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

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.

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.

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.

Weight average approaches for predicting dynamical properties of biomolecules

Recent advances in atomistic molecular dynamics (MD) simulations of biomolecules allow us to explore their conformational spaces widely, observing large-scale conformational fluctuations or transitions between distinct structures. To reproduce or refine experimental data using MD simulations, structure ensembles, which are characterized by multiple structures and their statistical weights on the rugged free-energy landscapes, are often used. Here, we summarize weight average approaches for various experimental measurements. Weight average approaches are now applied to hybrid quantum mechanics/molecular mechanics MD simulations to predict fast vibrational motions in a protein with a high accuracy for better understanding of molecular functions from atomic structures.

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.

Combining Experimental Data and Computational Methods for the Non-Computer Specialist

Experimental methods are indispensable for the study of the function of biological macromolecules, not just as static structures, but as dynamic systems that change conformation, bind partners, perform reactions, and respond to different stimulus. However, providing a detailed structural interpretation of the results is often a very challenging task. While experimental and computational methods are often considered as two different and separate approaches, the power and utility of combining both is undeniable. The integration of the experimental data with computational techniques can assist and enrich the interpretation, providing new detailed molecular understanding of the systems. Here, we briefly describe the basic principles of how experimental data can be combined with computational methods to obtain insights into the molecular mechanism and expand the interpretation through the generation of detailed models.