStuckBead.vi and calculates the mirror calibration. The calibrations willneed to be multiplied by -1 before inputting them by hand into PZTCalMulti.dat
located in C:\users\perkins\trap\data\.
Typical parameters: Inputs the output file of CalibratePZTMirrorUsingStageAndStuckBead.vi, first y data then x data.
Zcal 2 beams 1 bead Rezero.vi
Location: .\Z calibration\
Description: This program measures the position of one or two fiducial marks
using two lasers. The user will first align the two lasers to look at one fiducial
mark or two fiducial marks. Then the program centers the lasers and calibrates
the fiducial mark position. Finally, the program measures fiducial position vs.
time until the “Stop” button is pressed. The program will output the differential

154
measurement and will also actively stabilize the fiducial position.
Typical parameters: The user defines the “DAQ rate”, typically 10.4 kHz, and“DAQ Num pnts to avg”, typically 104. These two numbers define the feedback
loop rate, which works the best at 100 Hz. The user also need to define the“beam PZT”, which is the beam that will be calibrated by moving the PZT
mirror (850), and the “beam control”, which is the beam that will be calibrated
by moving the stage (785).
StageDrift 1 Beam Multi.vi
Location: .\JILA\StageDrift\
Description: This program takes positional calibration curves in 3D. The program centers the fiducial mark and then outputs the calibration curve. If any ofthe position calibration subvi’s are stopped during data acquisition then sometimes the LabVIEW stage program will freeze. This is because the stage istrying to send data while LabVIEW is writing data. To fix this, run the program E710 Recieve.vi.
Typical parameters: The user defines the “beam control” laser to detect position, usually 850 or 785. To save the calibration data the user will need to flag
the various subvi’s with a true write statement.
DNAPulling v1.vi
Location: .\JILA\DNA stretching\
Description: This routine takes a DNA elasticity curve. First, a DNA-tethered
bead is trapped and bead position is calibrated. Then the program moves thestage in y to stretch the tether. This continues until the bead reaches the “clamp
position”, at which time, the stage continues to move while the stiffness in thetrap increases to maintain bead position. The program stops stretching whenthe “high force” is reached and begins stretching in the opposite direction. The

155
resulting elasticity curve is fit with a modified Marko-Siggia formula [71] todetermine the tether point, DNA contour length, and DNA persistence length.
The stage is readjusted in y to center the tether point. The program thenrepeats the stretching measurement in x. Usually two stretching measurements
will center the tetherpoint, while the last stretching measurement will take thefinal DNA elasticity curves.
Typical parameters: “clamp position” is typically 70 nm, while “high force” isusually between 6–10 pN. “Bead Radius” is 0.16 µm. “Moving Beam” is 1064
and ”Beam to measure” is set to 785.
Measure freebead with steps.vi
Location: .\JILA\freebead meas\
Description: This routine measures the trapped bead position and thus thename of the vi is somewhat of a misnomer. The trapped bead position iscalibrated and then position vs. time is measured until the “Stop” button ispressed.
Typical parameters: “Beam Detect” is 785. “beam PZT” is 1064. “Bead Height”
is either 0.3 µm or 1.0 µm.
InfiniteBWForceClamp ys.vi
Location: .\JILA\inf bandwidth clamp ys\InfiniteBWForceClamp ys\
Description: This is a passive force clamp used to take the DNA hairpin data.
First, a DNA-tethered bead is trapped and bead position is calibrated. Second,
multiple DNA elasticity measurements are taken to center the tether point relative to the laser beam. Next, the PZT mirror centers a detection laser on afiducial mark. Then the stage is moved to stretch the DNA and pull the beadto an intermediary position where position is recalibrated. The stage moves
further, stretching the DNA and pulling the bead out of the trap, until each156
stage movement moves the bead out of the trap the same amount (bead position= ∼240 nm). At this point, there is a corresponding move of the PZT mirror
to recenter the laser onto the fiducial mark and fiducial mark position is calibrated. Finally, the program begins taking bead positional data vs. time andcalculating the corresponding DNA contour length vs. time. While taking data,
the program actively stabilizes the stage while clamping the bead position bychanging the trap stiffness. For taking DNA hairpin data without the passive
force clamp we used a clamped bead position of 70 nm, instead of 240 nm. The
output “.tim” data file can be viewed using NA Tanalysis.ipf.
Typical parameters: The user defines the “DAQ rate”, typically 4 kHz, and“DAQ Num pnts to avg”, typically 40. These two numbers define the feedback
loop rate, which works the best at 100 Hz. “Bead Radius” is typically 0.16
µm. The “Desired stiffness value” is the force at which you want to pull (6 pN)
divided by the “Clamp position” (240 nm), 0.025 pN/nm. “Moving Beam” is1064 and ”Beam to measure” is set to 785.
RecBCDPulling v1.vi
Location: .\JILA\RecBCD\RecBCDPulling v1\
Description: This routine measures DNA contour length vs. time using active
stabilization. The program was used to take control measurements of DNA
tethers, as well as RecBCD data. First, a tethered bead is trapped and beadposition is calibrated. Second, multiple DNA elasticity measurements are taken
to center the tether point relative to the laser beam. Next, the PZT mirror centers a detection laser on a fiducial mark. Then the stage moves in y, stretching
the DNA and pulling the bead out of the trap until the bead position is at the“Clamp position”; there is a corresponding move of the PZT mirror to keep thedetection laser centered on the fiducial mark. To make sure, the fiducial mark157
position is calibrated at this point. Finally, the program begins taking beadpositional data vs. time and calculating the corresponding DNA contour lengthvs. time. While taking data, the program actively stabilizes the stage, if thebead position changes by more than 10 nm, the stage and mirror are readjusted
so that bead position returns to the initial value. This clamp on bead positionis termed the pseudo clamp. The output “.dat” data file can be viewed using
AnalyzeDNAPulling.ipf.
Typical parameters: The user defines the “DAQ rate”, typically 4 kHz, and“DAQ Num pnts to avg”, typically 40. These two numbers define the feedback
loop rate, which works the best at 100 Hz. “Bead Radius” is typically 0.16
µm. The “Desired stiffness value” is the force at which you want to pull (6 pN)
divided by the “Clamp position” (70 nm), 0.086 pN/nm. The “Feedback Modecontrol” is pseudo. “Moving Beam” is 1064 and ”Beam to measure” is set to785.
calibrate free bead.vi
Location: .\Description: This program measures stiffness using the drag method. The user
positions a trapped bead at one end of the stage range. The program begins
moving the stage at a particular velocity, which displaces the bead from thetrap center. Using this measurement, the program calculates the stiffness ofthe trap at the current intensity servo voltage. The program will need to berepeated over several voltages to get a calibration for stiffness to voltage.
Typical parameters: “End Velocity” sets the velocity and depends on the force
you want to use. “Range” is how many microns you want to move the stage
and is typically 90 µm. “dz/dx” is the tilt of the stage and can be found bymeasuring the change in fiducial mark z position as the stage is moved laterally.

158“Angle” picks whether to move the stage in x or y, 0 degrees = x and 90 degrees
= y.

C.2

AFM experiment

Gavin 1beam Rezero.vi
Location: .\Z calibration\
Description: This program measures the position of one or two fiducial marks
using two lasers. The user will first align the two lasers to look at one fiducial
mark or two fiducial marks. Then the program centers the lasers and calibrates
the fiducial mark position. Finally, the program measures fiducial position vs.
time until the “Stop” button is pressed. The program plots the differential
measurement and will also actively stabilize the fiducial position. It is also
outfitted to allow for an optional linear crosstalk compensation, scanning of thesample, and back-and-forth movement of the sample. The output “.dtf” data
file can be viewed using AnalyzeStabData.ipf.
Typical parameters: The user defines the “DAQ rate”, typically 10.4 kHz, and“DAQ Num pnts to avg”, typically 104. These two numbers define the feedback
loop rate, which works the best at 100 Hz.
AFM 3D stabilization.vi
Location: .\JILA\Gavin\AFM 3D Stabilization\
Description: This routine measures the position of the tip using two lasers. The
user will first align the two lasers to look at one tip. Then the program moves
the tip stage back-and-forth relative to both lasers, while the user moves the tip
to center it. The program calibrates the tip position and measures the crosstalk.
Finally, the program measures tip position vs. time using a linear algorithm tocompensate for crosstalk. Active stabilization of the tip is optional. The output

159“.dtf” data file can be viewed using AnalyzeStabData.ipf.
Typical parameters: The user defines the “DAQ rate”, typically 10.4 kHz, and“DAQ Num pnts to avg”, typically 104. These two numbers define the feedback
loop rate, which works the best at 100 Hz. The 810-nm beam measures the
AFM tip, while the 845-nm beam measures the fiducial mark.
AA Top Level 77PicoDrift 2D stabilization Multi wiggle FPGA.vi
Location: .\JILA\Gavin\AFM VI’s Reorganized 20070713\
Description: This is a surface imaging program using the stabilized AFM. A
more in depth description is elsewhere [20]. Briefly, the program centers boththe tip and fiducial mark to their respective lasers and calibrates position (witha crosstalk compensation method). Then the program calibrates the AFM tip
position using the optical lever arm. Active stabilization of both the tip in 3D
and sample in 2D is controlled through writes to a field-programmable gatearray card. The sample position in z is locked using the optical lever arm tomaintain a constant force on the tip. The sample is scanned while the z error
signal is output as the surface map. To view the “.stm” data file use AnalyzeAFMImage.ipf or sub routine of this procedure.

Appendix D

Hardware Index

This is an index of the custom-built hardware on the optical trapping instrument. Hardware for the AFM experiment will be described elsewhere [20]. There are
drawings and designs of various machined microscope and optics mounts, as well as
electronic diagrams for our custom electronics. These items do not represent my original work and were mostly made by the JILA machine and electronic shops, please see
the Acknowledgements for a more complete reference. The drawings are included forcompleteness.

161

Figure D.1: Building the microscope part 1.

162

Figure D.2: Building the microscope part 2.

163

Figure D.3: Building the microscope part 3.

164

Figure D.4: Building the microscope part 4.

165

Figure D.5: Building the microscope part 5.

166

Figure D.6: Building the diode laser system part 1.

167

Figure D.7: Building the diode laser system part 2.

168

Figure D.8: Building the diode laser system part 3.

169

Figure D.9: Microscope base plate.

170

Figure D.10: Condenser arm focusing plate adapter.

171

Figure D.11: Condenser arm focusing plate spacer.

172

Figure D.12: Detection mount off condenser arm.

173

Figure D.13: Detection mount off condenser arm picture.

174

Figure D.14: Upside down lens adaptor plate part 1.

175

Figure D.15: Upside down lens adaptor plate part 2.

176

Figure D.16: Upside down lens adaptor plate part 3.

177

Figure D.17: Microscope bridge plate part 1.

178

Figure D.18: Microscope bridge plate part 2.

179

Figure D.19: Microscope bridge plate part 3.

180

Figure D.20: Microscope bridge plate part 4.

181

Figure D.21: Microscope bridge plate part 5.

182

Figure D.22: Objective holder part 1.

183

Figure D.23: Objective holder part 2.

184

Figure D.24: Riser for 733.3D Physik Instrumente stage.

185

Figure D.25: Microscope dichroic holder part 1.

186

Figure D.26: Microscope dichroic holder part 2.

187

Figure D.27: Microscope dichroic holder part 3.

188

Figure D.28: Microscope camera mount.

189

Figure D.29: Color filter holder.

190

Figure D.30: Lens mount.

191

Figure D.31: Mercury lamp to liquid light guide mount part 1.

192

Figure D.32: Mercury lamp to liquid light guide mount part 2.

193

Figure D.33: Mercury lamp to liquid light guide mount part 3.

194

Figure D.34: Mercury lamp to liquid light guide mount part 4.

195

Figure D.35: Mercury lamp to liquid light guide mount part 5.

196

Figure D.36: Mercury lamp to liquid light guide mount part 6.

197

Figure D.37: Mercury lamp to liquid light guide mount picture.

198

Figure D.38: Gimbal mirror mount part 1. The height is incorrect for the opticaltrapping experiment part 1.

199

Figure D.39: Gimbal mirror mount part 2.

200

Figure D.40: Fiber launch to 3D translation stage adaptor.

201

Figure D.41: Double dichroic mount part 1.

202

Figure D.42: Double dichroic mount part 2.

203

Figure D.43: Double dichroic mount part 3.

204

Figure D.44: Double dichroic mount part 4.

205

Figure D.45: Double dichroic mount part 5.

206

Figure D.46: Double dichroic mount part 6.

207
PT004A3.sch-1 - Tue Oct 28 15:33:48 2008

Figure D.47: Intensity servo electronic diagram.

208

Figure D.48: Intensity servo picture.

Appendix E

Protocol Index

This is a protocol index that lists detailed, step-by-step instructions for various
preparations. Most protocols have been developed to prepare a biological assay. However, there are some protocols for how to use various instruments at JILA requiredin sample preparation and other protocols on how to do various procedures on our
instrument. The protocols do not represent my original work, please see the Acknowledgements for a more complete reference. They are included for completeness.

E.1

Potassium hydroxide-clean cover slips(1) Put on protective clothing: eyewear, lab coat, gloves, and close-toed shoes.
(2) Put small stir bar, 250 mL denatured ethanol, 80 g potassium hydroxide pellets
into a 1 L washed beaker. Cover with parafilm.
(3) Put on stirrer. Set at medium stirring speed (slow enough so that there is nosloshing), no heat.
(4) Load cover slip basket with cover slips and attach handle.
(5) Fill Branson 5200 degasser quarter full with distilled water using autoclaved
beaker.
(6) Place two 1 L washed beakers half full of distilled water in degasser.

210(7) Place potassium hydroxide-alcohol solution beaker in degasser. Hold potassiumhydroxide beaker down with tape. Turn on degasser power, but not heat.
(8) Using cover slip basket, place cover slips in solution for 3 min, and invigorate
cover slips by moving basket up and down and side to side.
(9) Rinse cover slips over sink with distilled water squirt bottle.
(10) Place cover slips in beaker of distilled water in degasser for 3 min.
(11) Rinse over sink with distilled water again.
(12) Place in other beaker of distilled water in degasser for 3 minutes.
(13) Rinse over sink with distilled water and shake water off.
(14) Dry in microwave, checking ever 30 s or so to see if dry, usually 5 min.
(15) Place in plastic container and remove handle. Write the date on the plastic
container.
(16) Repeat steps 8-14 for the rest of the cover slips, changing the distilled water inthe beakers in the degasser every three baskets.
(17) Clean-up. Dispose of distilled water in sink, potassium hydroxide solution inorganic hazardous waste, and clean empty beakers.

E.2

Piranha-clean cover slips(1) Put on protective clothing: eyewear, lab coat, two pairs of gloves (nitrile andrubber), and closed-toed shoes.
(2) In the fume hood, Pour ∼400 mL piranha solution (15 drops hydrogen peroxide
per 100 mL sulfuric acid) into a 1 L beaker and heat on a hot plate. Set athigh heat so that piranha begins to slowly bubble. Do not get piranha too hot

211
as this is dangerous. The hood should be empty; make sure there are not any
alcohols as this mixture is highly reactive.
(3) Load cover slip basket with cover slips and attach the long handle.
(4) Place cover slip basket in piranha for 10 min. There should be many small
bubbles around the basket for a good etch. If not, add more hydrogen peroxide.
Solution should be clear when etch is finished.
(5) Remove cover slip basket from piranha and place in 1 L beaker of distilled water.
Turn off hot plate.
(6) Rinse cover slip basket in sink with distilled water for 1 min, followed by denatured ethanol for 1 min. Place in microwave for 2 min to dry.
(7) Remove piranha from hot plate and allow to cool. Once cool, pour the piranha into a teflon or glass container with a loose teflon lid. Store in secondary
containment in fume hood. Piranha can be used multiple times.
(8) Clean used 1 L beakers.

E.3

Affix stuck beads(1) Prepare 100X diluted 770 nm beads in distilled water.
(2) Prepare sodium bicarbonate solution (84–90 mg of sodium bicarbonate and 10
ml of distilled water). You don’t need to measure it precisely.
(3) Mix 480 µL of sodium bicarbonate solution with 20 µL of beads. Vortex.
(4) Introduce this bead-solution to a preassembled sample chamber. Wait at least
10–20 min. Check under microscope to see if there are a decent number of stuckbeads for your application.

212(5) Wash out bead-solution from the sample chamber with 200 µL of 100 mM
magnesium acetate, 10 mM Tris, and 100 mM potassium chloride. Wait atleast 30 min.
(6) Dry out the sample chamber with ethanol (i.e., take 20 µL of ethanol and flow
it through, sucking out all the liquid completely). This prevents clumping ofstuck beads since the water surface tension is large enough to move the stuckbeads if allowed to evaporate. Wait 10 min.
(7) Put the sample chamber in the oven at 110 ◦ C for 13 min. Let cool for 30 min.
(8) Repeat last step three more times, but bake for only 7 min to avoid “pancake”
stuck beads.

E.4

Fabricate HSQ fiducial marks(1) Piranha clean cover slips for 10 min.
(2) Pre-bake on hotplate at 200 ◦ C for 2 min.
(3) Spin HSQ on to cover slip at 1200 rpm for 60 s, make 1-µm-tall post.
(4) Post-bake on hotplate at 120 ◦ C for 2 min and again at 200 ◦ C for 2 min.
(5) Thermally evaporate 15 nm of aluminum on to cover slip. HSQ is sensitive tolight and electron beams so the evaporation must be thermal and the cover slips
should be covered when leaving the clean room.
(6) Use the scanning electron microscope to expose an array of dots. Use the run
file to pattern a 1.5 mm X 1.5 mm array of dots with a diameter of 750 nm anda 15-µm spacing. Dosage is 450 µC/cm2 ; current is 25 pA; voltage is 38 keV.
(7) Etch the aluminum in a solution with 80 mL phosphoric acid, 5 mL acetic acid,
5 mL nitric acid, and 10 mL distilled water for about 10 s or until aluminum

213
disappears. Rinse in distilled water and nitrogen dry.
(8) Develop HSQ in tetramethylammonium hydroxide (2% solution) for 10 min; the
25% solution is better and takes 2 min. Place in beaker of 9:1 isopropyl alcohol
to tetramethylammonium hydroxide for 30 s, then in isopropyl alcohol, andfinally, in distilled water. Rinse in distilled water and nitrogen dry. Check posts
under microscope to see if development is complete. If not, repeat development.
(9) Cure in oven at 400 ◦ C for 60 min. Cover slips will need to be placed in glass
racks below oven in clean room; teflon will melt.
(10) Piranha clean cover slips for 10 min.

E.5

Fabricate silicon fiducial marks
This protocol can also be used as a guide to evaporation with the electron gun.

(1) Load sample holder with four masks and four cover slips. Load the masks sothat the window is over the opening in the rubber pad. Load cover slips so they
abut the alignment pins. Pull down the sample holder arm and lightly tighten
the screw to clamp, do not touch the screw that holds the spring-loaded pad.
(2) Vent the evaporator by pushing “Vent”. Make sure the gate between the upperand lower chamber is open.
(3) Load the silicon crucible into the crucible holder. Push “Remote” to open
shutter before installing crucible, then push “Remote” again to close shutter.
(4) Load sample holder into upper evaporator chamber. Unscrew the 8 pins that
hold the side flange on and remove flange. Remove the thermal evaporator
sample rod. Gently place the sample holder into the upper chamber and alignto the flange screw holes. Screw the 8 pins into the sample holder. Place theflange off to the side.

214(5) Close the upper and lower chamber door.
(6) Pump down the chamber by pressing “Cycle”. Pump down to 10−7 Torr.
(7) Check program parameters. Density should by 2.32 for silicon; amount to deposit is 150 nm.
(8) Turn on electron gun. Make sure set to “1”, then push “On/off” and wait for
power light, and then press “Gun” and wait for gun light. Turn on current to
30 and slowly ramp it up. The crucible should glow red hot.
(9) Deposit material. Wait until crystal shows 1 nm/s and then push “Run”. When
150 nm have been deposited turn gun current down to 30 and let sit for 1 min.
(10) Turn off gun. Press “gun” and then “On/off”.
(11) To do another sample you only need to vent and pump the upper chamber. Vent
the upper chamber by pushing “Gate close” and “Vent”. Take out evaporator
holder, load, and replace. Close the upper chamber door. Press “Rough” andwait until pressure is at 3X10−1 . Press “Hi Vac” and wait for two clicks. Push
“Gate open”, “Reset”, “Process”, and wait until chamber pumps down to 10−7 .
Then follow steps 7-10.
(12) Turn off when finished. Vent the upper chamber by pushing “Gate close” and“Vent”. Take out evaporator holder and replace the flange. Close the upper
chamber door. Press “Rough” and wait until pressure is at 3X10−1 . Press “Hi
Vac” and wait for two clicks. Push “Gate open”, “Reset”, “Vent”, and thefull chamber should vent. When vented take silicon crucible out of the lower
chamber and replace rod. Pump down by pressing “Cycle”. Make sure chamberpumps down to 10−7 .

215

E.6

Fabricate etched holes
Please see Theresa Ulrich’s notebook for a more detailed procedure.

(1) Piranha clean cover slips for 2 min.
(2) Thermally evaporate 15 nm of chromium on to the bottom of coverslip.
(3) Spin isopropyl alcohol on the cover slip at 4000 rpm for 45 s.
(4) Pre-bake cover slip on hotplate at 180 ◦ C for 20 min.
(5) Spin polymethyl methacrylate resist at 4000 rpm for 45 s.
(6) Post-bake cover slip on hotplate at 180 ◦ C for 5 min.
(7) Thermally evaporate 15 nm of aluminum.
(8) Use the scanning electron microscope to expose an array of filled circles. Use
the run file “perkdot4” to pattern a 2 mm X 2 mm array of filled circles withwidths of 50 nm, 100 nm, and 150 nm and 6 µm spacing. Dosage is 350 µC/cm2 ;voltage is 38 keV; current is 10 pA; magnification is 500X.
(9) Etch the aluminum in a solution with 20 mL distilled water and 3 mL sodiumhydroxide (50% w/w) for about 10 s or until aluminum disappears. Rinse indistilled water and nitrogen dry. Sodium hydroxide solution can go down thedrain with extra water.
(10) Develop the resist using 1:3 methyl isobutyl ketone to isopropyl alchohol for 3
min, 1:9 solution for 15 s, and distilled water for 30 s. Nitrogen dry. Check forholes in resist using microscope.
(11) Etch in buffered hydrofluoric acid. Wear neoprene gloves. Put 40 mL bufferedhydrofluoric acid in 50 mL beaker with stir bar on stirrer at medium stir speed.

216
Dip coverslip in acid for an amount of time appropriate for the depth of holeneeded (1 µm per min etch rate). Rinse in beaker of water for 30 s, rinse in
sink, nitrogen dry.
(12) Remove resist. Heat “Nano Remover PG” to 60 ◦ C (flash point is 88 ◦ C). Hold
cover slip over remover for 10 s to heat it up and prevent cracking, before placing
in remover for 5 min. Rinse in beaker of water for 30 s, rinse in sink, nitrogendry.
(13) Remove the chromium layer. Place in beaker of “Amtron ETC-212S chrome
photomask etchant” (perchloric acid) until chromium disappears. Rinse in
beaker of water for 30 s, rinse in sink, nitrogen dry.

E.7

Prepare DNA tethered particle assays(1) Prepare 10 mL of WB. To a 15 mL falcon tube add: 8.45 mL distilled water, 250µL 1 M Tris pH = 7.5, 10 µL 1 M magnesium acetate, 10 µL 1 M sodium chloride,
400 µL 10% Tween-20, 870 µL 35 mg/mL bovine serum albumin (filtered), 10µL 1 M dithiothreitol. To make 10 mL 35 mg/mL bovine serum albumin add
the following to a 15 mL falcon tube: 9.4 mL distilled water, 200 µL 1 M Tris
pH = 7.5, 400 µL 10% Tween-20, 350 mg bovine serum albumin. Hand mix thebovine serum albumin solution and filter using a 10 mL syringe and a 0.2-µm
filter.
(2) Vortex streptavidin bead stock.
(3) Add 30 µL streptavidin bead stock (408 pM 440-nm-diameter beads; 920 pM,
320-nm-diameter beads) to an eppendorf tube per 2 slides.
(4) Wash beads three times. Add 200 µL 0.4% phos-tween, centrifuge (400-nm
bead, 5 min, 10 krpm; 500-nm bead, 5 min, 7 krpm; 320-nm bead, 2 min,

217
12krpm), and remove supernatant.
(5) Resuspend in 30 µL of WB (400-nm beads, 408 pM; 320-nm beads, 920 pM).
(6) Sonicate beads for 40 mins at 20 ◦ C. Parafilm the tube before sonicating. Pulse
mode (2 s on, 2 s off).
(7) In the mean time, make flow chambers and allow epoxy to dry.
(8) Once sonication is done, check beads for monodispersion. Dilute 1 µL of beads
in 100 µL of WB. Flow through a slide and check under the microscope.
(9) Make 30 µL of 100 pM DNA in WB per two slides. If two dilutions are necessary,
first dilution should be in 10 mM Tris (this dilution can be kept and used forweeks). For the second dilution, dilute into WB. This solution can be used thatday.
(10) Mix 30 µL bead solution (400-nm bead, 408 pM; 320-nm bead 920 pM) with 30µL 100 pM DNA per two slides. Mix by pipetting. Let sit for 60 min at room
temperature.
(11) Concurrently, make 100 µL of 20 µg/mL anti-digoxigenin solution (90 µL 100
mM sodium phosphate buffer pH = 7, 10 µL of 200 µg/mL anti-digoxigenin full
antibody) per 2 slides. Spin anti-digoxigenin stock and then mix by vortexing
before using. Vortex final solution as well.
(12) Flow 50 muL per slide of 20 µg/mL anti-dig solution through slides. Sit for 60
min in humidity chamber at room temperature.
(13) Wash 2 times per slide with 200 µL WB. Sit for 10 min.
(14) Flow 30 µL of bead/DNA mixture per slide. Sit 60 min at room temperature.
(15) Wash 2 times with 200 µL of WB.

218

E.8

Prepare RecBCD assays(1) Make flow chambers and allow epoxy to dry.
(2) Dilute 200 µL of 125 µg/mL biotinylated bovine serum albumin solution (195µL 100 mM sodium phosphate buffer pH = 7, 5 µL of 5 mg/mL solution), whichmakes enough for 10 slides.
(3) Flow 20 µL per slide of 125 µg/mL biotinylated bovine serum albumin solution
through slides. Sit for 20 min in humidity chamber at room temperature.
(4) Prepare 10 mL of WB. To a 15 mL falcon tube add: 8.45 mL distilled water, 250µL 1 M Tris pH = 7.5, 10 µL 1 M magnesium acetate, 10 µL 1 M sodium chloride,
400 µL 10% Tween-20, 870 µL 35 mg/mL bovine serum albumin (filtered), 10µL 1 M dithiothreitol. To make 10 mL 35 mg/mL bovine serum albumin add
the following to a 15 mL falcon tube: 9.4 mL distilled water, 200 µL 1 M Tris
pH = 7.5, 400 µL 10% Tween-20, 350 mg bovine serum albumin. Hand mix thebovine serum albumin solution and filter using a 10 mL syringe and a 0.2-µm
filter.
(5) Wash 2 times per slide with 200 µL WB. Sit for 10 min.
(6) Make 300 µL of 10 µg/mL streptavidin solution (297 µL WB, 3 µL of 1 mg/mL
streptavidin), which makes enough for 6 slides.
(7) Flow 50 µL per slide of 10 µg/mL streptavidin solution. Sit for 20 min in
humidity chamber at room temperature.
(8) Concurrent with flow chamber preparation, begin preparing beads. Vortex
streptavidin bead stock.
(9) Add 30 µL streptavidin bead stock (408 pM 440-nm-diameter beads; 920 pM,
320-nm-diameter beads) to an eppendorf tube per 2 slides.

219(10) Wash beads three times. Add 200 µL 0.4% phos-tween, centrifuge (400-nm
bead, 5 min, 10 krpm; 500-nm bead, 5 min, 7 krpm; 320-nm bead, 2 min,12krpm), and remove supernatant.
(11) Resuspend in 30 µL of WB (400-nm beads, 408 pM; 320-nm beads, 920 pM).
(12) Sonicate beads for 40 mins at 20 ◦ C. Parafilm the tube before sonicating. Pulse
mode (2 s on, 2 s off).
(13) By this time the streptavidin solution incubating in the flow chamber should be
done. Wash 2 times per slide with 200 µL of WB. Sit for 10 min.
(14) Make 600 µL of 15 nM biotinylated RecBCD solution (600 µL WB, 0.45 µL 10µM or 34 µM biotinylated RecBCD).
(15) Flow 20 µL 15 nM biotinylated RecBCD solution. Sit for 2 hours in humidity
chamber at room temperature.
(16) Wait for the bead sonication to finish. Once it is done, check beads for monodispersion. Dilute 1 µL of beads in 100 µL of WB. Flow through a slide and checkunder the microscope.
(17) Make 30 µL of 100 pM DNA in WB per two slides. If two dilutions are necessary,
first dilution should be in 10 mM Tris (this dilution can be kept and used forweeks). For the second dilution, dilute into WB. This solution can be used thatday.
(18) Mix 30 µL bead solution (400-nm bead, 408 pM; 320-nm bead 920 pM) with 30µL 100 pM DNA per two slides. Mix by pipetting. Let sit for 60 min at room
temperature.
(19) When biotinylated RecBCD is done incubating, wash 2 times with 200 µL of
WB. Sit for 10 min.

220(20) Flow 30 µL of bead/DNA mixture per slide. Sit for 40 min in humidity chamberat room temperature.
(21) Wash 2 times with 200 µL of WB.

E.9

How to guide: thermal evaporator(1) Align sample (i.e. cover slips) on sample holder and affix with metal pins.
(2) Vent chamber with “Vent” button.
(3) Need to remove the electron beam gun and line the gun area with aluminum
foil. Generally, Dave Alchenburger does this. Put a sign on the evaporator thatsays that thermal evaporation is underway.
(4) Insert the thermal crucible with what you would like to evaporate (e.g. one
pellet of aluminum).
(5) Screw the sample rod into the upper chamber through the tube between thelower and upper chambers.
(6) Insert sample holder into the rod using an M6 screw and by holding the rod
fixed from above the evaporator.
(7) Check quartz crystal to see if it needs replacing.
(8) Make sure the shutter is closed and on auto (push “S1” and “Remote” in).
(9) Close the door and pump down the chamber by pushing “Cycle”. If the vacuum
remains at 10−8 press “Cycle” again. Chamber pressure should decrease to 10−7 .
(10) Check system parameters: density (aluminum is 2.7), tooling (1.3), termination
depth (15 nm).

221(11) Heat crucible. Turn knob to “LT” and begin slowly increasing current. The
outer surface of the material will melt and fall to the bottom of the crucible
when it is time to evaporate. Be careful not to turn up the current too muchbecause the material will wick around the side of the crucible and leak out.
(12) Press “Run” to start the evaporation. This should automatically open the
shutter and the crystal will record the amount of deposition. Tune the current
so that 1 nm of material per second is deposited. The shutter will automaticallyclose when finished.
(13) Turn the current slowly down and move the knob back to “0”. Wait until thechamber temperature reaches ∼40 ◦ C to vent the chamber by pushing “Vent”.
(14) Remove sample from chamber and insert the electron beam gun back into thechamber.
(15) Close the door and pump down the chamber by pushing “Cycle”. If the vacuum
remains at 10−8 press “Cycle” again. Chamber pressure should decrease to 10−7 .

E.10

How to guide: scanning electron microscope(1) Make sure vacuum is sufficient (10−6 Torr). If not, fill trap with liquid nitrogen.
(2) Log on to computer. Turn on the “SEM Motion Controller” (stage software),“NPGS menu” (run file editor), and “Flashbus” (video) programs.
(3) Check instrument settings (see Figs. E.1, E.2, E.3, and E.4 for a detailed description of instrument. Turn on the chamber camera by flipping the unlabeledswitch, unless sample is sensitive to light. Turn up the brightness and contrast
on both monitors. Press “FAST” to switch to fast monitor updating. Bring up
the “EOS menu” on the right monitor and the standard screen on the left monitor. Check the parameters on the “EOS menu” to see if correct; voltage = 38

222
keV, condenser lens coarse adjust = 8–10, magnification = 80–200X. Make surethe “SEM/NPGS” switch is in the “SEM” position. The filament knob shouldbe all the way counter-clockwise and “Accel Voltage” should be off. Check thatthe manual stage knobs are at 25, 35, 39, for x, y, and z.
(4) Mount the cover slip on the machined cover slip holder so that the calibration
standard is at the bottom. Wear gloves. Unscrew the clamps and push thecover slip against the alignment posts located on the right and bottom sides.
Screw in the clamps. Screw in the sample loading stick.
(5) Load the sample. Insert the sample with the loading stick into the outer chamber. Press the white button which pumps down the outer chamber. Wait for
two clicks (this when the roughing pump switches over to the fine pump). Openthe outer chamber gate using the “open” knob, and slide the sample into theinner chamber stage. Unscrew the loading stick and detract it to the outerchamber. Close the gate and push the white button.
(6) Turn the z knob from 39 to 8, raising the sample. In the “EOS menu” change
the working distance to 8 mm.
(7) Move the stage to a safe place on your sample or to the calibration standard
using the “SEM Motion Controller”. Should also be a place where there arefeatures.
(8) Turn on the filament. To do this, turn on the “Accel Voltage”. “Fila” button
should be glowing green, if not press the button. Change the standard screen on
the monitor to a line scan. Slowly turn up the filament current while watching
the feature amplitude in the line scan. If there are not any features, check to
see if the magnification is low enough (100X), the current is high enough (60pA), and you are at the correct spot on your sample. The linescan amplitude

223
should increase, then decrease, then increase, and finally plateau. Leave thefilament current right at the start of the plateau. Change the monitor back tothe standard image screen.
(9) Tune the electron beam for high resolution images and writes. Find a feature on
the surface and increase the magnification while tuning the focus knob. Oncea feature is in focus at 70,000X, slowly turn the x and y astigmatism knobs tomore clearly focus the image. The “Wobbler” will wobble the focus for easier
tuning of the astigmatism knobs. When the beam is tuned, the feature will be
sharp at 100,000X.
(10) Turn on the “PCD”, which blanks the beam, and move to a location on yoursample that is close to the write field. Turn off the “PCD” to image. Make surethat a feature is still in focus at 100,000X.
(11) Turn on the “PCD” button and move to the center of the cover slip or the startof the write field.
(12) Set the correct probe current for the write (10-12 pA).
(13) Set the correct magnification for the write (500X).
(14) Switch “SEM/NPGS” to “NPGS”.
(15) Switch “Beam Blanking” to “EXT”.
(16) Turn off the “PCD”.
(17) Select the correct run file in the “NPGS menu” and push start. The pattern
will begin writing.
(18) Once the writing is done, turn off the beam. Slowly turn the filament knob tothe full counter-clockwise position. Turn off “Accel Voltage”. Return the “SEM

224
Motion Controller” to absolute home. “Beam Blanking” to off. “SEM/NPGS”
switch to “SEM”. Turn off “PCD”.
(19) Remove the sample. Move the z manual knob to 39. Reverse load the sample.
Unscrew the clamps to remove the cover slip from the sample holder.
(20) Shut down the instrument. Clear both monitors and turn the contrast andbrightness down. Turn off the camera. Press “PF5”.

E.11

How to guide: fiber alignment(1) Using the translatable lens or an imaging system collimate the free-space laser
beam at a diameter that would produce a focal beam width that matches thecore diameter of the fiber. Typically beam diameters can be selected to match
either the numerical aperture of the fiber or the core diameter. We match thecore diameter to minimize the effects of beam translations while still maintaining
reasonable power efficiency through the fiber.
(2) Without the fiber attached to the fiber mount, maximize the output power
through the mount using the mirrors.
(3) Attach a fiber-coupled laser to the fiber mount such that the fiber-coupled laser
beam is output where the free-space laser beam is input. Move the fiber mounttip, tilt, and axial stage such that the fiber-coupled laser beam aligns with the
input free-space laser.
(4) Disconnect the fiber laser from the mount and connect the fiber, measuring thelight out of the fiber with a power meter.
(5) If there is not any measurable output light recheck steps 2–4.

225

Figure E.1: Scanning electron microscope (SEM) display and controls. (1) Vacuum
inside the specimen chamber. (2) Current in nA. (3) Enable switch. (4) SEM Motion
Controller Program. (5) Printer for SEM images. (6) Portion of the SEM auxiliary
control panel. (7) Analog monitor. (8) Digital monitor. (9) The ”standard display”
on a monitor. (10) Auxiliary control panel. (11) SEM control keyboard. (12) Primarycontrol panel. (13) Brightness and contrast dials for the analog and digital monitors.
(14) ”ON” button for ACCEL VOLTAGE. (15) SEM computer keyboard. Figure credit:
Theresa Ulrich.

226

Figure E.2: SEM column. (1) Dewar for liquid nitrogen sits on the floor here. (2) Funnel
for liquid nitrogen. (3) Location of small pipe that gets filled with liquid nitrogen. (4)Coarse z control for the stage. (5) Condenser controls. (6) Tilt controls. (7) White
button to push when loading a sample. (8) ”Open” knob for opening the gate into
the specimen chamber. (9) Outer chamber for initial loading of sample. (10) Rotation
controls. (11) x control. (12) Fine z control. (13) y control. Figure credit: Theresa
Ulrich.

227

Figure E.3: SEM auxiliary control panel. (1) SEM/NPGS switch. (2) Press this button
to see your pattern writing on the analog screen. (3) Speed control for the joystickmotion controller. (4) Joystick motion controller. (5) Beam blanking switch. (6) PCD
button. (7) Chamber View System switch to turn on the camera. (8) Filament gauge,
lit on the right side. (9) Filament button. (10) Filament knob. (11) Scan Rotation
knob. Figure credit: Theresa Ulrich.

228

Figure E.4: SEM primary control panel. (1) PIC and MODE buttons, useful during
filament saturation. (2) Magnification knob. (3) x astigmatism knob. (4) y astigmatism
knob. (5) WFM button, useful for checking brightness and contrast values. (6) D-MAG
button, useful for focusing at high magnification. (7) FREZ button, useful for freezing
the screen. (8) Speed controls to change scan rate from FAST to SLOW. (9) Coarse/Fineswitch for the focus knob. (10) Focus knob. (11) Probe Current knob. (12) Brightness
and Contrast knobs. Figure credit: Theresa Ulrich.

229(6) Translate the fiber mount axially by turning the three z screws equally. The
measured power should reach a maximum value and then decline, go throughthe maximum and then back to it.
(7) Move the fiber mount in x and y in tiny increments until the power is maximized;
do not move more than one turn and do not touch these screws again.
(8) Begin moving the three z screws individually and in order while maximizing thepower each time. Two screws you will not have to turn very much, while thethird screw, the “magic” screw, will be rotated more. This is because the fiber
is angle-cleaved and the “magic” screw is tilting the mount to accommodate forthis angle.
(9) Once the power has reached 10% of the input value begin adjusting the twomirrors individually and in order along with the three fiber mount z screws.
(10) Once the power has reached ∼70% of the input power begin translating the lensin small increments while adjusting the mirror and fiber screws to maximize thepower at each lens position. This should experimentally determine the widthof the beam at the fiber input. Once this procedure is done there should be∼80% of the input light at the fiber output. One important note: do not get
frustrated, sometimes things have to get worse before they get better.

E.12

How to guide: intensity servo tuning(1) To tune the servo, the fine and coarse gain along with the proportional-integral
corner were turned all of the way down. For this intensity servo the proportionalintegral corner is somewhat of a misnomer since the corner is really between asingle integral (20 dB per decade) and a double integral (40 dB per decade).
(2) The in-loop photodiode voltage was T-ed off to an electronic spectrum analyzer

230
operating over the bandwidth of 0–1 MHz.
(3) While monitoring the noise using the electronic spectrum analyzer, the coarse
gain was turned up until the system began to oscillate and then backed off.
(4) Step 3 was then repeated with the fine gain and, finally, the proportional-integral
corner.
(5) To further make sure the system wasn’t oscillating, the photodiode output voltage was checked using an oscilloscope.
(6) When finished, the spectrum analyzer should show a noise peak at the bandwidth of the feedback loop (200 kHz for all three lasers), and a measurement of
the noise level should reproduce the quoted values in Section 2.1.4.