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

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.

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.

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.

Recombinant protein linker production as a basis for non-invasive determination of single-cell yeast age in heterogeneous yeast populations

The physiological and metabolic diversity of a yeast culture is the sum of individual cell phenotypes. As well as environmental conditions, genetics, and numbers of cell divisions, a major factor influencing cell characteristics is cell age. A postcytokinesis bud scar on the mother cell, a benchmark in the replicative life span, is a quantifiable indicator of cell age, characterized by significant amounts of chitin. We developed a binding process for visualizing the bud scars of Saccharomyces pastorianus var. carlsbergensis using a protein linker containing a polyhistidine tag, a superfolder green fluorescent protein (sfGFP), and a chitin-binding domain (His6-SUMO-sfGFP-ChBD). The binding did not affect yeast viability; thus, our method provides the basis for non-invasive cell age determination using flow cytometry. The His6-SUMO-sfGFP-ChBD protein was synthesized in Escherichia coli, purified using two-stage chromatography, and checked for monodispersity and purity. Linker-cell binding and the characteristics of the bound complex were determined using flow cytometry and confocal laser scanning microscopy (CLSM). Flow cytometry showed that protein binding increased to 60 455 ± 2706 fluorescence units per cell. The specific coupling of the linker to yeast cells was additionally verified by CLSM and adsorption isotherms using yeast cells, E. coli cells, and chitin resin. We found a relationship between the median bud scar number, the median of the fluorescence units, and the chitin content of yeast cells. A fast measurement of yeast population dynamics by flow cytometry is possible, using this protein binding technique. Rapid qualitative determination of yeast cell age distribution can therefore be performed.

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.