Accurate and Transferable Reactive Molecular Dynamics Models from Constrained Density Functional Theory
Chemical reactions constitute the central feature of many liquid, material, and biomolecular processes. Conventional molecular dynamics (MD) is inadequate for simulating chemical reactions given the fixed bonding topology of most force fields, while modeling chemical reactions using ab initio molecular dynamics is limited to shorter time and length scales given its high computational cost. As such, the multiscale reactive molecular dynamics method provides one promising alternative for simulating complex chemical systems at atomistic detail on a reactive potential energy surface. However, the parametrization of such models is a key barrier to their applicability and success. In this work, we present reactive MD models derived from constrained density functional theory that are both accurate and transferable. We illustrate the features of these models for proton dissociation reactions of amino acids in both aqueous and protein environments. Specifically, we present models for ionizable glutamate and lysine that predict accurate absolute pKa values in water as well as their significantly shifted pKa in staphylococcal nuclease (SNase) without any modification of the models. As one outcome of the new methodology, the simulations show that the deprotonation of ionizable residues in SNase can be closely coupled with side chain rotations, which is a concept likely generalizable to many other proteins. Furthermore, the present approach is not limited to only pKa prediction but can enable the fully atomistic simulation of many other reactive systems along with a determination of the key aspects of the reaction mechanisms.
Using Constrained Density Functional Theory to Track Proton Transfers and to Sample Their Associated Free Energy Surface
Ab initio molecular dynamics (AIMD) and quantum mechanics/molecular mechanics (QM/MM) methods are powerful tools for studying proton solvation, transfer, and transport processes in various environments. However, due to the high computational cost of such methods, achieving sufficient sampling of rare events involving excess proton motion—especially when Grotthuss proton shuttling is involved—usually requires enhanced free energy sampling methods to obtain informative results. Moreover, an appropriate collective variable (CV) that describes the effective position of the net positive charge defect associated with an excess proton is essential both for tracking the trajectory of the defect and for the free energy sampling of the processes associated with the resulting proton transfer and transport. In this work, such a CV is derived from first principles using constrained density functional theory (CDFT). This CV is applicable to a broad array of proton transport and transfer processes as studied via AIMD and QM/MM simulations.
Formin Cdc12’s specific actin assembly properties are tailored for cytokinesis in fission yeast
Formins generate unbranched actin filaments by a conserved, processive actin assembly mechanism. Most organisms express multiple formin isoforms that mediate distinct cellular processes and facilitate actin filament polymerization by significantly different rates, but how these actin assembly differences correlate to cellular activity is unclear. We used a computational model of fission yeast cytokinetic ring assembly to test the hypothesis that particular actin assembly properties help tailor formins for specific cellular roles. Simulations run in different actin filament nucleation and elongation conditions revealed that variations in formin’s nucleation efficiency critically impact both the probability and timing of contractile ring formation. To probe the physiological importance of nucleation efficiency, we engineered fission yeast formin chimera strains in which the FH1-FH2 actin assembly domains of full-length cytokinesis formin Cdc12 were replaced with the FH1-FH2 domains from functionally and evolutionarily diverse formins with significantly different actin assembly properties. Although Cdc12 chimeras generally support life in fission yeast, quantitative live-cell imaging revealed a range of cytokinesis defects from mild to severe. In agreement with the computational model, chimeras whose nucleation efficiencies are least similar to Cdc12 exhibit more severe cytokinesis defects, specifically in the rate of contractile ring assembly. Together, our computational and experimental results suggest that fission yeast cytokinesis is ideally mediated by a formin with properly tailored actin assembly parameters.
Synthesis, Characterization, and Simulation of Four-Armed Megamolecules
This paper describes the synthesis, characterization, and modeling of a series of molecules having four protein domains attached to a central core. The molecules were assembled with the “megamolecule” strategy, wherein enzymes react with their covalent inhibitors that are substituted on a linker. Three linkers were synthesized, where each had four oligo(ethylene glycol)-based arms terminated in a para-nitrophenyl phosphonate group that is a covalent inhibitor for cutinase. This enzyme is a serine hydrolase and reacts efficiently with the phosphonate to give a new ester linkage at the Ser-120 residue in the active site of the enzyme. Negative-stain transmission electron microscopy (TEM) images confirmed the architecture of the four-armed megamolecules. These cutinase tetramers were also characterized by X-ray crystallography, which confirmed the active-site serine-phosphonate linkage by electron-density maps. Molecular dynamics simulations of the tetracutinase megamolecules using three different force field setups were performed and compared with the TEM observations. Using the Amberff99SB-disp + pH7 force field, the two-dimensional projection distances of the megamolecules were found to agree with the measured dimensions from TEM. The study described here, which combines high-resolution characterization with molecular dynamics simulations, will lead to a comprehensive understanding of the molecular structures and dynamics for this new class of molecules.
Advanced Materials for Energy-Water Systems: The Central Role of Water/Solid Interfaces in Adsorption, Reactivity, and Transport
The structure, chemistry, and charge of interfaces between materials and aqueous fluids play a central role in determining properties and performance of numerous water systems. Sensors, membranes, sorbents, and heterogeneous catalysts almost uniformly rely on specific interactions between their surfaces and components dissolved or suspended in the water—and often the water molecules themselves—to detect and mitigate contaminants. Deleterious processes in these systems such as fouling, scaling (inorganic deposits), and corrosion are also governed by interfacial phenomena. Despite the importance of these interfaces, much remains to be learned about their multiscale interactions. Developing a deeper understanding of the molecular- and mesoscale phenomena at water/solid interfaces will be essential to driving innovation to address grand challenges in supplying sufficient fit-for-purpose water in the future. In this Review, we examine the current state of knowledge surrounding adsorption, reactivity, and transport in several key classes of water/solid interfaces, drawing on a synergistic combination of theory, simulation, and experiments, and provide an outlook for prioritizing strategic research directions.
Structural Characterization of Protonated Water Clusters Confined in HZSM-5 Zeolites
A molecular description of the structure and behavior of water confined in aluminosilicate zeolite pores is a crucial component for understanding zeolite acid chemistry under hydrous conditions. In this study, we use a combination of ultrafast two-dimensional infrared (2D IR) spectroscopy and ab initio molecular dynamics (AIMD) to study H2O confined in the pores of highly hydrated zeolite HZSM-5 (∼13 and ∼6 equivalents of H2O per Al atom). The 2D IR spectrum reveals correlations between the vibrations of both terminal and H-bonded O–H groups and the continuum absorption of the excess proton. These data are used to characterize the hydrogen-bonding network within the cluster by quantifying single-, double-, and non-hydrogen-bond donor water molecules. These results are found to be in good agreement with the statistics calculated from an AIMD simulation of an H+(H2O)8 cluster in HZSM-5. Furthermore, IR spectral assignments to local O–H environments are validated with DFT calculations on clusters drawn from AIMD simulations. The simulations reveal that the excess charge is detached from the zeolite and resides near the more highly coordinated water molecules in the cluster. When they are taken together, these results unambiguously assign the complex IR spectrum of highly hydrated HZSM-5, providing quantitative information on the molecular environments and hydrogen-bonding topology of protonated water clusters under extreme confinement.
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.
Key computational findings reveal proton transfer as driving the functional cycle in the phosphate transporter PiPT
Proton- or sodium-coupled transporters within the major facilitator superfamily are essential for nutrient uptake in all forms of life. We focus on a high-affinity eukaryotic proton-coupled phosphate symporter using extensive classical molecular dynamics (MD) simulations and quantum mechanics/molecular mechanics MD combined with free energy sampling and confirm the role of a key residue, D324, at the molecular level. The results explain the exit direction of the proton once dissociated from D324 and reveal a perspective on proton-coupled transporters, showing that titratable substrates can be involved in the proton transport process as a key aspect of the functional cycle. Mutagenesis and phosphate transport confirm the essential nature of the key D45 residue in the protonation pathway.
The hopping mechanism of the hydrated excess proton and its contribution to proton diffusion in water
In this work, a series of analyses are performed on ab initio molecular dynamics simulations of a hydrated excess proton in water to quantify the relative occurrence of concerted hopping events and “rattling” events and thus to further elucidate the hopping mechanism of proton transport in water. Contrary to results reported in certain earlier papers, the new analysis finds that concerted hopping events do occur in all simulations but that the majority of events are the product of proton rattling, where the excess proton will rattle between two or more waters. The results are consistent with the proposed “special-pair dance” model of the hydrated excess proton wherein the acceptor water molecule for the proton transfer will quickly change (resonate between three equivalent special pairs) until a decisive proton hop occurs. To remove the misleading effect of simple rattling, a filter was applied to the trajectory such that hopping events that were followed by back hops to the original water are not counted. A steep reduction in the number of multiple hopping events is found when the filter is applied, suggesting that many multiple hopping events that occur in the unfiltered trajectory are largely the product of rattling, contrary to prior suggestions. Comparing the continuous correlation function of the filtered and unfiltered trajectories, we find agreement with experimental values for the proton hopping time and Eigen–Zundel interconversion time, respectively.
Compressive and Tensile Deformations Alter ATP Hydrolysis and Phosphate Release Rates in Actin Filaments
Actin filament networks in eukaryotic cells are constantly remodeled through nucleotide state controlled interactions with actin binding proteins, leading to macroscopic structures such as bundled filaments, branched filaments, and so on. The nucleotide (ATP) hydrolysis, phosphate release, and polymerization/depolymerization reactions that lead to the formation of these structures are correlated with the conformational fluctuations of the actin subunits at the molecular scale. The resulting structures generate and experience varying levels of force and impart cells with several functionalities such as their ability to move, divide, transport cargo, etc. Models that explicitly connect the structure to reactions are essential to elucidate a fundamental level of understanding of these processes. In this regard, a bottom-up Ultra-Coarse-Grained (UCG) model of actin filaments that can simulate ATP hydrolysis, inorganic phosphate release (Pi), and depolymerization reactions is presented in this work. In this model, actin subunits are represented using coarse-grained particles that evolve in time and undergo reactions depending on the conformations sampled. The reactions are represented through state transitions, with each state represented by a unique effective coarse-grained potential. Effects of compressive and tensile strains on the rates of reactions are then analyzed. Compressive strains tend to unflatten the actin subunits, reduce the rate of ATP hydrolysis, and increase the Pi release rate. On the other hand, tensile strain flattens subunits, increases the rate of ATP hydrolysis, and decrease the Pi release rate. Incorporating these predictions into a Markov State Model highlighted that strains alter the steady-state distribution of subunits with ADPPi and ADP nucleotide, thus identifying possible additional factors underlying the cooperative binding of regulatory proteins to actin filaments.
Structural basis of fast- and slow-severing actin–cofilactin boundaries
Members of the ADF/cofilin family of regulatory proteins bind actin filaments cooperatively, locally change actin subunit conformation and orientation, and sever filaments at “boundaries” between bare and cofilin-occupied segments. A cluster of bound cofilin introduces two distinct classes of boundaries due to the intrinsic polarity of actin filaments, one at the “pointed” end side and the other at the “barbed” end-side of the cluster; severing occurs more readily at the pointed end side of the cluster (“fast-severing” boundary) than the barbed end side (“slow-severing” boundary). A recent electron-cryomicroscopy (cryo-EM) model of the slow-severing boundary revealed structural “defects” at the interface that potentially contribute to severing. However, the structure of the fast-severing boundary remains uncertain. Here, we use extensive molecular dynamics simulations to produce atomic resolution models of both severing boundaries. Our equilibrated simulation model of the slow-severing boundary is consistent with the cryo-EM structural model. Simulations indicate that actin subunits at both boundaries adopt structures intermediate between those of bare and cofilin-bound actin subunits. These “intermediate” states have compromised intersubunit contacts, but those at the slow-severing boundary are stabilized by cofilin bridging interactions, accounting for its lower fragmentation probability. Simulations where cofilin proteins are removed from cofilactin filaments favor a mechanism in which a cluster of two contiguously bound cofilins is needed to fully stabilize the cofilactin conformation, promote cooperative binding interactions, and accelerate filament severing. Together, these studies provide a molecular-scale foundation for developing coarse-grained and theoretical descriptions of cofilin-mediated actin filament severing.
Constructing many-body dissipative particle dynamics models of fluids from bottom-up coarse-graining
Since their emergence in the 1990s, mesoscopic models of fluids have been widely used to study complex organization and transport phenomena beyond the molecular scale. Even though these models are designed based on results from physics at the meso- and macroscale, such as fluid mechanics and statistical field theory, the underlying microscopic foundation of these models is not as well defined. This paper aims to build such a systematic connection using bottom-up coarse-graining methods. From the recently developed dynamic coarse-graining scheme, we introduce a statistical inference framework of explicit many-body conservative interaction that quantitatively recapitulates the mesoscopic structure of the underlying fluid. To further consider the dissipative and fluctuation forces, we design a novel algorithm that parameterizes these forces. By utilizing this algorithm, we derive pairwise decomposable friction kernels under both non-Markovian and Markovian limits where both short- and long-time features of the coarse-grained dynamics are reproduced. Finally, through these new developments, the many-body dissipative particle dynamics type of equations of motion are successfully derived. The methodologies developed in this work thus open a new avenue for the construction of direct bottom-up mesoscopic models that naturally bridge the meso- and macroscopic physics.
Coarse-Grained Force Fields from the Perspective of Statistical Mechanics: Better Understanding of the Origins of a MARTINI Hangover
The popular MARTINI coarse-grained model is used as a test case to analyze the adherence of top-down coarse-grained molecular dynamics models (i.e., models primarily parametrized to match experimental results) to the known features of statistical mechanics for the underlying all-atom representations. Specifically, the temperature dependence of various pair distribution functions, and hence their underlying potentials of mean force via the reversible work theorem, are compared between MARTINI 2.0, Dry MARTINI, and all-atom simulations mapped onto equivalent coarse-grained sites for certain lipid bilayers. It is found that the MARTINI models do not completely capture the lipid structure seen in atomistic simulations as projected onto the coarse-grained mappings and that issues of accuracy and temperature transferability arise due to an incorrect enthalpy–entropy decomposition of these potentials of mean force. The potential of mean force for the association of two amphipathic helices in a lipid bilayer is also calculated, and especially at shorter ranges, the MARTINI and all-atom projection results differ substantially. The former is much less repulsive and hence will lead to a higher probability of MARTINI helix association in the MARTINI bilayer than occurs in the actual all-atom case. Additionally, the bilayer height fluctuation spectra are calculated for the MARTINI model, and compared to the all-atom results, it is found that the magnitude of thermally averaged amplitudes at intermediate length scales are quite different, pointing to a number of possible consequences for realistic modeling of membrane processes. Taken as a whole, the results presented here show disagreement in the enthalpic and entropic driving forces driving lateral structure in lipid bilayers as well as quantitative differences in association of embedded amphipathic helices, which can help direct future efforts to parametrize CG models with better agreement to the all-atom systems they aspire to represent.
A Multiscale Coarse-Grained Model of the SARS-CoV-2 Virion
Significance: This study reports the construction of a molecular model for the SARS-CoV-2 virion and details our multiscale approach toward model refinement. The resulting model and methods can be applied to and enable the simulation of SARS-CoV-2 virions.
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.
A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). II. Temperature transferability and structural properties at low temperature
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.
Experiment directed simulation (EDS) is a method within a class of techniques seeking to improve molecular simulations by minimally biasing the system Hamiltonian to reproduce certain experimental observables. In a previous application of EDS to ab initio molecular dynamics (AIMD) simulation based on electronic density functional theory (DFT), the AIMD simulations of water were biased to reproduce its experimentally derived solvation structure. In particular, by solely biasing the O–O pair correlation function, other structural and dynamical properties that were not biased were improved. In this work, the hypothesis is tested that directly biasing the O–H pair correlation (and hence the H–O···H hydrogen bonding) will provide an even better improvement of DFT-based water properties in AIMD simulations. The logic behind this hypothesis is that for most electronic DFT descriptions of water the hydrogen bonding is known to be deficient due to anomalous charge transfer and over polarization in the DFT. Using recent advances to the EDS learning algorithm, we thus train a minimal bias on AIMD water that reproduces the O–H radial distribution function derived from the highly accurate MB-pol model of water. It is then confirmed that biasing the O–H pair correlation alone can lead to improved AIMD water properties, with structural and dynamical properties even closer to experiment than the previous EDS-AIMD model.
Atomic-scale characterization of mature HIV-1 capsid stabilization by inositol hexakisphosphate (IP6)
Inositol hexakisphosphates (IP6) are cellular cofactors that promote the assembly of mature capsids of HIV. These negatively charged molecules coordinate an electropositive ring of arginines at the center of pores distributed throughout the capsid surface. Kinetic studies indicate that the binding of IP6 increases the stable lifetimes of the capsid by several orders of magnitude from minutes to hours. Using all-atom molecular dynamics simulations, we uncover the mechanisms that underlie the unusually high stability of mature capsids in complex with IP6. We find that capsid hexamers and pentamers have differential binding modes for IP6. Ligand density calculations show three sites of interaction with IP6 including at a known capsid inhibitor binding pocket. Free energy calculations demonstrate that IP6 preferentially stabilizes pentamers over hexamers to enhance fullerene modes of assembly. These results elucidate the molecular role of IP6 in stabilizing and assembling the retroviral capsid.
Density Functional Theory-Based Quantum Mechanics/Coarse-Grained Molecular Mechanics: Theory and Implementation
Quantum mechanics/molecular mechanics (QM/MM) is a standard computational tool for describing chemical reactivity in systems with many degrees of freedom, including polymers, enzymes, and reacting molecules in complex solvents. However, QM/MM is less suitable for systems with complex MM dynamics due to associated long relaxation times, the high computational cost of QM energy evaluations, and expensive long-range electrostatics. Recently, a systematic coarse graining of the MM part was proposed to overcome these QM/MM limitations in the form of the quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM) approach. Herein, we recast QM/CG-MM in the density functional theory formalism and, by employing the force-matching variational principle, assess the method performance for the two model systems: QM CCl4 in the MM CCl4 liquid and the reaction of tert-butyl hypochlorite with the benzyl radical in the MM CCl4 solvent. We find that density functional theory (DFT)-QM/CG-MM accurately reproduces DFT-QM/MM radial distribution functions and three-body correlations between the QM and CG-MM subsystems. The free-energy profile of the reaction is also described well, with an error <1–2 kcal/mol. DFT-QM/CG-MM is a general, systematic, and computationally efficient approach to include chemical reactivity in coarse-grained molecular models.
Anisotropic Motions of Fibrils Dictated by Their Orientations in the Lamella: A Coarse-Grained Model of a Plant Cell Wall
Plant cell walls are complex systems that exhibit the characteristics of both rigid and soft material depending on their external perturbations. The three main polymeric components in a plant primary cell wall are cellulose fibrils, hemicellulose, and pectins. These components interact in a hierarchical fashion giving rise to mesoscale structural features such as cellulose bundles, lamella stacking, and so on. Although several studies have focused on understanding these unique structural features, a clear picture linking them to cell wall mechanics is still lacking. As a first step toward this goal, a phenomenological model of plant cell wall has been developed in this work by using available experimental data to investigate the underlying connections between mesoscale structural features and the motions of fibrils during deformation. In this model cellulose fibrils exhibit motions such as angular reorientations and kinking upon forced stretching. These motions are dependent on the orientation of fibrils with respect to the stretch direction, i.e., fibrils that are at an angle to the stretch direction exhibit predominant angular reorientations, while fibrils transverse to the stretch direction undergo kinking as a result of transverse compression. Varying the chain length of pectin had negligible effects on these motions. One of the main contributions from this work is the development of a simple model that can be easily fine-tuned to test other hypotheses and extended to include additional experimental knowledge about the structural aspects of cell walls in the future.
Structural basis for polarized elongation of actin filaments
Actin filaments elongate and shorten much faster at their barbed end than their pointed end, but the molecular basis of this difference has not been understood. We use all-atom molecular dynamics simulations to investigate the properties of subunits at both ends of the filament. The terminal subunits tend toward conformations that resemble actin monomers in solution, while contacts with neighboring subunits progressively flatten the conformation of internal subunits. At the barbed end the terminal subunit is loosely tethered by its DNase-1 loop to the third subunit, because its monomer-like conformation precludes stabilizing contacts with the penultimate subunit. The motions of the terminal subunit make the partially flattened penultimate subunit accessible for binding monomers. At the pointed end, unique contacts between the penultimate and terminal subunits are consistent with existing cryogenic electron microscopic (cryo-EM) maps, limit binding to incoming monomers, and flatten the terminal subunit, which likely promotes ATP hydrolysis and rapid phosphate release. These structures explain the distinct polymerization kinetics of the two ends.
Temperature and Phase Transferable Bottom-up Coarse-Grained Models
Despite the high fidelity of bottom-up coarse-grained (CG) approaches to recapitulate the structural correlations in atomistic simulations, the general use of bottom-up CG methods is limited because of the nontransferable nature of these CG models under different thermodynamic conditions. Because bottom-up CG potentials usually correspond to configuration-dependent free energies of the system, recent studies have focused on adjusting enthalpic or entropic contributions to account for issues with transferability. However, these approaches can require a manual adjustment of the CG interaction a priori and are usually limited to constant volume ensembles. To overcome these limitations, we construct temperature and phase transferable CG models under constant pressure by developing the ultra-coarse-graining (UCG) methodology in the mean-field limit. In the mean-field ansatz, an embedded semi-global order parameter recapitulates global changes to the system by automatically adjusting the effective CG interactions, thus bridging free energy decompositions with UCG theory. The method presented is designed to faithfully capture structural correlations under different thermodynamic conditions, using a single UCG model. Specifically, we test the applicability of the developed theory in three distinct cases: (1) different temperatures at constant pressure in liquids, (2) different temperatures across thermodynamic phases, and (3) liquid/vapor interfaces. We demonstrate that the systematic construction of both temperature and phase transferable bottom-up CG models is possible using this generalized UCG theory. Based on our findings, this approach significantly extends the transferability and applicability of the bottom-up CG theory and method.
Influenza A M2 Inhibitor Binding Understood through Mechanisms of Excess Proton Stabilization and Channel Dynamics
Prevalent resistance to inhibitors that target the influenza A M2 proton channel has necessitated a continued drug design effort, supported by a sustained study of the mechanism of channel function and inhibition. Recent high-resolution X-ray crystal structures present the first opportunity to see how the adamantyl amine class of inhibitors bind to M2 and disrupt and interact with the channel’s water network, providing insight into the critical properties that enable their effective inhibition in wild-type M2. In this work, we examine the hypothesis that these drugs act primarily as mechanism-based inhibitors by comparing hydrated excess proton stabilization during proton transport in M2 with the interactions revealed in the crystal structures, using the Multiscale Reactive Molecular Dynamics (MS-RMD) methodology. MS-RMD, unlike classical molecular dynamics, models the hydrated proton (hydronium-like cation) as a dynamic excess charge defect and allows bonds to break and form, capturing the intricate interactions between the hydrated excess proton, protein atoms, and water. Through this, we show that the ammonium group of the inhibitors is effectively positioned to take advantage of the channel’s natural ability to stabilize an excess protonic charge and act as a hydronium mimic. Additionally, we show that the channel is especially stable in the drug binding region, highlighting the importance of this property for binding the adamantane group. Finally, we characterize an additional hinge point near Val27, which dynamically responds to charge and inhibitor binding. Altogether, this work further illuminates a dynamic understanding of the mechanism of drug inhibition in M2, grounded in the fundamental properties that enable the channel to transport and stabilize excess protons, with critical implications for future drug design efforts.
Molecular Origins of the Barriers to Proton Transport in Acidic Aqueous Solution
The self-consistent iterative multistate empirical valence bond (SCI-MS-EVB) method is used to analyze the structure, thermodynamics, and dynamics of hydrochloric acid solutions. The reorientation time scales of irreversible proton transport are elucidated by simulating 0.43, 0.85, 1.68, and 3.26 M HCl solutions at 270, 285, 300, 315, and 330 K. The results indicate increased counterion pairing with increasing concentration, which manifests itself via reduced hydronium oxygen–chloride (O*–Cl) structuring in the radial distribution functions. Increasing ionic concentration also reduces the diffusion of the hydrated excess protons, principally by reducing the contribution of the Grotthuss proton hopping (shuttling) mechanism to the overall diffusion process. In agreement with prior experimental findings, a decrease in the activation energy of reorientation time scales was also observed, which is explicitly explained by using activated rate theory and an energy–entropy decomposition of the state-averaged radial distribution functions. These results provide atomistic verification of suggestions from recent two-dimensional infrared spectroscopy experiments that chloride anions (as opposed to hydrated excess protons) create entropic barriers to proton transport.
Interfacial Solvation and Slow Transport of Hydrated Excess Protons in Non-Ionic Reverse Micelles
This work employs molecular dynamics simulations to investigate the solvation and transport properties of hydrated excess protons (with a hydronium-like core structure) in non-ionic Igepal CO-520 reverse micelles of various sizes in a non-polar solvent. Multiscale Reactive Molecular Dynamics (MS-RMD) simulations were used to describe vehicular and hopping diffusion during the proton transport process. As detailed herein, an excess proton shows a marked tendency to localize in the interfacial region of micellar water pools. Slow proton transport was observed which becomes faster with increasing micellar size. Further analysis reveals that the slow diffusion of an excess proton is a combined result of slow water diffusion and the low proton hopping rate. This study also confirms that a low proton hopping rate in reverse micelles stems from the interfacial solvation of hydrated excess protons and the immobilization of interfacial water. The low water density in the interfacial region makes it difficult to form a complete hydrogen bond network near the hydrated excess proton, and therefore locks in the orientation of hydrated proton cations. The immobilization of the interfacial water also slows the relaxation of the overall hydrogen bond network.
Reactive Coarse-Grained Molecular Dynamics
Coarse-grained (CG) models have allowed for the study of long time and length scale properties of a variety of systems. However, when a system undergoes chemical reactions, current CG models are not able to capture this behavior because of their fixed bonding topology. In order to develop CG models capable of taking into account such chemical changes, a model must be able to adapt its bonding topology and CG site–site interactions to switch between multiple bonding structures (i.e., topologies). This challenge particularly impacts “bottom-up” CG models developed from the fundamental underlying atomistic-scale interactions. In this paper, a reactive coarse-grained (RCG) method is developed which utilizes all-atom (AA) data to create a CG model able to represent chemical reactions by undergoing changes in bonding topology. As an example, the RCG method was applied to a model of SN2 reactions of 1-chlorobutane with a chloride ion and 1-iodobutane with an iodide ion in a methanol solvent. An asymmetric reaction was also modeled by incorporating a constant energy offset to the 1-iodobutane model. In each case, the calculated CG potential of mean force (PMF) results in good agreement with the fully AA PMF for the reactions.
Water-Assisted Proton Transport in Confined Nanochannels
Hydrated excess protons under hydrophobic confinement are a critical component of charge transport behavior and reactivity in nanoporous materials and biomolecular systems. Herein, excess proton confinement effects are computationally investigated for sub-2 nm hydrophobic nanopores by varying the diameters (d = 0.81, 0.95, 1.09, 1.22, 1.36, 1.63, and 1.90 nm), lengths (l ∼3 and ∼5 nm), curvature, and chirality of cylindrical carbon nanotube (CNT) nanopores. CNTs with a combination of different diameter segments are also explored. The spatial distribution of water molecules under confinement is diameter-dependent; however, proton solvation and transport are consistently found to occur in the water layer adjacent to the pore wall, showing an “amphiphilic” character of the hydrated excess proton hydronium-like structure. The proton transport free energy barrier also decreases significantly as the nanopore diameter increases and proton transport becomes almost barrierless in the d > 1 nm nanopores. Among the nanopores studied, the Zundel cation (H5O2+) is populated only in the d = 0.95 nm CNT (7,7) nanopore. The presence of the hydrated excess proton and K+ inside the CNT (7,7) nanopore induces a water density increase by 40 and 20%, respectively. The K+ transport through CNT nanopores is also consistently higher in the free energy barrier than proton transport. Interestingly, the evolution of excess protonic charge defect distribution reveals a “frozen” single water wire configuration in the d = 0.81 nm CNT (6,6) nanopore (or segment), through which hydrated excess protons can only shuttle via the Grotthuss mechanism. Vehicular diffusion becomes relevant to proton transport in the “flat” free energy regions and in the wider nanopores, where protons do not primarily shuttle in the axial direction
What Coordinate Best Describes the Affinity of the Hydrated Excess Proton for the Air–Water Interface?
Molecular dynamics simulations and free energy sampling are employed in this work to investigate the surface affinity of the hydrated excess proton with two definitions of the interface: The Gibbs dividing interface (GDI) and the Willard–Chandler interface (WCI). Both the multistate empirical valence bond (MS-EVB) reactive molecular dynamics method and the density functional theory-based ab initio molecular dynamics (AIMD) were used to describe the hydrated excess proton species, including “vehicular” (standard diffusion) transport and (Grotthuss) proton hopping transport and associated structures of the hydrated excess proton net positive charge defect. The excess proton is found to exhibit a similar trend and quantitative free energy behavior in terms of its surface affinity as a function of the GDI or WCI. Importantly, the definitions of the two interfaces in terms of the excess proton charge defect are highly correlated and far from independent of one another, thus undermining the argument that one interface is superior to the other when describing the proton interface affinity. Moreover, the hydrated excess proton and its solvation shell significantly influence the location and local curvature of the WCI, making it difficult to disentangle the interfacial thermodynamics of the excess proton from the influence of that species on the instantaneous surface curvature.
Microtubule Simulations Provide Insight into the Molecular Mechanism Underlying Dynamic Instability
The dynamic instability of microtubules (MTs), which refers to their ability to switch between polymerization and depolymerization states, is crucial for their function. It has been proposed that the growing MT ends are protected by a “GTP cap” that consists of GTP-bound tubulin dimers. When the speed of GTP hydrolysis is faster than dimer recruitment, the loss of this GTP cap will lead the MT to undergo rapid disassembly. However, the underlying atomistic mechanistic details of the dynamic instability remains unclear. In this study, we have performed long-time atomistic molecular dynamics simulations (1 μs for each system) for MT patches as well as a short segment of a closed MT in both GTP- and GDP-bound states. Our results confirmed that MTs in the GDP state generally have weaker lateral interactions between neighboring protofilaments (PFs) and less cooperative outward bending conformational change, where the difference between bending angles of neighboring PFs tends to be larger compared with GTP ones. As a result, when the GDP state tubulin dimer is exposed at the growing MT end, these factors will be more likely to cause the MT to undergo rapid disassembly. We also compared simulation results between the special MT seam region and the remaining material and found that the lateral interactions between MT PFs at the seam region were comparatively much weaker. This finding is consistent with the experimental suggestion that the seam region tends to separate during the disassembly process of an MT.
A Helical Assembly of Human ESCRT-I Scaffolds Reverse-Topology Membrane Scission
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 the 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.
TRIM5α self-assembly and compartmentalization of the HIV-1 viral capsid
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.
Anisotropic Motions of Fibrils Dictated by Their Orientations in the Lamella: A Coarse-Grained Model of a Plant Cell Wall
Plant cell walls are complex systems that exhibit the characteristics of both rigid and soft material depending on their external perturbations. The three main polymeric components in a plant primary cell wall are cellulose fibrils, hemicellulose, and pectins. These components interact in a hierarchical fashion giving rise to mesoscale structural features such as cellulose bundles, lamella stacking, and so on. Although several studies have focused on understanding these unique structural features, a clear picture linking them to cell wall mechanics is still lacking. As a first step toward this goal, a phenomenological model of plant cell wall has been developed in this work by using available experimental data to investigate the underlying connections between mesoscale structural features and the motions of fibrils during deformation. In this model cellulose fibrils exhibit motions such as angular reorientations and kinking upon forced stretching. These motions are dependent on the orientation of fibrils with respect to the stretch direction, i.e., fibrils that are at an angle to the stretch direction exhibit predominant angular reorientations, while fibrils transverse to the stretch direction undergo kinking as a result of transverse compression. Varying the chain length of pectin had negligible effects on these motions. One of the main contributions from this work is the development of a simple model that can be easily fine-tuned to test other hypotheses and extended to include additional experimental knowledge about the structural aspects of cell walls in the future.
Local Conformational Dynamics Regulating Transport Properties of a Cl–/H+ Antiporter
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.
Compatible observable decompositions for coarse-grained representations of real molecular systems
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.
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.
Dynamic Protonation Dramatically Affects the Membrane Permeability of Drug-like Molecules
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.
Proton-Induced Conformational and Hydration Dynamics in the Influenza A M2 Channel
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.
Unusual Organization of I-BAR Proteins on Tubular and Vesicular Membranes
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
Multiscale Model of Integrin Adhesion Assembly
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.
Coarse-Graining of Many-Body Path Integrals: Theory and Numerical Approximations
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.
Multiconfigurational Coarse-Grained Molecular Dynamics
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-Graining Involving Virtual Sites: Centers of Symmetry Coarse-Graining
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.
Systematic Coarse-Grained Lipid Force Fields with Semiexplicit Solvation via Virtual Sites
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.
Coarse-Grained Simulation of Full-Length Integrin Activation
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.
Dynamic Protonation Dramatically Affects the Membrane Permeability of Drug-like Molecules
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.
Gating mechanisms during actin filament elongation by formins
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.
Multiscale simulation of actin filaments and actin-associated proteins
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.
Ultra-Coarse-Grained Liquid State Models with Implicit Hydrogen Bonding
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.
Mesopic coarse-grained representation of fluids rigorously derived from atomistic models
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.
Entropic forces drive clustering and spatial localization of influenza A M2 during viral budding
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.
Insights into the Cooperative Nature of ATP Hydrolysis in Actin Filaments
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.
Ultra-Coarse-Grained Models Allow for an Accurate and Transferable Treatment of Interfacial Systems
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.
Coarse-grained Directed Simulation
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.
Improved Ab Initio Molecular Dynamics by Minimally Biasing with Experimental Data
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.
Highly Coarse-Grained Representations of Transmembrane Proteins
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.
The Origin of Coupled Chloride and Proton Transport in a Cl–/H+Antiporter
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.
Acid Activation Mechanism of the Influenza A M2 Proton Channel
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
Fascin and α-Actinin-bundled Networks Contain Intrinsic Structural Features That Drive Protein Sorting
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 that allows us to predict the energetic barrier for switching from one domain to another by comparison of the model results to experimental domain sizes.
On the Representability Problem and the Physical Meaning of Coarse-Grained Models
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.
Multiscale Simulations of Protein Facilitated Membrane Remodeling
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.
Multiscale Simulations Reveal Key Features of the Proton Pumping Mechanism in Cytochrome c Oxidase
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.
Cations Stiffen Actin Filaments by Adhering a Key Structural Element to Adjacent Subunits
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.