Representation of Protein Dynamics Disentangled by Time-Structure-Based Prior.

Representation learning (RL) is a universal technique for deriving low-dimensional disentangled representations from high-dimensional observations, aiding in a multitude of downstream tasks. RL has been extensively applied to various data types, including images and natural language. Here, we analyze molecular dynamics (MD) simulation data of biomolecules in terms of RL. Currently, state-of-the-art RL techniques, mainly motivated by the variational principle, try to capture slow motions in the representation (latent) space. Here, we propose two methods based on an alternative perspective on the disentanglement in the latent space. By disentanglement, we here mean the separation of underlying factors in the simulation data, aiding in detecting physically important coordinates for conformational transitions. The proposed methods introduce a simple prior that imposes temporal constraints in the latent space, serving as a regularization term to facilitate the capture of disentangled representations of dynamics. Comparison with other methods via the analysis of MD simulation trajectories for alanine dipeptide and chignolin validates that the proposed methods construct Markov state models (MSMs) whose implied time scales are comparable to those of the state-of-the-art methods. Using a measure based on total variation, we quantitatively evaluated that the proposed methods successfully disentangle physically important coordinates, aiding the interpretation of folding/unfolding transitions of chignolin. Overall, our methods provide good representations of complex biomolecular dynamics for downstream tasks, allowing for better interpretations of the conformational transitions.

Evaluation for Ion Heating of H2A-H2B Dimer in Ion Mobility Spectrometry-Mass Spectrometry.

Ion mobility spectrometry-mass spectrometry (IMS-MS) provides m/z values and collision cross sections (CCSs) of gas-phase ions. In our previous study, an intrinsically disordered protein, the H2A-H2B dimer, was analyzed using IMS-MS, resulting in two conformational populations of CCS. Based on experimental and theoretical approaches, this resulted from a structural diversity of intrinsically disordered regions. We predicted that this phenomenon is related to ion heating in the IMS-MS instrument. In this study, to reveal the effect of ion heating from parameters in the IMS-MS instrument on the conformational population of the H2A-H2B dimer, we investigated the arrival time distributions of the H2A-H2B dimer by changing values of three instrumental parameters, namely, cone voltage located in the first vacuum chamber, trap collision energy (trap CE) for tandem mass spectrometry, and trap bias voltage for the entrance of IMS. These results revealed that the two populations observed for the H2A-H2B dimer were due to the trap bias voltage. Furthermore, to evaluate the internal energies of the analyte ions with respect to each parameter, benzylpyridinium derivatives were used as temperature-sensitive probes. The results showed that the trap CE voltage imparts greater internal energy to the ions than the trap bias voltage. In addition, this slight change in the internal energy caused by the trap bias voltage resulted in the structural diversity of the H2A-H2B dimer. Therefore, the trap bias voltage should be set with attention to the properties of the analytes, even if the effect of the trap bias voltage on the internal energy is negligible.

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.

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 .

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.

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.

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.

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

High-speed (HS) atomic force microscopy (AFM) is a prominent imaging technology that observes large-scale structural dynamics of biomolecules near the physiological condition, but the AFM data are limited to the surface shape of specimens. Rigid-body fitting methods were developed to obtain molecular structures that fit to an AFM image, without accounting for conformational changes. Here, we developed a method to fit flexibly a three-dimensional (3D) biomolecular structure into an AFM image. First, we describe a method to produce a pseudo-AFM image from a given 3D structure in a differentiable form. Then, using a correlation function between the experimental AFM image and the computational pseudo-AFM image, we developed a flexible fitting molecular dynamics (MD) simulation method by which we obtain protein structures that well fit to the given AFM image. We first test it with a twin experiment; using an AFM image produced from a protein structure different from its native conformation as a reference, we performed the flexible fitting MD simulations to sample conformations that fit well the reference AFM image, and the method was confirmed to work well. Then, parameter dependence in the protocol was discussed. Finally, we applied the method to a real experimental HS-AFM image for a flagellar protein FlhA, demonstrating its applicability. We also test the rigid-body fitting of a molecular structure to an AFM image. Our method will be a general tool for dynamic structure modeling based on HS-AFM images and is publicly available through the CafeMol software.

Cooperative DNA Binding of the Plasmid Partitioning Protein TubR from the Bacillus cereus pXO1 Plasmid.

Tubulin/FtsZ-like GTPase TubZ is responsible for maintaining the stability of pXO1-like plasmids in virulent Bacilli. TubZ forms a filament in a GTP-dependent manner, and like other partitioning systems of low-copy-number plasmids, it requires the centromere-binding protein TubR that connects the plasmid to the TubZ filament. Systems regulating TubZ partitioning have been identified in Clostridium prophages as well as virulent Bacillus species, in which TubZ facilitates partitioning by binding and towing the segrosome: the nucleoprotein complex composed of TubR and the centromere. However, the molecular mechanisms of segrosome assembly and the transient on-off interactions between the segrosome and the TubZ filament remain poorly understood. Here, we determined the crystal structure of TubR from Bacillus cereus at 2.0-Å resolution and investigated the DNA-binding ability of TubR using hydroxyl radical footprinting and electrophoretic mobility shift assays. The TubR dimer possesses 2-fold symmetry and binds to a 15-bp palindromic consensus sequence in the tubRZ promoter region. Continuous TubR-binding sites overlap each other, which enables efficient binding of TubR in a cooperative manner. Interestingly, the segrosome adopts an extended DNA-protein filament structure and likely gains conformational flexibility by introducing non-consensus residues into the palindromes in an asymmetric manner. Together, our experimental results and structural model indicate that the unique centromere recognition mechanism of TubR allows transient complex formation between the segrosome and the dynamic polymer of TubZ.

Structural Diversity of Nucleosomes Characterized by Native Mass Spectrometry.

Histone tails, which protrude from nucleosome core particles (NCPs), play crucial roles in the regulation of DNA transcription, replication, and repair. In this study, structural diversity of nucleosomes was investigated in detail by analyzing the observed charge states of nucleosomes reconstituted with various lengths of DNA using positive-mode electrospray ionization mass spectrometry (ESI-MS) and molecular dynamics (MD) simulation. Here, we show that canonical NCPs, having 147 bp DNA closely wrapped around a histone octamer, can be classified into three groups by charge state, with the least-charged group being more populated than the highly charged and intermediate groups. Ions with low charge showed small collision cross sections (CCSs), suggesting that the histone tails are generally compact in the gas phase, whereas the minor populations with higher charges appeared to have more loosened structure. Overlapping dinucleosomes, which contain 14 histone proteins closely packed with 250 bp DNA, showed similar characteristics. In contrast, mononucleosomes reconstituted with a histone octamer and longer DNA (≥250 bp), which have DNA regions uninvolved in the core-structure formation, showed only low-charge ions. This was also true for dinucleosomes with free DNA regions. These results suggest that free DNA regions affect the nucleosome structures. To investigate the possible structures of NCP observed in ESI-MS, computational structural calculations in solution and in vacuo were performed. They suggested that conformers with large CCS values have slightly loosened structure with extended tail regions, which might relate to the biological function of histone tails.

CLASP2 Has Two Distinct TOG Domains That Contribute Differently to Microtubule Dynamics.

CLIP-associated proteins CLASPs are mammalian microtubule (MT) plus-end tracking proteins (+TIPs) that promote MT rescue in vivo. Their plus-end localization is dependent on other +TIPs, EB1 and CLIP-170, but in the leading edge of the cell, CLASPs display lattice-binding activity. MT association of CLASPs is suggested to be regulated by multiple TOG (tumor overexpressed gene) domains and by the serine-arginine (SR)-rich region, which contains binding sites for EB1. Here, we report the crystal structures of the two TOG domains of CLASP2. Both domains consist of six HEAT repeats, which are similar to the canonical paddle-like tubulin-binding TOG domains, but have arched conformations. The degrees and directions of curvature are different between the two TOG domains, implying that they have distinct roles in MT binding. Using biochemical, molecular modeling and cell biological analyses, we have investigated the interactions between the TOG domains and αß-tubulin and found that each domain associates differently with αß-tubulin. Our findings suggest that, by varying the degrees of domain curvature, the TOG domains may distinguish the structural conformation of the tubulin dimer, discriminate between different states of MT dynamic instability and thereby function differentially as stabilizers of MTs.

Mass spectrometric approach for characterizing the disordered tail regions of the histone H2A/H2B dimer.

The histone H2A/H2B dimer is a component of nucleosome core particles (NCPs). The structure of the dimer at the atomic level has not yet been revealed. A possible reason for this is that the dimer has three intrinsically disordered tail regions: the N- and C-termini of H2A and the N-terminus of H2B. To investigate the role of the tail regions of the H2A/H2B dimer structure, we characterized behaviors of the H2A/H2B mutant dimers, in which these functionally important disordered regions were depleted, using mass spectrometry (MS). After verifying that the acetylation of Lys residues in the tail regions had little effect on the gas-phase conformations of the wild-type dimer, we prepared two histone H2A/H2B dimer mutants: an H2A/H2B dimer depleted of both N-termini (dN-H2A/dN-H2B) and a dimer with the N- and C-termini of H2A and the N-terminus of H2B depleted (dNC-H2A/dN-H2B). We analyzed these mutants using ion mobility-mass spectrometry (IM-MS) and hydrogen/deuterium exchange mass spectrometry (HDX-MS). With IM-MS, reduced structural diversity was observed for each of the tail-truncated H2A/H2B mutants. In addition, global HDX-MS proved that the dimer mutant dNC-H2A/dN-H2B was susceptible to deuteration, suggesting that its structure in solution was somewhat loosened. A partial relaxation of the mutant's structure was demonstrated also by IM-MS. In this study, we characterized the relationship between the tail lengths and the conformations of the H2A/H2B dimer in solution and gas phases, and demonstrated, using mass spectrometry, that disordered tail regions play an important role in stabilizing the conformation of the core region of the dimer in both phases.

Slow dynamics of a protein backbone in molecular dynamics simulation revealed by time-structure based independent component analysis.

We recently proposed the method of time-structure based independent component analysis (tICA) to examine the slow dynamics involved in conformational fluctuations of a protein as estimated by molecular dynamics (MD) simulation [Y. Naritomi and S. Fuchigami, J. Chem. Phys. 134, 065101 (2011)]. Our previous study focused on domain motions of the protein and examined its dynamics by using rigid-body domain analysis and tICA. However, the protein changes its conformation not only through domain motions but also by various types of motions involving its backbone and side chains. Some of these motions might occur on a slow time scale: we hypothesize that if so, we could effectively detect and characterize them using tICA. In the present study, we investigated slow dynamics of the protein backbone using MD simulation and tICA. The selected target protein was lysine-, arginine-, ornithine-binding protein (LAO), which comprises two domains and undergoes large domain motions. MD simulation of LAO in explicit water was performed for 1 µs, and the obtained trajectory of C(α) atoms in the backbone was analyzed by tICA. This analysis successfully provided us with slow modes for LAO that represented either domain motions or local movements of the backbone. Further analysis elucidated the atomic details of the suggested local motions and confirmed that these motions truly occurred on the expected slow time scale.

Gas-phase structure of the histone multimers characterized by ion mobility mass spectrometry and molecular dynamics simulation.

The minimum structural unit of chromatin is the nucleosome core particle (NCP), consisting of 146 bp of DNA wrapped around a histone octamer, which itself contains two H2A/H2B dimers and one (H3/H4)2 tetramer. These multimers possess functionally important tail regions that are intrinsically disordered. In order to elucidate the mechanisms behind NCP assembly and disassembly processes, which are highly related to gene expression, structural characterization of the H2A/H2B dimer and (H3/H4)2 tetramer will be of importance. In the present study, human histone multimers with disordered tail regions were characterized by electrospray ionization (ESI) ion mobility-mass spectrometry (IM-MS) and molecular dynamics (MD) simulation. Experimentally obtained arrival times of these histone multimer ions showed rather wide distributions, implying that multiple conformers exist for each histone multimer in the gas phase. To examine their structures, MD simulations of the histone multimers were performed first in solution and then in vacuo at four temperatures, resulting in a variety of histone multimer structures. Theoretical collision cross-section (CCS) values calculated for the simulated structures revealed that structural models with smaller CCS values had more compact tail regions than those with larger CCS values. This implied that variation of the CCS values of the histone multimers were primarily due to the random behaviors of the tail regions in the gas phase. The combination of IM-MS and MD simulation enabled clear and comprehensive characterization of the gas-phase structures of histone multimers containing disordered tails.

Classification and annotation of the relationship between protein structural change and ligand binding.

The causal relationship between protein structural change and ligand binding was classified and annotated for 839 nonredundant pairs of crystal structures in the Protein Data Bank-one with and the other without a bound low-molecular-weight ligand molecule. Protein structural changes were first classified into either domain or local motions depending on the size of the moving protein segments. Whether the protein motion was coupled with ligand binding was then evaluated based on the location of the ligand binding site and by application of the linear response theory of protein structural change. Protein motions coupled with ligand binding were further classified into either closure or opening motions. This classification revealed the following: (i) domain motions coupled with ligand binding are dominated by closure motions, which can be described by the linear response theory; (ii) local motions frequently accompany order-disorder or α-helix-coil conformational transitions; and (iii) transferase activity (Enzyme Commission number 2) is the predominant function among coupled domain closure motions. This could be explained by the closure motion acting to insulate the reaction site of these enzymes from environmental water.

Slow dynamics in protein fluctuations revealed by time-structure based independent component analysis: the case of domain motions.

Protein dynamics on a long time scale was investigated using all-atom molecular dynamics (MD) simulation and time-structure based independent component analysis (tICA). We selected the lysine-, arginine-, ornithine-binding protein (LAO) as a target protein and focused on its domain motions in the open state. A MD simulation of the LAO in explicit water was performed for 600 ns, in which slow and large-amplitude domain motions of the LAO were observed. After extracting domain motions by rigid-body domain analysis, the tICA was applied to the obtained rigid-body trajectory, yielding slow modes of the LAO's domain motions in order of decreasing time scale. The slowest mode detected by the tICA represented not a closure motion described by a largest-amplitude mode determined by the principal component analysis but a twist motion with a time scale of tens of nanoseconds. The slow dynamics of the LAO were well described by only the slowest mode and were characterized by transitions between two basins. The results show that tICA is promising for describing and analyzing slow dynamics of proteins.

Latent dynamics of a protein molecule observed in dihedral angle space.

Dihedral angles are alternative set of variables to Cartesian coordinates for representing protein dynamics. The two sets of variables exhibit extremely different behavior. Motions in dihedral angle space are characterized by latent dynamics, in which motion induced in each dihedral angle is always compensated for by motions of many other dihedral angles, in order to maintain a rigid globular shape. Using molecular dynamics simulations, we propose a molecular mechanism for the latent dynamics in dihedral angle space. It was found that, due to the unique structure of dihedral principal components originating in the globular shape of the protein, the dihedral principal components with large (small) amplitudes are highly correlated with the eigenvectors of the metric matrix with small (large) eigenvalues. Such an anticorrelation in the eigenmode structures minimizes the mean square displacement of Cartesian coordinates upon rotation of dihedral angles. In contrast, a short peptide, deca-alanine in this study, does not show such behavior of the latent dynamics in the dihedral principal components, but shows similar behaviors to those of the Cartesian principal components, due to the absence of constraints to maintain a rigid globular shape.

Normal mode analysis of protein dynamics in a non-Eckart frame.

Normal mode analysis, with the all-atom or coarse-grained elastic network model, represents the equilibrium fluctuation of protein molecule in the Eckart frame, where contributions from external motions (translation and rotation) of the entire protein molecule are eliminated. On the other hand, domain motion is frequently exhibited by the relative motion of one domain to the other. Such a representation of fluctuations in the non-Eckart frame cannot be achieved by conventional normal mode analysis. Here, we propose normal mode analysis in a non-Eckart frame, where the external degrees of freedom are fixed for any portion of the system. In this analysis, the covariance matrix in the Eckart frame is transformed into one in the non-Eckart frame. Using a molecular dynamics simulation, we have confirmed the validity of the transformation formula and discussed the physical implication of the formula.

Molecular modeling of the HAMP domain of sensory rhodopsin II transducer from Natronomonas pharaonis.

The halobacterial transducer of sensory rhodopsin II (HtrII) is a photosignal transducer associated with phototaxis in extreme halophiles. The HAMP domain, a linker domain in HtrII, is considered to play an important role in transferring the signal from the membrane to the cytoplasmic region, although its structure in the complex remains undetermined. To establish the structural basis for understanding the mechanism of signal transduction, we present an atomic model of the structure of the N-terminal HAMP domain from Natronomonas pharaonis (HtrII: 84-136), based on molecular dynamics (MD) simulations. The model was built by homology modeling using the NMR structure of Af1503 from Archaeoglobus fulgidus as a template. The HAMP domains of Af1503 and HtrII were stable during MD simulations over 100 ns. Quantitative analyses of inter-helical packing indicated that the Af1503 HAMP domain stably maintained unusual knobs-to-knobs packing, as observed in the NMR structure, while the bulky side-chains of HtrII shifted the packing state to canonical knobs-into-holes. The role of the connector loop in maintaining structural stability was also discussed using MD simulations of loop deletion mutants.

Multivariate frequency domain analysis of protein dynamics.

Multivariate frequency domain analysis (MFDA) is proposed to characterize collective vibrational dynamics of protein obtained by a molecular dynamics (MD) simulation. MFDA performs principal component analysis (PCA) for a bandpass filtered multivariate time series using the multitaper method of spectral estimation. By applying MFDA to MD trajectories of bovine pancreatic trypsin inhibitor, we determined the collective vibrational modes in the frequency domain, which were identified by their vibrational frequencies and eigenvectors. At near zero temperature, the vibrational modes determined by MFDA agreed well with those calculated by normal mode analysis. At 300 K, the vibrational modes exhibited characteristic features that were considerably different from the principal modes of the static distribution given by the standard PCA. The influences of aqueous environments were discussed based on two different sets of vibrational modes, one derived from a MD simulation in water and the other from a simulation in vacuum. Using the varimax rotation, an algorithm of the multivariate statistical analysis, the representative orthogonal set of eigenmodes was determined at each vibrational frequency.