Developing and applying new theoretical and computational methods to study complex condensed phase systems
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Multi-scale Coarse-graining (MS-CG) Force Matching (FM) code is now publicly available for download
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.
ClC‐ec1 is a Cl−/H+ antiporter that exchanges Cl− and H+ ions across the membrane. Experiments have demonstrated that several mutations, including I109F, decrease the Cl− and H+ transport rates by order of magnitude. Using reactive molecular dynamics simulations of explicit proton transport across the central region in the I109F mutant, a two‐dimensional free energy profile has been constructed that is consistent with the experimental transport rates. The importance of a phenylalanine gate formed by F109 and F357 and its influence on hydration connectivity through the central proton transport pathway is revealed. This work demonstrates how seemingly subtle changes in local conformational dynamics can dictate hydration changes and thus transport properties.
Coarse-grained (CG) observable expressions, such as pressure or potential energy, are generally different than their fine-grained (FG, e.g., atomistic) counterparts. Recently, we analyzed this so-called “representability problem” in Wagner et al. [J. Chem. Phys. 145, 044108 (2016)]. While the issue of representability was clearly and mathematically stated in that work, it was not made clear how to actually determine CG observable expressions from the underlying FG systems that can only be simulated numerically. In this work, we propose minimization targets for the CG observables of such systems. These CG observables are compatible with each other and with structural observables. Also, these CG observables are systematically improvable since they are variationally minimized. Our methods are local and data efficient because we decompose the observable contributions. Hence, our approaches are called the multiscale compatible observable decomposition (MS-CODE) and the relative entropy compatible observable decomposition (RE-CODE), which reflect two main approaches to the “bottom-up” coarse-graining of real FG systems. The parameterization of these CG observable expressions requires the introduction of new, symmetric basis sets and one-body terms. We apply MS-CODE and RE-CODE to 1-site and 2-site CG models of methanol for the case of pressure, as well as to 1-site methanol and acetonitrile models for potential energy.
Adversarial-Residual-Coarse-Graining: Applying Machine Learning Theory to Systematic Molecular Coarse-Graining
In this paper, connections between molecular coarse-graining (CG) approaches and implicit generative models in machine learning used to describe a new framework for systematic molecular CG. Focus is placed on the formalism encompassing generative adversarial networks. The resulting method enables a variety of model parameterization strategies, some of which show similarity to previous CG methods. We demonstrate that the resulting framework can rigorously parameterize CG models containing CG sites with no prescribed connection to the reference atomistic system (termed virtual sites); however, this advantage is offset by the lack of a closed-form expression for the CG Hamiltonian at the resolution obtained after integration over the virtual CG sites. Computational examples are provided for cases in which these methods ideally return identical parameters as relative entropy minimization CG but where traditional relative entropy minimization CG optimization equations are not applicable.
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.
Permeability (Pm) across biological membranes is of fundamental importance and a key factor in drug absorption, distribution, and development. Although the majority of drugs will be charged at some point during oral delivery, our understanding of membrane permeation by charged species is limited. The canonical model assumes that only neutral molecules partition into and passively permeate across membranes, but there is mounting evidence that these processes are also facile for certain charged species. However, it is unknown whether such ionizable permeants dynamically neutralize at the membrane surface or permeate in their charged form. To probe protonation-coupled permeation in atomic detail, we herein apply continuous constant-pH molecular dynamics along with free energy sampling to study the permeation of a weak base propranolol (PPL), and evaluate the impact of including dynamic protonation on Pm. The simulations reveal that PPL dynamically neutralizes at the lipid–tail interface, which dramatically influences the permeation free energy landscape and explains why the conventional model overestimates the assigned intrinsic permeability. We demonstrate how fixed-charge-state simulations can account for this effect, and propose a revised model that better describes pH-coupled partitioning and permeation. Our results demonstrate how dynamic changes in protonation state may play a critical role in the permeation of ionizable molecules, including pharmaceuticals and drug-like molecules, thus requiring a revision of the standard picture.
The influenza A M2 protein is an acid-activated proton channel responsible for acidification of the inside of the virus, a critical step in the viral life cycle. This channel has four central histidine residues that form an acid-activated gate, binding protons from the outside until an activated state allows proton transport to the inside. While previous work has focused on proton transport through the channel, the structural and dynamic changes that accompany proton flux and enable activation have yet to be resolved. In this study, extensive Multiscale Reactive Molecular Dynamics simulations with explicit Grotthuss-shuttling hydrated excess protons are used to explore detailed molecular-level interactions that accompany proton transport in the +0, + 1, and +2 histidine charge states. The results demonstrate how the hydrated excess proton strongly influences both the protein and water hydrogen-bonding network throughout the channel, providing further insight into the channel’s acid-activation mechanism and rectification behavior. We find that the excess proton dynamically, as a function of location, shifts the protein structure away from its equilibrium distributions uniquely for different pH conditions consistent with acid-activation. The proton distribution in the xy-plane is also shown to be asymmetric about the channel’s main axis, which has potentially important implications for the mechanism of proton conduction and future drug design efforts.
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 from 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 a low surface concentration that adds insight into how I-BAR domain proteins may contribute to certain aspects of membrane remodeling in cells
The ability of adherent cells to form adhesions is critical to numerous phases of their physiology. Several types of integrins mediate the assembly of adhesions. These integrins differ in physical properties, including the rate of diffusion on the plasma membrane, rapidity of changing conformation from bent to extended, an affinity for extracellular matrix ligands, and lifetimes of their ligand-bound states. However, how nanoscale physical properties of integrins ensure proper adhesion assembly remains elusive. We observe experimentally that both β-1 and β-3 integrins localize in nascent adhesions at the cell leading edge. To understand how different nanoscale parameters of β-1 and β-3 integrins mediate proper adhesion assembly, we, therefore, develop a coarse-grained computational model. Results from the model demonstrate that morphology and distribution of nascent adhesions depend on ligand binding affinity and strength of pairwise interactions. The organization of nascent adhesions depends on the relative amounts of integrins with different bond kinetics. Moreover, the model shows that the architecture of an actin filament network does not perturb the total quantity of integrin clustering and ligand binding; however, only bundled actin architectures favor adhesion stability and ultimately maturation. Together, our results support the view that cells can finely tune the expression of different integrin types to determine both the structural and dynamic properties of adhesions.
Off-Pathway Assembly: A Broad-Spectrum Mechanism of Action for Drugs That Undermine Controlled HIV-1 Viral Capsid Formation
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 are 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.
Feynman's imaginary time path integral approach to quantum statistical mechanics provides a theoretical formalism for including nuclear quantum effects (NQEs) in a simulation of condensed matter systems. Sinitskiy and Voth [J. Chem. Phys. 143, 094104 (2015)] have presented the coarse-grained path integral (CG-PI) theory, which provides a reductionist coarse-grained representation of the imaginary time path integral based on the quantum-classical isomorphism. In this paper, the many-body generalization of the CG-PI theory is presented. It is shown that the N interacting particles obeying quantum Boltzmann statistics can be represented as a system of N pairs of classical-like pseudoparticles coupled to each other analogous to the pseudoparticle pair of the one-body theory. Moreover, we present a numerical CG-PI (n-CG-PI) method applying a simple approximation to the coupling scheme between the pseudoparticles due to the numerical challenges of directly implementing the full many-body CG-PI theory. Structural correlations of two liquid systems are investigated to demonstrate the performance of the n-CG-PI method. Both the many-body CG-PI theory and the n-CG-PI method not only present reductionist views of the many-body quantum Boltzmann statistics but also provide theoretical and numerical insight into how to explicitly incorporate NQEs in the representation of condensed matter systems with minimal additional degrees of freedom.further extend the current view of CG modeling into predictive multiscale modeling.
Standard low-resolution coarse-grained modeling techniques have difficulty capturing multiple configurations of protein systems. Here, we present a method for creating accurate coarse-grained (CG) models with multiple configurations using a linear combination of functions or “states”. Individual CG models are created to capture the individual states, and the approximate coupling between the two states is determined from an all-atom potential of mean force. We show that the resulting multiconfiguration coarse-graining (MCCG) method accurately captures the transition state as well as the free energy between the two states. We have tested this method on the folding of dodecaalanine, as well as the amphipathic helix of endophilin.
Coarse-grained (CG) models allow efficient molecular simulation by reducing the degrees of freedom in the system. To recapitulate important physical properties, including many-body correlations at the CG resolution, an appropriate mapping from the atomistic to CG level is needed. Symmetry exhibited by molecules, especially when aspherical, can be lost upon coarse-graining due to the use of spherically symmetric CG effective potentials. This mismatch can be efficiently amended by imposing symmetry using virtual CG sites. However, there has been no rigorous bottom-up approach for constructing a many-body potential of mean force that governs the distribution of virtual CG sites. Herein, we demonstrate a statistical mechanical framework that extends a mapping scheme of CG systems involving virtual sites to provide a thermodynamically consistent CG model in the spirit of the principle of maximum entropy. Utilizing the extended framework, this work defines a center of symmetry (COS) mapping and applies it to benzene and toluene systems such that the planar symmetry of the aromatic ring is preserved by constructing two virtual sites along a normal vector. Compared to typical center of mass (COM) CG models, COS CG models correctly recapitulate radial and higher order correlations, e.g., orientational and three-body correlations. Moreover, we find that COS CG interactions from bulk phases are transferable to mixture phases, whereas conventional COM models deviate between the two states. This result suggests a systematic approach to construct more transferable CG models by conserving molecular symmetry, and the new protocol is further expected to capture other many-body correlations by utilizing virtual sites.