Reconstruction of low-resolution molecular structures from simulated atomic force microscopy images

Analyzing atomic force microscopy images of virus-like particles by expectation-maximization

Analysis of virus-like particles (VLPs) is an essential task in optimizing their implementation as vaccine antigens for virus-initiated diseases. Interrogating VLP collections for elasticity by probing with a rigid atomic force microscopy (AFM) tip is a potential method for determining VLP morphological changes. During VLP morphological change, it is not expected that all VLPs would be in the same state. This leads to the open question of whether VLPs may change in a continuous or stepwise fashion. For continuous change, the statistical distribution of observed VLP properties would be expected as a single distribution, while stepwise change would lead to a multimodal distribution of properties. This study presents the application of a Gaussian mixture model (GMM), fit by the Expectation-Maximization (EM) algorithm, to identify different states of VLP morphological change observed by AFM imaging.

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.

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 .

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.

A hybrid approach to study large conformational transitions of biomolecules from single particle XFEL diffraction data

X-ray free-electron laser (XFEL) is the latest generation of the X-ray source that could become an invaluable technique in structural biology. XFEL has ultrashort pulse duration, extreme peak brilliance, and high spatial coherence, which could enable the observation of the biological molecules in near nature state at room temperature without crystallization. However, for biological systems, due to their low diffraction power and complexity of sample delivery, experiments and data analysis are not straightforward, making it extremely challenging to reconstruct three-dimensional (3D) structures from single particle XFEL data. Given the current limitations to the amount and resolution of the data from such XFEL experiments, we propose a new hybrid approach for characterizing biomolecular conformational transitions by using a single 2D low-resolution XFEL diffraction pattern in combination with another known conformation. In our method, we represent the molecular structure with a coarse-grained model, the Gaussian mixture model, to describe large conformational transitions from low-resolution XFEL data. We obtain plausible 3D structural models that are consistent with the XFEL diffraction pattern by deforming an initial structural model to maximize the similarity between the target pattern and the simulated diffraction patterns from the candidate models. We tested the proposed algorithm on two biomolecules of different sizes with different complexities of conformational transitions, adenylate kinase, and elongation factor 2, using synthetic XFEL data. The results show that, with the proposed algorithm, we can successfully describe the conformational transitions by flexibly fitting the coarse-grained model of one conformation to become consistent with an XFEL diffraction pattern simulated from another conformation. In addition, we showed that the incident beam orientation has some effect on the accuracy of the 3D structure modeling and discussed the reasons for the inaccuracies for certain orientations. The proposed method could serve as an alternative approach for retrieving information on 3D conformational transitions from the XFEL diffraction patterns to interpret experimental data. Since the molecules are represented by Gaussian kernels and no atomic structure is needed in principle, such a method could also be used as a tool to seek initial models for 3D reconstruction algorithms.

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.

Biological and methodological complexities of beta-amyloid peptide: Implications for Alzheimer's disease research

Although controversial, the amyloid cascade hypothesis remains central to the Alzheimer's disease (AD) field and posits amyloid-beta (Aβ) as the central factor initiating disease onset. In recent years, there has been an increase in emphasis on studying the role of low molecular weight aggregates, such as oligomers, which are suggested to be more neurotoxic than fibrillary Aβ. Other Aβ isoforms, such as truncated Aβ, have also been implicated in disease. However, developing a clear understanding of AD pathogenesis has been hampered by the complexity of Aβ biochemistry in vitro and in vivo. This review explores factors contributing to the lack of consistency in experimental approaches taken to model Aβ aggregation and toxicity and provides an overview of the different techniques available to analyse Aβ, such as electron and atomic force microscopy, nuclear magnetic resonance spectroscopy, dye-based assays, size exclusion chromatography, mass spectrometry and SDS-PAGE. The review also explores how different types of Aβ can influence Aβ aggregation and toxicity, leading to variation in experimental outcomes, further highlighting the need for standardisation in Aβ preparations and methods used in current research.

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.

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.

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.