Lipids, which are amphipathic biomolecules that assemble into cellular membranes, are central to many biophysical processes. To understand the fundamental molecular mechanisms that dictate the macroscopic behavior of lipid assemblies, we introduce a novel procedure for the systematic development of low-resolution coarse-grained (CG) lipid models that will enable simulations of biologically-relevant spatiotemporal scales with molecular fidelity. The central idea is to represent the structural features of the solvent-lipid interface through the introduction of virtual CG sites. We then leverage two systematic coarse-graining approaches, multiscale coarse-graining (MS-CG) and relative entropy minimization (REM), in a hybrid fashion to derive the effective interactions of our virtual-site CG (VCG) models from reference all-atom simulations. We demonstrate that VCG models recapitulate the rich biophysics of lipids, which enable self-assembly, morphological diversity, and multiple phases. Our findings further suggest that the VCG framework is a powerful approach for an investigation into macromolecular biophysics.
Integrin conformational dynamics are critical to their receptor and signaling functions in many cellular processes, including spreading, adhesion, and migration. However, assessing integrin conformations is both experimentally and computationally challenging because of limitations in resolution and dynamic sampling. Thus, structural changes that underlie transitions between conformations are largely unknown. Here, focusing on integrin αv β 3, we developed a modified form of the coarse-grained heterogeneous elastic network model (hENM), which allows sampling conformations at the onset of activation by formally separating local fluctuations from global motions. Both local fluctuations and global motions are extracted from all-atom molecular dynamics simulations of the full-length αv β 3 bent integrin conformer, but whereas the former are incorporated in the hENM as effective harmonic interactions between groups of residues, the latter emerge by systematically identifying and treating weak interactions between long-distance domains with flexible and anharmonic connections. The new hENM model allows integrins and single-point mutant integrins to explore various conformational states, including the initiation of separation between α- and β-subunit cytoplasmic regions, headpiece extension, and legs opening.
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 complex interactions between actin and actin binding proteins regulate actin filament formation within the cytoskeletal network. A central part of this regulatory system is composed of formins, which are highly conserved multidomain proteins that nucleate and elongate unbranched actin filaments. In this paper, we utilize multiscale simulation techniques to understand the underlying factors that cause the difference in the formin-mediated polymerization rate of actin by studying the interactions between actin and the FH2 domains of the formins Cdc12, Bni1, and mDia1. These formins slow elongation of actin filament by 5 to 95% depending on the particular species. We found two mechanisms that can influence the rate of actin polymerization mediated by formins from our all-atom molecular dynamics and bottom-up coarse-grained simulations. According to these mechanisms, formins can sterically block the addition of new actin subunits, or flatten the helical twist of the terminal actin subunits. Making the filament ends unfavorable for the addition of a new actin subunit. Our findings help to explain why Cdc12 FH2 domains slow elongation of the actin filament much more than Bni1 and mDia1.
In this review, we gave an overview of the work mostly done in the Voth group that was highly motivated by the important contributions of Tom Pollard to understand the essential structural and chemical aspects of the actin cytoskeleton. We have discussed the use of various simulation techniques to understand the key structural and chemical features of actin, which are associated with biological processes occurring at different scales such as actin filament polymerization, the hydrolysis of bound nucleotide ATP and phosphate release. These simulation techniques include detailed atomistic simulations and advanced free energy sampling techniques to understand structural transformation of actin subunits, advanced coarse-graining methods such as ED-CG, hENM, and the UCG to model actin at various resolutions of coarse-graining, and hybrid quantum mechanics/molecular mechanics approach to study ATP hydrolysis. Furthermore, we summarized the modeling of actin binding proteins such as the Arp2/3 complex and formin to have a molecular level understanding of the fundamental mechanisms affecting the architecture of actin network at different length and time scales by using these methods. Many of these studies were a direct result of a collaboration with Tom Pollard and his group or inspired by informal interactions with him.
Modulating the Chemical Transport Properties of a Transmembrane Antiporter via Alternative Anion Flux
CIC is a family of proteins crucial to the homeostasis of ion concentrations and pH gradients in bacteria as well as in the human body. ClC-ec1, as a prototypical ClC protein, exchanges Cl– for H+ across the membrane. Other polyatomic anions, such as NO3– and SCN–, are also permeable through the protein, but with partially or entirely uncoupled H+ flux. In this work, we characterized the potential of mean forces of the proton transport (PT) process in ClC-ec1 and the essential mechanism of H+ transport affected by the alternative anion flux. We revealed that the energy barrier is related to the water connectivity along the PT pathway in the presence of the excess proton, which is significantly affected by the nature of the bound anion. This piece of work shows how chemical engineering can regulate PT in proteins by changing the hydration behavior.
Reproducibility in the coarse-grained model is essential, especially when vital information below the CG resolution is lost during the CG process. In the case of a two-site methanol molecule, this problem becomes apparent since the hydrogen-bonding topology (either donor or acceptor) among -OH beads is lost, resulting in inaccurate local structures. To surmount this challenge, we apply the Ultra-Coarse-Grained (UCG) theory to construct a high-fidelity CG model with implicit hydrogen-bonding. Since hydrogen bonding is a local phenomenon, the internal states of the hydrogen-bonding participating CG sites are determined by the local density of the CG sites. This strategy is then applied to two different hydrogen bonding motifs: chain-like and ring-like. For both motifs including amino acid building blocks, the UCG models show better structural correlations (pair, triplet, and local number density) compared to the conventional MS-CG models. These results strongly suggest that the UCG theory can significantly improve the reproducibility of the CG model in the complex condensed system.
In this work, we built up the first rigorous bridge between atomistic and supramolecular mesoscopic models of fluids. A delicate dynamic coarse-graining mapping scheme, whose idea originates from the centroidal Voronoi tesellation algorithm in computational geometry, was designed to account for the microscopic momentum transport that governs the fluid motion at mesoscale. Besides, a systematic parameterization method based on Mori-Zwanzig formalism was developed and faithfully reproduces the statistical and dynamical characteristics of the coarse-grained trajectory. The new dynamical coarse-grained mapping scheme and the parameterization protocol open up an avenue for direct bottom-up construction of mesoscopic models of complex fluids in a Lagrangian description.
Molecular transport through membranes: Accurate permeability coefficients from multidimensional potentials of mean force and local diffusion constants
Estimating the permeability coefficient of small molecules through lipid bilayer membranes plays an essential role in the development of effective drug candidates. However, the absolute permeability coefficients obtained from pre-existing computer simulation methods are usually off by orders of magnitude, mostly due to the poor convergence of permeation free energy profiles and over-simplified diffusion models. To overcome these obstacles, we describe the permeation process using multiple reaction coordinates and estimate the permeability along the minimum free energy path of the multidimensional potential of mean force. A combination of cutting-edge metadynamics enhanced sampling techniques, and improved representation of the permeation process leads to a considerably more accurate estimation of permeability coefficients compared to pre-existing methods.
For influenza virus to release from the infected host cell, controlled viral budding must finalize with membrane scission of the viral envelope. Curiously, influenza carries its own protein, M2, which can sever the membrane of the constricted budding neck. Here we elucidate the physical mechanism of clustering and spatial localization of the M2 scission proteins through a combined computational and experimental approach.
Hydrolysis of the nucleotide bound to each subunit of actin serves as an important clock that governs the remodeling of the cytoskeletal network. Whether the hydrolysis and the subsequent phosphate release act independently or are somehow coupled across different subunits in the filament network has been debated for over three decades. Here, we developed a systematic multi-scale modeling framework by combining atomistic simulations, the Ultra-Coarse-Graining approach, and Markov State Modeling, that addresses this issue.
In this work, we have demonstrated the application of the recently developed Ultra-CG (UCG) theory to heterogeneous systems: liquid/vapor and liquid/liquid interfaces. Due to the inhomogeneous nature of an interfacial system, the conventional MS-CG framework fails to capture the structure and directionality of molecules, resulting in the breakdown of the interfacial density profile. In order to resolve the limitation of the MS-CG method, we have designed the UCG framework to systematically distinguish different local environments in interfacial systems and faithfully recapitulates structural correlations in the interfacial systems. More fascinatingly, the CG interactions obtained by the UCG methodology are transferable to corresponding bulk states. This transferability was observed in both liquid/vapor and liquid/liquid systems: the UCG methodology can impart transferable CG models while retaining high accuracy.
Immature HIV-1 lattice assembly dynamics are regulated by scaffolding from nucleic acid and the plasma membrane
In this work, we use coarse-grained molecular models to simulate the early stages of viral assembly, packaging, and budding during HIV-1 replication. In collaboration with the Lippincott-Schwartz Group at the NIH and HHMI, we provide a molecular-level view into the dynamics of this process and show that Gag polyproteins engage with viral RNA and deformations along the cell membrane to both instigate and control its self-assembly into the immature HIV-1 lattice. We further demonstrate the importance of specific features of the modeled Gag domains. Taken together, our findings elucidate a simple regulatory network of interactions that may contain viable targets for antivirals.
In this work, we show that using minimal bias methods, we can simulate a protein in solution and have it behave as if embedded in a different environment, such as a large protein complex. This is done by learning a bias on coarse-grained observables, such as distances or angles between beads representing large collections of atoms in the protein. The bias is targeted such that these observables sample the correct mean and variance from simulations in the whole complex. We apply this to the protein actin in solution, and discuss how this would be useful for future expensive sampling or QM/MM simulations performed on actin, previously done with rigid constraints that pollute the protein's dynamics.
In this work, we apply the Experiment Directed Simulation (EDS) method to improve the properties of water simulated with Ab Initio Molecular Dynamics (AIMD) simulations at a poor/cheap DFT level of theory. A simple classical bias is learned on-the-fly from the O-O radial distribution function, which causes the AIMD water to match much better the structural properties of water seen in experiment, including diffusion. Applying this bias to a hydrated excess proton in water also significantly improves the properties of that system, without the need for learning a new bias potential.
Development of Reactive Force Fields Using Ab Initio Molecular Dynamics Simulation Minimally Biased to Experimental Data
By using relative entropy minimization (REM) and minimally biased ab initio molecular dynamics (AIMD) simulations, we have developed two new multiscale reactive molecular dynamics force fields for a hydrated excess proton. We show that both of these models closely reproduce the solvation structure of the reference AIMD data, and we also demonstrate the capabilities of REM to develop reactive force-fields.
Extending the Range and Physical Accuracy of Coarse-grained Models: Order Parameter Dependent Interactions
The choice of basis function is an important decision that must go into the construction of a coarse-grained model. Coarse-grained models are usually built using a basis set of pairwise interactions for non-bonded interactions and expanding into 3-body and on to expand the basis set. This paper introduces the use of order parameters, particularly local density and absolute position, as an efficient alternative to expand basis sets. The order parameter basis set allows for a drastically improved description of liquid-vapor interfaces in coarse-grained methanol.
Internal symmetry in transmembrane protein — exact or approximate — is common and it has consequences for the Gaussian fluctuations around the equilibrium structure of the proteins. We substantiate that a coarse-grained mapping must preserve the underlying structural symmetries (both structural symmetry groups and modular repeats in the secondary structure, depending on the resolution) and show that this can be used as a design principle to construct coarse-grained mappings.
ClC-ec1, a Cl- /H+ antiporter, is critical for maintaining ion concentrations and PH gradients in bacteria in acidic environments. In this work, we computationally characterized the rate-limiting step of the overall proton transport process in ClC-ec1 and the essential mechanism of the Cl-/H+ coupling. We found that the highest barrier for PT is located at the deprotonation of E148, and this barrier is significantly reduced by the binding of Cl- in the central site, which displaces E148 and thereby facilitates its deprotonation.
Molecular Modeling and Assignment of IR Spectra of the Hydrated Excess Proton in Isotopically Dilute Water
We developed a mixed quantum-classical model for the vibrational spectroscopy of the excess proton in isotopically dilute water. The model is useful for decomposing IR spectra into contributions from different aqueous proton configurations as validated by our experimental collaborator Andrei Tokmakoff (UChicago). We find that the shift from Eigen to Zundel-like configurations is distinguished by a decrease in the O—H transition frequency.
The influenza A M2 channel (AM2) transports protons into the influenza virus upon acid activation. MS-RMD simulations were performed to characterize the free energy profiles of the proton transport events in the M2 channel. Our results show that decreasing pH causes the Trp41 gate to open, which decreases the deprotonation barrier of the His37 tetrad. This leads to channel activation, which is characterized by increased proton conductance.
Transition-Tempered Metadynamics is a Promising Tool for Studying the Permeation of Drug-like Molecules through Membranes
The recently developed transition-tempered metadynamics (TTMetaD) has been proven to converge asymptotically without sacrificing exploration of the collective variable space in the early stages of simulations. We applied TTMetaD to study the permeation of drug-like molecules through a lipid bilayer to investigate its usefulness in medicinal chemistry. Compared to other enhanced sampling methods, TTMetaD is able to predict the most accurate and reliable estimate of the potential of mean force in the early stages of the simulations. We also show that using multiple randomly initialized replicas allows convergence analysis and provides an efficient means to converge the simulations in shorter wall times and CPU times
Actin-binding protein sorting is critical for the self-organization of diverse dynamic actin cytoskeleton networks within a common cytoplasm. In this work it was shown using in vitro reconstitution techniques including biomimetic assays and single-molecule multi-color total internal reflection fluorescence microscopy, that the sorting of the prominent actin-bundling proteins fascin and α-actinin mutually exclude each other by promoting their own recruitment and inhibiting recruitment of the other, resulting in the formation of distinct domains. We designed a lattice model which allows us to predict the energetic barrier for switching from one domain to another by comparison of the model results to experimental domain sizes.
We discuss the relationship between coarse-grained (CG) observables and the corresponding fine-grained (FG) or experimental observables in the framework of systematic bottom-up CG modeling. The importance of this issue is illustrated with a simple polymer system that has implications for the coarse-graining of intramolecular degrees of freedom.
Many crucial biological processes, such as cell division, protein trafficking, and cell signaling, involve large-scale membrane shape and topology changes that are facilitated by complex membrane-protein interactions. In this Review we discuss the recent advances of our group in multiscale computational approaches for studying protein-mediated large-scale membrane remodeling.
We used MS-RMD simulations to characterize the free energy profiles of the proton transport events in the cytochrome c oxidase (CcO) that enable proton pumping and chemical reaction. Our results show that the transfer of both the pumped and chemical protons are thermodynamically driven by electron transfer, and explain how proton back leakage is avoided by kinetic gating.
In this work, we use molecular dynamics simulations and coares-grained techniques to study actin filaments which have incorporated magnesium ions into recently predicted binding sites between actin subunits. Binding of a magnesium ion into a predicted "stiffness site" adheres the actin DNase-binding loop (D-loop) to its long-axis neighbor, which increases the filament torsional stiffness and bending persistence length. Our analysis shows that bound D-loops occupy a smaller region of accessible conformational space and that cation occupancy buries key conserved residues of the D-loop, restricting accessibility to regulatory proteins and enzymes that target these amino acids.