Flexible Fitting of Biomolecular Structures to Atomic Force Microscopy Images via Biased Molecular Simulations

The conformational space of RNase P RNA in solution

RNA conformational diversity has fundamental biological roles1-5, but direct visualization of its full conformational space in solution has not been possible using traditional biophysical techniques. Using solution atomic force microscopy, a deep neural network and statistical analyses, we show that the ribonuclease P (RNase P) RNA adopts heterogeneous conformations consisting of a conformationally invariant core and highly flexible peripheral structural elements that sample a broad conformational space, with amplitudes as large as 20-60 Å in a multitude of directions, with very low net energy cost. Increasing Mg2+ drives compaction and enhances enzymatic activity, probably by narrowing the conformational space. Moreover, analyses of the correlations and anticorrelations between spatial flexibility and sequence conservation suggest that the functional roles of both the structure and dynamics of key regions are embedded in the primary sequence. These findings reveal the structure-dynamics basis for the embodiment of both enzymatic precision and substrate promiscuity in the RNA component of the RNase P. Mapping the conformational space of the RNase P RNA demonstrates a new general approach to studying RNA structure and dynamics.

Determining structures of RNA conformers using AFM and deep neural networks

Much of the human genome is transcribed into RNAs1, many of which contain structural elements that are important for their function. Such RNA molecules-including those that are structured and well-folded2-are conformationally heterogeneous and flexible, which is a prerequisite for function3,4, but this limits the applicability of methods such as NMR, crystallography and cryo-electron microscopy for structure elucidation. Moreover, owing to the lack of a large RNA structure database, and no clear correlation between sequence and structure, approaches such as AlphaFold5 for protein structure prediction do not apply to RNA. Therefore, determining the structures of heterogeneous RNAs remains an unmet challenge. Here we report holistic RNA structure determination method using atomic force microscopy, unsupervised machine learning and deep neural networks (HORNET), a novel method for determining three-dimensional topological structures of RNA using atomic force microscopy images of individual molecules in solution. Owing to the high signal-to-noise ratio of atomic force microscopy, this method is ideal for capturing structures of large RNA molecules in distinct conformations. In addition to six benchmark cases, we demonstrate the utility of HORNET by determining multiple heterogeneous structures of RNase P RNA and the HIV-1 Rev response element (RRE) RNA. Thus, our method addresses one of the major challenges in determining heterogeneous structures of large and flexible RNA molecules, and contributes to the fundamental understanding of RNA structural biology.

Finite element modelling of atomic force microscopy imaging on deformable surfaces

Atomic force microscopy (AFM) provides a three-dimensional topographic representation of a sample surface, at nanometre resolution. Computational simulations can aid the interpretation of such representations, but have mostly been limited to cases where both the AFM probe and the sample are hard and not compressible. In many applications, however, the sample is soft and therefore deformed due to the force exerted by the AFM tip. Here we use finite element modelling (FEM) to study how the measured AFM topography relates to the surface structures of soft and compressible materials. Consistent with previous analytical studies, the measured elastic modulus in AFM is generally found to deviate from the elastic modulus of the sample material. By the analysis of simple surface geometries, the FEM modelling shows how measured mechanical and topographic features in AFM images depend on a combination of tip-sample geometry and indentation of the tip into the sample. Importantly for the interpretation of AFM data, nanoparticles may appear larger or smaller by a factor of two depending on tip size and indentation force; and a higher spatial resolution in AFM images does not necessarily coincide with a more accurate representation of the sample surface. These observations on simple surface geometries also extend to molecular-resolution AFM, as illustrated by comparing FEM results with experimental data acquired on DNA. Taken together, the FEM results provide a framework that aids the interpretation of surface topography and local mechanics as measured by AFM.

Modeling Conformational Transitions of Biomolecules from Atomic Force Microscopy Images using Normal Mode Analysis

Observing a single biomolecule performing its function is fundamental in biophysics as it provides important information for elucidating the mechanism. High-speed atomic force microscopy (HS-AFM) is a unique and powerful technique that allows the observation of biomolecular motion in a near-native environment. However, the spatial resolution of HS-AFM is limited by the physical size of the cantilever tip, which restricts the ability to obtain atomic details of molecules. In this study, we propose a novel computational algorithm designed to derive atomistic models of conformational dynamics from AFM images. Our method uses normal-mode analysis to describe the expected motions of the molecule, allowing these motions to be represented with a limited number of coordinates. This approach mitigates the problem of overinterpretation inherent in the analysis of AFM images with limited resolution. We demonstrate the effectiveness of our algorithm, NMFF-AFM, using synthetic data sets for three proteins that undergo significant conformational changes. NMFF-AFM is a fast and user-friendly program that requires minimal setup and has the potential to be a valuable tool for biophysical studies using HS-AFM.

Deciphering the actin structure-dependent preferential cooperative binding of cofilin

The mechanism underlying the preferential and cooperative binding of cofilin and the expansion of clusters toward the pointed-end side of actin filaments remains poorly understood. To address this, we conducted a principal component analysis based on available filamentous actin (F-actin) and C-actin (cofilins were excluded from cofilactin) structures and compared to monomeric G-actin. The results strongly suggest that C-actin, rather than F-ADP-actin, represented the favourable structure for binding preference of cofilin. High-speed atomic force microscopy explored that the shortened bare half helix adjacent to the cofilin clusters on the pointed end side included fewer actin protomers than normal helices. The mean axial distance (MAD) between two adjacent actin protomers along the same long-pitch strand within shortened bare half helices was longer (5.0-6.3 nm) than the MAD within typical helices (4.3-5.6 nm). The inhibition of torsional motion during helical twisting, achieved through stronger attachment to the lipid membrane, led to more pronounced inhibition of cofilin binding and cluster formation than the presence of inorganic phosphate (Pi) in solution. F-ADP-actin exhibited more naturally supertwisted half helices than F-ADP.Pi-actin, explaining how Pi inhibits cofilin binding to F-actin with variable helical twists. We propose that protomers within the shorter bare helical twists, either influenced by thermal fluctuation or induced allosterically by cofilin clusters, exhibit characteristics of C-actin-like structures with an elongated MAD, leading to preferential and cooperative binding of cofilin.

Advancing biomolecular simulation through exascale HPC, AI and quantum computing

Biomolecular simulation can act as both a digital microscope and a crystal ball; offering the potential for a deeper understanding of experimental observations whilst also presenting a forward-looking avenue for the in silico design and evaluation of hitherto unsynthesized compounds. Indeed, as the intricacy of our scientific inquiries has grown, so too has the computational prowess we seek to deploy in our pursuit of answers. As we enter the Exascale era, this mini-review surveys the computational landscape from both the point of view of the development of new and ever more powerful systems, and the simulations that are run on them. Moreover, as we stand on the cusp of a transformative phase in computational biology, this article offers a contemplative glance into the future, speculating on the profound implications of artificial intelligence and quantum computing for large-scale biomolecular simulations.

Computation of topographic and three-dimensional atomic force microscopy images of biopolymers by calculating forces

Atomic force microscopy (AFM) is widely utilized to visualize the molecular motions of biomolecules. Comparison of experimentally measured AFM images with simulated AFM images based on known structures of biomolecules is often necessary to elucidate what is actually resolved in the images. Experimental AFM images are generated by force measurements; however, conventional AFM simulation has been based on geometrical considerations rather than calculating forces using molecular dynamics simulations due to limited computation time. This letter summarizes recently developed methods to simulate topographic and three-dimensional AFM (3D-AFM) images of biopolymers such as chromosomes and cytoskeleton fibers. Scanning such biomolecules in AFM measurements usually results in nonequilibrium-type work being performed. As such, the Jarzynski equality was employed to relate the nonequilibrium work to the free energy profiles, and the forces were calculated by differentiating the free energy profiles. The biomolecules and probes were approximated using a supra-coarse-grained model, allowing the simulation of force-distance curves in feasible time. It was found that there is an optimum scanning velocity and that some of polymer structures are resolved in the simulated 3D-AFM images. The theoretical background adopted to rationalize the use of small probe radius in the conventional AFM simulation of biomolecules is clarified.

Crystal structure of Escherichia coli thiamine pyrophosphate-sensing riboswitch in the apo state

The thiamine pyrophosphate (TPP)-sensing riboswitch is one of the earliest discovered and most widespread riboswitches. Numerous structural studies have been reported for this riboswitch bound with various ligands. However, the ligand-free (apo) structure remains unknown. Here, we report a 3.1 Å resolution crystal structure of Escherichia coli TPP riboswitch in the apo state, which exhibits an extended, Y-shaped conformation further supported by small-angle X-ray scattering data and driven molecular dynamics simulations. The loss of ligand interactions results in helical uncoiling of P5 and disruption of the key tertiary interaction between the sensory domains. Opening of the aptamer propagates to the gene-regulatory P1 helix and generates the key conformational flexibility needed for the switching behavior. Much of the ligand-binding site at the three-way junction is unaltered, thereby maintaining a partially preformed pocket. Together, these results paint a dynamic picture of the ligand-induced conformational changes in TPP riboswitches that confer conditional gene regulation.

Particle Smoother to Assimilate Asynchronous Movie Data of High-Speed AFM with MD Simulations

High-speed (HS) atomic force microscopy (AFM) can be used to observe structural dynamics of biomolecules under near-physiological conditions. In the AFM measurement, the probe tip scans an area of interest and acquires height data pixel by pixel so that the obtained AFM image contains a measurement time difference. In this study, to integrate molecular dynamics simulations with asynchronous HS-AFM movie data, we developed a particle smoother (PS) method for Bayesian data assimilation, one of the machine learning approaches, by extending the previous particle filter method. With a twin experiment with an asynchronous pseudo HS-AFM movie of a nucleosome, we found that the PS method with the pixel-by-pixel data acquisition reproduced the dynamic behavior of a nucleosome better than the previous particle filter method that ignored the data asynchronicity. We examined several frequencies of particle resampling in the PS method, and found that resampling once per one frame was optimal for reproducing the dynamic behavior. Thus, we found that the PS method with an appropriate resampling frequency is a powerful method for estimating the dynamic behavior of a target molecule from HS-AFM data with low spatiotemporal resolution.

Protein dynamics by the combination of high-speed AFM and computational modeling

High-speed atomic force microscopy (HS-AFM) allows direct observation of biological molecules in dynamic action. However, HS-AFM has no atomic resolution. This article reviews recent progress of computational methods to infer high-resolution information, including the construction of 3D atomistic structures, from experimentally acquired resolution-limited HS-AFM images.

BioAFMviewer software for simulation atomic force microscopy of molecular structures and conformational dynamics

Atomic force microscopy (AFM) and high-speed scanning have significantly advanced real time observation of biomolecular dynamics, with applications ranging from single molecules to the cellular level. To facilitate the interpretation of resolution-limited imaging, post-experimental computational analysis plays an increasingly important role to understand AFM measurements. Data-driven simulation of AFM, computationally emulating experimental scanning, and automatized fitting has recently elevated the understanding of measured AFM topographies by inferring the underlying full 3D atomistic structures. Providing an interactive user-friendly interface for simulation AFM, the BioAFMviewer software has become an established tool within the Bio-AFM community, with a plethora of applications demonstrating how the obtained full atomistic information advances molecular understanding beyond topographic imaging. This graphical review illustrates the BioAFMviewer capacities and further emphasizes the importance of simulation AFM to complement experimental observations.

Visualizing RNA conformational and architectural heterogeneity in solution

RNA flexibility is reflected in its heterogeneous conformation. Through direct visualization using atomic force microscopy (AFM) and the adenosylcobalamin riboswitch aptamer domain as an example, we show that a single RNA sequence folds into conformationally and architecturally heterogeneous structures under near-physiological solution conditions. Recapitulated 3D topological structures from AFM molecular surfaces reveal that all conformers share the same secondary structural elements. Only a population-weighted cohort, not any single conformer, including the crystal structure, can account for the ensemble behaviors observed by small-angle X-ray scattering (SAXS). All conformers except one are functionally active in terms of ligand binding. Our findings provide direct visual evidence that the sequence-structure relationship of RNA under physiologically relevant solution conditions is more complex than the one-to-one relationship for well-structured proteins. The direct visualization of conformational and architectural ensembles at the single-molecule level in solution may suggest new approaches to RNA structural analyses.

End-to-end differentiable blind tip reconstruction for noisy atomic force microscopy images

Observing the structural dynamics of biomolecules is vital to deepening our understanding of biomolecular functions. High-speed (HS) atomic force microscopy (AFM) is a powerful method to measure biomolecular behavior at near physiological conditions. In the AFM, measured image profiles on a molecular surface are distorted by the tip shape through the interactions between the tip and molecule. Once the tip shape is known, AFM images can be approximately deconvolved to reconstruct the surface geometry of the sample molecule. Thus, knowing the correct tip shape is an important issue in the AFM image analysis. The blind tip reconstruction (BTR) method developed by Villarrubia (J Res Natl Inst Stand Technol 102:425, 1997) is an algorithm that estimates tip shape only from AFM images using mathematical morphology operators. While the BTR works perfectly for noise-free AFM images, the algorithm is susceptible to noise. To overcome this issue, we here propose an alternative BTR method, called end-to-end differentiable BTR, based on a modern machine learning approach. In the method, we introduce a loss function including a regularization term to prevent overfitting to noise, and the tip shape is optimized with automatic differentiation and backpropagations developed in deep learning frameworks. Using noisy pseudo-AFM images of myosin V motor domain as test cases, we show that our end-to-end differentiable BTR is robust against noise in AFM images. The method can also detect a double-tip shape and deconvolve doubled molecular images. Finally, application to real HS-AFM data of myosin V walking on an actin filament shows that the method can reconstruct the accurate surface geometry of actomyosin consistent with the structural model. Our method serves as a general post-processing for reconstructing hidden molecular surfaces from any AFM images. Codes are available at https://github.com/matsunagalab/differentiable_BTR .

Combining Biophysical Methods for Structure-Function Analyses of RNA in Solution

RNA-level regulation by riboswitches relies on the specific binding of small metabolites to the aptamer domain to trigger substantial conformational changes that affect transcription or translation. Although several biophysical methods have been employed to study such RNAs, the utility of any one single method is limited. Hybrid approaches, therefore, are essential to better characterize these intrinsically dynamic molecules and elucidate their regulatory mechanisms driven by ligand-induced conformational changes. This chapter outlines procedures for biochemical and biophysical characterization of RNA that employs a combination of solution-based methods: isothermal titration calorimetry (ITC), small-angle X-ray scattering (SAXS), and atomic force microscopy (AFM). Collectively, these tools provide a semi-quantitative assessment of the thermodynamics associated with ligand binding and subsequent conformational changes.

Development of hidden Markov modeling method for molecular orientations and structure estimation from high-speed atomic force microscopy time-series images

High-speed atomic force microscopy (HS-AFM) is a powerful technique for capturing the time-resolved behavior of biomolecules. However, structural information in HS-AFM images is limited to the surface geometry of a sample molecule. Inferring latent three-dimensional structures from the surface geometry is thus important for getting more insights into conformational dynamics of a target biomolecule. Existing methods for estimating the structures are based on the rigid-body fitting of candidate structures to each frame of HS-AFM images. Here, we extend the existing frame-by-frame rigid-body fitting analysis to multiple frames to exploit orientational correlations of a sample molecule between adjacent frames in HS-AFM data due to the interaction with the stage. In the method, we treat HS-AFM data as time-series data, and they are analyzed with the hidden Markov modeling. Using simulated HS-AFM images of the taste receptor type 1 as a test case, the proposed method shows a more robust estimation of molecular orientations than the frame-by-frame analysis. The method is applicable in integrative modeling of conformational dynamics using HS-AFM data.

Recent advances in RNA structurome

RNA structures are essential to support RNA functions and regulation in various biological processes. Recently, a range of novel technologies have been developed to decode genome-wide RNA structures and novel modes of functionality across a wide range of species. In this review, we summarize key strategies for probing the RNA structurome and discuss the pros and cons of representative technologies. In particular, these new technologies have been applied to dissect the structural landscape of the SARS-CoV-2 RNA genome. We also summarize the functionalities of RNA structures discovered in different regulatory layers-including RNA processing, transport, localization, and mRNA translation-across viruses, bacteria, animals, and plants. We review many versatile RNA structural elements in the context of different physiological and pathological processes (e.g., cell differentiation, stress response, and viral replication). Finally, we discuss future prospects for RNA structural studies to map the RNA structurome at higher resolution and at the single-molecule and single-cell level, and to decipher novel modes of RNA structures and functions for innovative applications.

Inferring Conformational State of Myosin Motor in an Atomic Force Microscopy Image via Flexible Fitting Molecular Simulations

High-speed atomic force microscopy (HS-AFM) is a powerful technique to image the structural dynamics of biomolecules. We can obtain atomic-resolution structural information from the measured AFM image by superimposing a structural model on the image. We previously developed a flexible fitting molecular dynamics (MD) simulation method that allows for modest conformational changes when superimposed on an AFM image. In this study, for a molecular motor, myosin V (which changes its chemical state), we examined whether the conformationally distinct state in each HS-AFM image could be inferred via flexible fitting MD simulation. We first built models of myosin V bound to the actin filament in two conformational states, the “down-up” and “down-down” states. Then, for the previously obtained HS-AFM image of myosin bound to the actin filament, we performed flexible-fitting MD simulations using the two states. By comparing the fitting results, we inferred the conformational and chemical states from the AFM image.

Simulation atomic force microscopy for atomic reconstruction of biomolecular structures from resolution-limited experimental images

Atomic force microscopy (AFM) can visualize the dynamics of single biomolecules under near-physiological conditions. However, the scanning tip probes only the molecular surface with limited resolution, missing details required to fully deduce functional mechanisms from imaging alone. To overcome such drawbacks, we developed a computational framework to reconstruct 3D atomistic structures from AFM surface scans, employing simulation AFM and automatized fitting to experimental images. We provide applications to AFM images ranging from single molecular machines, protein filaments, to large-scale assemblies of 2D protein lattices, and demonstrate how the obtained full atomistic information advances the molecular understanding beyond the original topographic AFM image. We show that simulation AFM further allows for quantitative molecular feature assignment within measured AFM topographies. Implementation of the developed methods into the versatile interactive interface of the BioAFMviewer software, freely available at www.bioafmviewer.com, presents the opportunity for the broad Bio-AFM community to employ the enormous amount of existing structural and modeling data to facilitate the interpretation of resolution-limited AFM images.

Highly Reliable Method to Obtain a Correlation Coefficient Unaffected by the SEM Noise Component for Examining the Degree of Specimen Damage due to Electron Beam Irradiation

A correlation coefficient is often used as a measure of the strength of a linear relationship (i.e., the degree of similarity) between two sets of data in a variety of fields. However, in the field of scanning electron microscopy (SEM), it is frequently difficult to properly use the correlation coefficient because SEM images generally include severe noise, which affects the measurement of this coefficient. The current study describes a method of obtaining a correlation coefficient that is unaffected by SEM noise in principle. This correlation coefficient is obtained from a total of four SEM images, comprising two sets of two images with identical views, by calculating several covariance values. Numerical experiments confirm that the measured correlation coefficients obtained using the proposed method for noisy images are equal to those for noise-free images. Furthermore, the present method can be combined with a highly accurate and noise-robust position alignment as needed. As one application, we show that it is possible to immediately examine the degree of specimen damage due to electron beam irradiation during a certain SEM observation, which has been difficult until now.

Reconstruction of Three-Dimensional Conformations of Bacterial ClpB from High-Speed Atomic-Force-Microscopy Images

ClpB belongs to the cellular disaggretase machinery involved in rescuing misfolded or aggregated proteins during heat or other cellular shocks. The function of this protein relies on the interconversion between different conformations in its native condition. A recent high-speed-atomic-force-microscopy (HS-AFM) experiment on ClpB from Thermus thermophilus shows four predominant conformational classes, namely, open, closed, spiral, and half-spiral. Analyses of AFM images provide only partial structural information regarding the molecular surface, and thus computational modeling of three-dimensional (3D) structures of these conformations should help interpret dynamical events related to ClpB functions. In this study, we reconstruct 3D models of ClpB from HS-AFM images in different conformational classes. We have applied our recently developed computational method based on a low-resolution representation of 3D structure using a Gaussian mixture model, combined with a Monte-Carlo sampling algorithm to optimize the agreement with target AFM images. After conformational sampling, we obtained models that reflect conformational variety embedded within the AFM images. From these reconstructed 3D models, we described, in terms of relative domain arrangement, the different types of ClpB oligomeric conformations observed by HS-AFM experiments. In particular, we highlighted the slippage of the monomeric components around the seam. This study demonstrates that such details of information, necessary for annotating the different conformational states involved in the ClpB function, can be obtained by combining HS-AFM images, even with limited resolution, and computational modeling.

Rigid-body fitting to atomic force microscopy images for inferring probe shape and biomolecular structure

Atomic force microscopy (AFM) can visualize functional biomolecules near the physiological condition, but the observed data are limited to the surface height of specimens. Since the AFM images highly depend on the probe tip shape, for successful inference of molecular structures from the measurement, the knowledge of the probe shape is required, but is often missing. Here, we developed a method of the rigid-body fitting to AFM images, which simultaneously finds the shape of the probe tip and the placement of the molecular structure via an exhaustive search. First, we examined four similarity scores via twin-experiments for four test proteins, finding that the cosine similarity score generally worked best, whereas the pixel-RMSD and the correlation coefficient were also useful. We then applied the method to two experimental high-speed-AFM images inferring the probe shape and the molecular placement. The results suggest that the appropriate similarity score can differ between target systems. For an actin filament image, the cosine similarity apparently worked best. For an image of the flagellar protein FlhA_C, we found the correlation coefficient gave better results. This difference may partly be attributed to the flexibility in the target molecule, ignored in the rigid-body fitting. The inferred tip shape and placement results can be further refined by other methods, such as the flexible fitting molecular dynamics simulations. The developed software is publicly available.

Observation of functional dynamics of individual biomolecules is important to understand molecular mechanisms of cellular phenomena. High-speed (HS) atomic force microscopy (AFM) is a powerful tool that enables us to visualize the real-time dynamics of working biomolecules under near-physiological conditions. However, the information available by the AFM images is limited to the two-dimensional surface shape detected via the force to the probe. While the surface information is affected by the shape of the probe tip, the probe shape itself cannot be directly measured before each AFM measurement. To overcome this problem, we have developed a computational method to simultaneously infer the probe tip shape and the molecular placement from an AFM image. We show that our method successfully estimates the effective AFM tip shape and visualizes a structure with a more accurate placement. The estimation of a molecular placement with the correct probe tip shape enables us to obtain more insights into functional dynamics of the molecule from HS-AFM images.

Modeling of DNA binding to the condensin hinge domain using molecular dynamics simulations guided by atomic force microscopy

The condensin protein complex compacts chromatin during mitosis using its DNA-loop extrusion activity. Previous studies proposed scrunching and loop-capture models as molecular mechanisms for the loop extrusion process, both of which assume the binding of double-strand (ds) DNA to the hinge domain formed at the interface of the condensin subunits Smc2 and Smc4. However, how the hinge domain contacts dsDNA has remained unknown. Here, we conducted atomic force microscopy imaging of the budding yeast condensin holo-complex and used this data as basis for coarse-grained molecular dynamics simulations to model the hinge structure in a transient open conformation. We then simulated the dsDNA binding to open and closed hinge conformations, predicting that dsDNA binds to the outside surface when closed and to the outside and inside surfaces when open. Our simulations also suggested that the hinge can close around dsDNA bound to the inside surface. Based on these simulation results, we speculate that the conformational change of the hinge domain might be essential for the dsDNA binding regulation and play roles in condensin-mediated DNA-loop extrusion.

Case Report: Bayesian Statistical Inference of Experimental Parameters via Biomolecular Simulations: Atomic Force Microscopy

The atomic force microscopy (AFM) is a powerful tool for imaging structures of molecules bound on surfaces. To gain high-resolution structural information, one often superimposes structure models on the measured images. Motivated by high flexibility of biomolecules, we previously developed a flexible-fitting molecular dynamics (MD) method that allows protein structural changes upon superimposing. Since the AFM image largely depends on the AFM probe tip geometry, the fitting process requires accurate estimation of the parameters related to the tip geometry. Here, we performed a Bayesian statistical inference to estimate a tip radius of the AFM probe from a given AFM image via flexible-fitting molecular dynamics (MD) simulations. We first sampled conformations of the nucleosome that fit well the reference AFM image by the flexible-fitting with various tip radii. We then estimated an optimal tip parameter by maximizing the conditional probability density of the AFM image produced from the fitted structure.

BioAFMviewer: An interactive interface for simulated AFM scanning of biomolecular structures and dynamics

We provide a stand-alone software, the BioAFMviewer, which transforms biomolecular structures into the graphical representation corresponding to the outcome of atomic force microscopy (AFM) experiments. The AFM graphics is obtained by performing simulated scanning over the molecular structure encoded in the corresponding PDB file. A versatile molecular viewer integrates the visualization of PDB structures and control over their orientation, while synchronized simulated scanning with variable spatial resolution and tip-shape geometry produces the corresponding AFM graphics. We demonstrate the applicability of the BioAFMviewer by comparing simulated AFM graphics to high-speed AFM observations of proteins. The software can furthermore process molecular movies of conformational motions, e.g. those obtained from servers which model functional transitions within a protein, and produce the corresponding simulated AFM movie. The BioAFMviewer software provides the platform to employ the plethora of structural and dynamical data of proteins in order to help in the interpretation of biomolecular AFM experiments.

Nowadays nanotechnology allows to observe single proteins at work. Under atomic force microscopy (AFM), e.g., their surface can be rapidly scanned and functional motions monitored, which is of great importance for applications in all fields of Life science. The analysis and interpretation of experimental results remains however challenging, because the resolution of obtained images or molecular movies is far from perfect. On the other side, high-resolution static structures of most proteins are known and their conformational dynamics can be computed in molecular simulations. This enormous amount of available data offers a great opportunity to better understand the outcome of resolution-limited scanning experiments. Our software provides the computational package towards this goal. The BioAFMviewer computationally emulates the scanning of any biomolecular structure to produce graphical images that mimic the outcome of AFM experiments. This makes the comparison of all available structural data and computational molecular movies to AFM results possible. We demonstrate that simulated AFM images are of great value to facilitate the interpretation of high-speed AFM observations. With its versatile interactive interface and rich functionality, the BioAFMviewer provides a convenient platform for the broad Bio-AFM community to better understand experiments.

Resolving the data asynchronicity in high-speed atomic force microscopy measurement via the Kalman Smoother

High-speed atomic force microscopy (HS-AFM) is a scanning probe microscopy that can capture structural dynamics of biomolecules in real time at single molecule level near physiological condition. Albeit much improvement, while scanning one frame of HS-AFM movies, biomolecules often change their conformations largely. Thus, the obtained frame images can be hampered by the time-difference, the asynchronicity, in the data acquisition. Here, to resolve this data asynchronicity in the HS-AFM movie, we developed Kalman filter and smoother methods, some of the sequential Bayesian filtering approaches. The Kalman filter/smoother methods use alternative steps of a short time-propagation by a linear dynamical system and a correction by the likelihood of AFM data acquired pixel by pixel. We first tested the method using a toy model of a diffusing cone, showing that the Kalman smoother method outperforms to reproduce the ground-truth movie. We then applied the Kalman smoother to a synthetic movie for conformational change dynamics of a motor protein, i.e., dynein, confirming the superiority of the Kalman smoother. Finally, we applied the Kalman smoother to two real HS-AFM movies, FlhA_C and centralspindlin, reducing distortion and noise in the AFM movies. The method is general and can be applied to any HS-AFM movies.

The molecular structure of long non-coding RNAs: emerging patterns and functional implications

Long non-coding RNAs (lncRNAs) are recently-discovered transcripts that regulate vital cellular processes and are crucially connected to diseases. Despite their unprecedented molecular complexity, it is emerging that lncRNAs possess distinct structural motifs. Remarkably, the 3D shape and topology of full-length, native lncRNAs have been visualized for the first time in the last year. These studies reveal that lncRNA structures dictate lncRNA functions. Here, we review experimentally determined lncRNA structures and emphasize that lncRNA structural characterization requires synergistic integration of computational, biochemical and biophysical approaches. Based on these emerging paradigms, we discuss how to overcome the challenges posed by the complex molecular architecture of lncRNAs, with the goal of obtaining a detailed understanding of lncRNA functions and molecular mechanisms in the future.

Particle Filter Method to Integrate High-Speed Atomic Force Microscopy Measurements with Biomolecular Simulations

High-speed atomic force microscopy (HS-AFM) can be used to observe the structural dynamics of biomolecules at the single-molecule level in real time under near-physiological conditions; however, its spatiotemporal resolution is limited. Complementarily, molecular dynamics (MD) simulations have higher spatiotemporal resolutions, albeit with some artifacts. Here, to integrate HS-AFM data and coarse-grained molecular dynamics (CG-MD) simulations, we develop a particle filter method that implements a sequential Bayesian data assimilation approach. We test the method in a twin experiment. First, we generate a reference HS-AFM movie from the CG-MD trajectory of a test molecule, a nucleosome; this serves as the "experimental measurement". Then, we perform a particle filter simulation with 512 particles, which captures the large-scale nucleosome structural dynamics compatible with the AFM movie. Comparing particle filter simulations with 8-8192 particles, we find that using greater numbers of particles consistently increases the likelihood of the whole AFM movie. By comparing the likelihoods for different ionic concentrations and time scale mappings, we find that the "true" concentration and time scale mapping can be inferred as the largest likelihood of the whole AFM movie but not that of each AFM image. The particle filter method provides a general approach for integrating HS-AFM data with MD simulations.

Visualizing the functional 3D shape and topography of long noncoding RNAs by single-particle atomic force microscopy and in-solution hydrodynamic techniques

Long noncoding RNAs (lncRNAs) are recently discovered transcripts that regulate vital cellular processes, such as cellular differentiation and DNA replication, and are crucially connected to diseases. Although the 3D structures of lncRNAs are key determinants of their function, the unprecedented molecular complexity of lncRNAs has so far precluded their 3D structural characterization at high resolution. It is thus paramount to develop novel approaches for biochemical and biophysical characterization of these challenging targets. Here, we present a protocol that integrates non-denaturing lncRNA purification with in-solution hydrodynamic analysis and single-particle atomic force microscopy (AFM) imaging to produce highly homogeneous lncRNA preparations and visualize their 3D topology at ~15-Å resolution. Our protocol is suitable for imaging lncRNAs in biologically active conformations and for measuring structural defects of functionally inactive mutants that have been identified by cell-based functional assays. Once optimized for the specific target lncRNA of choice, our protocol leads from cloning to AFM imaging within 3-4 weeks and can be implemented using state-of-the-art biochemical and biophysical instrumentation by trained researchers familiar with RNA handling and supported by AFM and small-angle X-ray scattering (SAXS) experts.