Multiscale Bayesian simulations reveal functional chromatin condensation of gene loci.

Chromatin, the complex assembly of DNA and associated proteins, plays a pivotal role in orchestrating various genomic functions. To aid our understanding of the principles underlying chromatin organization, we introduce Hi-C metainference, a Bayesian approach that integrates Hi-C contact frequencies into multiscale prior models of chromatin. This approach combines both bottom-up (the physics-based prior) and top-down (the data-driven posterior) strategies to characterize the 3D organization of a target genomic locus. We first demonstrate the capability of this method to accurately reconstruct the structural ensemble and the dynamics of a system from contact information. We then apply the approach to investigate the Sox2, Pou5f1, and Nanog loci of mouse embryonic stem cells using a bottom-up chromatin model at 1 kb resolution. We observe that the studied loci are conformationally heterogeneous and organized as crumpled globules, favoring contacts between distant enhancers and promoters. Using nucleosome-resolution simulations, we then reveal how the Nanog gene is functionally organized across the multiple scales of chromatin. At the local level, we identify diverse tetranucleosome folding motifs with a characteristic distribution along the genome, predominantly open at cis-regulatory elements and compact in between. At the larger scale, we find that enhancer-promoter contacts are driven by the transient condensation of chromatin into compact domains stabilized by extensive internucleosome interactions. Overall, this work highlights the condensed, but dynamic nature of chromatin in vivo, contributing to a deeper understanding of gene structure-function relationships.

Extension of the iSoLF implicit-solvent coarse-grained model for multicomponent lipid bilayers.

iSoLF is a coarse-grained (CG) model for lipid molecules with the implicit-solvent approximation used in molecular dynamics (MD) simulations of biological membranes. Using the original iSoLF (iSoLFv1), MD simulations of lipid bilayers consisting of either POPC or DPPC and these bilayers, including membrane proteins, can be performed. Here, we improve the original model, explicitly treating the electrostatic interactions between different lipid molecules and adding CG particle types. As a result, the available lipid types increase to 30. To parameterize the potential functions of the new model, we performed all-atom MD simulations of each lipid at three different temperatures using the CHARMM36 force field and the modified TIP3P model. Then, we parameterized both the bonded and non-bonded interactions to fit the area per lipid and the membrane thickness of each lipid bilayer by using the multistate Boltzmann Inversion method. The final model reproduces the area per lipid and the membrane thickness of each lipid bilayer at the three temperatures. We also examined the applicability of the new model, iSoLFv2, to simulate the phase behaviors of mixtures of DOPC and DPPC at different concentrations. The simulation results with iSoLFv2 are consistent with those using Dry Martini and Martini 3, although iSoLFv2 requires much fewer computations. iSoLFv2 has been implemented in the GENESIS MD software and is publicly available.

Micelle-like clusters in phase-separated Nanog condensates: A molecular simulation study.

The phase separation model for transcription suggests that transcription factors (TFs), coactivators, and RNA polymerases form biomolecular condensates around active gene loci and regulate transcription. However, the structural details of condensates remain elusive. In this study, for Nanog, a master TF in mammalian embryonic stem cells known to form protein condensates in vitro, we examined protein structures in the condensates using residue-level coarse-grained molecular simulations. Human Nanog formed micelle-like clusters in the condensate. In the micelle-like cluster, the C-terminal disordered domains, including the tryptophan repeat (WR) regions, interacted with each other near the cluster center primarily via hydrophobic interaction. In contrast, hydrophilic disordered N-terminal and DNA-binding domains were exposed on the surface of the clusters. Electrostatic attractions of these surface residues were responsible for bridging multiple micelle-like structures in the condensate. The micelle-like structure and condensate were dynamic and liquid-like. Mutation of tryptophan residues in the WR region which was implicated to be important for a Nanog function resulted in dissolution of the Nanog condensate. Finally, to examine the impact of Nanog cluster to DNA, we added DNA fragments to the Nanog condensate. Nanog DNA-binding domains exposed to the surface of the micelle-like cluster could recruit more than one DNA fragments, making DNA-DNA distance shorter.

Postsynaptic protein assembly in three and two dimensions studied by mesoscopic simulations.

Recently, cellular biomolecular condensates formed via phase separation have received considerable attention. While they can be formed either in cytosol (denoted as 3D) or beneath the membrane (2D), the underlying difference between the two has not been well clarified. To compare the phase behaviors in 3D and 2D, postsynaptic density (PSD) serves as a model system. PSD is a protein condensate located under the postsynaptic membrane that influences the localization of glutamate receptors and thus contributes to synaptic plasticity. Recent in vitro studies have revealed the formation of droplets of various soluble PSD proteins via liquid-liquid phase separation. However, it is unclear how these protein condensates are formed beneath the membrane and how they specifically affect the localization of glutamate receptors in the membrane. In this study, focusing on the mixture of a glutamate receptor complex, AMPAR-TARP, and a ubiquitous scaffolding protein, PSD-95, we constructed a mesoscopic model of protein-domain interactions in PSD and performed comparative molecular simulations. The results showed a sharp contrast in the phase behaviors of protein assemblies in 3D and those under the membrane (2D). A mixture of a soluble variant of the AMPAR-TARP complex and PSD-95 in the 3D system resulted in a phase-separated condensate, which was consistent with the experimental results. However, with identical domain interactions, AMPAR-TARP embedded in the membrane formed clusters with PSD-95, but did not form a stable separated phase. Thus, the cluster formation behaviors of PSD proteins in the 3D and 2D systems were distinct. The current study suggests that, more generally, stable phase separation can be more difficult to achieve in and beneath the membrane than in 3D systems.

Removing the parachuting artifact using two-way scanning data in high-speed atomic force microscopy.

The high-speed atomic force microscopy (HS-AFM) is a unique and prominent method to observe structural dynamics of biomolecules at single molecule level at near-physiological condition. To achieve high temporal resolution, the probe tip scans the stage at high speed which can cause the so-called parachuting artifact in the HS-AFM images. Here, we develop a computational method to detect and remove the parachuting artifact in HS-AFM images using the two-way scanning data. To merge the two-way scanning images, we employed a method to infer the piezo hysteresis effect and to align the forward- and backward-scanning images. We then tested our method for HS-AFM videos of actin filaments, molecular chaperone, and duplex DNA. Together, our method can remove the parachuting artifact from the raw HS-AFM video containing two-way scanning data and make the processed video free from the parachuting artifact. The method is general and fast so that it can easily be applied to any HS-AFM videos with two-way scanning data.

Histone chaperone Nap1 dismantles an H2A/H2B dimer from a partially unwrapped nucleosome.

DNA translocases, such as RNA polymerases, inevitably collide with nucleosomes on eukaryotic chromatin. Upon these collisions, histone chaperones are suggested to facilitate nucleosome disassembly and re-assembly. In this study, by performing in vitro transcription assays and molecular simulations, we found that partial unwrapping of a nucleosome by an RNA polymerase dramatically facilitates an H2A/H2B dimer dismantling from the nucleosome by Nucleosome Assembly Protein 1 (Nap1). Furthermore, the results uncovered molecular mechanisms of Nap1 functions in which the highly acidic C-terminal flexible tails of Nap1 contribute to the H2A/H2B binding by associating with the binding interface buried and not accessible to Nap1 globular domains, supporting the penetrating fuzzy binding mechanism seemingly shared across various histone chaperones. These findings have broad implications for the mechanisms by which histone chaperones process nucleosomes upon collisions with translocases in transcription, histone recycling and nucleosomal DNA repair.

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 .

FO-F1 coupling and symmetry mismatch in ATP synthase resolved in every FO rotation step.

FOF1 ATP synthase, a ubiquitous enzyme that synthesizes most ATP in living cells, is composed of two rotary motors: a membrane-embedded proton-driven FO motor and a catalytic F1 motor. These motors share both central and peripheral stalks. Although both FO and F1 have pseudo-symmetric structures, their symmetries do not match. How symmetry mismatch is solved remains elusive because of the missing intermediate structures of the rotational steps. Here, for the case of Bacillus PS3 ATP synthases with three- and 10-fold symmetries in F1 and FO, respectively, we uncovered the mechanical couplings between FO and F1 at every 36° rotation step via molecular dynamics simulations and comparative studies of cryoelectron microscopy (cryo-EM) structures from three species. We found that the mismatch could be solved using several elements: 1) the F1 head partially rotates relative to the FO a subunit via elastic distortion of the b subunits, 2) the rotor is twisted, and 3) comparisons of cryo-EM structures further suggest that the c ring rotary angles can deviate from the symmetric ones. In addition, the F1 motor may have non-canonical structures, relieving stronger frustration. Thus, we provide new insights for solving the symmetry mismatch problem.

The stoichiometric interaction model for mesoscopic MD simulations of liquid-liquid phase separation.

Liquid-liquid phase separation (LLPS) has received considerable attention in recent years for explaining the formation of cellular biomolecular condensates. The fluidity and the complexity of their components make molecular simulation approaches indispensable for gaining structural insights. Domain-resolution mesoscopic model simulations have been explored for cases in which condensates are formed by multivalent proteins with tandem domains. One problem with this approach is that interdomain pairwise interactions cannot regulate the valency of the binding domains. To overcome this problem, we propose a new potential, the stoichiometric interaction (SI) potential. First, we verified that the SI potential maintained the valency of the interacting domains for the test systems. We then examined a well-studied LLPS model system containing tandem repeats of SH3 domains and proline-rich motifs. We found that the SI potential alone cannot reproduce the phase diagram of LLPS quantitatively. We had to combine the SI and a pairwise interaction; the former and the latter represent the specific and nonspecific interactions, respectively. Biomolecular condensates with the mixed SI and pairwise interaction exhibited fluidity, whereas those with the pairwise interaction alone showed no detectable diffusion. We also compared the phase diagrams of the systems containing different numbers of tandem domains with those obtained from the experiments and found quantitative agreement in all but one case.

Molecular dynamics simulations for the study of chromatin biology.

The organization of Eukaryotic DNA into chromatin has profound implications for the processing of genetic information. In the past years, molecular dynamics (MD) simulations proved to be a powerful tool to investigate the mechanistic basis of chromatin biology. We review recent all-atom and coarse-grained MD studies revealing how the structure and dynamics of chromatin underlie its biological functions. We describe the latest method developments; the structural fluctuations of nucleosomes and the various factors affecting them; the organization of chromatin fibers, with particular emphasis on its liquid-like character; the interactions and dynamics of transcription factors on chromatin; and how chromatin organization is modulated by molecular motors acting on DNA.

Rotational Mechanism of FO Motor in the F-Type ATP Synthase Driven by the Proton Motive Force.

In FOF1 ATP synthase, driven by the proton motive force across the membrane, the FO motor rotates the central rotor and induces conformational changes in the F1 motor, resulting in ATP synthesis. Recently, many near-atomic resolution structural models have been obtained using cryo-electron microscopy. Despite high resolution, however, static information alone cannot elucidate how and where the protons pass through the FO and how proton passage is coupled to FO rotation. Here, we review theoretical and computational studies based on FO structure models. All-atom molecular dynamics (MD) simulations elucidated changes in the protonation/deprotonation of glutamate-the protein-carrier residue-during rotation and revealed the protonation states that form the "water wire" required for long-range proton hopping. Coarse-grained MD simulations unveiled a free energy surface based on the protonation state and rotational angle of the rotor. Hybrid Monte Carlo and MD simulations showed how proton transfer is coupled to rotation.

Coarse-grained molecular dynamics simulations of base-pair mismatch recognition protein MutS sliding along DNA.

DNA mismatches are frequently generated by various intrinsic and extrinsic factors including DNA replication errors, oxygen species, ultraviolet, and ionizing radiation. These mismatches should be corrected by the mismatches repair (MMR) pathway to maintain genome integrity. In the Escherichia coli (E. coli) MMR pathway, MutS searches and recognizes a base-pair mismatch from millions of base-pairs. Once recognized, ADP bound to MutS is exchanged with ATP, which induces a conformational change in MutS. Previous single-molecule fluorescence microscopy studies have suggested that ADP-bound MutS temporarily slides along double-stranded DNA in a rotation-coupled manner to search a base-pair mismatch and so does ATP-bound MutS in a rotation-uncoupled manner. However, the detailed structural dynamics of the sliding remains unclear. In this study, we performed coarse-grained molecular dynamics simulations of the E. coli MutS bound on DNA in three different conformations: ADP-bound (MutSADP), ATP-bound open clamp ( M u t S O p e n A T P ), and ATP-bound closed clamp ( M u t S C l o s e d A T P ) conformations. In the simulations, we observed conformation-dependent diffusion of MutS along DNA. MutSADP and M u t S C l o s e d A T P diffused along DNA in a rotation-coupled manner with rare and frequent groove-crossing events, respectively. In the groove-crossing events, MutS overcame an edge of a groove and temporarily diffused in a rotation-uncoupled manner. It was also indicated that mismatch searches by M u t S O p e n A T P is inefficient in terms of mismatch checking even though it diffuses along DNA and reaches unchecked regions more rapidly than MutSADP.

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.

Implementation of residue-level coarse-grained models in GENESIS for large-scale molecular dynamics simulations.

Residue-level coarse-grained (CG) models have become one of the most popular tools in biomolecular simulations in the trade-off between modeling accuracy and computational efficiency. To investigate large-scale biological phenomena in molecular dynamics (MD) simulations with CG models, unified treatments of proteins and nucleic acids, as well as efficient parallel computations, are indispensable. In the GENESIS MD software, we implement several residue-level CG models, covering structure-based and context-based potentials for both well-folded biomolecules and intrinsically disordered regions. An amino acid residue in protein is represented as a single CG particle centered at the Cα atom position, while a nucleotide in RNA or DNA is modeled with three beads. Then, a single CG particle represents around ten heavy atoms in both proteins and nucleic acids. The input data in CG MD simulations are treated as GROMACS-style input files generated from a newly developed toolbox, GENESIS-CG-tool. To optimize the performance in CG MD simulations, we utilize multiple neighbor lists, each of which is attached to a different nonbonded interaction potential in the cell-linked list method. We found that random number generations for Gaussian distributions in the Langevin thermostat are one of the bottlenecks in CG MD simulations. Therefore, we parallelize the computations with message-passing-interface (MPI) to improve the performance on PC clusters or supercomputers. We simulate Herpes simplex virus (HSV) type 2 B-capsid and chromatin models containing more than 1,000 nucleosomes in GENESIS as examples of large-scale biomolecular simulations with residue-level CG models. This framework extends accessible spatial and temporal scales by multi-scale simulations to study biologically relevant phenomena, such as genome-scale chromatin folding or phase-separated membrane-less condensations.

Cooperation among c-subunits of FoF1-ATP synthase in rotation-coupled proton translocation.

In FoF1-ATP synthase, proton translocation through Fo drives rotation of the c-subunit oligomeric ring relative to the a-subunit. Recent studies suggest that in each step of the rotation, key glutamic acid residues in different c-subunits contribute to proton release to and proton uptake from the a-subunit. However, no studies have demonstrated cooperativity among c-subunits toward FoF1-ATP synthase activity. Here, we addressed this using Bacillus PS3 ATP synthase harboring a c-ring with various combinations of wild-type and cE56D, enabled by genetically fused single-chain c-ring. ATP synthesis and proton pump activities were decreased by a single cE56D mutation and further decreased by double cE56D mutations. Moreover, activity further decreased as the two mutation sites were separated, indicating cooperation among c-subunits. Similar results were obtained for proton transfer-coupled molecular simulations. The simulations revealed that prolonged proton uptake in mutated c-subunits is shared between two c-subunits, explaining the cooperation observed in biochemical assays.

Cells need to be able to store and transfer energy to fuel their various activities. To do this, they produce a small molecule called ATP to carry the energy, which is then released when the ATP is broken down. An enzyme found in plants, animals and bacteria, called F_oF₁ ATP synthase, can both create and use ATP. When it does this, protons, or positive hydrogen ions, are transported across cellular boundaries called membranes. The region of the enzyme that is responsible for pumping the protons contains different parts known as the c-ring and the a-subunit. The movement of protons drives the c-ring to rotate relative to the a-subunit, which leads to producing ATP. Previous research using simulations and the protein structures found there are two or three neighbouring amino acids in the c-ring that face the a-subunit, suggesting that these amino acids act together to drive the rotation. To test this hypothesis, Mitome et al. mutated these amino acids to examine the effect on the enzyme's ability to produce ATP. A single mutation reduced the production of ATP, which decreased even further with mutations in two of the amino acids. The extent of this decrease depended on the distance between the two mutations in the c-ring. Simulations of these changes also found similar results. This indicates there is coordination between different parts of the c-ring to increase the rate of ATP production. This study offers new insights into the molecular processes controlling ATP synthesis and confirms previous theoretical research. This will interest specialists in bioenergetics because it addresses a fundamental biological question with broad impact.

Modeling DNA Opening in the Eukaryotic Transcription Initiation Complexes via Coarse-Grained Models.

Recently, the molecular mechanisms of transcription initiation have been intensively studied. Especially, the cryo-electron microscopy revealed atomic structure details in key states in the eukaryotic transcription initiation. Yet, the dynamic processes of the promoter DNA opening in the pre-initiation complex remain obscured. In this study, based on the three cryo-electron microscopic yeast structures for the closed, open, and initially transcribing complexes, we performed multiscale molecular dynamics (MD) simulations to model structures and dynamic processes of DNA opening. Combining coarse-grained and all-atom MD simulations, we first obtained the atomic model for the DNA bubble in the open complexes. Then, in the MD simulation from the open to the initially transcribing complexes, we found a previously unidentified intermediate state which is formed by the bottleneck in the fork loop 1 of Pol II: The loop opening triggered the escape from the intermediate, serving as a gatekeeper of the promoter DNA opening. In the initially transcribing complex, the non-template DNA strand passes a groove made of the protrusion, the lobe, and the fork of Rpb2 subunit of Pol II, in which several positively charged and highly conserved residues exhibit key interactions to the non-template DNA strand. The back-mapped all-atom models provided further insights on atomistic interactions such as hydrogen bonding and can be used for future simulations.

Corrigendum: Modeling DNA Opening in the Eukaryotic Transcription Initiation Complexes via Coarse-Grained Models.

[This corrects the article DOI: 10.3389/fmolb.2021.772486.].

Modeling lipid-protein interactions for coarse-grained lipid and Cα protein models.

Biological membranes that play major roles in diverse functions are composed of numerous lipids and proteins, making them an important target for coarse-grained (CG) molecular dynamics (MD) simulations. Recently, we have developed the CG implicit solvent lipid force field (iSoLF) that has a resolution compatible with the widely used Cα protein representation [D. Ugarte La Torre and S. Takada, J. Chem. Phys. 153, 205101 (2020)]. In this study, we extended it and developed a lipid-protein interaction model that allows the combination of the iSoLF and the Cα protein force field, AICG2+. The hydrophobic-hydrophilic interaction is modeled as a modified Lennard-Jones potential in which parameters were tuned partly to reproduce the experimental transfer free energy and partly based on the free energy profile normal to the membrane surface from previous all-atom MD simulations. Then, the obtained lipid-protein interaction is tested for the configuration and placement of transmembrane proteins, water-soluble proteins, and peripheral proteins, showing good agreement with prior knowledge. The interaction is generally applicable and is implemented in the publicly available software, CafeMol.

Semi-Implicit Time Integration with Hessian Eigenvalue Corrections for a Larger Time Step in Molecular Dynamics Simulations.

In molecular dynamics simulations, the limited time step size has been a barrier to simulating long-time behaviors. Implicit time integration methods allow markedly larger time steps than the standard explicit time method, although they have major drawbacks such as overheads solving linear systems and instability of Newton iterations. To overcome these issues, we propose a semi-implicit time integration scheme, the semi-implicit Hessian correction (SimHec) scheme, for overdamped Langevin dynamics. The method focuses on the Hessian matrices of bonded and nonbonded interactions, where components with large negative Hessian eigenvalues are cut off in the linear approximation of momentum equations to avoid instability. The narrow band Hessian matrix enables an efficient parallelized linear solution with an overlapping approximation. We tested SimHec for the interdomain fluctuations in adenylate kinase and the powerstroke transition of myosin II using a coarse-grained protein model. SimHec reproduced the same dynamics as the explicit method, although the transition dynamics tended to be accelerated and fluctuations in bonded potentials were slightly reduced. These deviations were corrected using a hybrid method, SimHec-H, which adds explicit time steps after the semi-implicit time step. The proposed scheme allowed us to use time steps 50-200 times larger than those in explicit time integration, which resulted in a speedup factor of 7-30 taking the overhead into account.