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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5338_Библиотеки_им_академика_М_И_Перельмана
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258 S. Fuchigami and S. Takada
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Fig. 15.1 Examples of applying the flexible fitting method to HS-AFM images of FlhAc monomer.
A, E Experimental AFM images [
mental AFM images and the corresponding pseudo-AFM images in the background. C, G PseudoAFM images generated from the snapshots. D, H Probability distributions obtained by the simula-
tion. The correlation for the initial structures and the positions of the most correlated snapshots are
indicated by dotted lines and arrows, respectively (Reprinted with permission from [
29]. B, F Snapshots showing the highest correlation to the experi-
])
21
15.2.2 Rigid-Body Fitting to AFM Images for Inferring
Probe Shape and Biomolecular Structure
An AFM image is based on the placement of a biomolecule on the surface and
also depends on the shape of AFM probe tip. It is easy to search the biomolecular
structure placement best-fit to a given AFM image using rigid-body fitting [
23–26].
On the other hand, it is possible to experimentally measure the probe tip shape,
but it is rarely measured in usual AFM observations and is normally unknown.
However, to accurately and successfully infer the molecular structure from an AFM
image, the knowledge of probe tip shape is required. To address this requirement,
a computational method, called exhaustive search rigid-body fitting method, have
been developed to simultaneously infer the biomolecular structure placement and
22
the probe tip shape from an AFM image [
].
The developed method finds the optimal combination of biomolecular placement and the probe tip shape for generating a pseudo-AFM image that most closely
resembles an experimental AFM image by exhaustively searching the discretized
biomolecule position (orientation and translation) and the discretized probe tip shape
(radius and half-apex angle). In addition, to determine the best similarity score of
AFM images for this method, four similarity scores (cosine similarity, correlation
coefficient, pixel-RMSD, and penalty function) were examined through twin experiments using four biomolecules (dynein, myosin, actin monomer, and actin filament),
finding that the cosine similarity worked best generally and that the correlation
coefficient and the pixel-RMSD were also useful.
15 Data Assimilation to Integrate High-Speed Atomic Force Microscopy … 259
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Moreover, the developed method was applied to experimental HS-AFM images
of two biomolecules (actin filament and flagellar protein FlhA
ring) to infer the
C
biomolecular placement and the probe tip shape. As a result, the effective probe tip
shapes were estimated successfully and biomolecular structures were visualized with
accurate placement (Fig.
15.2). Interestingly, the results indicated that the appropriate
similarity scores were different between the two target biomolecules. In the case of
the actin filament, the cosine similarity worked best apparently. In contrast, for an
AFM image of the flagellar protein FlhA
ring, the correlation coefficient gave better
C
results. This difference may be partly due to the flexibility of the target biomolecules,
which was ignored in rigid-body fitting. The developed method is publicly available
30
through the software, afmize [
].
Fig. 15.2 Example of applying the exhaustive search rigid-body fitting method to a HS-AFM
image of FlhA
tilt. C AFM image used for rigid-body fitting. D Pseudo-AFM image corresponding to panel C.
E Absolute difference between panels C and D. F Fitted structure with the corresponding AFM
image in the background. G–I Similarity scores of structures fitted using cosine similarity (G),
pixel-RMSD (H), and correlation coefficient (I) (Reprinted with permission from [
ring [29
c
]. A Estimated stage surface. B AFM image corrected for stage surface
22])
260 S. Fuchigami and S. Takada
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15.3 Image Analysis from HS-AFM Measurement Data
Before the structural analysis, or independently from the structural analysis, some
image analyses of raw HS-AFM images can be of high value. Many standard image
processing methods have been applied, such as denoising and averaging. In this
section, we present two image processing methods recently developed [
31, 32].
15.3.1 Resolving the Data Asynchronicity in HS-AFM
Measurement via the Kalman Smoother
HS-AFM has a spatiotemporal resolution sufficient to observe a single biomolecular
motion at work. However, the temporal resolution is not necessarily high enough to
obtain a snapshot of the observed biomolecule; an AFM image could be distorted
when a biomolecule changes its conformation significantly during the scanning of
a single frame of HS-AFM movie. This limitation of the temporal resolution is an
inevitable problem inherent to observation by scanning probe microscopy and results
in the measurement time difference, i.e. data asynchronicity, in HS-AFM movies.
To resolve this problem of HS-AFM movies and to generate synchronous HS-AFM
movies, Kalman filter and smoother methods based on a sequential Bayesian data
assimilation approach have been developed [
In applying the Kalman filter and smoother methods to HS-AFM movies, a shorttime evolution of HS-AFM images by a linear dynamical system (LDS), called
“prediction”, and a modification of HS-AFM images using the likelihood of HSAFM data acquired pixel-by-pixel, termed “filtering”, are repeated alternately. The
Kalman filter method uses an LDS for the time evolution of HS-AFM images at the
current time as well as the past time points and thus can be applied on-the-fly. On the
other hand, when a whole time series of HS-AFM images are available, the Kalman
filter method can be extended to use not only current and past data but also future
data, which is called the Kalman smoother method.
The Kalman filter and smoother methods implemented for HS-AFM movies were
first tested using a toy model of a diffusing cone in a twin experiment, confirming
that both methods can reduce image distortion and noise and that the Kalman
smoother method outperforms significantly. To further confirm the advantage of
the Kalman smoother method, another twin experiment was performed using a
synthetic HS-AFM movie of a motor protein, dynein. In molecular dynamics simulation, dynein showed a rapid conformational change, called power stroke, but the
conformational change was hardly detected in the raw HS-AFM movie (Fig.
By contrast, the HS-AFM movie estimated by the Kalman smoother method showed
weak but detectable power stroke conformational change (Fig.
the superiority of the Kalman smoother method. Furthermore, the effectiveness
of the Kalman smoother method in reducing distortion and noise was confirmed
31].
15.3).
15.3), confirming
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through its application to two experimental HS-AFM movies of FlhAC monomer
and centralspindlin.
15.3.2 End-To-End Differentiable Blind Tip Reconstruction
for Noisy HS-AFM Images
Sample surface measured by AFM is different and deformed from the actual surface
by the effect of AFM probe tip geometry and interactions between the sample and the
probe tip. Once the probe tip shape is known, the surface geometry of the sample can
be reconstructed approximately by deconvolution of the AFM image. Thus, correct
knowledge of the probe tip shape is important and essential information for AFM
image analysis. As an algorithm to estimate and prove tip shape only from AFM
images, Villarrubia developed the blind tip reconstruction (BTR) method [
The BTR method works perfectly well for noise-free AFM images but is susceptible
to noise and does not perform adequately for noisy AFM images, which are often
found in HS-AFM measurement. To overcome this problem, Matsunaga et al. have
proposed an alternative BTR method, called end-to-end differentiable BTR method,
based on a modern machine learning approach [
The end-to-end differentiable BTR method introduces an appropriate loss function
for inverted probe tip shape, p, including a regularization term to prevent overfitting
to noise with parameter
λ as
32].
33, 34].
MSE(p) + λp
where MSE(p) is the mean square error of AFM images in the transformation called
“opening” using an inverted probe tip shape, p, and
“opening” transformation, the sample surface is first estimated by removing the
effect of the probe tip from an AFM image (this procedure is called “erosion”),
followed by estimating an AFM image using the probe tip shape, p, from the estimated
sample surface (“dilation”) (Fig.
is optimized with automatic differentiation and backpropagations developed in deep
learning frameworks.
By performing twin experiments using noisy pseudo-AFM images of myosin V
motor domain, it was confirmed that the end-to-end differentiable BTR method is
robust to noise in AFM images and is less parameter dependence than the original
BTR method. In addition, the developed method could correctly detect a doubletip shape, which is frequently occurred artifact in AFM measurement, and could
transform a doubled sample image into a normal image. Finally, by applying the
method to actual HS-AFM data of myosin V walking on actin filament, it was shown
that the developed method could accurately reconstruct the surface of actomyosin
consistent with the structural model obtained by flexible fitting MD simulation [
15.4). Using the loss function, a probe tip shape
2
2 is the L2 norm. In the
(15.2)
35].
262 S. Fuchigami and S. Takada
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Fig. 15.3 Example of applying the Kalman smoother method to a synthetic AFM movie of a
motor protein, dynein. A Power-stroke motion of dynein. B Snapshot structures and C–E the
corresponding synthetic AFM images. Power-stroke motion occurred between the 1st and the 4th
frames. C Ground-truth, D noisy, and E Kalman-smoother-estimated AFM images with contours
(Reprinted with permission from [
31])
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30
25
20
Y coordinate [nm]
15
15 20 25 30
X coordinate [nm]
Input
AFM
image
8
6
4
2
0
Erosion
with p
Identical when probe tip shape p is correct
Probe tip shape p is optimized by minimizing MSE
L2 regularization is imposed to obtain a blunt probe tip
Reconstructed
molecular surface
30
25
20
Y coordinate [nm]
15
15 20 25 30
X coordinate [nm]
Dilation
with p
30
25
20
Y coordinate [nm]
15
15 20 25 30
X coordinate [nm]
Output
AFM
image
Fig. 15.4 Schematic of end-to-end differentiable BTR (Modified and reprinted with permission
from [
32])
The end-to-end differentiable BTR method serves as a post-processing step to reconstruct sample surfaces from AFM images. A set of codes for the developed method
is publicly available at
https://github.com/matsunagalab/differentiable_BTR.
15.4 Data Assimilation Combining HS-AFM Measurement
and Molecular Simulation
8
6
4
2
0
While remarkable protein structural dynamics have successfully been observed by
HS-AFM, its spatiotemporal resolution is not always high enough. One possible
solution to the analysis of higher-resolution phenomena is data assimilation using MD
simulation, which can provide the high spatiotemporal resolution required. In this
section, we present four-dimensional structural analysis methods to understand and
elucidate the behavior of biomolecules observed by HS-AFM in detail by assimilating
data from HS-AFM movies and MD simulation [
36, 37].
15.4.1 Particle Filter and Smoother Methods to Integrate
HS-AFM Measurements with Biomolecular
Simulations
Considering the time resolution of HS-AFM measurements, it is better to use CG
molecular model for the simulations. Attempts to develop methodologies for integrating HS-AFM data and CG-MD simulation have been made using the particle
filter and smoother methods that implement a s equential Bayesian data assimilation approach [
36, 37]. In both methods, a probability distribution of biomolecule
264 S. Fuchigami and S. Takada
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structures at a time is represented as a finite set of structure samples, referred to as
“particles”.
In the particle filter method, CG-MD simulation of each particle is performed by
CafeMol [
two consecutive HS-AFM image acquisitions in a procedure called “prediction”.
Then, the likelihood of the HS-AFM images is estimated for each particle, and particles are resampled according to the estimated likelihoods in the so-called “filtering”
procedure. By repeating these two procedures alternately, an ensemble of structural
dynamics that is compatible with the experimental time series data is obtained. This
protocol of the particle filter method was validated by a twin experiment using a
synthetic HS-AFM movie of a nucleosome as the “experimental measurement” [
Particle filter simulations with 512 particles successfully captured the large-scale
nucleosome structural dynamics compatible with the HS-AFM movie. The reproducibility of the experimental HS-AFM movie improved as the number of particles
increased, but even with 8192 particles, the problem of degeneracy, where only one
particle is resampled, was not resolved. However, this problem is not considered
serious because the results obtained are totally consistent with the HS-AFM movie.
It was also found that by performing particle filter simulations with different ion
concentrations or time scale mappings and comparing their likelihoods, the “true”
ion concentration and time scale mapping could be inferred.
which was generated from a single biomolecular structure, but actual HS-AFM
images do not measure all pixels at the time, but rather at different times. Therefore, the particle filter method was extended to the particle smoother method that
takes the measurement time difference into account, and a twin experiment was
performed using an asynchronous pseudo-HS-AFM movie of a nucleosome [
First, particle smoother simulations with two types of data acquisition, pixel-bypixel (PS-PBP simulation) and all-at-once (PS-AAO simulation), were performed at
the same once-per-one-frame resampling frequency as the particle filter simulation,
and the results of both methods were compared. As a result, it was confirmed that
the PS-PBP method reproduced the dynamic behavior of a nucleosome better than
the PS-AAO method (Fig.
pixel, one line, five lines, one frame, two frames, and ten frames) in the particle
smoother simulations were examined, founding that resampling once-per-one-frame
was optimal for the robust inference.
28] over a short period of time corresponding to the time interval between
36
The above particle filter simulations used a series of HS-AFM images, each of
37].
15.5). Next, six resampling frequencies (once per one
].
15.4.2 Hidden Markov Model Analysis of Myosin V Walking
Observed by High-Speed Atomic Force Microscopy
As described in the previous subsection, data assimilation approach to HS-AFM
data using particle filter and smoother methods has achieved a measure of success,
but these methods are computationally expensive to simulate functional motion of
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Fig. 15.5 Comparison of PS-PBP and PS-AAO methods. A Mean squared error (MSE) trajectories
of AFM images for PS-PBP (purple) and PS-AAO (red) trajectories. Moving averages of each
trajectory are shown by thick lines. B Accumulated MSE of AFM images for three trajectories with
the largest likelihood of each method (Reprinted with permission from [
37])
biomolecules. One approach that is less demanding on the computer and that allows
broader applications is to use a Markov state model (MSM), which can easily investigate the dynamic behavior of biomolecules over a longer period of time [
16, 17].
In this model, the long-term dynamics is represented as a series of stochastic transitions between discrete Markov states. Furthermore, based on the constructed MSM,
data assimilation of a HS-AFM movie can be performed by using a hidden Markov
model (HMM) to estimate detailed information on molecular dynamics at the atomic
level, such as the pathway of molecular structural change. The MSM and HMM have
been applied to the walking motion of myosin V along actin filament to reveal the
detailed dynamics of myosin V walking observed in HS-AFM movies (This work is
unpublished).
First, model structures of tail-truncated myosin V and actin 31-mer filament
were constructed by homology modeling, respectively. Then, molecular models of
the actin–myosin complex in four different conformational states (two-head bound
down-up state, one-head bound up-up state, two-head bound down-down state, and
one-head bound up-down state) were prepared for two possible pathways of structural state changes in myosin V walking. Many CG-MD simulations of these complex
28
structures were performed using CafeMol software [
]. In CG-MD simulations in
two one-head bound states, actin binding site on the unbound head was observed to
move in the direction of walking motion. In the up-up state, the unbound head did
not rebind to the actin filament, but, in the up-down state, rebinding of the unbound
head was successfully achieved, reproducing the entire walking motion from the
detachment of the head from actin filament to its rebinding.
An MSM was then constructed using a number of structures obtained from the CGMD simulations of the four conformational states of myosin V. In the obtained MSM,
all Markov states in the four states were connected, but a set of Markov states in four
266 S. Fuchigami and S. Takada
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conformational states were properly separated from each other, yielding a plausible
model that could discuss the details of walking dynamics of myosin V. Based on this
MSM, MSMs for each conformational states were reconstructed, and an extended
MSM was constructed by distinguishing each Markov states by conformational states
and adding transitions between Markov states in different conformational states. The
added transitions were represented using one parameter for each pair of conformational states, and suitable values of state transitions were estimated by the maximum
likelihood method using five HS-AFM movies of one-step walking of myosin V [
38].
The maximum likelihood paths can be determined for each HS-AFM movie by the
Viterbi algorithm.
15.5 Improvement of Performance and Functionality
of High-Speed Atomic Force Microscopy
In AFM measurement, a probe tip attached at the end of the cantilever scans a stage
surface on which the specimen is tethered and detects the mechanical interaction
between the probe and the specimen-tethered surface (the stage plain is set as the
xy-plain). The cantilever xy-position relative to the surface is moved by x- and yscanners made by piezoelectric elements. During the xy-plain scanning, the probe tip
moves up and down in the z-direction weakly touching the surface, which is realized
by the z-scanner, another piezoelectric element (Fig.
Among several operation modes, the AFM for biomolecules nearly always employ
the tapping mode [
2]. While scanning, the probe tip is forced to oscillate normal to the
surface (the z-direction) with a high and fixed frequency and a fixed amplitude. The
interaction with the specimen-tethered surface modulates the oscillation amplitude
of the probe tip, which is measured by the laser light applied to the cantilever. At
15.6A).
Fig. 15.6 A Schematic picture of the feedback loop in HS-AFM apparatus. B The design of the
z-scanner booster (Reprinted with permission from [
permission from [
40
])
39]). C The DB-A2 circuit (Reprinted with
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each xy-position, the AFM apparatus searches the probe tip height in z-direction that
causes a certain modulation, termed the set point, of the oscillation amplitude. In this
way, the probe can detect the envelop of the specimen-tethered surface.
While the conventional AFM takes on the order of minutes for a single scanning
of the surface, the HS-AFM was developed to speed up the frame rate by orders of
magnitude: It takes tens to hundreds of milliseconds to scan the surface in HS-AFM.
This high speed enables us to monitor the dynamic motions of target biomolecules
at work, which is the major advantage of the HS-AFM compared to the conventional
one. Notably, however, this time resolution, tens of millisecond, is not always high
enough. Proteins and other biomolecules change their conformations in a broad range
of time scales from submicroseconds to seconds. Some fast motions cannot directly
be observed even with the HS-AFM.
How is the frame rate of HS-AFM determined? As described above, at each xyposition, the probe tip searches the height that causes a certain modulation of the
probe tip oscillation amplitude. This requires the feedback loop [
2] (Fig. 15.6A).
First, the probe tip tapping is measured by the laser light. Second, using the time
course of the tip height, the amplitude is estimated. Third, from the amplitude, the
desired change in the probe height is calculated. Fourth, the z-scanner is moved to
realize the desired height of the probe tip. At the updated probe tip height, the tapping
is measured again, which corresponds to the first step of completing the feedback
loop. The time required for this feedback loop is the sum of times of all these steps
and determines the time resolution for a single point measurement. The time f or one
frame is simply obtained by the product of the single-point measurement time and
the number of points to be measured on the surface.
The HS-AFM has been developed and modified to reduce the time for this feedback loop by numerous technological devises. Here, we describe the most recent
devises realized in the last five years.
First, Shimizu et al. developed the z-scanner booster to increase the resonance
frequency to 1.1 MHz [
39] (Fig. 15.6B), which is about 6 times as high as the previous
generation of the setup. The z-scanner booster uses the latest and small piezoelectric
element. In addition, it supports the piezoelectric element at the 4 vertexes, rather
than the entire bottom plain, which significantly increased the resonance frequency.
Second, Umeda et al. developed a new and fast amplitude detector, called
differential-based square amplitude (DB-A
) method [40
15.6C). Given the
] (Fig.
2
detected probe oscillation A sin(ωt), this method uses the differentiation device to
2
obtain A cos(ωt). Then, with A
sin2(ωt) + A2 cos2(ωt) = A2, one can determine the
amplitude A. While the conventional approach requires significant fractions of the
oscillation period to determine the amplitude, the new method can estimate the amplitude almost instantaneously. The new method was shown to speed up the amplitude
detection time by less than half of the previous best approach.
Third, Kodera group made a cantilever markedly smaller than the previous
one using the FIB (focused ion beam) technology, which increases the resonance
frequency of the cantilever by a factor 10–20. Together with some additional technical advances, Kodera group succeeded to increase the time resolution by a factor
of ~7, reaching to the feedback loop with ~500 kHz (2 microseconds). Notably, the
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