Faster high-speed atomic force microscopy
for imaging of biomolecular processes
Cite as: Rev. Sci. Instrum. 92, 033705 (2021); https://doi.org/10.1063/5.0032948
Submitted: 12 October 2020 . Accepted: 20 February 2021 . Published Online: 12 March 2021
Shingo Fukuda, andToshio AndoRev. Sci. Instrum. 92, 033705 (2021); https://doi.org/10.1063/5.0032948© 2021 Author(s).

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Faster high-speed atomic force microscopy
for imaging of biomolecular processes
Cite as: Rev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948
Submitted: 12 October 2020 • Accepted: 20 February 2021 •Published Online: 12 March 2021
Shingo Fukuda

and Toshio Andoa)

AFFILIATIONS
Nano Life Science Institute (WPI-NanoLSI), Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japana)

Author to whom correspondence should be addressed: tando@staff.kanazawa-u.ac.jp

ABSTRACT

High-speed atomic force microscopy (HS-AFM) has enabled observing protein molecules during their functional activity at rates of 1–12.5
frames per second (fps), depending on the imaging conditions, sample height, and fragility. To meet the increasing demand for the great
expansion of observable dynamic molecular processes, faster HS-AFM with less disturbance is imperatively needed. However, even a 50%
improvement in the speed performance imposes tremendous challenges, as the optimization of major rate-limiting components for their fast
response is nearly matured. This paper proposes an alternative method that can lower the feedback control error and thereby enhance theimaging rate. This method can be implemented in any HS-AFM system by minor modifications of the software and hardware. The resulting
faster and less-disturbing imaging capabilities are demonstrated by the imaging of relatively fragile actin filaments and microtubules near thevideo rate, and of actin polymerization that occurs through weak intermolecular interactions, at ∼8 fps.
© 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0032948

I. INTRODUCTION
High-speed atomic force microscopy (HS-AFM) operating in
the amplitude-modulation (AM) mode was established in 2008
through the development of various components and control techniques,1 such as small cantilevers,2,4 optical beam deflection detectors optimized for small cantilevers,3,5 fast deflection-to-amplitude
converters,1,2 fast scanners,6,7 active vibration damping techniques,8and dynamic feedback controllers capable of automatic gain tuning during imaging.9 In the AM mode, the cantilever oscillation
amplitude is maintained at its set point value by feedback Zscanning of the sample stage (or the cantilever chip). The feedback
control error increases with increasing X-scan velocity. In particular, the error becomes large in the step height (edge) regions.
When the error exceeds a certain level depending on the sample
fragility, the tip–sample contact disturbs the biological functionof the sample and can even destroy the sample. Several strategies
have been employed to minimize disturbance to a sample. For filamentous protein assemblies, filaments oriented approximately along
the fast X-scanning direction have been adopted for imaging. Thisorientation minimizes step height changes, thereby reducing boththe tip–sample contact strength and tip parachuting (i.e., complete loss of tip–sample contact), as exemplified in the imaging ofRev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948© Author(s) 2021

myosin V walking on actin filaments at 7 frames per second (fps).10
Meanwhile, the surface density of globular proteins on a substrate
has been increased to narrow their inter-molecular gaps, producing
a smaller step height, as demonstrated by the imaging of double-ring
GroEL of height ∼15 nm interacting with its co-chaperonin GroES
at 1–2 fps.6,11 Alternatively, the lateral scan size can be minimized
to reduce the X-scan velocity, allowing an increased imaging rate,
as illustrated by the imaging of F1 -ATPase lacking the γ-subunit at
12.5 fps.12 Moreover, when a molecular process proceeds througha second-order reaction, the concentration of species involved in
the reaction is lowered for slower dynamics, allowing for slowerand hence less disturbing imaging. This strategy has been used in
the imaging of conformational changes of ATPases6,10–13 and selfassembly processes.14–16 By adapting these means to an end (whennecessary and possible), HS-AFM has been successfully used to visualize various protein molecules in dynamic action at 1–12.5 fps (seeRefs. 17–20 and references therein).
Although the highest possible imaging rate of HS-AFM in the
AM-mode depends on the imaging conditions, such as the scan
range and number of scan lines, major imaging-rate determinants
are the feedback bandwidth of the HS-AFM system, including thecantilever, as well as the sample fragility and height.21 It is possible toimage at > 30 fps low-height samples, such as membrane-embedded

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membrane proteins with small protrusions (<∼1 nm) from themembrane surface22 and highly disordered, intrinsically disordered
proteins with diameters of ∼0.15 nm,23 and robust molecules, suchas dsDNA. However, most proteins do not meet these conditions.
Moreover, many biomolecular processes occur in a shorter timescale (<0.1 s) and/or through weak intermolecular interactions. In
particular, protein self-assembly processes often occur through weakintermolecular interactions; imaging them with HS-AFM is infeasible, as demonstrated in a study of the centriolar scaffold protein
SAS-6.24 Therefore, there is a growing need for further improvement
toward faster and less disturbing imaging capabilities. Even after
the establishment of HS-AFM, several efforts have been made to
optimize components (except cantilevers) for a faster response.25–27
Nonetheless, even a 50% increase in the imaging rate has been difficult because the cantilever resonant frequency has become thedominant determinant of the feedback bandwidth. Furthermore,
it is difficult to fabricate smaller cantilevers with a resonant frequency higher than ∼1.5 MHz in water and a small spring constant(∼0.1 N/m).
In this study, we explored an alternative approach to achievea faster and less disturbing performance. Based on our observation that retrace imaging during backward x-scanning produces
larger feedback error than trace imaging, we eliminated retrace
imaging and shortened the time of backward scanning. This elimination and the time reduction could be carried out by simple
modifications of the hardware and software of our HS-AFM system. This method can be easily implemented in any HS-AFM
system.

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II. RESULTS AND DISCUSSIONS
A. Feedback error comparison between traceand retrace scanning processes
In AFM imaging, the sample stage (or the cantilever chip) is
generally raster scanned; along the fast scan X axis, the sample istraced and retraced with the tip in the forward and backward directions, respectively. The X axis is set parallel to the longitudinal axisof the projection of the cantilever beam onto the substrate surface.
This arrangement can avoid twisting of the cantilever beam around
its longitudinal axis. Assuming that the tip is attached to the left endof the cantilever beam, trace imaging is generally carried out fromleft to right of the sample, whereas retrace imaging is carried out
from right to left [see Fig. 1(a)]. Because images acquired in the traceand retrace scanning processes are almost identical in the AM mode,
as well as in other AC modes, only images acquired during tracescanning are generally recorded. However, the similarity between
the trace and retrace images has only been checked using slow AFM.
In this study, we first examined this issue using HS-AFM. We used
relatively fragile actin filaments and microtubules (MTs) as the test
samples. The former were bound to phalloidin and the latter to taxol,
unless stated otherwise. These chemicals prevent depolymerizationof the respective polymers upon dilution for HS-AFM imaging.
To evaluate the feedback control error, we first imaged aglutaraldehyde-treated actin filament (height h0 ≈ 8 nm) attached
onto an amino-silane-coated mica surface [Fig. 1(b)] using a shortcantilever (AC10DS, Olympus) with an electron beam deposited(EBD) tip of ∼0.7 μm in length grown on the original tip of ∼2 μm.

FIG. 1. Difference in feedback control error between the trace and retrace scanning processes. (a) Schematic of the trace and retrace scanning processes. [(b) and (c)]Topography (top) and error (middle) images of the actin filament (b) and MT (c) captured at 5 fps during trace and retrace scanning processes. The graphs (bottom) represent
the error signal profiles measured along the broken lines shown in the error images.

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This cantilever (length: 10 μm and width: 2 μm) has a spring constant kc ≈ 0.1 N/m, resonant frequency f c ≈ 500 kHz in water, andquality factor Qc ≈ 1.5 in water. In this imaging at 5 fps, we chose an
actin filament oriented nearly along the Y axis. This orientation produces a relatively large feedback error in the positive and negative
step height regions of the sample. The imaging parameters were set
as follows: X-scan velocity V x = 110 μm/s, scan area = 200 × 100 nm2 ,
cantilever free oscillation amplitude Af = 2.25 nm, and cantilever set
point amplitude As = 0.85 × Af . The trace and retrace topography
images appeared similar [Fig. 1(b), top]. However, the error images
obtained during the trace (forward) and retrace (backward) scanning processes [Fig. 1(b), middle] differ remarkably in the positive
step height regions. Specifically, the right edge of the actin filament
appeared darker in the error image acquired during backward scanning, compared with its left counterpart acquired during forward
scanning. Note that we took the error signal ε as ε = (A – As ), whereA represents the cantilever oscillation amplitude measured during
imaging. Therefore, pixels in the error image appear darker when A< As and brighter when A > As . The error signal profiles along the
X axis clearly indicated a large error difference between the traceand retrace scanning processes [Fig. 1(b), bottom]. Note that theerror in the negative step height region diminished rapidly. This isbecause our system is equipped with a dynamic feedback controllerthat can suppress tip parachuting at a negative step height. The peakerror at the positive step height (−0.6 V) in the retrace image corresponds to ε = −0.9 nm based on the amplitude detection sensitivity of
1.5 nm/V. In contrast, in the trace image, the peak error at thepositive step height is −0.2 V, corresponding to ε = −0.3 nm. We
confirmed a similar error signal difference between the trace andretrace scanning processes by imaging a glutaraldehyde-treated
MT of larger height (h0 ≈ 25 nm) using the same imaging conditions as those for the actin filament [Fig. 1(c)]. Remarkably,
the errors in the trace and retrace images detected in the respective positive step height regions were, however, almost identicalto those observed for the actin filament [Figs. 1(b) and 1(c), bottom]. We will discuss later this error similarity between the two
samples.
What does create the error difference between the trace andretrace scanning processes? Under the conditions used above (V x
= 110 μm/s and f c = 500 kHz), the X-scanner is displaced by
0.22 nm during a single cycle of cantilever oscillation. The peak-topeak free oscillation amplitude (2 × Af = 4.5 nm) is less than theheights of an actin filament and an MT. Therefore, during imaging of
their steep positive step height regions, the tip can be laterally pushedfrom the sample by ∼0.1–0.2 nm during a single cycle of oscillation.
Although this distance is not significantly large, the opposite directions of the lateral forces exerted on the tip in the trace and retracescanning processes could possibly lead to different behaviors of thecantilever, as intuitively speculated below. In the trace scanning process, the torque resulting from the lateral force exerted on the tip
is produced in the same direction as the torque produced by thevertical force from the sample [Fig. 2(a)]. The torque produced by
the lateral force decreases the slope near the end of the cantilever
beam [Fig. 2(a)]. The amplitude measurement based on optical beam
deflection sensing interprets this slope change as a reduction in theoscillation amplitude. The resulting amplitude signal is smaller thanthe case where only a vertical force acts on the tip; thus, the Zscanner (and hence the sample) is displaced away from the tip byRev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948© Author(s) 2021

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feedback control [Fig. 2(a)]. In contrast, in the retrace scanning
process, the torque resulting from the lateral force is produced in the
direction opposite to the torque produced by the vertical force fromthe sample [Fig. 2(b)]. The lateral force increases the slope near theend of the cantilever beam [Fig. 2(b)], which is interpreted as risein the oscillation amplitude. The resulting amplitude signal is larger
than the case where only a vertical force acts on the tip from thesample; thus, the Z-scanner is displaced toward the tip by feedback
control [Fig. 2(b)]. Although this Z-displacement reduces the error
signal, both the lateral and vertical forces (as well as their resultant
force) become larger.
To closely inspect the mechanism that produces the error difference between the trace and retrace scanning processes, we simultaneously recorded the cantilever deflection and error signals as wellas the feedback controller output during imaging under the conditions used above [Figs. 2(c) and 2(e) and supplementary material,
Fig. S1 shows these signals recorded during imaging at 6.7 fps]. Notethat the values of f c , tip-end radius, and tip cone angle moderately
vary with the cantilever used. In the typical data recorded during
retrace imaging of an actin filament [Fig. 2(c), third from the left], apositive peak error of ∼0.55 V (i.e., A – As ≈ 0.83 nm) first appearedat the time indicated by arrow-1. This error then became approximately zero or slightly negative during ∼15 cycles of cantilever
oscillation. As the feedback bandwidth of our system including thecantilever is 30–40 kHz, the feedback control does not work within
a single cycle of cantilever oscillation. Therefore, the quick error
reduction immediately after the positive error peak must be caused
mainly by tip–sample interactions. Immediately after this period of∼15 oscillation cycles, a negative peak error of ∼−0.7 V (i.e., A – As
≈ −1.05 nm) suddenly appeared at the time indicated by arrow-2.
The positive error at arrow-1 suggests that the tip was pushed laterally at the rightmost sample edge. This lateral force resulted ina downward bending of the cantilever beam hence in an increased
amplitude signal. In the next ∼15 oscillation cycles corresponding to∼38 μs and an X-displacement of ∼4 nm, the tip was pushed bothvertically and laterally from the sample. Note that because of thetip size effect, the ∼4 nm displacement does not imply that the tip
end was brought by this X-displacement to the uppermost positionof the actin filament with the radius of ∼4 nm. The upward deflection caused by the vertical force was largely canceled by the downward deflection caused by the lateral force. Therefore, during thisperiod, feedback Z-scanning was performed only in a small extent(see the green line) despite a strong resultant force from the vertical and lateral forces acting on the sample. The negative peak error
at arrow-2 suggests that the lateral force exerted on the tip by thistime was largely removed, resulting in the sudden appearance of alarge amplitude reduction caused by the strong vertical force. In fact,
the deflection signal on the bottom-half side was largely reduced
around the time point of arrow-2. At and after this time point, nolarge lateral force acted on the tip; therefore, the feedback control
operated properly. In other records of error signals during retrace
imaging of actin filaments, the positive and negative peak errors at
the time points of arrow-1 and arrow-2 and the error level between
these time points varied in a moderate range (see supplementarymaterial, Fig. S1). However, the positive and negative peak errors
appeared consistently in this order, and the time interval between
the peaks remained almost constant for a given cantilever tip. In
the cases of trace imaging of an actin filament and a MT, the error

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FIG. 2. Feedback error, deflection, and feedback control signals recorded during trace and retrace imaging at 5 fps. [(a) and (b)] Schematics showing torques T x and T zcaused by lateral and vertical forces F x and F z , respectively, exerted on the tip from the sample during trace (a) and retrace (b) imaging in sample edge regions. The arrows
denoted by Zx and Zz indicate the directions in which the Z-scanner is displaced to minimize errors caused by F x and F z , respectively. [(c) and (e)] Feedback error (red,blue), deflection (purple), and feedback control (green) signals recorded during trace and retrace imaging of actin filament (c) and MT (e); left: error signal in the entire scanrage (red and blue rectangles indicate scanning in positive step height regions), middle: during trace imaging of the positive step height regions, and right: during retrace
imaging of the positive step height regions. [(d) and (f)] Dependence of negative peak error (mean ± s.d.; n = 30 for each plot) on X-scan velocity measured for actin
filaments (d) and MTs (f).

signals were smaller than those in the retrace imaging and did notshow clear responses indicative of lateral force effects [Figs. 2(c) and2(e), second from the left].
Furthermore, retrace imaging of the positive step height regionof a MT showed positive and negative peak errors in this order, while
the interval between the peaks was longer, i.e., ∼57 μs, corresponding to an X-scanner displacement of ∼6.3 nm [Fig. 2(e), third fromthe left], due to the larger diameter of the MT. However, in the time
region between the two error peaks, the error gradually became negative, which was remarkably caused by a gradual decrease in deflection on the upper-half side. After this period, the deflection on theupper-half side gradually recovered, while that on the bottom-halfside gradually decreased. Then, the deflection on both sides gradually recovered, resulting in a smaller error approaching approximately zero. These behaviors of the error and deflection signals canbe interpreted as follows [see Fig. 3(a)]. Around the time of the negative error peak [Fig. 3, (ii)], the tip is largely inclined inward by astrong lateral force from the sample. By this inclination, the verticaloscillations of the tip are accompanied by lateral vibrations (in the Xdirection). However, the outward displacement in the X-direction ishampered by the sample, and hence, the upward deflection is alsoRev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948© Author(s) 2021

hampered [see Fig. 3(a), top, (ii)], resulting in the suppression of
cantilever deflection on the upper-half side. In contrast, the inward
displacement in the X-direction is not hampered by the sample,
and therefore, the downward deflection is not suppressed. In addition, the inward inclination of the tip is accompanied by downwardbending of the cantilever beam at its end region, which increases
the deflection signal on the bottom-half side. These interpretations
are consistent with the observed deflection signals [Fig. 3(b), (ii)].
After the time of the negative error peak, the tip gradually makes
contact with the sample at the tip-end region, while the side contact gradually diminishes. Therefore, the suppressed deflection on
the upper-half side gradually recovers, while the deflection on thebottom-half side reduces gradually [see Fig. 3(a), (iii)], consistent
with the observed deflection signal [Fig. 3(b), (iii)].
Next, glutaraldehyde-treated actin filaments and MTs runningnearly along the Y axis were imaged at different X-scan velocities, during which the cantilever deflection and error signals wererecorded. Figures 2(d) and 2(f) show the negative peak errors (mean± s.d.) appearing during the trace and retrace imaging of the actin
filaments [Fig. 2(d)] and MTs [Fig. 2(f)] at the respective X-scanvelocities. Note that data were collected only for the cases in which

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FIG. 3. Interpretation of error and deflection signals that appeared during retrace
imaging of MT. (a) Cantilever oscillation and deflection depending on thelateral force exerted on the tip; top:schematics for cantilever oscillations in
the respective time domains (i–iv) shownin (b), middle: deflection patterns in therespective time domains, and bottom:
schematics showing cantilever deflection and tip inclination in the respective
time domains. (b) Time domain classification by features of error and deflection signals [identical to those shown in
Fig. 2(e), third from the left].

the glutaraldehyde-treated samples were not broken during imaging.
The error difference between the trace and retrace imaging processes
increased with increasing X-scan velocity. In addition, for different
X-scan velocities and the trace and retrace scanning processes, therespective errors were almost identical between the two samples,
despite their height difference of ∼3-times. The error ratio (actin
vs MT) was 0.95:1 for trace imaging and 0.82:1 for retrace imaging, on average. When lateral force effects are not considered, themaximum feedback control error εmax can be theoretically expressed
as εmax = h0 × sin(πV x τ 0 /λ), where τ 0 and 1/λ represent the delay
time in the closed feedback loop and the spatial frequency of the
tip-detected sample surface topography, respectively.21 When thevalue of πV x τ 0 /λ is smaller than ∼π/4, the maximum error becomesapproximately proportional to h0 /λ. Similar values of h0 /λ for thetwo samples in their positive step height regions were confirmed by
calculating the spatial frequencies for the simulated surface topographies of the samples (supplementary material, Note S1 and Figs. S2and S3). From the error similarity between the two samples observedin retrace imaging, the influence of lateral forces on the negative
peak error is also likely to be approximately proportional to h0 /λ.
However, this issue requires further investigation. When a custommade cantilever with f c ≈ 1 MHz in water was used for imaging ofactin filaments, the error was reduced by 30%–40% (supplementary material, Fig. S4: dotted lines). This improvement is due toan increased feedback bandwidth and a shorter tip-sample contact
time.
B. New X-scanning mode
From the observed feedback error difference between the traceand retrace scanning processes, the elimination of imaging during backward (retrace) scanning enables less disturbance and hence

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faster imaging. To achieve this “only trace imaging” (OTI) mode, a
DC offset signal (Aos < 0) was added to the true amplitude signal (A)during backward scanning, and the resulting false amplitude signal
was fed to the feedback controller [Fig. 4(a)]. This operation withdraws the sample stage completely from the cantilever tip during
backward scanning, except for the small left- and right-edge regionsof the scan area. Moreover, the OTI mode enables further faster
imaging by reducing the backward scan period. To achieve this, we
can use a quasi-sawtooth waveform for X-scanning. This waveformwith a period T and amplitude X 0 is expressed as
X(t)
1
=
t
X0
αT
X(t)/X0 = −(0 ≤ t ≤ αT),

(1)

1
1
t+
(αT ≤ t ≤ T),(1 − α)T(1 − α)(2)where α is 0.5 < α < 1. The Fourier series of this function is given by
X(t)/X0 =1 ∞ −1 + cos(2nπα)2π+∑[cos(n t)2 n=1 2n2 π2 α(1 − α)T+sin(2nπα)2πsin(n t)].
2n2 π2 α(1 − α)T(3)Because the vertices of X(t) contain high-frequency components,
driving the X-scanner with X(t) would easily generate vibrationsin the X-scanner. We rounded the vertices using the finite Fourier
series containing the first nine terms, which approximated the quasisawtooth waveform for α = 0.8, and even for α = 0.9 [Fig. 4(b),top]. However, the bottom vertex position slightly shifted in theright and upward directions, whereas the top peak position slightly

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FIG. 4. Implementation of the OTI mode. (a) Circuit diagram for implementation of the OTI mode. (b) Wave forms constructed with finite Fourier series (containing thefirst nine terms) of quasi-sawtooth wave forms having α = 0.8 and 0.9 (top) and those obtained after compensation for vertex position shifts caused by the finite Fourier
series (bottom). (c) Driving signal for X-scanner (top), DC offset signal added to true amplitude signal (middle), and Z-scanner displacement (bottom). (d) Driving signal of
10.5 kHz for the X-scanner in the OTI mode after inverse compensation for vibrations (top) and measured displacement of X-scanner (bottom).

shifted in the left and downward directions. These shifts could easily be compensated for, as shown at the bottom of Fig. 4(b) andin supplementary material, Fig. S5. The compensation method is
described in detail in supplementary material, Note S2. Figure 4(c)shows an X-scanner driving signal (T = 3 ms and α = 0.8) constructed in this manner (top), together with the DC offset signal
added to the true amplitude signal (middle) and the Z-scanner displacement (bottom). Our X-scanner with a resonant frequency of
47 kHz [supplementary material, Fig. S6(a)] and stroke range of
1.6 μm moved smoothly in the quasi-sawtooth waveform with
α = 0.8 [supplementary material, Fig. S6(b)], when driven at
f x = 1.05 kHz, corresponding to an imaging rate of 10 fps for thenumber of scan lines N = 100 (note that the time required for Yscanning toward the origin of the scan area after one frame acquisition, 5/f x , is considered). Although the X-scanner exhibited vibrations when driven at 10.5 kHz (corresponding to 100 fps for N= 100) [supplementary material, Fig. S6(c)], the vibrations werecompletely suppressed using an inverse feedforward compensation
method [Fig. 4(d) and supplementary material, Fig. S6(d)].28,29
C. Improved performances in “only trace imaging”(OTI) mode
To demonstrate the less disturbing/invasive and faster imaging capability of the OTI method, we first imaged an actin filament.
Note that we hereafter used protein samples that were not treatedRev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948© Author(s) 2021

with glutaraldehyde. As shown at the top of Fig. 5(a) (Multimedia view), an actin filament oriented nearly along the Y axis could
be imaged at 12.5 fps in the OTI mode, without disrupting the filament. In contrast, when the imaging mode was switched to theconventional scanning mode, the same actin filament was immediately broken under identical imaging conditions including the imaging rate [Fig. 5(a), bottom (Multimedia view)]. This clear differenceis because of the elimination of retrace imaging in the OTI mode
and, in part, because of the ∼38% slower forward X-scan velocity
in the OTI mode compared with that in the conventional mode
under the same imaging rate. When “only retrace imaging” was conducted with a rounded quasi-sawtooth waveform having α = 0.8, theactin filaments broke even at 10 fps (supplementary material, Fig.
S7). The improved imaging capability of the OTI mode was further
confirmed by imaging of a MT oriented nearly along the Y axis at
14.3 fps [Fig. 5(b), top (Multimedia view)]. In the conventionalmode, the MT immediately broke at the same imaging rate [Fig. 5(b),bottom (Multimedia view)].
Next, we quantitatively evaluated the less disturbing/invasive
and faster imaging capability of the OTI mode by measuring thenon-breaking probability (PNB ) with which actin filaments and MTs
could be imaged without breaking in a given time window (10 s). In
this evaluation, the samples oriented nearly along the Y axis wereimaged for an area of 200 × 100 nm2 with 100 × 50 pixels at different
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FIG. 5. Comparison of the OTI and conventional modes. (a) HS-AFM images of an actin filament captured at 12.5 fps in the OTI and conventional modes. (b) HS-AFM
images of a MT captured at 14.3 fps in the OTI and conventional modes. Multimedia Views: https://doi.org/10.1063/5.0032948.1; https://doi.org/10.1063/5.0032948.2;
https://doi.org/10.1063/5.0032948.3; https://doi.org/10.1063/5.0032948.4

sample breakage (N NB ), and we obtained PNB as PNB = N NB /(N B+ N NB ). Figures 6(a) and 6(d) clearly show the faster scanning capability of the OTI mode. The X-scan velocity that produced PNB = 50%
was enhanced by the OTI mode from 179 to 240 μm/s (34% faster)for the actin filaments and from 205 to 299 μm/s (46% faster) for theMTs. As expected, the imaging rate that produced PNB = 50% was
more significantly improved by the OTI mode [Figs. 6(b) and 6(e)]from 8.2 to 16.4 fps for the actin filaments and from 9.3 to 22.4 fps
for the MTs.

Subsequently, the amount of tip–sample interaction energy
required to break actin filaments and MTs was quantitatively evaluated under the assumption that the energy lost from the oscillating cantilever by tip–sample contact is transferred to the sample.
Because we could not measure the feedback control error at the time
when these samples were broken, we estimated the error at a given
X-scan velocity by extrapolation or interpolation from the relationships of the negative peak error vs X-scan velocity obtained for the
trace and retrace imaging processes [Figs. 2(d) and 2(e)]. From the

FIG. 6. Comparison of the OTI and conventional modes. Relationships of PNB vs V x [(a) and (d)], PNB vs imaging rate [(b) and (e)], and PNB vs E ts [(c) and (f)] measured byimaging of the samples in the OTI and conventional modes. All measurements were repeated 27–52 times for each plot. The imaging conditions were as follows: imaging
area = 200 nm × 100 nm; number of pixels = 100 × 50, Af = 2.5 nm; and As = 0.85 × Af . The black broken lines in (c) and (f) represent the results obtained by imaging at
0.5 fps for 10 s using different set points. The measurements were repeated 21–32 times for each plot. The widths shown with the red and blue stripes in (c) and (f) present
the standard deviations derived from those of the error signals at different X-scan velocities shown in Figs. 2(d) and 2(f).

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ARTICLEerror ε (<0) in nm, we estimated the tip–sample interaction energy
Ets as follows:17,30
1
Ets = γ × kc × [A2f − (As + ε)2 ]/Qc ,2(4)where γ (∼0.9 for actin filaments and ∼1.0 for MTs) is a correction factor for the amplitude reduction caused by a resonant frequency shift of the cantilever. We estimated the frequency shift froma phase shift measured using a fast phase detector31 (supplementarymaterial, Note S3). In this way, the relationships between PNB andV x [Figs. 6(a) and 6(d)] could be converted to those between PNB
and Ets , as shown in Figs. 6(c) and 6(f). Here, the broken lines inFig. 6(c) for the actin filaments and in Fig. 6(f) for the MTs indicate
the PNB –Ets relationships obtained by control experiments where
PNB was measured by imaging at 0.5 fps with Af = 2.5 nm and various values of As (0.45–0.85 × Af ). Note that the feedback control
error is negligible at this low imaging rate. The data obtained in thecontrol experiments indicated that the actin filaments and MTs were
disrupted with Ets values of ∼35 and ∼38 kB T, respectively (kB , Boltzmann constant; T = 298 K). The PNB –Ets relationships obtained fromimaging in the OTI mode agreed approximately with those obtained
from the control data, suggesting that the negative peak error ismostly caused by the vertical tip–sample interaction force and thatthe sample breakage is determined by the amount of energy lost fromthe oscillating cantilever by the tip–sample contact. Meanwhile, the
PNB –Ets relationships obtained from imaging in the conventional
imaging mode shifted toward higher energy by ∼3.3 kB T for the actin
filaments and ∼5 kB T for the MTs, compared with the cases measured in the OTI mode. These shifts suggest that the negative peakerror in retrace imaging does not precisely correspond to the energy
required for sample breakage and that the samples might have beenbroken before the error reached the negative peak error.

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Figs. 7(a) and 7(b) (Multimedia view), the OTI mode enabled imaging of the actin filaments at 25 fps (n = 28) and the MTs at 30 fps(n = 28), without breaking them (PNB > 90%). In the conventional imaging mode, the actin filaments and MTs oriented nearly
along the X-direction were easily broken at these imaging rates (PNB
< 40% for actin filaments and PNB < 60% for MTs; n = 24 for both
samples). Thus, the OTI mode enhances the speed performance of
HS-AFM ∼2.5 times, indicating that trace imaging is further lessdisturbing/invasive than retrace imaging for protein samples withrelatively small surface corrugations and low spatial frequencies.
To observe the polymerization processes of actin filaments, partially biotinylated actin filaments were attached onto the surface of
two-dimensionally crystalized tamavidin 2-LPI, which has a strongly
affinity for biotin. Unlabeled G-actin (actin monomers) was added
to the solution (final concentration: 0.5 μM), without phalloidin. In
the case of MTs, they were attached onto a bare mica surface, andtubulin dimers were added (final concentration: 0.5 μM), without

D. Effectiveness of OTI mode
Finally, we demonstrated the effectiveness of the OTI mode by
performing fast imaging of actin filaments and MTs oriented nearly
along the X-direction and observing their polymerization processes
that occur through weak protein–protein interactions. As shown in

FIG. 7. Faster and less invasive imaging capability of the OTI mode. [(a) and(b)] HS-AFM images of an actin filament (a) and a MT (b) oriented nearly
along the X-direction, captured in the OTI mode at 25 fps and 30 fps, respectively, with number of pixels = 100 × 50, Af = 2.0 nm, and As = 1.7 nm.
These imaging experiments were repeated 28 times for each sample to obtainthe value of PNB (>90%). Multimedia views: https://doi.org/10.1063/5.0032948.5;
https://doi.org/10.1063/5.0032948.6

Rev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948© Author(s) 2021

FIG. 8. Comparison of the OTI and conventional modes. (a) HS-AFM images
showing breakage of an actin filament and subsequent polymerization from thebroken filament ends in the presence of G-actin. Just before t = 2.4 s, As waschanged from 1.3 to 1.9 nm (Af = 2.2 nm), and imaging in the conventional mode
was continued up to t = 10.8 s (left). Then, the imaging mode was switched to
the OTI mode (right). (b) HS-AFM images showing tubulin polymerization fromends of protofilaments within a broken MT in the presence of tubulin dimers.
After breakage of a MT under As = 1.5 nm (Af = 2.5 nm), the broken MT was
first imaged in the conventional mode at 3.3 fps with As = 2.1 nm (left). Then,the imaging mode was switched to the OTI mode (right). (c) HS-AFM images
showing actin polymerization from one end of a broken actin filament in thepresence of G-actin. The imaging was performed in the OTI mode at 7.7 fps, with
Af = 2.2 nm and As = 1.9 nm. (d) Time course of length change of the actin
filament shown in (c). (e) Distribution of length change occurring during intervals of
0.13 s obtained from (d). Multimedia views: https://doi.org/10.1063/5.0032948.7;
https://doi.org/10.1063/5.0032948.8; https://doi.org/10.1063/5.0032948.9;
https://doi.org/10.1063/5.0032948.10; https://doi.org/10.1063/5.0032948.11

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taxol. For the partial breakage of these polymers and the subsequent observation of polymerization processes at the polymer ends,
the polymer samples oriented nearly in the diagonal direction werechosen. To break the polymers, they were imaged at 5 fps in theconventional imaging mode with the cantilever set point adjusted
at ∼1.3 nm (Af = 2.2 nm). Then, the set point was readjusted to
1.9 nm. As shown in the left of Fig. 8(a) at 6.0 s and 10.0 s (Multimedia view), actin polymerization from the broken filament ends
could not be observed in the conventional imaging mode even at
5 fps. This is because the tip disturbed the weak association of Gactin with the polymer ends: K d ≈ 0.1 and 0.5 μM at the plus andminus ends, respectively.32 In fact, when the imaging mode wasswitched to the OTI mode, asymmetric polymerization was observed
at 5 fps [Fig. 8(a), right, 0–5 s] (Multimedia view)]. In a separate
experiment, polymerization was observed at 7.7 fps in the OTI mode
[Fig. 8(c) (Multimedia view)], where discreet elongation and shortening with a step size of ∼5 nm were evident [Figs. 8(d) and 8(e)]. In
the case of MTs, polymerization could not be observed in the conventional imaging mode, even at 3.3 fps [Fig. 8(b), left (Multimediaview)]. This is because the K d value for the binding of tubulin dimers
to the ends of a protofilament is large (K d = 5.0 μM for tubulins frombovine brain),33 and the association between α and β tubulins is weak
(K d = 0.8 μM for tubulins from bovine brain).34 When the imaging
mode was switched to the OTI mode, polymerization was observed
at 3.3 fps [Fig. 8(b), right (Multimedia view)].

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circuit were newly added to the system to generate the DC offset signal and add the offset signal to the true amplitude signal of
the oscillating cantilever, respectively. The voltage and duration of
the DC offset signal were changed using a lab-developed software
program in Igor Pro (Wave Metrics Inc., USA.) These parameters
were adjusted according to the X-scan velocity. Commercially available cantilevers (AC10DS, Olympus, Japan) with a spring constantof ∼0.1 N/m, resonance frequency of ∼500 kHz in water, and quality factor of ∼1.5 in water were used. An EBD tip was grown for
1.5 min on the original tip in an atmosphere of sublimated ferrocene vapor using a field emission scanning electron microscope(SUPRA40VP, Zeiss, Germany). The grown tip was sharpened byradiofrequency plasma etching for 1 min at 15 W in an argon environment using a plasma cleaner (Tergeo Plasma Cleaner, Pie Scientific, USA). In addition, custom-made cantilevers (BL-AC7DS-KU2,
Olympus, Japan) with a spring constant of 0.15–0.2 N/m, resonancefrequency of ∼1 MHz in water, and quality factor of 2–3 in water
were used to check the dependence of the feedback control error
on the cantilever resonant frequency. The imaging conditions used,such as the number of scan lines and the values of Af and As , aredescribed in figure legends. Procedures for EBD tip preparationand HS-AFM imaging have been described in detail in a previous
article.35

B. Preparation of protein samples
III. CONCLUSIONSIn this study, we first observed that the feedback control error
is larger in retrace imaging than in trace imaging. Based on thisfinding, we developed the OTI mode. This mode allows for not
only less disturbing/invasive imaging but also faster imaging. For
samples with high spatial frequency, the highest possible imaging
rate is doubled by the OTI mode. For samples with low spatial frequency, the imaging rate is improved by a factor of ∼2.5, as demonstrated through the imaging of actin filaments and MTs oriented
nearly along the X-direction at 25 and 30 fps, respectively. Even for
dynamic actin polymerization processes that occur through weakprotein–protein interactions, the OTI mode enables faster imaging
at ∼8 fps. In the current state, where even a 50% improvement in
the speed performance of HS-AFM is very difficult, the alternative
method developed in this study is highly advantageous. We expectthat our simple and highly effective method will soon be installedin the existing and upcoming HS-AFM systems and will improvea wide range of HS-AFM imaging studies in biophysics and otherfields.

IV. MATERIALS AND METHODS
A. HS-AFM system and imaging
We used a lab-built HS-AFM apparatus1 with slight modifications for this study. Our HS-AFM system is equipped with a dynamic
feedback controller that can automatically adjust the gain parameters during imaging so that tip parachuting is suppressed evenunder the condition of weak tip–sample contact.9 Only a digital-toanalog convertor board (PCI3305, Interface, Japan) and an addition

Rev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948© Author(s) 2021

Actin was prepared from rabbit skeletal muscles as described
previously.36 Actin filaments were bound to an equimolar amountof phalloidin (Thermo Fisher, USA). For HS-AFM imaging of actin
filaments, freshly cleaved mica was treated with 0.1% 3-aminopropyl
triethoxysilane (Sigma Aldrich, USA) for 3 min, unless stated otherwise. After the surface was washed with pure water (200 μl),
actin filaments (1 μM) were deposited on the surface and incubatedfor 10 min. After the surface was washed with F-Buffer containing
20 mM imidazole-HCl (pH 7.6), 50 mM KCl, 2 mM MgCl2 , and
1 mM EGTA, all measurements were performed in F-Buffer, unlessstated otherwise. To measure the error signals (Figs. 1 and 2),
the surface-attached actin filaments were treated with 0.1% glutaraldehyde for 15 min and then washed with F-Buffer. For the HSAFM observation of actin polymerization (Fig. 8), actin filaments
were formed from unlabeled G-actin and biotinylated G-actin at
the molar ratio of 0.8:0.2 and then stabilized with an equimolar
amount of phalloidin. Biotinylation of G-actin was performed in
G-buffer containing 10 mM TES-KOH (pH 7.0), 0.2 mM CalCl2 ,0.1 mM NaN3 , and 0.2 mM ATP using a 5 M excess biotin-PEAC5 maleimide (Dojindo, Japan). Then, the biotinylated G-actin was filtered with a centrifugal filter (Amicon Ultra, Millipore Corp., USA)to remove free biotin-PEAC5 -maleimide. The partially biotinylated
actin filaments were placed on the surface of two-dimensional crystals of tamavidin two-LPI (Wako Chemicals, Japan) directly formed
on a mica surface, as described previously.37 Then, 0.5 μM G-actin,
0.2 mM ATP, and 1 mM DTT were added to the sample chamber solution containing an additional 50 mM KCl in F-buffer. MTs
were prepared by the polymerization of porcine brain tubulin dimers(Cytoskeleton, Inc., USA). Tubulin proteins (1 mg/ml) were incubated with GTP (1 mM) for 15 min at 37 ○ C in PEM buffer containing 80 mM PIPES-NaOH (pH 6.9), 1 mM MgCl2 , and 1 mM

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EGTA, followed by the addition of taxol (200 μM). After incubation for 15 min at 37 ○ C, the MTs were purified using a centrifugal filter (Amicon Ultra, Millipore Corp., USA). To measure theerror signals (Figs. 1 and 2), glutaraldehyde (0.1%) was added to
the MTs and incubated for 10 min before centrifugation. The MTs
were then deposited onto freshly cleaved mica and incubated for
30 min. After the surface was washed with PEM buffer, all measurements were performed in PEM buffer. For the HS-AFM observation of tubulin polymerization from the ends of a broken MT(Figs. 8), 0.5 μM tubulin dimers and 100 μM GTP were added to thesolution.
SUPPLEMENTARY MATERIAL
The following data are available as the supplementary material: captions for Supplementary Movies S1–S11; feedback control
error, cantilever deflection, and feedback controller output signals
recorded during retrace imaging of an actin filament and a MT at
6.7 fps; calculations of the spatial frequencies of tip-detected
topographies of the modeled actin filament and MT; twodimensional modeled tip shape and its contact with the X–Z crosssections of modeled actin filament and MT oriented along the Y
axis; calculations of tip-convoluted topographies of modeled actin
filament and MT and their spatial frequencies; dependence of
feedback control error on cantilever resonant frequency; detailed
method of compensation for peak shifts in rounded quasi-sawtoothwave; quasi-sawtooth waves rounded by finite Fourier series containing the first nine terms; displacement of Z-scanner driven by
rounded quasi-sawtooth wave and effect of inverse compensationon the displacement; detailed method to estimate the contribution of cantilever resonant frequency shift to amplitude reduction
by tip–sample interactions; and comparison between “only trace
imaging” and “only retrace imaging” modes for breakage of actin
filaments.
Movie S1 shows the capability of the OTI mode to image an
actin filament aligned along the Y axis at 12.5 fps without breakage;
Movie S2, the breakage of an actin filament aligned along the Y axis
during imaging in the conventional imaging mode at 12.5 fps; Movie
S3, the capability of the OTI mode to image a MT aligned along the
Y axis at 14.3 fps without breakage; Movie S4, the breakage of a MTaligned along the Y axis during imaging in the conventional imaging
mode at 14.3 fps; Movie S5, the capability of the OTI mode to image
actin filaments aligned along the X axis at 25 fps without breakage;
Movie S6, the capability of the OTI mode to image MTs aligned
along the X axis at 30 fps without breakage; Movie S7, the incapability of the conventional imaging mode to image actin polymerization
at 5 fps; Movie S8, the capability of the OTI mode to image actin
polymerization at 5 fps; Movie S9, the capability of the OTI mode
to image the actin polymerization process at 7.7 fps; Movie S10,
the incapability of the conventional imaging mode to image tubulin
polymerization at 3.3 fps; and Movie S11, the capability of the OTImode to image tubulin polymerization at 3.3 fps.
ACKNOWLEDGMENTS
This work was supported by the JSPS KAKENHI (Grant Nos.
17H0621 to T.A. and 20K15140 to S.F.) and the Human Frontier
Science Program Grant (to T.A.).

Rev. Sci. Instrum. 92, 033705 (2021); doi: 10.1063/5.0032948© Author(s) 2021

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DATA AVAILABILITY
The data that support the findings of this study are available
within the article and its supplementary material. The source codefor the OTI mode will be provided upon request.
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