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.

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.

Construction of a Humanized Artificial VHH Library Reproducing Structural Features of Camelid VHHs for Therapeutics.

A variable domain of heavy chain antibody (VHH) has different binding properties than conventional antibodies. Conventional antibodies prefer binding to the convex portion of the antigen, whereas VHHs prefer epitopes, such as crevices and clefts on the antigen. Therefore, developing candidates with the binding characteristics of camelid VHHs is important. Thus, To this end, a synthetic VHH library that reproduces the structural properties of camelid VHHs was constructed. First, the characteristics of VHHs were classified according to the paratope formation based on crystal structure analyses of the complex structures of VHHs and antigens. Then, we classified 330 complementarity-determining region 3 (CDR3) structures of VHHs from the Protein Data Bank (PDB) into three loop structures: Upright, Half-Roll, and Roll. Moreover, these structures depended on the number of amino acid residues within CDR3. Furthermore, in the Upright loops, several amino acid residues in the FR2 are involved in the paratope formation, along with CDR3, suggesting that the FR2 design in the synthetic library is important. A humanized synthetic VHH library, comprising two sub-libraries, Upright and Roll, was constructed and named PharmaLogical. A validation study confirmed that our PharmaLogical library reproduces VHHs with the characteristics of the paratope formation of the camelid VHHs, and shows good performance in VHH screening.

Use of multistate Bennett acceptance ratio method for free-energy calculations from enhanced sampling and free-energy perturbation.

Multistate Bennett acceptance ratio (MBAR) works as a method to analyze molecular dynamics (MD) simulation data after the simulations have been finished. It is widely used to estimate free-energy changes between different states and averaged properties at the states of interest. MBAR allows us to treat a wide range of states from those at different temperature/pressure to those with different model parameters. Due to the broad applicability, the MBAR equations are rather difficult to apply for free-energy calculations using different types of MD simulations including enhanced conformational sampling methods and free-energy perturbation. In this review, we first summarize the basic theory of the MBAR equations and categorize the representative usages into the following four: (i) perturbation, (ii) scaling, (iii) accumulation, and (iv) full potential energy. For each, we explain how to prepare input data using MD simulation trajectories for solving the MBAR equations. MBAR is also useful to estimate reliable free-energy differences using MD trajectories based on a semi-empirical quantum mechanics/molecular mechanics (QM/MM) model and ab initio QM/MM energy calculations on the MD snapshots. We also explain how to use the MBAR software in the GENESIS package, which we call mbar_analysis, for the four representative cases. The proposed estimations of free-energy changes and thermodynamic averages are effective and useful for various biomolecular systems.

Enhanced Conformational Sampling of Nanobody CDR H3 Loop by Generalized Replica-Exchange with Solute Tempering.

The variable domains of heavy-chain antibodies, known as nanobodies, are potential substitutes for IgG antibodies. They have similar affinities to antigens as antibodies, but are more heat resistant. Their small size allows us to exploit computational approaches for structural modeling or design. Here, we investigate the applicability of an enhanced sampling method, a generalized replica-exchange with solute tempering (gREST) for sampling CDR-H3 loop structures of nanobodies. In the conventional replica-exchange methods, temperatures of only a whole system or scaling parameters of a solute molecule are selected for temperature or parameter exchange. In gREST, we can flexibly select a part of a solute molecule and a part of the potential energy terms as a parameter exchange region. We selected the CDR-H3 loop and investigated which potential energy term should be selected for the efficient sampling of the loop structures. We found that the gREST with dihedral terms can explore a global conformational space, but the relaxation to the global equilibrium is slow. On the other hand, gREST with all the potential energy terms can sample the equilibrium distribution, but the structural exploration is slower than with dihedral terms. The lessons learned from this study can be applied to future studies of loop modeling.

Structural and energetic analysis of metastable intermediate states in the E1P-E2P transition of Ca2+-ATPase.

Sarcoplasmic reticulum (SR) Ca2+-ATPase transports two Ca2+ ions from the cytoplasm to the SR lumen against a large concentration gradient. X-ray crystallography has revealed the atomic structures of the protein before and after the dissociation of Ca2+, while biochemical studies have suggested the existence of intermediate states in the transition between E1P⋅ADP⋅2Ca2+ and E2P. Here, we explore the pathway and free energy profile of the transition using atomistic molecular dynamics simulations with the mean-force string method and umbrella sampling. The simulations suggest that a series of structural changes accompany the ordered dissociation of ADP, the A-domain rotation, and the rearrangement of the transmembrane (TM) helices. The luminal gate then opens to release Ca2+ ions toward the SR lumen. Intermediate structures on the pathway are stabilized by transient sidechain interactions between the A- and P-domains. Lipid molecules between TM helices play a key role in the stabilization. Free energy profiles of the transition assuming different protonation states suggest rapid exchanges between Ca2+ ions and protons when the Ca2+ ions are released toward the SR lumen.

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 FlhAC, 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.

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins.

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

Use of single-molecule time-series data for refining conformational dynamics in molecular simulations.

Atomically detailed description of conformational dynamics in biomolecules is often essential to understand biological functions. Combining experimental measurements with molecular simulations significantly improves the outcome. Ensemble refinements, where the simulations are utilized to refine ensemble averaged data in NMR, SAXS, or cryo-EM, are a popular approach in integrative structural biology. Single-molecule time-series data contain rich temporal information of biomolecular dynamics. However, direct usage of the time-series data together with molecular simulations is just beginning. Here, we review data-assimilation approaches linking molecular simulations with experimental time-series data and discuss current limitations and potential applications of this approach in integrative structural biology.

Building a macro-mixing dual-basin Go model using the Multistate Bennett Acceptance Ratio.

The dual-basin Go-model is a structural-based coarsegrained model for simulating a conformational transition between two known structures of a protein. Two parameters are required to produce a dual-basin potential mixed using two single-basin potentials, although the determination of mixing parameters is usually not straightforward. Here, we have developed an efficient scheme to determine the mixing parameters using the Multistate Bennett Acceptance Ratio (MBAR) method after short simulations with a set of parameters. In the scheme, MBAR allows us to predict observables at various unsimulated conditions, which are useful to improve the mixing parameters in the next round of iterative simulations. The number of iterations that are necessary for obtaining the converged mixing parameters are significantly reduced in the scheme. We applied the scheme to two proteins, the glutamine binding protein and the ribose binding protein, for showing the effectiveness in the parameter determination. After obtaining the converged parameters, both proteins show frequent conformational transitions between open and closed states, providing the theoretical basis to investigate structure-dynamics-function relationships of the proteins.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions.

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Linking time-series of single-molecule experiments with molecular dynamics simulations by machine learning.

Single-molecule experiments and molecular dynamics (MD) simulations are indispensable tools for investigating protein conformational dynamics. The former provide time-series data, such as donor-acceptor distances, whereas the latter give atomistic information, although this information is often biased by model parameters. Here, we devise a machine-learning method to combine the complementary information from the two approaches and construct a consistent model of conformational dynamics. It is applied to the folding dynamics of the formin-binding protein WW domain. MD simulations over 400 µs led to an initial Markov state model (MSM), which was then "refined" using single-molecule Förster resonance energy transfer (FRET) data through hidden Markov modeling. The refined or data-assimilated MSM reproduces the FRET data and features hairpin one in the transition-state ensemble, consistent with mutation experiments. The folding pathway in the data-assimilated MSM suggests interplay between hydrophobic contacts and turn formation. Our method provides a general framework for investigating conformational transitions in other proteins.

Energetics and conformational pathways of functional rotation in the multidrug transporter AcrB.

The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive. Here, calculating the minimum free energy pathway of the functional rotation for the complete AcrB trimer, we describe the structural and energetic basis behind the coupling between the functional rotation and the proton translocation at atomic resolution. Free energy calculations show that protonation of Asp408 in the transmembrane portion of the drug-bound protomer drives the functional rotation. The conformational pathway identifies vertical shear motions among several transmembrane helices, which regulate alternate access of water in the transmembrane as well as peristaltic motions that pump drugs in the periplasm.

Tumor invasion to the arteries feeding the gallbladder as a novel risk factor for cholecystitis after metallic stent placement in distal malignant biliary obstruction.

BACKGROUND AND AIM: Cholecystitis is a major complication after self-expandable metallic stent (SEMS) placement for malignant biliary obstruction. Ischemia is one of the risk factors for cholecystitis, but little is known about the influence of tumor invasion to the feeding artery of the gallbladder on the onset of cholecystitis after SEMS placement. The aim of the present study was to identify risk factors for cholecystitis after SEMS placement. METHODS: Incidence and nine predictive factors of cholecystitis were retrospectively evaluated in 107 patients who underwent SEMS placement for unresectable distal malignant biliary obstruction at Kyoto University Hospital and Otsu Red Cross Hospital between January 2012 and June 2016. RESULTS: Cholecystitis occurred in 13 of 107 patients (12.1%) after SEMS placement during the median follow-up period of 262 days. Univariate analyses showed that tumor invasion to the feeding artery of the gallbladder and tumor involvement to the orifice of the cystic duct were significant predictors of cholecystitis (P = 0.001 and P < 0.001). Multivariate analysis confirmed that these two factors were significant and independent risks for cholecystitis with odds ratios of 22.13 (95% CI, 3.57-137.18; P = 0.001) and 25.26 (95% CI, 4.12-154.98; P < 0.001), respectively. CONCLUSIONS: This study showed for the first time that tumor invasion to the feeding artery of the gallbladder as well as tumor involvement to the orifice of the cystic duct are independent risk factors for cholecystitis after SEMS placement.

GENESIS 1.1: A hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms.

GENeralized-Ensemble SImulation System (GENESIS) is a software package for molecular dynamics (MD) simulation of biological systems. It is designed to extend limitations in system size and accessible time scale by adopting highly parallelized schemes and enhanced conformational sampling algorithms. In this new version, GENESIS 1.1, new functions and advanced algorithms have been added. The all-atom and coarse-grained potential energy functions used in AMBER and GROMACS packages now become available in addition to CHARMM energy functions. The performance of MD simulations has been greatly improved by further optimization, multiple time-step integration, and hybrid (CPU + GPU) computing. The string method and replica-exchange umbrella sampling with flexible collective variable choice are used for finding the minimum free-energy pathway and obtaining free-energy profiles for conformational changes of a macromolecule. These new features increase the usefulness and power of GENESIS for modeling and simulation in biological research. © 2017 Wiley Periodicals, Inc.

Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein.

Collective variables (CVs) are often used in molecular dynamics simulations based on enhanced sampling algorithms to investigate large conformational changes of a protein. The choice of CVs in these simulations is essential because it affects simulation results and impacts the free-energy profile, the minimum free-energy pathway (MFEP), and the transition-state structure. Here we examine how many CVs are required to capture the correct transition-state structure during the open-to-close motion of adenylate kinase using a coarse-grained model in the mean forces string method to search the MFEP. Various numbers of large amplitude principal components are tested as CVs in the simulations. The incorporation of local coordinates into CVs, which is possible in higher dimensional CV spaces, is important for capturing a reliable MFEP. The Bayesian measure proposed by Best and Hummer is sensitive to the choice of CVs, showing sharp peaks when the transition-state structure is captured. We thus evaluate the required number of CVs needed in enhanced sampling simulations for describing protein conformational changes.

Domain Motion Enhanced (DoME) Model for Efficient Conformational Sampling of Multidomain Proteins.

Large conformational changes of multidomain proteins are difficult to simulate using all-atom molecular dynamics (MD) due to the slow time scale. We show that a simple modification of the structure-based coarse-grained (CG) model enables a stable and efficient MD simulation of those proteins. "Motion Tree", a tree diagram that describes conformational changes between two structures in a protein, provides information on rigid structural units (domains) and the magnitudes of domain motions. In our new CG model, which we call the DoME (domain motion enhanced) model, interdomain interactions are defined as being inversely proportional to the magnitude of the domain motions in the diagram, whereas intradomain interactions are kept constant. We applied the DoME model in combination with the Go model to simulations of adenylate kinase (AdK). The results of the DoME-Go simulation are consistent with an all-atom MD simulation for 10 µs as well as known experimental data. Unlike the conventional Go model, the DoME-Go model yields stable simulation trajectories against temperature changes and conformational transitions are easily sampled despite domain rigidity. Evidently, identification of domains and their interfaces is useful approach for CG modeling of multidomain proteins.

Extended Phase-Space Methods for Enhanced Sampling in Molecular Simulations: A Review.

Molecular Dynamics simulations are a powerful approach to study biomolecular conformational changes or protein-ligand, protein-protein, and protein-DNA/RNA interactions. Straightforward applications, however, are often hampered by incomplete sampling, since in a typical simulated trajectory the system will spend most of its time trapped by high energy barriers in restricted regions of the configuration space. Over the years, several techniques have been designed to overcome this problem and enhance space sampling. Here, we review a class of methods that rely on the idea of extending the set of dynamical variables of the system by adding extra ones associated to functions describing the process under study. In particular, we illustrate the Temperature Accelerated Molecular Dynamics (TAMD), Logarithmic Mean Force Dynamics (LogMFD), and Multiscale Enhanced Sampling (MSES) algorithms. We also discuss combinations with techniques for searching reaction paths. We show the advantages presented by this approach and how it allows to quickly sample important regions of the free-energy landscape via automatic exploration.

Sequential data assimilation for single-molecule FRET photon-counting data.

Data assimilation is a statistical method designed to improve the quality of numerical simulations in combination with real observations. Here, we develop a sequential data assimilation method that incorporates one-dimensional time-series data of smFRET (single-molecule Förster resonance energy transfer) photon-counting into conformational ensembles of biomolecules derived from "replicated" molecular dynamics (MD) simulations. A particle filter using a large number of "replicated" MD simulations with a likelihood function for smFRET photon-counting data is employed to screen the conformational ensembles that match the experimental data. We examine the performance of the method using emulated smFRET data and coarse-grained (CG) MD simulations of a dye-labeled polyproline-20. The method estimates the dynamics of the end-to-end distance from smFRET data as well as revealing that of latent conformational variables. The particle filter is also able to correct model parameter dependence in CG MD simulations. We discuss the applicability of the method to real experimental data for conformational dynamics of biomolecules.