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.

Protein hydrogels represent an important and growing biomaterial for a multitude of applications, including diagnostics and drug delivery. We have previously explored the ability to engineer the thermoresponsive supramolecular assembly of coiled–coil proteins into hydrogels with varying gelation properties, where we have defined important parameters in the coiled–coil hydrogel design. Using Rosetta energy scores and Poisson–Boltzmann electrostatic energies, we iterate a computational design strategy to predict the gelation of coiled–coil proteins while simultaneously exploring five new coiled–coil protein hydrogel sequences. Provided this library, we explore the impact of in silico energies on structure and gelation kinetics, where we also reveal a range of blue autofluorescence that enables hydrogel disassembly and recovery. As a result of this library, we identify the new coiled–coil hydrogel sequence, Q5, capable of gelation within 24 h at 4 °C, a more than 2-fold increase over that of our previous iteration Q2. The fast gelation time of Q5 enables the assessment of structural transition in real time using small-angle X-ray scattering (SAXS) that is correlated to coarse-grained and atomistic molecular dynamics simulations revealing the supramolecular assembling behavior of coiled–coils toward nanofiber assembly and gelation. This work represents the first system of hydrogels with predictable self-assembly, autofluorescent capability, and a molecular model of coiled–coil fiber formation.

The outer membrane in Gram-negative bacteria consists of an asymmetric phospholipid—lipopolysaccharide bilayer that is densely packed with outer-membrane β-barrel proteins (OMPs) and lipoproteins The architecture and composition of this bilayer is closely monitored and is essential to cell integrity and survival Here we find that SlyB, a lipoprotein in the PhoPQ stress regulon, forms stable stress-induced complexes with the outer-membrane proteome. SlyB comprises a 10 kDa periplasmic β-sandwich domain and a glycine zipper domain that forms a transmembrane α-helical hairpin with discrete phospholipid- and lipopolysaccharide-binding sites. After loss in lipid asymmetry, SlyB oligomerizes into ring-shaped transmembrane complexes that encapsulate β-barrel proteins into lipid nanodomains of variable size. We find that the formation of SlyB nanodomains is essential during lipopolysaccharide destabilization by antimicrobial peptides or acute cation shortage, conditions that result in a loss of OMPs and compromised outer-membrane barrier function in the absence of a functional SlyB. Our data reveal that SlyB is a compartmentalizing transmembrane guard protein that is involved in cell-envelope proteostasis and integrity, and suggest that SlyB represents a larger family of broadly conserved lipoproteins with 2TM glycine zipper domains with the ability to form lipid nanodomains.

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.

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.

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.

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.

Lipid droplets (LDs) are organelles formed in the endoplasmic reticulum (ER) to store triacylglycerol (TG) and sterol esters. The ER protein seipin is key for LD biogenesis. Seipin forms a cage-like structure, with each seipin monomer containing a conserved hydrophobic helix and two transmembrane (TM) segments. How the different parts of seipin function in TG nucleation and LD budding is poorly understood. Here, we utilized molecular dynamics simulations of human seipin, along with cell-based experiments, to study seipin’s functions in protein–lipid interactions, lipid diffusion, and LD maturation. An all-atom simulation indicates that seipin TM segment residues and hydrophobic helices residues located in the phospholipid tail region of the bilayer attract TG. Simulating larger, growing LDs with coarse-grained models, we find that the seipin TM segments form a constricted neck structure to facilitate conversion of a flat oil lens into a budding LD. Using cell experiments and simulations, we also show that conserved, positively charged residues at the end of seipin’s TM segments affect LD maturation. We propose a model in which seipin TM segments critically function in TG nucleation and LD growth.

The molecular events that permit the spike glycoprotein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to bind and enter cells are important to understand for both fundamental and therapeutic reasons. Spike proteins consist of S1 and S2 domains, which recognize angiotensin-converting enzyme 2 (ACE2) receptors and contain the viral fusion machinery, respectively. Ostensibly, the binding of spike trimers to ACE2 receptors promotes dissociation of the S1 domains and exposure of the fusion machinery, although the molecular details of this process have yet to be observed. We report the development of bottom-up coarse-grained (CG) models consistent with cryo-electron tomography data, and the use of CG molecular dynamics simulations to investigate viral binding and S2 core exposure. We show that spike trimers cooperatively bind to multiple ACE2 dimers at virion-cell interfaces in a manner distinct from binding between soluble proteins, which processively induces S1 dissociation. We also simulate possible variant behavior using perturbed CG models, and find that ACE2-induced S1 dissociation is primarily sensitive to conformational state populations and the extent of S1/S2 cleavage, rather than ACE2 binding affinity. These simulations reveal an important concerted interaction between spike trimers and ACE2 dimers that primes the virus for membrane fusion and entry.

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.

A number of studies have constructed coarse-grained (CG) models of water to understand its anomalous properties. Most of these properties emerge at low temperatures, and an accurate CG model needs to be applicable to these low-temperature ranges. However, direct use of CG models parameterized from other temperatures, e.g., room temperature, encounters a problem known as transferability, as the CG potential essentially follows the form of the many-body CG free energy function. Therefore, temperature-dependent changes to CG interactions must be accounted for. The collective behavior of water at low temperature is generally a many-body process, which often motivates the use of expensive many-body terms in the CG interactions. To surmount the aforementioned problems, we apply the Bottom-Up Many-Body Projected Water (BUMPer) CG model constructed from Paper I to study the low-temperature behavior of water. We report for the first time that the embedded three-body interaction enables BUMPer, despite its pairwise form, to capture the growth of ice at the ice/water interface with corroborating many-body correlations during the crystal growth. Furthermore, we propose temperature transferable BUMPer models that are indirectly constructed from the free energy decomposition scheme. Changes in CG interactions and corresponding structures are faithfully recapitulated by this framework. We further extend BUMPer to examine its ability to predict the structure, density, and diffusion anomalies by employing an alternative analysis based on structural correlations and pairwise potential forms to predict such anomalies. The presented analysis highlights the existence of these anomalies in the low-temperature regime and overcomes potential transferability problems.

Water is undoubtedly one of the most important molecules for a variety of chemical and physical systems, and constructing precise yet effective coarse-grained (CG) water models has been a high priority for computer simulations. To recapitulate important local correlations in the CG water model, explicit higher-order interactions are often included. However, the advantages of coarse-graining may then be offset by the larger computational cost in the model parameterization and simulation execution. To leverage both the computational efficiency of the CG simulation and the inclusion of higher-order interactions, we propose a new statistical mechanical theory that effectively projects many-body interactions onto pairwise basis sets. The many-body projection theory presented in this work shares similar physics from liquid state theory, providing an efficient approach to account for higher-order interactions within the reduced model. We apply this theory to project the widely used Stillinger–Weber three-body interaction onto a pairwise (two-body) interaction for water. Based on the projected interaction with the correct long-range behavior, we denote the new CG water model as the Bottom-Up Many-Body Projected Water (BUMPer) model, where the resultant CG interaction corresponds to a prior model, the iteratively force-matched model. Unlike other pairwise CG models, BUMPer provides high-fidelity recapitulation of pair correlation functions and three-body distributions, as well as N-body correlation functions. BUMPer extensively improves upon the existing bottom-up CG water models by extending the accuracy and applicability of such models while maintaining a reduced computational cost.

The CA (capsid) domain of immature HIV-1 Gag and the adjacent spacer peptide 1 (SP1) play a key role in viral assembly by forming a lattice of CA hexamers, which adapts to viral envelope curvature by incorporating small lattice defects and a large gap at the site of budding. This lattice is stabilized by intrahexameric and interhexameric CA-CA interactions, which are important in regulating viral assembly and maturation. We applied subtomogram averaging and classification to determine the oligomerization state of CA at lattice edges and found that CA forms partial hexamers. These structures reveal the network of interactions formed by CA-SP1 at the lattice edge. We also performed atomistic molecular dynamics simulations of CA-CA interactions stabilizing the immature lattice and partial CA-SP1 helical bundles. Free energy calculations reveal increased propensity for helix-to-coil transitions in partial hexamers compared to complete six-helix bundles. Taken together, these results suggest that the CA dimer is the basic unit of lattice assembly, partial hexamers exist at lattice edges, these are in a helix-coil dynamic equilibrium, and partial helical bundles are more likely to unfold, representing potential sites for HIV-1 maturation initiation.

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.

Collective action by inverse-Bin/Amphiphysin/Rvs (I-BAR) domains drive micron-scale membrane remodeling. The macroscopic curvature sensing and generation behavior of I-BAR domains is well characterized, and computational models have suggested various mechanisms on simplified membrane systems, but there remain missing connections between the complex environment of the cell and the models proposed thus far. Here, we show a connection between the role of protein curvature and lipid clustering in the relaxation of large membrane deformations. When we include phosphatidylinositol 4,5-bisphosphate-like lipids that preferentially interact with the charged ends of an I-BAR domain, we find clustering of phosphatidylinositol 4,5-bisphosphate-like lipids that induce a directional membrane-mediated interaction between membrane-bound I-BAR domains. Lipid clusters mediate I-BAR domain interactions and cause I-BAR domain aggregates that would not arise through membrane fluctuation-based or curvature-based interactions. Inside of membrane protrusions, lipid cluster-mediated interaction draws long side-by-side aggregates together, resulting in more cylindrical protrusions as opposed to bulbous, irregularly shaped protrusions.

The ESCRT complexes drive membrane scission in HIV-1 release, autophagosome closure, multivesicular body biogenesis, cytokinesis, and other cell processes. ESCRT-I is the most upstream complex and bridges the system to HIV-1 Gag in virus release. The crystal structure of the headpiece of human ESCRT-I comprising TSG101–VPS28–VPS37B–MVB12A was determined, revealing an ESCRT-I helical assembly with a 12-molecule repeat. Electron microscopy confirmed that ESCRT-I subcomplexes form helical filaments in solution. Mutation of VPS28 helical interface residues blocks filament formation in vitro and autophagosome closure and HIV-1 release in human cells. Coarse-grained (CG) simulations of ESCRT assembly at HIV-1 budding sites suggest that formation of a 12-membered ring of ESCRT-I molecules is a geometry-dependent checkpoint during late stages of Gag assembly and HIV-1 budding and templates ESCRT-III assembly for membrane scission. These data show that ESCRT-I is not merely a bridging adaptor; it has an essential scaffolding and mechanical role in its own right.

The tripartite-motif protein, TRIM5α, is an innate immune sensor that potently restricts retrovirus infection by binding to human immunodeficiency virus capsids. Higher-ordered oligomerization of this protein forms hexagonally patterned structures that wrap around the viral capsid, despite an anomalously low affinity for the capsid protein (CA). Several studies suggest TRIM5α oligomerizes into a lattice with a symmetry and spacing that matches the underlying capsid, to compensate for the weak affinity, yet little is known about how these lattices form. Using a combination of computational simulations and electron cryo-tomography imaging, we reveal the dynamical mechanisms by which these lattices self-assemble. Constrained diffusion allows the lattice to reorganize, whereas defects form on highly curved capsid surfaces to alleviate strain and lattice symmetry mismatches. Statistical analysis localizes the TRIM5α binding interface at or near the CypA binding loop of CA. These simulations elucidate the molecular-scale mechanisms of viral capsid cellular compartmentalization by TRIM5α.

Coarse-grained (CG) models facilitate efficient simulation of complex systems by integrating out the atomic, or fine-grained (FG), degrees of freedom. Systematically derived CG models from FG simulations often attempt to approximate the CG potential of mean force (PMF), an inherently multidimensional and many-body quantity, using additive pairwise contributions. However, they currently lack fundamental principles that enable their extensible use across different thermodynamic state points, i.e., transferability. In this work, we investigate the explicit energy–entropy decomposition of the CG PMF as a means to construct transferable CG models. In particular, despite its high-dimensional nature, we find for liquid systems that the entropic component to the CG PMF can similarly be represented using additive pairwise contributions, which we show is highly coupled to the CG configurational entropy. This approach formally connects the missing entropy that is lost due to the CG representation, i.e., translational, rotational, and vibrational modes associated with the missing degrees of freedom, to the CG entropy. By design, the present framework imparts transferable CG interactions across different temperatures due to the explicit definition of an additive entropic contribution. Furthermore, we demonstrate that transferability across composition state points, such as between bulk liquids and their mixtures, is also achieved by designing combining rules to approximate cross-interactions from bulk CG PMFs. Using the predicted CG model for liquid mixtures, structural correlations of the fitted CG model were found to corroborate a high-fidelity combining rule. Our findings elucidate the physical nature and compact representation of CG entropy and suggest a new approach for overcoming the transferability problem. We expect that this approach will further extend the current view of CG modeling into predictive multiscale modeling.

The early and late stages of human immunodeficiency virus (HIV) replication are orchestrated by the capsid (CA) protein, which self-assembles into a conical protein shell during viral maturation. Small molecule drugs known as capsid inhibitors (CIs) impede the highly regulated activity of CA. Intriguingly, a few CIs, such as PF-3450074 (PF74) and GS-CA1, exhibit effects at multiple stages of the viral lifecycle at effective concentrations in the pM to nM regimes, while the majority of CIs target a single stage of the viral lifecycle and are effective at nM to μM concentrations. In this work, we use coarse-grained molecular dynamics simulations to elucidate the molecular mechanisms that enable CIs to have such curious broad-spectrum activity. Our quantitatively analyzed findings show that CIs can have a profound impact on the hierarchical self-assembly of CA by perturbing populations of small CA oligomers. The self-assembly process is accelerated by the emergence of alternative assembly pathways that favor the rapid incorporation of CA pentamers, and leads to increased structural pleomorphism in mature capsids. Two relevant phenotypes are observed: (1) eccentric capsid formation that may fail to encase the viral genome and (2) rapid disassembly of the capsid, which express at late and early stages of infection, respectively. Finally, our study emphasizes the importance of adopting a dynamical perspective on inhibitory mechanisms and provides a basis for the design of future therapeutics that are effective at low stoichiometric ratios of drug to protein.

Protein-mediated membrane remodeling is a ubiquitous and critical process for proper cellular function. Inverse Bin/Amphiphysin/Rvs (I-BAR) domains drive local membrane deformation as a precursor to large-scale membrane remodeling. We employ a multiscale approach to provide the molecular mechanism of unusual I-BAR domain-driven membrane remodeling at a low protein surface concentration with near-atomistic detail. We generate a bottom-up coarse-grained model that demonstrates similar membrane-bound I-BAR domain aggregation behavior as our recent Mesoscopic Membrane with Explicit Proteins model. Together, these models bridge several length scales and reveal an aggregation behavior of I-BAR domains. We find that at low surface coverage (i.e., low bound protein density), I-BAR domains form transient, tip-to-tip strings on periodic flat membrane sheets. Inside of lipid bilayer tubules, we find linear aggregates parallel to the axis of the tubule. Finally, we find that I-BAR domains form tip-to-tip aggregates around the edges of membrane domes. These results are supported by in vitro experiments showing low curvature bulges surrounded by I-BAR domains on giant unilamellar vesicles. Overall, our models reveal new I-BAR domain aggregation behavior in membrane tubules and on the surface of vesicles at low surface concentration that add insight into how I-BAR domain proteins may contribute to certain aspects of membrane remodeling in cells.

Despite the central role of lipids in many biophysical functions, the molecular mechanisms that dictate macroscopic lipid behavior remain elusive to both experimental and computational approaches. As such, there has been much interest in the development of low-resolution, implicit-solvent coarse-grained (CG) models to dynamically simulate biologically relevant spatiotemporal scales with molecular fidelity. However, in the absence of solvent, a key challenge for CG models is to faithfully emulate solvent-mediated forces, which include both hydrophilic and hydrophobic interactions that drive lipid aggregation and self-assembly. In this work, we provide a new methodological framework to incorporate semiexplicit solvent effects through the use of virtual CG particles, which represent structural features of the solvent-lipid interface. To do so, we leverage two systematic coarse-graining approaches, multiscale coarse-graining (MS-CG) and relative entropy minimization (REM), in a hybrid fashion to construct our virtual-site CG (VCG) models. As a proof-of-concept, we focus our efforts on two lipid species, 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), which adopt a liquid-disordered and gel phase, respectively, at room temperature. Through our analysis, we also present, to our knowledge, the first direct comparison between the MS-CG and REM methods for a complex biomolecule and highlight each of their strengths and weaknesses. We further demonstrate that VCG models recapitulate the rich biophysics of lipids, which enable self-assembly, morphological diversity, and multiple phases. Our findings suggest that the VCG framework is a powerful approach for investigation into macromolecular biophysics.

Recent progress in coarse-grained (CG) molecular modeling and simulation has facilitated an influx of computational studies on biological macromolecules and their complexes. Given the large separation of length-scales and time-scales that dictate macromolecular biophysics, CG modeling and simulation are well-suited to bridge the microscopic and mesoscopic or macroscopic details observed from all-atom molecular simulations and experiments, respectively. In this review, we first summarize recent innovations in the development of CG models, which broadly include structure-based, knowledge-based, and dynamics-based approaches. We then discuss recent applications of different classes of CG models to explore various macromolecular complexes. Finally, we conclude with an outlook for the future in this ever-growing field of biomolecular modeling.

The packaging and budding of Gag polyprotein and viral RNA is a critical step in the HIV-1 life cycle. High-resolution structures of the Gag polyprotein have revealed that the capsid (CA) and spacer peptide 1 (SP1) domains contain important interfaces for Gag self-assembly. However, the molecular details of the multimerization process, especially in the presence of RNA and the cell membrane, have remained unclear. In this work, we investigate the mechanisms that work in concert between the polyproteins, RNA, and membrane to promote immature lattice growth. We develop a coarse-grained (CG) computational model that is derived from subnanometer resolution structural data. Our simulations recapitulate contiguous and hexameric lattice assembly driven only by weak anisotropic attractions at the helical CA–SP1 junction. Importantly, analysis from CG and single-particle tracking photoactivated localization (spt-PALM) trajectories indicates that viral RNA and the membrane are critical constituents that actively promote Gag multimerization through scaffolding, while overexpression of short competitor RNA can suppress assembly. We also find that the CA amino-terminal domain imparts intrinsic curvature to the Gag lattice. As a consequence, immature lattice growth appears to be coupled to the dynamics of spontaneous membrane deformation. Our findings elucidate a simple network of interactions that regulate the early stages of HIV-1 assembly and budding.

Electrochemical double layer capacitors, or supercapacitors, are high-power energy storage devices that consist of large surface area electrodes (filled with electrolyte) to accommodate ion packing in accordance with classical electric double layer (EDL) theory. Nanoporous carbons (NPCs) have recently emerged as a class of electrode materials with the potential to dramatically improve the capacitance of these devices by leveraging ion confinement. However, the molecular mechanisms underlying such enhancements are a clear departure from EDL theory and remain an open question. In this paper, we present the concept of ion reorganization kinetics during charge/discharge cycles, especially within highly confining subnanometer pores, which necessarily dictates the capacitance. Our molecular dynamics voltammetric simulations of ionic liquid immersed in NPC electrodes (of varying pore size distributions) demonstrate that the most efficient ion migration, and thereby largest capacitance, is facilitated by nonuniformity of shape (e.g., from cylindrical to slitlike) along nanopore channels. On the basis of this understanding, we propose that a new structural descriptor, coined as the pore shape factor, can provide a new avenue for materials optimization. These findings also present a framework to understand and evaluate ion migration kinetics within charged nanoporous materials.

High electrical conductivity and large accessible surface area, which are required for ideal electrode materials of energy conversion and storage devices, are opposed to each other in current materials. It is a long-term goal to solve this issue. Herein, we report highly conductive porous Na-embedded carbon (Na@C) nanowalls with large surface areas, which have been synthesized by an invented reaction of CO with liquid Na. Their electrical conductivities are 2 orders of magnitude larger than highly conductive 3D graphene. Furthermore, almost all their surface areas are accessible for electrolyte ions. These unique properties make them ideal electrode materials for energy devices, which significantly surpass expensive Pt. Consequently, the dye-sensitized solar cells (DSSCs) with the Na@C counter electrode has reached a high power conversion efficiency of 11.03%. The Na@C also exhibited excellent performance for supercapacitors, leading to high capacitance of 145 F g^–1 at current density of 1 A g^–1.

Over the past decade, interest in leveraging subnanometer pores for improved capacitance in electrochemical double layer capacitors (EDLCs) has readily grown. Correspondingly, many theoretical studies have endeavored to understand the mechanisms that dictate the capacitance enhancement once ions are confined within nanopores, typically within quasi-equilibrium conditions. However, a kinetic-based understanding of the capacitance may be important, especially since the dynamics of ion transport can exhibit dramatic differences under confinement compared to the bulk liquid phase; ion transport is driven by the competition between the electrostatic electrode–ion and ion–ion interactions, which can be comparable as the internal surface area to volume ratio increases. In this work, we study the relationship between the dynamics of 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIM/BF₄) ionic liquid and the capacitance within two idealized cylindrical subnanometer pores with diameters of 0.81 and 1.22 nm using classical molecular dynamics simulations. By adjusting the voltage scan rate, we find that the capacitance is highly sensitive to the formation of an electroneutral ionic liquid region; with rapid charging, consolidated anion–cation contact pairs, which remain trapped within the pore, restrict the local accumulation of charge carriers and, thereby, the capacitance. These findings highlight potential kinetic limitations that can mitigate the benefits from electrodes with subnanometer pores.

One important attribute of graphene that makes it attractive for high-performance electronics is its inherently large thermal conductivity (κ) for the purposes of thermal management. Using a combined density-functional theory and classical molecular-dynamics approach, we predict that the κ of graphene supported on hexagonal boron nitride (h-BN) can be as large as 90% of the κ of suspended graphene, in contrast to the significant suppression of κ (more than 70% reduction) on amorphous silica. Interestingly, we find that this enhanced thermal transport is largely attributed to increased lifetimes of the in-plane acoustic phonon modes, which is a notable contrast from the dominant contribution of out-of-plane acoustic modes in suspended graphene. This behavior is possible due to the charge polarization throughout graphene that induces strong interlayer adhesion between graphene and h-BN. These findings highlight the potential benefit of layered dielectric substrates such as h-BN for graphene-based thermal management, in addition to their electronic advantages. Furthermore, our study brings attention to the importance of understanding the interlayer interactions of graphene with layered dielectric materials which may offer an alternative technological platform for substrates in electronics.

The lowest possible thermal conductivity of silicon–germanium (SiGe) bulk alloys achievable through alloy scattering, or the so-called alloy limit, is important to identify for thermoelectric applications. However, this limit remains a subject of contention as both experimentally-reported and theoretically-predicted values tend to be widely scattered and inconclusive. In this work, we present a possible explanation for these discrepancies by demonstrating that the thermal conductivity can vary significantly depending on the degree of randomness in the spatial arrangement of the constituent atoms. Our study suggests that the available experimental data, obtained from alloy samples synthesized using ball-milling techniques, and previous first-principles calculations, restricted by small supercell sizes, may not have accessed the alloy limit. We find that low-frequency anharmonic phonon modes can persist unless the spatial distribution of Si and Ge atoms is completely random at the atomic scale, in which case the lowest possible thermal conductivity may be achieved. Our theoretical analysis predicts that the alloy limit of SiGe could be around 1–2 W m⁻¹ K⁻¹ with an optimal composition around 25 at% Ge, which is substantially lower than previously reported values from experiments and first-principles calculations.

Reduced graphene oxide (rGO) has been explored as an alternative to graphene as an electrode material for use in supercapacitors, which thus enables highly scalable solution-based processing. To understand the performance of rGO electrodes in supercapacitors, we theoretically investigate model systems by considering OH-functionalized graphene immersed in 1-ethyl-3-methylimidazolium bis(fluorosulfonyl)imide (EMIM/FSI) ionic liquid. Our specific interest is to understand the influence of varying the hydroxyl content (or O/C ratio) on both the quantum (C_Q) and electric double-layer (C_D) capacitances. Ultimately, the total interfacial capacitance is found to be sensitive to O/C, but is optimized when the suppression of C_D is most effectively mitigated by the enhancement in C_Q. Our findings clearly demonstrate that the use of GO materials has the potential to enhance supercapacitor performance significantly but will require careful control of both the concentration and composition of oxygen functional groups along the basal surface.

The dielectric constant or relative permittivity (ε_r) of a dielectric material, which describes how the net electric field in the medium is reduced with respect to the external field, is a parameter of critical importance for charging and screening in electronic devices. Such a fundamental material property is intimately related to not only the polarizability of individual atoms but also the specific atomic arrangement in the crystal lattice. In this Letter, we present both experimental and theoretical investigations on the dielectric constant of few-layer In₂Se₃ nanoflakes grown on mica substrates by van der Waals epitaxy. A nondestructive microwave impedance microscope is employed to simultaneously quantify the number of layers and local electrical properties. The measured ε_r increases monotonically as a function of the thickness and saturates to the bulk value at around 6–8 quintuple layers. The same trend of layer-dependent dielectric constant is also revealed by first-principles calculations. Our results of the dielectric response, being ubiquitously applicable to layered 2D semiconductors, are expected to be significant for this vibrant research field.

The thermal conductivity (κ) of graphene dramatically decreases once supported on a substrate, hindering its use for thermal management. To clarify the underlying mechanisms, we investigate the κ of graphene on amorphous SiO2 by using molecular dynamics with particular attention to the graphene-substrate topography. Our analysis reveals that the suppression in κ increases with the nonuniformity of the forces acting on graphene, which tends to increase as the substrate-surface roughness and graphene conformity increase. Our findings highlight the importance of the interfacial morphology on κ and can provide guidance on the design of substrates to improve thermal transport through graphene.

The electric double layer (C_D) and electrode quantum (C_Q) capacitances of graphene-based supercapacitors are investigated using a combined molecular dynamics and density functional theory approach. In particular, we compare an approach that includes electronic polarization to one that is polarization-free by evaluating both C_D and C_Q using [EMIM][BF₄] ionic liquid as a model electrolyte. Our results indicate that the inclusion of polarization effects can yield higher C_D values—in this study by up to 40% around ±2 V—which we attribute primarily to the presence of charge smearing at the electrode-electrolyte interface. On the other hand, we find that the polarization-induced distortion of the electronic structure of graphene does not noticeably alter the predicted C_Q. Our analysis suggests that an accurate description of the spatial charge distribution at the graphene interface due to polarization is necessary to improve our predictive capabilities, though more notably for C_D. However, the conventional polarization-free approximation can serve as an efficient tool to study trends associated with both the C_Q and C_D at the interface of various graphene-like materials.

The inherently large surface area and electrical conductivity of graphene-like electrodes have motivated extensive research for their use in supercapacitors. Although these properties are beneficial for the electric double layer (EDL) capacitance, the full utilization of graphene is curtailed by its intrinsically limited quantum capacitance due to the low density of electronic states near the neutrality point. While recent work has demonstrated that modifications to graphene can generally mitigate this limitation, a comprehensive analysis of the impact of graphene edges, which can be created during synthesis and post-treatment, has yet to be reported. Using a theoretical approach, we investigate the influence of graphene edges on both the quantum and EDL capacitances using edge-passivated zigzag graphene nanoribbons (ZGNRs) in [BMIM][PF₆] ionic liquid as model systems. Our findings show that the presence of edges improves the quantum capacitance by increasing the electronic density of states, which is further amplified as the ZGNR width decreases. Our analysis also reveals that the EDL microstructure can be noticeably altered by the edges, which in turn increases the EDL capacitance. Through comparisons with pristine graphene electrodes, our study clearly highlights that edge defects in graphene-like electrodes can enhance supercapacitor performance by dramatically augmenting both EDL and quantum capacitances.

Chemically doped graphene-based materials have recently been explored as a means to improve the performance of supercapacitors. In this work, we investigate the effects of 3d transition metals bound to vacancy sites in graphene with [BMIM][PF₆] ionic liquid on the interfacial capacitance; these results are compared to the pristine graphene case with particular attention to the relative contributions of the quantum and electric double layer capacitances. Our study highlights that the presence of metal-vacancy complexes significantly increases the availability of electronic states near the charge neutrality point, thereby enhancing the quantum capacitance drastically. In addition, the use of metal-doped graphene electrodes is found to only marginally influence the microstructure and capacitance of the electric double layer. Our findings indicate that metal-doping of graphene-like electrodes can be a promising route toward increasing the interfacial capacitance of electrochemical double layer capacitors, primarily by enhancing the quantum capacitance.

Graphene-based materials have been proposed as promising electrodes for electric double layer capacitors. Recently, it has been found that one of the limitations of graphene electrodes is the finite quantum capacitance at low applied voltage. In this work, we investigate the impact of having point-like topological defects in graphene on the electronic structure and quantum capacitance. Our results clearly show that the presence of defects, such as Stone Wales, di-vacancies, and di-interstitials, can substantially enhance the quantum capacitance when compared to pristine graphene, which is found to be due to defect-induced quasi-localized states near the Fermi level. In addition, the charging behavior tends to be asymmetric around the neutrality point. We also discuss the possibility of tuning the electronic structure and capacitance through mixtures of these defects. Our findings suggest that graphene-based electrodes with topological defects may demonstrate noteworthy capacitance but should be carefully selected for use as either the positive or negative electrode.

Carbon nanotube (CNT) electrodes in supercapacitors have recently demonstrated enhanced performance compared to conventional carbon-based electrodes; however, the underlying relationships between electrode curvature and capacitance remain unclear. Using computer simulations, we evaluate the capacitive performance of metallic (6,6), (10,10), and (16,16) CNTs in [BMIM][PF₆] ionic liquid (IL), with particular attention to the relative contributions of the electric double layer (EDL) capacitance (C_D) at the CNT/IL interface and the electrode quantum capacitance (C_Q). Our classical molecular dynamics simulations reveal that C_D improves with increasing electrode curvature, which we discuss in terms of how the curvature affects both the electric field strength and EDL microstructure. In addition, the C_Q of the CNTs is constant near the Fermi level and increases with curvature, as also demonstrated by density functional theory calculations. Our study shows that the electrode curvature effect on the total interfacial capacitance can be a strong function of applied voltage, which we attribute to the shifting contributions of C_Q and C_D.

Motivated by promising demonstrations of carbon nanotube (CNT) electrodes in supercapacitors, we evaluate the capacitive performance of a (6,6) CNT in [BMIM][PF₆] ionic liquid (IL), with particular attention to the relative contributions of the electric double layer (EDL) capacitance (C_D) at the CNT/IL interface and the quantum capacitance (C_Q) of the CNT. Our classical molecular dynamics simulations reveal that the use of the CNT improves C_D when compared to planar graphene, which we discuss in terms of how the electrode curvature affects both the electric field strength and IL packing density. In addition, according to density functional theory calculations, the C_Q of the CNT is constant and significantly larger than that of graphene near the Fermi level, which is a consequence of the larger number of available electron states in the CNT. Our study also shows that the relative performance of the CNT- and graphene-based electrodes can be a strong function of applied voltage, which we attribute to the shifting contributions of C_Q and C_D.

Graphene-based electrodes have been widely tested and used in electrochemical double layer capacitors due to their high surface area and electrical conductivity. Nitrogen doping of graphene has recently been demonstrated to significantly enhance capacitance, but the underlying mechanisms remain ambiguous. We present the doping effect on the interfacial capacitance between graphene and [BMIM][PF₆] ionic liquid, particularly the relative changes in the double layer and electrode (quantum) capacitances. The electrode capacitance change was evaluated based on density functional theory calculations of doping-induced electronic structure modifications in graphene, while the microstructure and capacitance of the double layers forming near undoped/doped graphene electrodes were calculated using classical molecular dynamics. Our computational study clearly demonstrates that nitrogen doping can lead to significant enhancement in the electrode capacitance as a result of electronic structure modifications while there is virtually no change in the double layer capacitance. This finding sheds some insight into the impact of the chemical and/or mechanical modifications of graphene-like electrodes on supercapacitor performance.

A combination of graphene-like electrodes and ionic liquid (IL) electrolytes has emerged as a viable and attractive choice for electrochemical double layer (EDL) capacitors. Based on combined classical molecular dynamics and density functional theory calculations, we present the interfacial capacitance between planar graphene and [BMIM][PF₆] IL, with particular attention to the relative contributions of the electric double layer capacitance at the graphene/IL interface and the quantum capacitance of graphene. The microstructure of [BMIM][PF₆] near the graphene electrode with varying charge densities are investigated to provide a molecular description of EDLs, including BMIM/PF₆ packing and orientation, cation-anion segregation, and electrode charge screening. Although the IL interfacial structures exhibit an alternative cation/anion layering extending a few nanometers, the calculated potential profiles provide evidence of one-ion thick compact EDL formation. The capacitance-potential curve of the EDL is convex- or bell-shaped, whereas the quantum capacitance of graphene is found to have concave- or U-shaped characteristics with a minimum of nearly zero. Consequently, we find that the total interfacial capacitance exhibits a U-shaped trend, consistent with existing experimental observations at a typical carbon/IL interface. Our work highlights the importance of the quantum capacitance in the overall performance of graphene-based EDL capacitors.

The single day operation and size of a seawater reverse osmosis (RO) plant subject to a half-hourly varying electricity price is optimized. The study herein is an extension of Ghobeity and Mitsos, 2010 Desalination. Their model is modified to have a variable plant size controlled by the number of modules. The operating and capital costs are calculated as a function of size and operation. The objective of the optimization is to minimize the total annualized cost of the plant. The number of modules and the half-hourly varying operating frequency constitute the decision variables. The operation and size are optimized for four different electricity price functions: constant, moderately fluctuating, highly fluctuating, and actual electricity prices from a given day in Spain. The results show that variable operation and oversizing can produce savings of up to 7% for a highly fluctuating electricity price. The plant has a higher operating frequency when electricity is cheap and shuts off during periods of high electricity price when oversized. The size and day-by-day operation are also optimized for one year subject to Spain's electricity price. Little savings via oversizing are obtainable for the day-by-day optimization due to low fluctuations in the electricity price during the year.