Vol 437|6 October 2005|doi:10.1038/nature04003

LETTERS
Direct observation of steps in rotation of thebacterial flagellar motor
Yoshiyuki Sowa1*, Alexander D. Rowe2*, Mark C. Leake2, Toshiharu Yakushi3, Michio Homma3,
Akihiko Ishijima1,4 & Richard M. Berry2

The bacterial flagellar motor is a rotary molecular machine thatrotates the helical filaments that propel many species of swimming
bacteria1,2. The rotor is a set of rings up to 45 nm in diameter in thecytoplasmic membrane3; the stator contains about ten torquegenerating units anchored to the cell wall at the perimeter of therotor4,5. The free-energy source for the motor is an inwarddirected electrochemical gradient of ions across the cytoplasmic
membrane, the protonmotive force or sodium-motive force forH1-driven and Na1-driven motors, respectively. Here we demonstrate a stepping motion of a Na1-driven chimaeric flagellar
motor in Escherichia coli6 at low sodium-motive force and with
controlled expression of a small number of torque-generating
units. We observe 26 steps per revolution, which is consistent withthe periodicity of the ring of FliG protein, the proposed site of
torque generation on the rotor7,8. Backwards steps despite theabsence of the flagellar switching protein CheY indicate a smallchange in free energy per step, similar to that of a single iontransit.
Direct observation of steps in ATP-driven molecular motors hasrevealed much about the fundamental mechanisms of these protein
machines9–11. Steps characteristic of the ATP-driven F1 part of ATP
synthase have been observed when the whole enzyme is driven by ion
flow in the FO part12, but steps have never been seen in a purely iondriven molecular machine. Steps have not previously been resolvedin the flagellar motor13 because of its high speed14,15, the presence ofmultiple stator units in a single motor4 and the small step size
predicted—either from structural data on rotor periodicity or frommechanical data obtained by dividing the free energy of one ioncrossing the membrane by the torque that the motor generates. We
took several measures to overcome these factors. We detectedrotation by back-focal-plane (BFP) interferometry of 500-nm diameter polystyrene beads attached to spontaneously sticky flagellar
filaments of E. coli, as described previously16, or by high-speed
video recording of 200-nm fluorescent beads attached in the sameway (Fig. 1b, c, inset). The structure and function of Hþ and Naþ
motors are similar, and functional chimaeras have been madecontaining different mixtures of Hþ and Naþ motor components17.
We slowed motor rotation to the point at which steps could be
resolved by decreasing the sodium-motive force (SMF) in E. coli cells
containing Naþ-driven chimaeric motors (in which the Hþ-driven
stator proteins MotA and MotB are replaced by the Naþ-driven
PomA and the chimaeric fusion protein PotB, respectively6; Fig. 1a).
We decreased the SMF by a low external Naþ concentration inexperiments with BFP detection and by cumulative photodamage
in fluorescence experiments. We controlled the number of stator
units by inducible expression of stator proteins in a strain withwild-type stator proteins deleted. We also deleted cheY and pilA to
avoid possible complications due to motor switching or sticking ofbeads to cell bodies, respectively. We obtained rotation speed bymeans of power spectra of the combined x and y signals16, and bead
angles by modelling the raw data as the projection of an oblique
circular orbit18.
Fast Naþ-dependent rotation and reduced speed when Liþ
replaced Naþ (data not shown) indicate that the chimaera behaves
as a typical Naþ motor15,19. For step experiments, we grew cells with
low inducer levels to produce fully energized motors with a small
initial number of stator units (typically three or four; Supplementary
Information). Reduction of the SMF, either by lowering the Naþconcentration in BFP experiments (Supplementary Information) orby photodamage in fluorescence experiments, led to a decrease inboth the number of stator units and the speed per unit. Figure 1b
shows the speed of a 500-nm bead in a typical BFP experiment. The
Naþ concentration was reduced from 5 mM to 0.1 mM for theinterval between the black arrows, during which the motor rotated
at about 1 Hz. This cell rotated with four stator units when firstobserved in 5 mM Naþ, but this number was decreased to one by aprevious reduction of [Naþ] (data not shown). Discrete speed
increments identical to those occurring after the induced expressionof stator proteins16 were typical during recovery after the transient

Figure 1 | Rotation measurements of chimaeric Na 1-driven flagellar motors
in E. coli. a, Diagram of the Naþ-driven chimaeric flagellar motor.
Components derived from V. alginolyticus (stators; PomA, PotB) and E. coli
(PotB, rotor) are indicated in white and grey, respectively. b, Reducing SMF
and motor speed by lowering the external Naþ concentration (from 5 mM to
0.1 mM and back; black arrows), with BFP detection (inset). c, Reducing
SMF and motor speed by photodamage, with fluorescent detection (inset,
lower).The speed doublings in b and c (red arrows; shown with expanded
scales in c, inset, top) indicate a change from one to two stators. Data
window lengths are 1 s (main figures) and 4 s (inset).

1
Department of Applied Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan. 2The Clarendon Laboratory,
Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, UK. 3Division of Biological Science, Graduate School of Science, Nagoya University, Furo-cho, Chikusaku, Nagoya, Aichi 464-8602, Japan. 4PRESTO, Japan Science and Technology Corporation (JST) 4-1-8, Honmachi, Kawagoe, Saitama 332-0012, Japan.
*These authors contributed equally to this work.

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NATURE|Vol 437|6 October 2005

removal of Naþ(Fig. 1b), indicating reversible inactivation of
stator units on disruption of the SMF. Similar phenomena havebeen reported for Hþ-driven motors of E. coli20 and Rhodobacter
sphaeroides21. Figure 1c shows the speed of a 200-nm fluorescent beadin a typical fluorescence experiment. We attribute periods of smooth
speed reduction to photodamage-induced reduction of the membrane voltage22, and discrete speed changes (inset) to the consequent
reversible inactivation of stator units. Speed doublings such as thosein Fig. 1b, c were interpreted as a change from one to two stators.
However, faster speed fluctuations were common and we were notalways able to assign a definite stator number.
Figure 2a shows a sequence of images of a rotating 200-nm
fluorescent bead with calculated bead centres superimposed(Methods). Figure 2b shows stepping rotation of 500-nm plain and
200-nm fluorescent beads attached to chimaeric flagellar motors.
The diameter of bead orbits (insets) is consistent with attachment toa short flagellar filament stub. Steps were detected at speeds below 7
and 40 Hz in BFP and fluorescence experiments, respectively, andwere not restricted to episodes with an estimated single stator unit.
Figure 3a shows expanded sections of the traces in Fig. 2b (moreexamples are given in Supplementary Information), with the output
of a step-finding algorithm (Methods) superimposed. Backwards
steps were observed in both BFP and fluorescence experiments, withhigher probability at lower speeds. As the strain lacks the switchinducing protein CheY and never rotated backwards at high Naþconcentration, backwards steps represent microscopic reversibility

Figure 2 | Stepping rotation. a, Selected frames at 21-ms intervals during
one rotation of a 200-nm fluorescent bead. Red and yellow dots mark the
calculated bead centre in the current and previous images respectively. Eachpixel is 80 nm square. b, Stepping rotation of flagellar motors with a range of
average speeds. Bead positions are shown in the insets (scales innanometres); bead angles are plotted against time in the main figure. Greylines indicate (360/26)8 in both main and inset figures. Blue and black traces
are from BFP and fluorescence experiments, respectively. Backwards andforwards steps were observed at all speeds.

rather than motor switching. Similar steps have been seen, althoughless frequently, in ATP-driven molecular motors10,11. Figure 3b shows
several revolutions of a 200-nm bead, the histogram of all dwell
angles during those revolutions and the power spectrum of that
histogram. The peak at 26 per revolution in the spectrum corresponds to steps of 13.88 and indicates that successive revolutions
show the same stopping angles.
We combined and analysed step data from different cells and bothexperimental techniques. Figure 4a shows the step-size histogram forall steps found. Assuming that larger steps are in fact unresolved
multiple steps, we fit the distribution as a sum of gaussian distributions with means equal to integer multiples of step size, allowing
different sizes and variances for forward and backward fits. The fitted
step sizes are 13.78 (26 per revolution) and 210.38 (35 per revolution) for forward and backward steps, respectively. The difference
between step sizes may be due to reorientation of the rotation axis on
reversal, or it may be an artefact of measurement and analysis.
Figure 4b shows the sum of histogram power spectra, similar to
those of Fig. 3b, for all step data. Histograms of the levels between
steps found by the step algorithm were also made; the sum of theirpower spectra is shown in the inset to Fig. 4b. The most striking peakis at 26 per revolution, with others at 11, 16 and 23 per revolution.
After subdivision of the data, neither step size nor periodicity
depended on the individual cell, experimental method, angle,
estimated number of stator units or average speed of rotation.
Stepping motion in ATP-driven molecular motors reflects both thediscrete molecular nature of the fuel and the periodicity of the ‘track’
along which the motor runs9–12. Our observation of 26 steps per

Figure 3 | Analysis of step size and periodicity. a, Selected sections of the
traces in Fig. 2b, with the output of a step-finding algorithm superimposed(red). Blue and black traces are from BFP and fluorescence experiments,
respectively, as in Fig. 2b. The dominant step size is about 148. b, Plot ofangle against time during three revolutions of a 200-nm bead, a histogram ofdwell angles for the same revolutions and the power spectrum of that
histogram. The peak at 26 per revolution corresponds to a step size of 13.88,
and shows that the motor stops at the same angles on successive revolutions.

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NATURE|Vol 437|6 October 2005

revolution is consistent with the periodicity of the ring of FliG
protein, the track on the rotor where torque is generated7,8. The
10-fold or 11-fold periodicity matches the filament and hook23; otherperiodicities observed may be due to interactions between othercomponents of the flagellum with as-yet undetermined symmetry.
Some cells in BFP experiments rotated at about 1 Hz even in 5 mM
Naþ. Steps were seen in these unusually slow episodes (data notshown), similar to or possibly slightly smaller than 1/26 of arevolution. Locking of one stator in one state of its mechanochemical
cycle while other stators continued normally could produce
steps with the periodicity of the locked state. Unusually slow episodes
are excluded from our data analysis, but we cannot entirely rule out apossible contribution of a locking effect. Interval length distributions
for data with a narrow range of average speed were sometimes, but
not always, single-exponential. The apparent independence of step
size on stator number, non-exponential interval length distributions
and the observation of occasional steps smaller than 1/26 of arevolution may require the revision of existing models of the flagellar
motor as a set of independent poisson-stepping stators16,24.
Our experiments cannot determine whether single steps correspond to single ion transits. Regardless of the nature of the stepping
process, the ratio of forwards to backwards step probabilities is
exp(2DG/kT), where DG is the free energy available to drive one
step and kT is the average thermal energy. In our experiments DG
ranged from 0 to 3kT, depending on rotation speed. This is equivalent
to the free energy of one ion transit through a SMF of up to 275 mV.
Measuring the SMF in E. coli under these conditions would reveal
whether the observed steps could be driven by single-ion transits.
However, previous data indicate that single ions in fully energizedwild-type motors cannot drive steps as large as 148. If about ten
torque-generating units pass 1,200 Hþ ions per revolution25,
then one ion in one unit should step about 38, assuming tightly
coupled independent units16. Energy conservation sets an upperbound to the angle coupled to one ion transit, equal to (free energy
per ion)/(maximum torque per unit). A wild-type E. coli cell with a

Figure 4 | Summary of step analysis. a, A histogram of step sizes found inall episodes of approximately constant speed (1,400 revolutions, 9 different
cells, 28,611 steps). A multiple-gaussian fit (red line) gives step sizes of 13.78(j ¼ 5.168) and 210.98 (j ¼ 3.98) for forward and backward steps,
respectively. b, The sum of histogram power spectra (see Fig. 3b) for thesame data set. Inset, summed spectra of histograms of mean levels between
found steps. The forward step size is in close agreement with the peak in thesummed spectra, confirming that there are 26 steps per revolution.
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protonmotive force of about 150 mV (6kT per ion)26 drives a 1-mm
bead with an estimated 280 pN nm per unit16, giving an upper boundof about 58. It is possible that stoichiometry changes at low SMF or
stator number or that smaller substeps will be resolved in future.
Alternatively, a mechanical step may be coupled to several ion
transits, requiring the accumulation either of ions or of mechanicalstrain between steps. The latter mechanism is believed to occur inATP-synthase, coupling three or four ion-driven steps in FO to asingle ATP-synthesizing step in F1. By combining high-resolution
measurements of flagellar rotation with manipulation of the SMF, thechimaeric flagellar motor described here will enable a detailed
comparison to be made between the mechanism of the bacterial
flagellar motor and those of its ATP-driven relatives.
METHODS
E. coli chimaera. E. coli strain YS34 (DcheY, fliC::Tn10, DpilA, DmotAmotB)
was derived from strain RP4979 (ref. 27) (DcheY) and transformed withplasmids pYS11 (fliC sticky filaments28, ampicillin resistance, pBR322 derivative) and pYS13 (pomApotB (ref. 6), isopropyl bD thiogalactoside inducible,
chloramphenicol resistance, pMMB206 derivative). Deletions of pilA and motAB
were made as described in ref. 29; fliC::Tn10 was transduced from HCB1271(ref. 16). Cells were grown for 5 h at 30 8C from frozen stocks, with shaking, in
tryptone broth (TB) containing antibiotics to preserve plasmids. IsopropylbD thiogalactoside (1–10 mM) was added for low-level expression of stator
proteins.
Rotation measurement. All experiments were performed at 23 8C. Speeds wereobtained from power spectra of combined (x,y) data16, using data windows oflength 1 or 4 s beginning at intervals of 0.1 s. Motor angles were obtained byfitting an ellipse to bead trajectories under the assumption that trajectories
represent the projection of a circular orbit onto the focal plane of the
microscope18.
For BFP experiments, polystyrene beads (diameter 535 nm; Polysciences)were attached to truncated flagella of immobilized cells, and bead position (x,y)
was measured by BFP laser interferometry (sample rate 4 kHz) as described16.
NaCl (or LiCl) was added to the Naþ-free motility medium in various
concentrations; the total concentration of added salt was adjusted to 85 mM
with KCl. Custom-made flow chambers allowed a complete exchange of medium
in about 5 s.
For fluorescence experiments, fluorescent polystyrene beads (diameter
227 nm, ‘yellow/green’; Molecular Probes) were attached as above. A mercuryarc lamp provided epifluorescence excitation (475-nm bandpass) at an intensityof about 1 W cm22. Images (16 £ 16 pixels, each 80 nm square in the sample
plane; 505 nm long-pass) were sampled at a frame rate of 2.4 kHz with a cooled,back-thinned, electron-multiplying charge-coupled device camera (iXon
DV860-BI, Andor Technology). Bead position was determined with a precisionof about 5 nm by a two-dimensional gaussian fit to the bead image.
Step resolution. The relaxation time of a 500-nm bead attached to an elastic
hook rotating about an axis 150 nm from its diameter is about 1.1 ms (ref. 30).
For a 200-nm bead the time is about 0.15 ms. These times are lower limits
assuming no contribution from the flagellar stub16, and they set upper limits ofabout 900 and 6,500 to the number of steps that can be detected per second in
BFP and fluorescence experiments respectively. Our actual limits were lower,
namely about 200 s21 and about 1,000 s21, respectively. The latter limit was
attained by analysis of dwell-time histograms.
Step analysis. A computer algorithm divided angle versus time records into
straight-line portions corresponding to episodes of constant average speed. A
second algorithm based on the method of J. W. Kerssemakers (personalcommunication) detected steps as follows. First, an entire episode was divided
into two intervals at the point giving the best least-squares fit to a single-stepfunction. Second, an excess of steps (N max per revolution on average) was
assigned by repeatedly dividing, as in the first step, the interval containing thelargest range of angles in the previous iteration. Third, a ‘quality factor’ Q was
defined for each assigned step as Q 2 ¼ (x 1 2 x 2)2/[(var.1/n 1) þ (var.2/n 2)],where x i, var.i and n i are the mean angle, the variance and the number ofpoints in an interval, respectively, and i ¼ 1 and i ¼ 2 indicate intervals
immediately before and after a step. The lowest-quality step was removed andadjacent intervals were concatenated, but only if the quality was below a
threshold Q min. Last, the previous step was repeated until no steps remainedwith Q , Q min. The accuracy and sensitivity of the algorithm were tested and asuitable value of Q min for each episode was chosen by applying the algorithm tosimulated data with N o ¼ 10, 20, 30, 40 and 80 Poisson-distributed steps per
revolution and brownian noise and average speed similar to real data.

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Received 1 April; accepted 11 July 2005.
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Supplementary Information is linked to the online version of the paper at
www.nature.com/nature.
Acknowledgements We thank H. Berg and K. Fahrner for the gift of strain
HCB1271. The research of R.B., M.L. and A.R. was supported by combined UK
research councils through an Interdisciplinary Research Collaboration in
Bionanotechnology, that of A.I., M.H. and T.Y. by Grants-in-Aid from the
Ministry of Education, Science, Sports, Culture and Technology of Japan, that of
M.H. and T.Y. by Soft Nano-Machine Project of JST, and that of Y.S. by JSPS
Research Fellowships for Young Scientists.
Author Contributions BFP experiments were performed by Y.S. and A.R.,
fluorescence experiments by A.R. and M.L., experimental design was by R.B.,
A.I., A.R. and Y.S., data analysis by R.B., Y.S. and A.R., and strain construction by
Y.S., T.Y. and M.H. Y.S. and A.R. contributed equally to this work.
Author Information Reprints and permissions information is available at
npg.nature.com/reprintsandpermissions. The authors declare no competing
financial interests. Correspondence and requests for materials should be
addressed to R.M.B. (r.berry1@physics.ox.ac.uk).

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