Coarse-grained simulation reveals key features of HIV-1 capsid self-assembly

Megamolecule Self-Assembly Networks: A Combined Computational and Experimental Design Strategy

This work describes the use of computational strategies to design megamolecule building blocks for the self-assembly of lattice networks. The megamolecules are prepared by attaching four Cutinase-SnapTag fusion proteins (CS fusions) to a four-armed linker, followed by functionalizing each fusion with a terpyridine linker. This functionality is designed to participate in a metal-mediated self-assembly process to give networks. This article describes a simulation-guided strategy for the design of megamolecules to optimize the peptide linker in the fusion protein to give conformations that are best suited for self-assembly and therefore streamlines the typically time-consuming and labor-intensive experimental process. We designed 11 candidate megamolecules and identified the most promising linker, (EAAAK)2, along with the optimal experimental conditions through a combination of all-atom molecular dynamics, enhanced sampling, and larger-scale coarse-grained molecular dynamics simulations. Our simulation findings were validated and found to be consistent with the experimental results. Significantly, this study offers valuable insight into the self-assembly of megamolecule networks and provides a novel and general strategy for large biomolecular material designs by using systematic bottom-up coarse-grained simulations.

Biomimetic Capsid-Like Nanoshells Self-Assembled from Homopolypeptides

The preparation of capsid-like nanoshells and the elucidation of their formation pathways are crucial for the application potential of capsid-like nanomaterials. In this study, we have prepared biomimetic capsid-like nanoshells (CLNs) through the solution self-assembly of poly (β-phenethyl-L-aspartate) homopolypeptide (PPLA). The formation of CLNs is governed by an aggregation-fusion mechanism. Initially, PPLA molecules self-assemble into small spherical assemblies as subunits and the initial nuclei are formed through fusing some subunits. Subsequently, additional subunits rapidly fuse onto these nuclei, leading to the growth of full or partial CLNs during the growth phase. Moreover, the suitable condition benefiting CLNs formation is clarified by a morphological phase diagram based on the initial PPLA concentration against water content. Molecular-level measurements suggest that the molecular flexibility of PPLA is a key factor in the arrangement and fusion of subunits for the formation of CLNs. These findings offer new perspectives for a deeper understanding of the formation pathways of capsid-like nanoshells derived from synthetic polymers.

Modeling reveals the strength of weak interactions in stacked-ring assembly

Cells employ many large macromolecular machines for the execution and regulation of processes that are vital for cell and organismal viability. Interestingly, cells cannot synthesize these machines as functioning units. Instead, cells synthesize the molecular parts that must then assemble into the functional complex. Many important machines, including chaperones such as GroEL and proteases such as the proteasome, comprise protein rings that are stacked on top of one another. While there is some experimental data regarding how stacked-ring complexes such as the proteasome self-assemble, a comprehensive understanding of the dynamics of stacked-ring assembly is currently lacking. Here, we developed a mathematical model of stacked-trimer assembly and performed an analysis of the assembly of the stacked homomeric trimer, which is the simplest stacked-ring architecture. We found that stacked rings are particularly susceptible to a form of kinetic trapping that we term "deadlock," in which the system gets stuck in a state where there are many large intermediates that are not the fully assembled structure but that cannot productively react. When interaction affinities are uniformly strong, deadlock severely limits assembly yield. We thus predicted that stacked rings would avoid situations where all interfaces in the structure have high affinity. Analysis of available crystal structures indicated that indeed the majority-if not all-of stacked trimers do not contain uniformly strong interactions. Finally, to better understand the origins of deadlock, we developed a formal pathway analysis and showed that, when all the binding affinities are strong, many of the possible pathways are utilized. In contrast, optimal assembly strategies utilize only a small number of pathways. Our work suggests that deadlock is a critical factor influencing the evolution of macromolecular machines and provides general principles for understanding the self-assembly efficiency of existing machines.

Evaluation of Essential Dynamics and Fixed-Length Coarse Graining for Multidomain Proteins

For multiscale modeling of biomolecules, reliable coarse-grained (CG) models can offer great potential to simulate larger temporal and spatial scales than traditional all-atom (AA) models. In this study, we explore the essential dynamics coarse graining (EDCG) and fixed-length coarse graining (FLCG) approaches for constructing highly coarse-grained models for multidomain proteins (MDPs), with 1 to 10 amino acid residues per CG site. In the studies of 13 MDPs, our data indicate that both EDCG and FLCG can preserve the protein dynamics of MDPs. FLCG, which restricts an equal number of residues in each CG site, represents an excellent approximation to EDCG and a straightforward approach for coarse-graining MDPs. Furthermore, FLCG is tested with a class B G-protein-coupled receptor protein, and the agreement with prior experiments suggests its general application to various MDPs in different environments or conditions. Finally, we demonstrate another application of FLCG through progressive backmapping, showcasing the ability to recover from lower-resolution CG models (6 residues/CG site) to higher-resolution ones (1 residue/CG site). These promising outcomes underscore the broad applicability of FLCG to construct highly or ultra-coarse-grained models of complex biomolecules for multiscale simulations.

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

IP6 and PF74 affect HIV-1 Capsid Stability through Modulation of Hexamer-Hexamer Tilt Angle Preference

The HIV-1 capsid is an irregularly shaped complex of about 1200 protein chains containing the viral genome and several viral proteins. Together, these components are the key to unlocking passage into the nucleus, allowing for permanent integration of the viral genome into the host cell genome. Recent interest into the role of the capsid in viral replication has been driven by the approval of the first-in-class drug lenacapavir, which marks the first drug approved to target a non-enzymatic HIV-1 viral protein. In addition to lenacapavir, other small molecules such as the drug-like compound PF74, and the anionic sugar inositolhexakisphosphate (IP6), are known to impact capsid stability, and although this is widely accepted as a therapeutic effect, the mechanisms through which they do so remain unknown. In this study, we employed a systematic atomistic simulation approach to study the impact of molecules bound to hexamers at the central pore (IP6) and the FG-binding site (PF74) on capsid oligomer dynamics, compared to apo hexamers and pentamers. We found that neither small molecule had a sizeable impact on the free energy of binding of the interface between neighboring hexamers but that both had impacts on the free energy profiles of performing angular deformations to the pair of oligomers akin to the variations in curvature along the irregular surface of the capsid. The IP6 cofactor, on one hand, stabilizes a pair of neighboring hexamers in their flattest configurations, whereas without IP6, the hexamers prefer a high tilt angle between them. On the other hand, having PF74 bound introduces a strong preference for intermediate tilt angles. These results suggest that structural instability is a natural feature of the HIV-1 capsid which is modulated by molecules bound in either the central pore or the FG-binding site. Such modulators, despite sharing many of the same effects on non-bonded interactions at the various protein-protein interfaces, have decidedly different effects on the flexibility of the complex. This study provides a detailed model of the HIV-1 capsid and its interactions with small molecules, informing structure-based drug design, as well as experimental design and interpretation.

Formalizing Coarse-Grained Representations of Anisotropic Interactions at Multimeric Protein Interfaces Using Virtual Sites

Molecular simulations of biomacromolecules that assemble into multimeric complexes remain a challenge due to computationally inaccessible length and time scales. Low-resolution and implicit-solvent coarse-grained modeling approaches using traditional nonbonded interactions (both pairwise and spherically isotropic) have been able to partially address this gap. However, these models may fail to capture the complex anisotropic interactions present at macromolecular interfaces unless higher-order interaction potentials are incorporated at the expense of the computational cost. In this work, we introduce an alternate and systematic approach to represent directional interactions at protein-protein interfaces by using virtual sites restricted to pairwise interactions. We show that virtual site interaction parameters can be optimized within a relative entropy minimization framework by using only information from known statistics between coarse-grained sites. We compare our virtual site models to traditional coarse-grained models using two case studies of multimeric protein assemblies and find that the virtual site models predict pairwise correlations with higher fidelity and, more importantly, assembly behavior that is morphologically consistent with experiments. Our study underscores the importance of anisotropic interaction representations and paves the way for more accurate yet computationally efficient coarse-grained simulations of macromolecular assembly in future research.

Pharmacologic hyperstabilisation of the HIV-1 capsid lattice induces capsid failure

The HIV-1 capsid has emerged as a tractable target for antiretroviral therapy. Lenacapavir, developed by Gilead Sciences, is the first capsid-targeting drug approved for medical use. Here, we investigate the effect of lenacapavir on HIV capsid stability and uncoating. We employ a single particle approach that simultaneously measures capsid content release and lattice persistence. We demonstrate that lenacapavir's potent antiviral activity is predominantly due to lethal hyperstabilisation of the capsid lattice and resultant loss of compartmentalisation. This study highlights that disrupting capsid metastability is a powerful strategy for the development of novel antivirals.

Mechanisms of allostery at the viral surface through the eyes of molecular simulation

The outermost surface layer of any virus is formed by either a capsid shell or envelope. Such layers have traditionally been thought of as immovable structures, but it is becoming apparent that they cannot be viewed exclusively as static architectures protecting the viral genome. A limited number of proteins on the virion surface must perform a multitude of functions in order to orchestrate the viral life cycle, and allostery can regulate their structures at multiple levels of organization, spanning individual molecules, protomers, large oligomeric assemblies, or entire viral surfaces. Here, we review recent contributions from the molecular simulation field to viral surface allostery, with a particular focus on the trimeric spike glycoprotein emerging from the coronavirus surface, and the icosahedral flaviviral envelope complex. As emerging viral pathogens continue to pose a global threat, an improved understanding of viral dynamics and allosteric regulation will prove crucial in developing novel therapeutic strategies.

Hexagonal Lattices of HIV Capsid Proteins Explored by Simulations Based on a Thermodynamically Consistent Model

HIV capsid proteins (CAs) may self-assemble into a variety of shapes under in vivo and in vitro conditions. Here, we employed simulations based on a residue-level coarse-grained (CG) model with full conformational flexibility to investigate hexagonal lattices, which are the underlying structural pattern for CA aggregations. Facilitated by enhanced sampling simulations to rigorously calculate CA dimerization and polymerization affinities, we calibrated our model to reproduce the experimentally measured affinities. Using the calibrated model, we performed unbiased simulations on several large systems consisting of 1512 CA subunits, allowing reversible binding and unbinding of the CAs in a thermodynamically consistent manner. In one simulation, a preassembled hexagonal CA sheet developed spontaneous curvatures reminiscent of those observed in experiments, and the edges of the sheet exhibited local curvatures larger than those of the interior. In other simulations starting with randomly distributed CAs at different concentrations, existing CA assemblies grew by binding free capsomeres to the edges and by merging with other assemblies. At high CA concentrations, rapid establishment of predominant aggregates was followed by much slower adjustments toward more regular hexagonal lattices, with increasing numbers of intact CA hexamers and pentamers being formed. Our approach of adapting a general CG model to specific systems by using experimental binding data represents a practical and effective strategy for simulating and elucidating intricate protein aggregations.

HIV-1 capsid shape, orientation, and entropic elasticity regulate translocation into the nuclear pore complex

Nuclear import and uncoating of the viral capsid are critical steps in the HIV-1 life cycle that serve to transport and release genomic material into the nucleus. Viral core import involves translocating the HIV-1 capsid at the nuclear pore complex (NPC). Notably, the central channel of the NPC appears to often accommodate and allow passage of intact HIV-1 capsid, though mechanistic details of the process remain to be fully understood. Here, we investigate the molecular interactions that operate in concert between the HIV-1 capsid and the NPC that regulate capsid translocation through the central channel. To this end, we develop a "bottom-up" coarse-grained (CG) model of the human NPC from recently released cryo-electron tomography structure and then construct composite membrane-embedded CG NPC models. We find that successful translocation from the cytoplasmic side to the NPC central channel is contingent on the compatibility of the capsid morphology and channel dimension and the proper orientation of the capsid approach to the channel from the cytoplasmic side. The translocation dynamics is driven by maximizing the contacts between phenylalanine-glycine nucleoporins at the central channel and the capsid. For the docked intact capsids, structural analysis reveals correlated striated patterns of lattice disorder likely related to the intrinsic capsid elasticity. Uncondensed genomic material inside the docked capsid augments the overall lattice disorder of the capsid. Our results suggest that the intrinsic "elasticity" can also aid the capsid to adapt to the stress and remain structurally intact during translocation.

pyCapsid: identifying dominant dynamics and quasi-rigid mechanical units in protein shells

SUMMARY

pyCapsid is a Python package developed to facilitate the characterization of the dynamics and quasi-rigid mechanical units of protein shells and other protein complexes. The package was developed in response to the rapid increase of high-resolution structures, particularly capsids of viruses, requiring multiscale biophysical analyses. Given a protein shell, pyCapsid generates the collective vibrations of its amino-acid residues, identifies quasi-rigid mechanical regions associated with the disassembly of the structure, and maps the results back to the input proteins for interpretation. pyCapsid summarizes the main results in a report that includes publication-quality figures.

AVAILABILITY AND IMPLEMENTATION

pyCapsid's source code is available under MIT License on GitHub. It is compatible with Python 3.8-3.10 and has been deployed in two leading Python package-management systems, PIP and Conda. Installation instructions and tutorials are available in the online documentation and in the pyCapsid's YouTube playlist. In addition, a cloud-based implementation of pyCapsid is available as a Google Colab notebook. pyCapsid Colab does not require installation and generates the same report and outputs as the installable version. Users can post issues regarding pyCapsid in the repository's issues section.

Transferable Implicit Solvation via Contrastive Learning of Graph Neural Networks

Implicit solvent models are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. Efforts are underway to develop accurate and transferable implicit solvent models and coarse-grained (CG) force fields in general, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to the lack of analytical expressions for the PMF and algorithmic limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent the solvation free energy and potential contrasting for parameter optimization. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside of the training data. Our study offers valuable insights for deriving systematically improvable implicit solvent models and CG force fields from a bottom-up perspective.

K-Means Clustering Coarse-Graining (KMC-CG): A Next Generation Methodology for Determining Optimal Coarse-Grained Mappings of Large Biomolecules

Coarse-grained (CG) molecular dynamics (MD) has become a method of choice for simulating various large scale biomolecular processes; therefore, the systematic definition of the CG mappings for biomolecules remains an important topic. Appropriate CG mappings can significantly enhance the representability of a CG model and improve its ability to capture critical features of large biomolecules. In this work, we present a systematic and more generalized method called K-means clustering coarse-graining (KMC-CG), which builds on the earlier approach of essential dynamics coarse-graining (ED-CG). KMC-CG removes the sequence-dependent constraints of ED-CG, allowing it to explore a more extensive space and thus enabling the discovery of more physically optimal CG mappings. Furthermore, the implementation of the K-means clustering algorithm can variationally optimize the CG mapping with efficiency and stability. This new method is tested in three cases: ATP-bound G-actin, the HIV-1 CA pentamer, and the Arp2/3 complex. In these examples, the CG models generated by KMC-CG are seen to better capture the structural, dynamic, and functional domains. KMC-CG therefore provides a robust and consistent approach to generating CG models of large biomolecules that can then be more accurately parametrized by either bottom-up or top-down CG force fields.

Gaussian representation of coarse-grained interactions of liquids: Theory, parametrization, and transferability

Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility.

OpenMSCG: A Software Tool for Bottom-Up Coarse-Graining

The "bottom-up" approach to coarse-graining, for building accurate and efficient computational models to simulate large-scale and complex phenomena and processes, is an important approach in computational chemistry, biophysics, and materials science. As one example, the Multiscale Coarse-Graining (MS-CG) approach to developing CG models can be rigorously derived using statistical mechanics applied to fine-grained, i.e., all-atom simulation data for a given system. Under a number of circumstances, a systematic procedure, such as MS-CG modeling, is particularly valuable. Here, we present the development of the OpenMSCG software, a modularized open-source software that provides a collection of successful and widely applied bottom-up CG methods, including Boltzmann Inversion (BI), Force-Matching (FM), Ultra-Coarse-Graining (UCG), Relative Entropy Minimization (REM), Essential Dynamics Coarse-Graining (EDCG), and Heterogeneous Elastic Network Modeling (HeteroENM). OpenMSCG is a high-performance and comprehensive toolset that can be used to derive CG models from large-scale fine-grained simulation data in file formats from common molecular dynamics (MD) software packages, such as GROMACS, LAMMPS, and NAMD. OpenMSCG is modularized in the Python programming framework, which allows users to create and customize modeling "recipes" for reproducible results, thus greatly improving the reliability, reproducibility, and sharing of bottom-up CG models and their applications.

Transferable Coarse Graining via Contrastive Learning of Graph Neural Networks

Coarse-grained (CG) force fields are essential for molecular dynamics simulations of biomolecules, striking a balance between computational efficiency and biological realism. These simulations employ simplified models grouping atoms into interaction sites, enabling the study of complex biomolecular systems over biologically relevant timescales. Efforts are underway to develop accurate and transferable CG force fields, guided by a bottom-up approach that matches the CG energy function with the potential of mean force (PMF) defined by the finer system. However, practical challenges arise due to many-body effects, lack of analytical expressions for the PMF, and limitations in parameterizing CG force fields. To address these challenges, a machine learning-based approach is proposed, utilizing graph neural networks (GNNs) to represent CG force fields and potential contrasting for parameterization from atomistic simulation data. We demonstrate the effectiveness of the approach by deriving a transferable GNN implicit solvent model using 600,000 atomistic configurations of six proteins obtained from explicit solvent simulations. The GNN model provides solvation free energy estimations much more accurately than state-of-the-art implicit solvent models, reproducing configurational distributions of explicit solvent simulations. We also demonstrate the reasonable transferability of the GNN model outside the training data. Our study offers valuable insights for building accurate coarse-grained models bottom-up.

Temporal control by cofactors prevents kinetic trapping in retroviral Gag lattice assembly

For retroviruses like HIV to proliferate, they must form virions shaped by the self-assembly of Gag polyproteins into a rigid lattice. This immature Gag lattice has been structurally characterized and reconstituted in vitro, revealing the sensitivity of lattice assembly to multiple cofactors. Due to this sensitivity, the energetic criterion for forming stable lattices is unknown, as are their corresponding rates. Here, we use a reaction-diffusion model designed from the cryo-ET structure of the immature Gag lattice to map a phase diagram of assembly outcomes controlled by experimentally constrained rates and free energies, over experimentally relevant timescales. We find that productive assembly of complete lattices in bulk solution is extraordinarily difficult due to the large size of this ∼3700 monomer complex. Multiple Gag lattices nucleate before growth can complete, resulting in loss of free monomers and frequent kinetic trapping. We therefore derive a time-dependent protocol to titrate or "activate" the Gag monomers slowly within the solution volume, mimicking the biological roles of cofactors. This general strategy works remarkably well, yielding productive growth of self-assembled lattices for multiple interaction strengths and binding rates. By comparing to the in vitro assembly kinetics, we can estimate bounds on rates of Gag binding to Gag and the cellular cofactor IP6. Our results show that Gag binding to IP6 can provide the additional time delay necessary to support smooth growth of the immature lattice with relatively fast assembly kinetics, mostly avoiding kinetic traps. Our work provides a foundation for predicting and disrupting formation of the immature Gag lattice via targeting specific protein-protein binding interactions.

Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles

Coarse-grained (CG) models parametrized using atomistic reference data, i.e., "bottom up" CG models, have proven useful in the study of biomolecules and other soft matter. However, the construction of highly accurate, low resolution CG models of biomolecules remains challenging. We demonstrate in this work how virtual particles, CG sites with no atomistic correspondence, can be incorporated into CG models within the context of relative entropy minimization (REM) as latent variables. The methodology presented, variational derivative relative entropy minimization (VD-REM), enables optimization of virtual particle interactions through a gradient descent algorithm aided by machine learning. We apply this methodology to the challenging case of a solvent-free CG model of a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer and demonstrate that introduction of virtual particles captures solvent-mediated behavior and higher-order correlations which REM alone cannot capture in a more standard CG model based only on the mapping of collections of atoms to the CG sites.

Structure of the HIV immature lattice allows for essential lattice remodeling within budded virions

For HIV virions to become infectious, the immature lattice of Gag polyproteins attached to the virion membrane must be cleaved. Cleavage cannot initiate without the protease formed by the homo-dimerization of domains linked to Gag. However, only 5% of the Gag polyproteins, termed Gag-Pol, carry this protease domain, and they are embedded within the structured lattice. The mechanism of Gag-Pol dimerization is unknown. Here, we use spatial stochastic computer simulations of the immature Gag lattice as derived from experimental structures, showing that dynamics of the lattice on the membrane is unavoidable due to the missing 1/3 of the spherical protein coat. These dynamics allow for Gag-Pol molecules carrying the protease domains to detach and reattach at new places within the lattice. Surprisingly, dimerization timescales of minutes or less are achievable for realistic binding energies and rates despite retaining most of the large-scale lattice structure. We derive a formula allowing extrapolation of timescales as a function of interaction free energy and binding rate, thus predicting how additional stabilization of the lattice would impact dimerization times. We further show that during assembly, dimerization of Gag-Pol is highly likely and therefore must be actively suppressed to prevent early activation. By direct comparison to recent biochemical measurements within budded virions, we find that only moderately stable hexamer contacts (-12kBT<∆G<-8kBT) retain both the dynamics and lattice structures that are consistent with experiment. These dynamics are likely essential for proper maturation, and our models quantify and predict lattice dynamics and protease dimerization timescales that define a key step in understanding formation of infectious viruses.

Understanding Virus Structure and Dynamics through Molecular Simulations

Viral outbreaks remain a serious threat to human and animal populations and motivate the continued development of antiviral drugs and vaccines, which in turn benefits from a detailed understanding of both viral structure and dynamics. While great strides have been made in characterizing these systems experimentally, molecular simulations have proven to be an essential, complementary approach. In this work, we review the contributions of molecular simulations to the understanding of viral structure, functional dynamics, and processes related to the viral life cycle. Approaches ranging from coarse-grained to all-atom representations are discussed, including current efforts at modeling complete viral systems. Overall, this review demonstrates that computational virology plays an essential role in understanding these systems.

Computer-aided drug design in seeking viral capsid modulators

Approved or licensed antiviral drugs have limited applications because of their drug resistance and severe adverse effects. By contrast, by stabilizing or destroying the viral capsid, compounds known as capsid modulators prevent viral replication by acting on new targets and, therefore, overcoming the problem of clinical drug resistance. For example. computer-aided drug design (CADD) methods, using strategies based on structures of biological targets (structure-based drug design; SBDD), such as docking, molecular dynamics (MD) simulations, and virtual screening (VS), have provided opportunities for fast and effective development of viral capsid modulators. In this review, we summarize the application of CADD in the discovery, optimization, and mechanism prediction of capsid-targeting small molecules, providing new insights into antiviral drug discovery modalities. Teaser: Computer-aided drug design will accelerate the development of viral capsid regulators, which brings new hope for the treatment of refractory viral diseases.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Critical mechanistic features of HIV-1 viral capsid assembly

The maturation of HIV-1 capsid protein (CA) into a cone-shaped lattice capsid is critical for viral infectivity. CA can self-assemble into a range of capsid morphologies made of ~175 to 250 hexamers and 12 pentamers. The cellular polyanion inositol hexakisphosphate (IP6) has recently been demonstrated to facilitate conical capsid formation by coordinating a ring of arginine residues within the central cavity of capsid hexamers and pentamers. However, the kinetic interplay of events during IP6 and CA coassembly is unclear. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanism of capsid formation, including the role played by IP6. We show that IP6, in small quantities at first, promotes curvature generation by trapping pentameric defects in the growing lattice and shifts assembly behavior toward kinetically favored outcomes. Our analysis also suggests that IP6 can stabilize metastable capsid intermediates and can induce structural pleomorphism in mature capsids.

Critical mechanistic features of HIV-1 viral capsid assembly

The maturation of HIV-1 capsid protein (CA) into a cone-shaped lattice capsid is critical for viral infectivity. CA can self-assemble into a range of capsid morphologies made of ~175 to 250 hexamers and 12 pentamers. The cellular polyanion inositol hexakisphosphate (IP6) has recently been demonstrated to facilitate conical capsid formation by coordinating a ring of arginine residues within the central cavity of capsid hexamers and pentamers. However, the kinetic interplay of events during IP6 and CA coassembly is unclear. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanism of capsid formation, including the role played by IP6. We show that IP6, in small quantities at first, promotes curvature generation by trapping pentameric defects in the growing lattice and shifts assembly behavior toward kinetically favored outcomes. Our analysis also suggests that IP6 can stabilize metastable capsid intermediates and can induce structural pleomorphism in mature capsids.

Critical mechanistic features of HIV-1 viral capsid assembly

The maturation of HIV-1 capsid protein (CA) into a cone-shaped lattice capsid is critical for viral infectivity. CA can self-assemble into a range of capsid morphologies made of ~175 to 250 hexamers and 12 pentamers. The cellular polyanion inositol hexakisphosphate (IP6) has recently been demonstrated to facilitate conical capsid formation by coordinating a ring of arginine residues within the central cavity of capsid hexamers and pentamers. However, the kinetic interplay of events during IP6 and CA coassembly is unclear. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanism of capsid formation, including the role played by IP6. We show that IP6, in small quantities at first, promotes curvature generation by trapping pentameric defects in the growing lattice and shifts assembly behavior toward kinetically favored outcomes. Our analysis also suggests that IP6 can stabilize metastable capsid intermediates and can induce structural pleomorphism in mature capsids.

Heat-induced transitions of an empty minute virus of mice capsid in explicit water: all-atom MD simulation

The capsid-like structure of the virus-based protein nanoparticles (NPs) can serve as bionanomaterials, with applications in biomedicines and nanotechnology. Release of packaged material from these nanocontainers is associated with subtle conformational changes of the NP structure, which in vitro, is readily accomplished by heating. Characterizing the structural changes as a function of temperature may provide fresh insights into nanomaterial/antiviral strategies. Here, we have calculated heat induced changes in the properties of an empty minute virus of mice particle using large-scale ≈ 3.0 × 10⁶ all-atom molecular dynamics simulations. We focus on two heat induced structural changes of the NP, namely, dynamical transition (DT) and breathing transition (BT), both characterized by sudden and sharp change of measured parameters at temperatures, T_DT and T_BT, respectively. While DT is assessed by mean-square fluctuation of hydrogen atoms of the NP, BT is monitored through internal volume and permeation rate of water molecules through the NP. Both the transitions, resulting primarily from collective atomistic motion, are found to occur at temperatures widely separated from one another (T_BT>T_DT). The breathing motions, responsible for the translocation events of the packaged materials through the NP to kick off, are further probed by computing atomic resolution stresses from NVE simulations. Distribution of equilibrium atomistic stresses on the NP reveals a largely asymmetric nature and suggests structural breathing may actually represent large dynamic changes in the hotspot regions, far from the NP pores, which is in remarkable resemblance with recently conducted hydrogen-deuterium exchange coupled to mass spectrometry experiment. Communicated by Ramaswamy H. Sarma.

Markov field models: Scaling molecular kinetics approaches to large molecular machines

With recent advances in structural biology, including experimental techniques and deep learning-enabled high-precision structure predictions, molecular dynamics methods that scale up to large biomolecular systems are required. Current state-of-the-art approaches in molecular dynamics modeling focus on encoding global configurations of molecular systems as distinct states. This paradigm commands us to map out all possible structures and sample transitions between them, a task that becomes impossible for large-scale systems such as biomolecular complexes. To arrive at scalable molecular models, we suggest moving away from global state descriptions to a set of coupled models that each describe the dynamics of local domains or sites of the molecular system. We describe limitations in the current state-of-the-art global-state Markovian modeling approaches and then introduce Markov field models as an umbrella term that includes models from various scientific communities, including Independent Markov decomposition, Ising and Potts models, and (dynamic) graphical models, and evaluate their use for computational molecular biology. Finally, we give a few examples of early adoptions of these ideas for modeling molecular kinetics and thermodynamics.

A Review of Mechanics-Based Mesoscopic Membrane Remodeling Methods: Capturing Both the Physics and the Chemical Diversity

Specialized classes of proteins, working together in a tightly orchestrated manner, induce and maintain highly curved cellular and organelles membrane morphology. Due to the various experimental constraints, including the resolution limits of imaging techniques, it is non-trivial to accurately elucidate interactions among the various components involved in membrane deformation. The spatial and temporal scales of the systems also make it formidable to investigate them using simulations with molecular details. Interestingly, mechanics-based mesoscopic models have been used with great success in recapitulating the membrane deformations observed in experiments. In this review, we collate together and discuss the various mechanics-based mesoscopic models for protein-mediated membrane deformation studies. In particular, we provide an elaborate description of a mesoscopic model where the membrane is modeled as a triangulated sheet and proteins are represented as either nematics or filaments. This representation allows us to explore the various aspects of protein-protein and protein-membrane interactions as well as examine the underlying mechanistic pathways for emergent behavior such as curvature-mediated protein localization and membrane deformation. We also put forward current efforts in the field towards back-mapping these mesoscopic models to finer-grained particle-based models-a framework that could be used to explore how molecular interactions propagate to physical scales and vice-versa. We end the review with an integrative-modeling-based road map where experimental imaging micrograph and biochemical data are combined with mesoscopic and molecular simulations methods in a theoretically consistent manner to faithfully recapitulate the multiple length and time scales in the membrane remodeling processes.

Human Immunodeficiency Virus Type 2 Capsid Protein Mutagenesis Reveals Amino Acid Residues Important for Virus Particle Assembly

Human immunodeficiency virus (HIV) Gag drives virus particle assembly. The capsid (CA) domain is critical for Gag multimerization mediated by protein-protein interactions. The Gag protein interaction network defines critical aspects of the retroviral lifecycle at steps such as particle assembly and maturation. Previous studies have demonstrated that the immature particle morphology of HIV-2 is intriguingly distinct relative to that of HIV-1. Based upon this observation, we sought to determine the amino acid residues important for virus assembly that might help explain the differences between HIV-1 and HIV-2. To do this, we conducted site-directed mutagenesis of targeted locations in the HIV-2 CA domain of Gag and analyzed various aspects of virus particle assembly. A panel of 31 site-directed mutants of residues that reside at the HIV-2 CA inter-hexamer interface, intra-hexamer interface and CA inter-domain linker were created and analyzed for their effects on the efficiency of particle production, particle morphology, particle infectivity, Gag subcellular distribution and in vitro protein assembly. Seven conserved residues between HIV-1 and HIV-2 (L19, A41, I152, K153, K157, N194, D196) and two non-conserved residues (G38, N127) were found to significantly impact Gag multimerization and particle assembly. Taken together, these observations complement structural analyses of immature HIV-2 particle morphology and Gag lattice organization as well as provide important comparative insights into the key amino acid residues that can help explain the observed differences between HIV immature particle morphology and its association with virus replication and particle infectivity.

Contrastive Learning of Coarse-Grained Force Fields

Coarse-grained models have proven helpful for simulating complex systems over long time scales to provide molecular insights into various processes. Methodologies for systematic parametrization of the underlying energy function or force field that describes the interactions among different components of the system are of great interest for ensuring simulation accuracy. We present a new method, potential contrasting, to enable efficient learning of force fields that can accurately reproduce the conformational distribution produced with all-atom simulations. Potential contrasting generalizes the noise contrastive estimation method with umbrella sampling to better learn the complex energy landscape of molecular systems. When applied to the Trp-cage protein, we found that the technique produces force fields that thoroughly capture the thermodynamics of the folding process despite the use of only α-carbons in the coarse-grained model. We further showed that potential contrasting could be applied over large data sets that combine the conformational ensembles of many proteins to improve force field transferability. We anticipate potential contrasting as a powerful tool for building general-purpose coarse-grained force fields.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Multiscale Modeling of Hepatitis B Virus Capsid Assembly and Its Dimorphism

Hepatitis B virus (HBV) is an endemic, chronic virus that leads to 800000 deaths per year. Central to the HBV lifecycle, the viral core has a protein capsid assembled from many copies of a single protein. The capsid protein adopts different (quasi-equivalent) conformations to form icosahedral capsids containing 180 or 240 proteins: T = 3 or T = 4, respectively, in Caspar-Klug nomenclature. HBV capsid assembly has become an important target for recently developed antivirals; nonetheless, the assembly pathways and mechanisms that control HBV dimorphism remain unclear. We describe computer simulations of the HBV assembly, using a coarse-grained model that has parameters learned from all-atom molecular dynamics simulations of a complete HBV capsid and yet is computationally tractable. Dynamical simulations with the resulting model reproduce experimental observations of HBV assembly pathways and products. By constructing Markov state models and employing transition path theory, we identify pathways leading to T = 3, T = 4, and other experimentally observed capsid morphologies. The analysis shows that capsid polymorphism is promoted by the low HBV capsid bending modulus, where the key factors controlling polymorphism are the conformational energy landscape and protein-protein binding affinities.

Accurate and Efficient Estimation of Lennard-Jones Interactions for Coarse-Grained Particles via a Potential Matching Method

The Lennard-Jones (LJ) energy functions are commonly used to describe the nonbonded interactions in bulk coarse-grained (CG) models, which contribute significantly to the stabilization of a local binding configuration or a self-assembly system. In many cases, systematic development of the LJ interaction parameters in a CG model requires a comprehensive sampling of the objective molecules at the all-atom (AA) level, which is therefore extremely time-consuming for large systems. Inspired by the concept of electrostatic potential (ESP), we define the LJ static potential (LJSP), by which the embedding potential energy surface can be constructed analytically. A semianalytic approach, namely, the LJSP matching method, is developed here to derive the CG parameters by minimizing the LJSP difference between the AA and the CG models, which provides a universal way to derive the CG LJ parameters from the AA models without doing presampling. The LJSP matching method is successful not only in deriving the LJ interaction energy landscape in the CG models for proteins, lipids, and DNA but also in reproducing the critical properties such as intermediate structures and enthalpy contributions as exemplified in simulating the self-assembly process of the dipalmitoylphosphatidylcholine (DPPC) lipids.

Inositol Hexakisphosphate (IP6) Accelerates Immature HIV-1 Gag Protein Assembly toward Kinetically Trapped Morphologies

During the late stages of the HIV-1 lifecycle, immature virions are produced by the concerted activity of Gag polyproteins, primarily mediated by the capsid (CA) and spacer peptide 1 (SP1) domains, which assemble into a spherical lattice, package viral genomic RNA, and deform the plasma membrane. Recently, inositol hexakisphosphate (IP6) has been identified as an essential assembly cofactor that efficiently produces both immature virions in vivo and immature virus-like particles in vitro. To date, however, several distinct mechanistic roles for IP6 have been proposed on the basis of independent functional, structural, and kinetic studies. In this work, we investigate the molecular influence of IP6 on the structural outcomes and dynamics of CA/SP1 assembly using coarse-grained (CG) molecular dynamics (MD) simulations and free energy calculations. Here, we derive a bottom-up, low-resolution, and implicit-solvent CG model of CA/SP1 and IP6, and simulate their assembly under conditions that emulate both in vitro and in vivo systems. Our analysis identifies IP6 as an assembly accelerant that promotes curvature generation and fissure-like defects throughout the lattice. Our findings suggest that IP6 induces kinetically trapped immature morphologies, which may be physiologically important for later stages of viral morphogenesis and potentially useful for virus-like particle technologies.

Single-molecule biophysics experiments in silico: Toward a physical model of a replisome

The interpretation of single-molecule experiments is frequently aided by computational modeling of biomolecular dynamics. The growth of computing power and ongoing validation of computational models suggest that it soon may be possible to replace some experiments outright with computational mimics. Here, we offer a blueprint for performing single-molecule studies in silico using a DNA-binding protein as a test bed. We demonstrate how atomistic simulations, typically limited to sub-millisecond durations and zeptoliter volumes, can guide development of a coarse-grained model for use in simulations that mimic single-molecule experiments. We apply the model to recapitulate, in silico, force-extension characterization of protein binding to single-stranded DNA and protein and DNA replacement assays, providing a detailed portrait of the underlying mechanics. Finally, we use the model to simulate the trombone loop of a replication fork, a large complex of proteins and DNA.

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Coarse-grained model derived from all-atom simulation recapitulates experiments

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Model reproduces the elastic response to force and exchange dynamics

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Model reveals structure of intermediate states usually inaccessible to experiment

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Model applied to viral replisome with trombone loop containing tens of SSB proteins

Cargo Release from Nonenveloped Viruses and Virus-like Nanoparticles: Capsid Rupture or Pore Formation

Virus-like nanoparticles are protein shells similar to wild-type viruses, and both aim to deliver their content into a cell. Unfortunately, the release mechanism of their cargo/genome remains elusive. Pores on the symmetry axes were proposed to enable the slow release of the viral genome. In contrast, cryo-EM images showed that capsids of nonenveloped RNA viruses can crack open and rapidly release the genome. We combined in vitro cryo-EM observations of the genome release of three viruses with coarse-grained simulations of generic virus-like nanoparticles to investigate the cargo/genome release pathways. Simulations provided details on both slow and rapid release pathways, including the success rates of individual releases. Moreover, the simulated structures from the rapid release pathway were in agreement with the experiment. Slow release occurred when interactions between capsid subunits were long-ranged, and the cargo/genome was noncompact. In contrast, rapid release was preferred when the interaction range was short and/or the cargo/genome was compact. These findings indicate a design strategy of virus-like nanoparticles for drug delivery.

Rotten to the core: antivirals targeting the HIV-1 capsid core

The capsid core of HIV-1 is a large macromolecular assembly that surrounds the viral genome and is an essential component of the infectious virus. In addition to its multiple roles throughout the viral life cycle, the capsid interacts with multiple host factors. Owing to its indispensable nature, the HIV-1 capsid has been the target of numerous antiretrovirals, though most capsid-targeting molecules have not had clinical success until recently. Lenacapavir, a long-acting drug that targets the HIV-1 capsid, is currently undergoing phase 2/3 clinical trials, making it the most successful capsid inhibitor to-date. In this review, we detail the role of the HIV-1 capsid protein in the virus life cycle, categorize antiviral compounds based on their targeting of five sites within the HIV-1 capsid, and discuss their molecular interactions and mechanisms of action. The diverse range of inhibition mechanisms provides insight into possible new strategies for designing novel HIV-1 drugs and furthers our understanding of HIV-1 biology.

Preservation of HIV-1 Gag Helical Bundle Symmetry by Bevirimat Is Central to Maturation Inhibition

The assembly and maturation of human immunodeficiency virus type 1 (HIV-1) require proteolytic cleavage of the Gag polyprotein. The rate-limiting step resides at the junction between the capsid protein CA and spacer peptide 1, which assembles as a six-helix bundle (6HB). Bevirimat (BVM), the first-in-class maturation inhibitor drug, targets the 6HB and impedes proteolytic cleavage, yet the molecular mechanisms of its activity, and relatedly, the escape mechanisms of mutant viruses, remain unclear. Here, we employed extensive molecular dynamics (MD) simulations and free energy calculations to quantitatively investigate molecular structure-activity relationships, comparing wild-type and mutant viruses in the presence and absence of BVM and inositol hexakisphosphate (IP6), an assembly cofactor. Our analysis shows that the efficacy of BVM is directly correlated with preservation of 6-fold symmetry in the 6HB, which exists as an ensemble of structural states. We identified two primary escape mechanisms, and both lead to loss of symmetry, thereby facilitating helix uncoiling to aid access of protease. Our findings also highlight specific interactions that can be targeted for improved inhibitor activity and support the use of MD simulations for future inhibitor design.

Curvature of the Retroviral Capsid Assembly Is Modulated by a Molecular Switch

During the maturation step, the retroviral capsid proteins (CAs) assemble into polymorphic capsids. Their acute curvature is largely determined by 12 pentamers inserted into the hexameric lattice. However, how the CA switches its conformation to control assembly curvature remains unclear. We report the high-resolution structural model of the Rous sarcoma virus (RSV) CA T = 1 capsid, established by molecular dynamics simulations combining solid-state NMR and prior cryoelectron tomography restraints. Comparing this with our previous model of the RSV CA tubular assembly, we identify the key residues for dictating the incorporation of acute curvatures. These residues undergo large torsion angle changes, resulting in a 34° rotation of the C-terminal domain relative to its N-terminal domain around the flexible interdomain linker, without substantial changes of either the conformation of individual domains or the assembly contact interfaces. This knowledge provides new insights to help decipher the mechanism of the retroviral capsid assembly.

Identifying crucial E-protein residues responsible for unusual stability of Zika virus envelope

An outbreak of Zika virus (ZIKV) infections in 2015-16 that caused microcephaly and other congenital abnormalities in newborns prompted intense research across the globe. These studies have suggested that ZIKV can survive high temperatures and harsh physiological conditions, unlike the other flaviviruses such as dengue virus (DENV). In contrast, recent cryo-electron microscopy studies have shown very similar architecture of the ZIKV and DENV envelopes that constitute the primary level of viral protection. Encouraged by these findings, here we attempt to identify the crucial protein residues that make the ZIKV envelope so robust by employing coarse-grained and all-atomic molecular dynamics simulations and computational mutagenesis studies. In accordance with more recent cryo-electron microscopy findings, our simulation results exhibited stable ZIKV envelope protein shell both at 29^oC and 40°C, whereas the DENV2 shell loosened up significantly at 40°C. Subsequently, we simulated a series of ZIKV variants to identify the specific domain and residues involved in maintaining the structural integrity of the viral protein shell at high temperatures. Our results suggest that the DIII domain-more specifically, the CD- and FG-loop residues of the ZIKV protein shell-play a crucial role in making the virus envelope thermostable by inducing strong raft-raft interactions. These findings can accelerate the rational design of ZIKV therapeutics.

Coarse-grained simulations of phase separation driven by DNA and its sensor protein cGAS

The enzyme cGAS functions as a sensor that recognizes the cytosolic DNA from foreign pathogen. The activation of the protein triggers the transcription of inflammatory genes, leading into the establishment of an antipathogen state. An interesting new discovery is that the detection of DNA by cGAS induced the formation of liquid-like droplets. However how cells regulate the formation of these droplets is still not fully understood. In order to unravel the molecular mechanism beneath the DNA-mediated phase separation of cGAS, we developed a polymer-based coarse-grained model which takes into accounts the basic structural organization in DNA and cGAS, as well as the binding properties between these biomolecules. This model was further integrated into a hybrid simulation algorithm. With this computational method, a multi-step kinetic process of aggregation between cGAS and DNA was observed. Moreover, we systematically tested the model under different concentrations and binding parameters. Our simulation results show that phase separation requires both cGAS dimerization and protein-DNA interactions, whereas polymers can be kinetically trapped in small aggregates under strong binding affinities. Additionally, we demonstrated that supramolecular assembly can be facilitated by increasing the number of functional modules in protein or DNA polymers, suggesting that multivalency and intrinsic disordered regions play positive roles in regulating phase separation. This is consistent to previous experimental evidences. Taken together, this is, to the best of our knowledge, the first computational model to study condensation of cGAS-DNA complexes. While the method can reach the timescale beyond the capability of atomic-level MD simulations, it still includes information about spatial arrangement of functional modules in biopolymers that is missing in the mean-field theory. Our work thereby adds a useful dimension to a suite of existing experimental and computational techniques to study the dynamics of phase separation in biological systems.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Fighting viruses with computers, right now

The synergistic conjunction of various technological revolutions with the accumulated knowledge and workflows is rapidly transforming several scientific fields. Particularly, Virology can now feed from accurate physical models, polished computational tools, and massive computational power to readily integrate high-resolution structures into biological representations of unprecedented detail. That preparedness allows for the first time to get crucial information for vaccine and drug design from in-silico experiments against emerging pathogens of worldwide concern at relevant action windows. The present work reviews some of the main milestones leading to these breakthroughs in Computational Virology, providing an outlook for future developments in capacity building and accessibility to computational resources.

Predicting the characteristics of defect transitions on curved surfaces

The energetically optimal position of lattice defects on intrinsically curved surfaces is a complex function of shape parameters. For open surfaces, a simple condition predicts the critical size for which a central disclination yields lower energy than a boundary disclination. In practice, this transition is modified by activation energies or more favorable intermediate defect positions. Here it is shown that these transition characteristics (continuous or discontinuous, first or second order) can also be inferred from analytical, general criteria evaluated from the surface shape. A universal scale of activation energy is found, and the criteria are generalized to predict transition order as surface shape symmetry is broken. The results give practical insight into structural transitions to disorder in many cellular materials of technological and biological importance.

A multiscale coarse-grained model of the SARS-CoV-2 virion

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the causative agent of the COVID-19 pandemic. Computer simulations of complete viral particles can provide theoretical insights into large-scale viral processes including assembly, budding, egress, entry, and fusion. Detailed atomistic simulations are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and ongoing development of a largely "bottom-up" coarse-grained (CG) model of the SARS-CoV-2 virion. Data from a combination of cryo-electron microscopy (cryo-EM), x-ray crystallography, and computational predictions were used to build molecular models of structural SARS-CoV-2 proteins, which were then assembled into a complete virion model. We describe how CG molecular interactions can be derived from all-atom simulations, how viral behavior difficult to capture in atomistic simulations can be incorporated into the CG models, and how the CG models can be iteratively improved as new data become publicly available. Our initial CG model and the detailed methods presented are intended to serve as a resource for researchers working on COVID-19 who are interested in performing multiscale simulations of the SARS-CoV-2 virion.

Compressive and Tensile Deformations Alter ATP Hydrolysis and Phosphate Release Rates in Actin Filaments

Actin filament networks in eukaryotic cells are constantly remodeled through nucleotide state controlled interactions with actin binding proteins, leading to macroscopic structures such as bundled filaments, branched filaments, and so on. The nucleotide (ATP) hydrolysis, phosphate release, and polymerization/depolymerization reactions that lead to the formation of these structures are correlated with the conformational fluctuations of the actin subunits at the molecular scale. The resulting structures generate and experience varying levels of force and impart cells with several functionalities such as their ability to move, divide, transport cargo, etc. Models that explicitly connect the structure to reactions are essential to elucidate a fundamental level of understanding of these processes. In this regard, a bottom-up Ultra-Coarse-Grained (UCG) model of actin filaments that can simulate ATP hydrolysis, inorganic phosphate release (Pi), and depolymerization reactions is presented in this work. In this model, actin subunits are represented using coarse-grained particles that evolve in time and undergo reactions depending on the conformations sampled. The reactions are represented through state transitions, with each state represented by a unique effective coarse-grained potential. Effects of compressive and tensile strains on the rates of reactions are then analyzed. Compressive strains tend to unflatten the actin subunits, reduce the rate of ATP hydrolysis, and increase the Pi release rate. On the other hand, tensile strain flattens subunits, increases the rate of ATP hydrolysis, and decrease the Pi release rate. Incorporating these predictions into a Markov State Model highlighted that strains alter the steady-state distribution of subunits with ADPPi and ADP nucleotide, thus identifying possible additional factors underlying the cooperative binding of regulatory proteins to actin filaments.