Systematic Coarse-Grained Lipid Force Fields with Semiexplicit Solvation via Virtual Sites

Rigorous Progress in Coarse-Graining

Low-resolution coarse-grained (CG) models provide remarkable computational and conceptual advantages for simulating soft materials. In principle, bottom-up CG models can reproduce all structural and thermodynamic properties of atomically detailed models that can be observed at the resolution of the CG model. This review discusses recent progress in developing theory and computational methods for achieving this promise. We first briefly review variational approaches for parameterizing interaction potentials and their relationship to machine learning methods. We then discuss recent approaches for simultaneously improving both the transferability and thermodynamic properties of bottom-up models by rigorously addressing the density and temperature dependence of these potentials. We also briefly discuss exciting progress in modeling high-resolution observables with low-resolution CG models. More generally, we highlight the essential role of the bottom-up framework not only for fundamentally understanding the limitations of prior CG models but also for developing robust computational methods that resolve these limitations in practice.

Optimizing Coarse-Grained Models for Large-Scale Membrane Protein Simulation

Coarse-grained (CG) models have been developed for studying membrane proteins at physiologically relevant scales. Such methods, including popular CG lipid models, exhibit stability and efficiency at moderate scales, but they can become impractical or even unusable beyond a critical size due to various technical issues. Here, we report that these scale-dependent issues can arise from progressively slower relaxation dynamics and become confounded by unforeseen instabilities observed only at larger scales. To address these issues, we systemically optimized a 4-site solvent-free CG lipid model that is suitable for conducting micron-scale molecular dynamics simulations of membrane proteins under various membrane properties. We applied this lipid model to explore the long-range membrane deformation induced by a large mechanosensitive ion channel, PIEZO. We show that the optimized CG models are powerful in elucidating the structural and dynamic interplay between PIEZO and the membrane. Furthermore, we anticipate that our methodological insights can prove useful for resolving issues stemming from scale-dependent limitations of similar CG methodologies.

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.

Computational Prediction of Coiled-Coil Protein Gelation Dynamics and Structure

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.

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.

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.

Mesoscale simulations: An indispensable approach to understand biomembranes

Computer simulation techniques form a versatile tool, a computational microscope, for exploring biological processes. This tool has been particularly effective in exploring different features of biological membranes. In recent years, thanks to elegant multiscale simulation schemes, some fundamental limitations of investigations by distinct simulation techniques have been resolved. As a result, we are now capable of exploring processes spanning multiple scales beyond the capacity of any single technique. In this perspective, we argue that mesoscale simulations require more attention and must be further developed to fill evident gaps in a quest toward simulating and modeling living cell membranes.

Flow-Matching: Efficient Coarse-Graining of Molecular Dynamics without Forces

Coarse-grained (CG) molecular simulations have become a standard tool to study molecular processes on time and length scales inaccessible to all-atom simulations. Parametrizing CG force fields to match all-atom simulations has mainly relied on force-matching or relative entropy minimization, which require many samples from costly simulations with all-atom or CG resolutions, respectively. Here we present flow-matching, a new training method for CG force fields that combines the advantages of both methods by leveraging normalizing flows, a generative deep learning method. Flow-matching first trains a normalizing flow to represent the CG probability density, which is equivalent to minimizing the relative entropy without requiring iterative CG simulations. Subsequently, the flow generates samples and forces according to the learned distribution in order to train the desired CG free energy model via force-matching. Even without requiring forces from the all-atom simulations, flow-matching outperforms classical force-matching by an order of magnitude in terms of data efficiency and produces CG models that can capture the folding and unfolding transitions of small proteins.

Cholesterol and M2 Rendezvous in Budding and Scission of Influenza A Virus

The cholesterol of the host cell plasma membrane and viral M2 protein plays a crucial role in multiple stages of infection and replication of the influenza A virus. Cholesterol is required for the formation of heterogeneous membrane microdomains (or rafts) in the budozone of the host cell that serves as assembly sites for the viral components. The raft microstructures act as scaffolds for several proteins. Cholesterol may further contribute to the mechanical forces necessary for membrane scission in the last stage of budding and help to maintain the stability of the virus envelope. The M2 protein has been shown to cause membrane scission in model systems by promoting the formation of curved lipid bilayer structures that, in turn, can lead to membrane vesicles budding off or scission intermediates. Membrane remodeling by M2 is intimately linked with cholesterol as it affects local lipid composition, fluidity, and stability of the membrane. Thus, both cholesterol and M2 protein contribute to the efficient and proper release of newly formed influenza viruses from the virus-infected cells.

A Core-Shell Approach for Systematically Coarsening Nanoparticle-Membrane Interactions: Application to Silver Nanoparticles

The continuous release of engineered nanomaterial (ENM) into the environment may bring about health concerns following human exposure. One important source of ENMs are silver nanoparticles (NPs) that are extensively used as anti-bacterial additives. The introduction of ENMs into the human body can occur via ingestion, skin uptake or the respiratory system. Therefore, evaluating how NPs translocate over bio-membranes is essential in assessing their primary toxicity. Unfortunately, data regarding membrane-NP interaction is still scarce, as is theoretical and in silico insight into what governs adhesion and translocation for the most relevant NPs and membranes. Coarse-grained (CG) molecular descriptions have the potential to alleviate this situation, but are hampered by the absence of a direct link to NP materials and membrane adhesion mechanisms. Here, we interrogate the relationship between the most common NP representation at the CG level and the adhesion characteristics of a model lung membrane. We find that this representation for silver NPs is non-transferable, meaning that a proper CG representation for one size is not suited for other sizes. We also identify two basic types of primary adhesion-(partial) NPs wrapping by the membrane and NP insertion into the membrane-that closely relate to the overall NP hydrophobicity and significantly differ in terms of lipid coatings. The proven non-transferability of the standard CG representation with size forms an inspiration for introducing a core-shell model even for bare NPs that are uniform in composition. Using existing all-atom molecular dynamics (MD) data as a reference, we show that this extension does allow us to reproduce size-dependent NP adhesion properties and lipid responses to NP binding at the CG level. The subsequent CGMD evaluation for 10 nm Ag NPs provides new insight into membrane binding for relevant NP sizes and into the role of water in trapping NPs into defected mixed monolayer-bilayer states. This development will be instrumental for simulating NP-membrane adhesion towards more experimentally relevant length and time scales for particular NP materials.

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.

Physical Characterization of Triolein and Implications for Its Role in Lipid Droplet Biogenesis

Lipid droplets (LDs) are neutral lipid-storing organelles surrounded by a phospholipid (PL) monolayer. At present, how LDs are formed in the endoplasmic reticulum (ER) bilayer is poorly understood. In this study, we present a revised all-atom (AA) triolein (TG) model, the main constituent of the LD core, and characterize its properties in a bilayer membrane to demonstrate the implications of its behavior in LD biogenesis. In bilayer simulations, TG resides at the surface, adopting PL-like conformations (denoted in this work as SURF-TG). Free energy sampling simulation results estimate the barrier for TG relocating from the bilayer surface to the bilayer center to be ∼2 kcal/mol in the absence of an oil lens. SURF-TG is able to modulate membrane properties by increasing PL ordering, decreasing bending modulus, and creating local negative curvature. The other neutral lipid, dioleoyl-glycerol (DAG), also reduces the membrane bending modulus and populates negative curvature regions. A phenomenological coarse-grained (CG) model is also developed to observe larger-scale SURF-TG-mediated membrane deformation. CG simulations confirm that TG nucleates between the bilayer leaflets at a critical concentration when SURF-TG is evenly distributed. However, when one monolayer contains more SURF-TG, the membrane bends toward the other leaflet, followed by TG nucleation if a concentration is higher than the critical threshold. The central conclusion of this study is that SURF-TG is a negative curvature inducer, as well as a membrane modulator. To this end, a model is proposed in which the accumulation of SURF-TG in the luminal leaflet bends the ER bilayer toward the cytosolic side, followed by TG nucleation.

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.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). I. General theory and model

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.

Coarse-grained implicit solvent lipid force field with a compatible resolution to the Cα protein representation

Biological membranes have been prominent targets for coarse-grained (CG) molecular dynamics simulations. While minimal CG lipid models with three beads per lipid and quantitative CG lipid models with >10 beads per lipid have been well studied, in between them, CG lipid models with a compatible resolution to residue-level CG protein models are much less developed. Here, we extended a previously developed three-bead lipid model into a five-bead model and parameterized it for two phospholipids, POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine). The developed model, iSoLF, reproduced the area per lipid, hydrophobic thickness, and phase behaviors of the target phospholipid bilayer membranes at the physiological temperature. The model POPC and DPPC membranes were in liquid and gel phases, respectively, in accordance with experiments. We further examined the spontaneous formation of a membrane bilayer, the temperature dependence of physical properties, the vesicle dynamics, and the POPC/DPPC two-component membrane dynamics of the CG lipid model, showing some promise. Once combined with standard Cα protein models, the iSoLF model will be a powerful tool to simulate large biological membrane systems made of lipids and proteins.

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, however, are constrained to shorter timescales and require billion-atom simulations for these processes. Here, we report the current status and on-going development of a largely "bottom-up" coarse-grained (CG) model of the SARS-CoV-2 virion. Structural 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 becomes 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.

Significance Statement

This study reports the construction of a molecular model for the SARS-CoV-2 virion and details our multiscale approach towards model refinement. The resulting model and methods can be applied to and enable the simulation of SARS-CoV-2 virions.

Dimerization energetics of the G-protein coupled bile acid receptor TGR5 from all-atom simulations

We describe the first extensive energetic evaluation of GPCR dimerization on the atomistic level by means of potential of mean force (PMF) computations and implicit solvent/implicit membrane end-point free energy calculations (MM-PBSA approach). Free energies of association computed from the PMFs show that the formation of both the 1/8 and 4/5 interface is energetically favorable for TGR5, the first GPCR known to be activated by hydrophobic bile acids and neurosteroids. Furthermore, formation of the 1/8 interface is favored over that of the 4/5 interface. Both results are in line with our previous FRET experiments in live cells. Differences in lipid-protein interactions are identified to contribute to the observed differences in free energies of association. A per-residue decomposition of the MM-PBSA effective binding energy reveals hot spot residues specific for both interfaces that form clusters. This knowledge may be used to guide the design of dimerization inhibitors or perform mutational studies to explore physiological consequences of distorted TGR5 association. Finally, we characterized the role of Y111, located in the conserved (D/E)RY motif, as a facilitator of TGR5 interactions. The types of computations performed here should be transferable to other transmembrane proteins that form dimers or higher oligomers as long as good structural models of the dimeric or oligomeric states are available. Such computations may help to overcome current restrictions due to an imperfect energetic representation of protein association at the coarse-grained level. © 2019 Wiley Periodicals, Inc.

Fat SIRAH: Coarse-Grained Phospholipids To Explore Membrane-Protein Dynamics

The capability to handle highly heterogeneous molecular assemblies in a consistent manner is among the greatest challenges faced when deriving simulation parameters. This is particularly the case for coarse-grained (CG) simulations in which chemical functional groups are lumped into effective interaction centers for which transferability between different chemical environments is not guaranteed. Here, we introduce the parametrization of a set of CG phospholipids compatible with the latest version of the SIRAH force field for proteins. The newly introduced lipid species include different acylic chain lengths and partial unsaturation, as well as polar and acidic head groups that show a very good reproduction of structural membrane determinants, such as areas per lipid, thickness, order parameter, etc., and their dependence with temperature. Simulation of membrane proteins showed unprecedented accuracy in the unbiased description of the thickness-dependent membrane-protein orientation in systems where this information is experimentally available (namely, the SarcoEndoplasmic Reticulum Calcium-SERCA-pump and its regulator Phospholamban). The interactions that lead to this faithful reproduction can be traced down to the single amino acid-lipid interaction level and show full agreement with biochemical data present in the literature. Finally, the present parametrization is implemented in the GROMACS and AMBER simulation packages facilitating its use by a wide portion of the biocomputing community.

Understanding Missing Entropy in Coarse-Grained Systems: Addressing Issues of Representability and Transferability

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.

Exploring the impact of proteins on the line tension of a phase-separating ternary lipid mixture

The separation of lipid mixtures into thermodynamically stable phase-separated domains is dependent on lipid composition, temperature, and system size. Using molecular dynamics simulations, the line tension between thermodynamically stable lipid domains formed from ternary mixtures of di-C16:0 PC:di-C18:2 PC:cholesterol at 40:40:20 mol. % ratio was investigated via two theoretical approaches. The line tension was found to be 3.1 ± 0.2 pN by capillary wave theory and 4.7 ± 3.7 pN by pressure tensor anisotropy approaches for coarse-grained models based on the Martini force field. Using an all-atom model of the lipid membrane based on the CHARMM36 force field, the line tension was found to be 3.6 ± 0.9 pN using capillary wave theory and 1.8 ± 2.2 pN using pressure anisotropy approaches. The discrepancy between estimates of the line tension based on capillary wave theory and pressure tensor anisotropy methods is discussed. Inclusion of protein in Martini membrane lipid mixtures was found to reduce the line tension by 25%-35% as calculated by the capillary wave theory approach. To further understand and predict the behavior of proteins in phase-separated membranes, we have formulated an analytical Flory-Huggins model and parameterized it against the simulation results. Taken together these results suggest a general role for proteins in reducing the thermodynamic cost associated with domain formation in lipid mixtures and quantifies the thermodynamic driving force promoting the association of proteins to domain interfaces.