Membrane free-energy landscapes derived from atomistic dynamics explain nonuniversal cholesterol-induced stiffening.

All lipid membranes have inherent morphological preferences and resist deformation. Yet adaptations in membrane shape can and do occur at multiple length scales. While this plasticity is crucial for cellular physiology, the factors controlling the morphological energetics of lipid bilayers and the dominant mechanisms of membrane remodeling remain to be fully understood. An ongoing debate regarding the universality of the stiffening effect of cholesterol underscores the challenges facing this field, both experimentally and theoretically, even for simple lipid mixtures. On the computational side, we have argued that enhanced-sampling all-atom molecular dynamics simulations are uniquely suited for the quantification of membrane conformational energetics, as they minimize a priori assumptions and permit analysis of bilayers in deformed states. To showcase this approach, we examine reported inconsistencies between alternative experimental measurements of bending moduli for cholesterol-enriched membranes. Specifically, we analyze lipid bilayers with different chain saturation and compute free-energy landscapes for curvature deformations distributed over areas from ∼5 to ∼60 nm2. These enhanced simulations, totaling over 100 µs of sampling time, enable us to directly quantify both bending and tilt moduli and to dissect the contributing factors and molecular mechanisms of curvature generation at each length scale. Our results show that the effects of cholesterol on bending rigidity are lipid-specific and suggest that this specificity arises from differences in the torsional dynamics of the acyl chains. In summary, we demonstrate that quantitative relationships can now be established between lipid structure and bending energetics, paving the way for addressing open fundamental questions in cell membrane mechanics.

Membrane free-energy landscapes derived from atomistic dynamics explain nonuniversal cholesterol-induced stiffening.

All lipid membranes have inherent morphological preferences and resist deformation. Yet adaptations in membrane shape can and do occur at multiple length scales. While this plasticity is crucial for cellular physiology, the factors controlling the morphological energetics of lipid bilayers and the dominant mechanisms of membrane remodeling remain unclear. An ongoing debate regarding the universality of the stiffening effect of cholesterol underscores the challenges facing this field, both experimentally and theoretically, even for simple lipid mixtures. On the computational side, we have argued that enhanced- sampling all-atom molecular dynamics simulations are uniquely suited for quantification of membrane conformational energetics, not only because they minimize a-priori assumptions, but also because they permit analysis of bilayers in deformed states. To showcase this approach, we examine reported inconsistencies between alternative experimental measurements of bending moduli for cholesterol-enriched membranes. Specifically, we analyze lipid bilayers with different chain saturation, and compute free-energy landscapes for curvature deformations distributed over areas from ∼5 to ∼60 nm 2 . These enhanced simulations, totaling over 100 microseconds of sampling time, enable us to directly quantify both bending and tilt moduli, and to dissect the contributing factors and molecular mechanisms of curvature generation at each length scale. Our results show that cholesterol effects are lipid-specific, in agreement with giantvesicle measurements, and explain why experiments probing nanometer scale lipid dynamics diverge. In summary, we demonstrate that quantitative structure-mechanics relationships can now be established for heterogenous membranes, paving the way for addressing open fundamental questions in cell membrane mechanics. Significance: Elucidating the energetics and mechanisms of membrane remodeling is an essential step towards understanding cell physiology. This problem is challenging, however, because membrane bending involves both large-scale and atomic-level dynamics, which are difficult to measure simultaneously. A recent controversy regarding the stiffening effect of cholesterol, which is ubiquitous in animal cells, illustrates this challenge. We show how enhanced molecular-dynamics simulations can bridge this length-scale gap and reconcile seemingly incongruent observations. This approach facilitates a conceptual connection between lipid chemistry and membrane mechanics, thereby providing a solid basis for future research on remodeling phenomena, such as in membrane trafficking or viral infection.

SPICA Force Field for Proteins and Peptides.

A coarse-grained (CG) model for peptides and proteins was developed as an extension of the Surface Property fItting Coarse grAined (SPICA) force field (FF). The model was designed to examine membrane proteins that are fully compatible with the lipid membranes of the SPICA FF. A preliminary version of this protein model was created using thermodynamic properties, including the surface tension and density in the SPICA (formerly called SDK) FF. In this study, we improved the CG protein model to facilitate molecular dynamics (MD) simulations with a reproduction of multiple properties from both experiments and all-atom (AA) simulations. An elastic network model was adopted to maintain the secondary structure within a single chain. The side-chain analogues reproduced the transfer free energy profiles across the lipid membrane and demonstrated reasonable association free energy (potential of mean force) in water compared to those from AA MD. A series of peptides/proteins adsorbed onto or penetrated into the membrane simulated by the CG MD correctly predicted the penetration depths and tilt angles of peripheral and transmembrane peptides/proteins as comparable to those in the orientations of proteins in membranes (OPM) database. In addition, the dimerization free energies of several transmembrane helices within a lipid bilayer were comparable to those from experimental estimation. Application studies on a series of membrane protein assemblies, scramblases, and poliovirus capsids demonstrated the good performance of the SPICA FF.

Human Learning for Molecular Simulations: The Collective Variables Dashboard in VMD.

The Collective Variables Dashboard is a software tool for real-time, seamless exploration of molecular structures and trajectories in a customizable space of collective variables. The Dashboard arises from the integration of the Collective Variables Module (also known as Colvars) with the visualization software VMD, augmented with a fully discoverable graphical interface offering interactive workflows for the design and analysis of collective variables. Typical use cases include a priori design of collective variables for enhanced sampling and free energy simulations as well as analysis of any type of simulation or collection of structures in a collective variable space. A combination of those cases commonly occurs when preliminary simulations, biased or unbiased, reveal that an optimized set of collective variables is necessary to improve sampling in further simulations. Then the Dashboard provides an efficient way to intuitively explore the space of likely collective variables, validate them on existing data, and use the resulting collective variable definitions directly in further biased simulations using the Collective Variables Module. Visualization of biasing energies and forces is proposed to help analyze or plan biased simulations. We illustrate the use of the Dashboard on two applications: discovering coordinates to describe ligand unbinding from a protein binding site and designing volume-based variables to bias the hydration of a transmembrane pore.

Bringing discrete-time Langevin splitting methods into agreement with thermodynamics.

In light of the recently published complete set of statistically correct Grønbech-Jensen (GJ) methods for discrete-time thermodynamics, we revise a differential operator splitting method for the Langevin equation in order to comply with the basic GJ thermodynamic sampling features, namely, the Boltzmann distribution and Einstein diffusion, in linear systems. This revision, which is based on the introduction of time scaling along with flexibility of a discrete-time velocity attenuation parameter, provides a direct link between the ABO splitting formalism and the GJ methods. This link brings about the conclusion that any GJ method has at least weak second order accuracy in the applied time step. It further helps identify a novel half-step velocity, which simultaneously produces both correct kinetic statistics and correct transport measures for any of the statistically sound GJ methods. Explicit algorithmic expressions are given for the integration of the new half-step velocity into the GJ set of methods. Numerical simulations, including quantum-based molecular dynamics (QMD) using the QMD suite Los Alamos Transferable Tight-Binding for Energetics, highlight the discussed properties of the algorithms as well as exhibit the direct application of robust, time-step-independent stochastic integrators to QMD.

Data-guided Multi-Map variables for ensemble refinement of molecular movies.

Driving molecular dynamics simulations with data-guided collective variables offer a promising strategy to recover thermodynamic information from structure-centric experiments. Here, the three-dimensional electron density of a protein, as it would be determined by cryo-EM or x-ray crystallography, is used to achieve simultaneously free-energy costs of conformational transitions and refined atomic structures. Unlike previous density-driven molecular dynamics methodologies that determine only the best map-model fits, our work employs the recently developed Multi-Map methodology to monitor concerted movements within equilibrium, non-equilibrium, and enhanced sampling simulations. Construction of all-atom ensembles along the chosen values of the Multi-Map variable enables simultaneous estimation of average properties, as well as real-space refinement of the structures contributing to such averages. Using three proteins of increasing size, we demonstrate that biased simulation along the reaction coordinates derived from electron densities can capture conformational transitions between known intermediates. The simulated pathways appear reversible with minimal hysteresis and require only low-resolution density information to guide the transition. The induced transitions also produce estimates for free energy differences that can be directly compared to experimental observables and population distributions. The refined model quality is superior compared to those found in the Protein Data Bank. We find that the best quantitative agreement with experimental free-energy differences is obtained using medium resolution density information coupled to comparatively large structural transitions. Practical considerations for probing the transitions between multiple intermediate density states are also discussed.

The challenge of stochastic Størmer-Verlet thermostats generating correct statistics.

In light of the recently developed complete GJ set of single random variable stochastic, discrete-time Størmer-Verlet algorithms for statistically accurate simulations of Langevin equations [N. Grønbech-Jensen, Mol. Phys. 118, e1662506 (2020)], we investigate two outstanding questions: (1) Are there any algorithmic or statistical benefits from including multiple random variables per time step and (2) are there objective reasons for using one or more methods from the available set of statistically correct algorithms? To address the first question, we assume a general form for the discrete-time equations with two random variables and then follow the systematic, brute-force GJ methodology by enforcing correct thermodynamics in linear systems. It is concluded that correct configurational Boltzmann sampling of a particle in a harmonic potential implies correct configurational free-particle diffusion and that these requirements only can be accomplished if the two random variables per time step are identical. We consequently submit that the GJ set represents all possible stochastic Størmer-Verlet methods that can reproduce time step-independent statistics of linear systems. The second question is thus addressed within the GJ set. Based on numerical simulations of complex molecular systems, as well as on analytic considerations, we analyze apparent friction-induced differences in the stability of the methods. We attribute these differences to an inherent, friction-dependent discrete-time scaling, which depends on the specific method. We suggest that the method with the simplest interpretation of temporal scaling, the GJ-I/GJF-2GJ method, be preferred for statistical applications.

Scalable molecular dynamics on CPU and GPU architectures with NAMD.

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

Coexistence of Lipid Phases Stabilizes Interstitial Water in the Outer Layer of Mammalian Skin.

The lipid matrix in the outer layer of mammalian skin, the stratum corneum, has been previously investigated by multiple biophysical techniques aimed at identifying hydrophilic and lipophilic pathways of permeation. Although consensus is developing over the microscopic structure of the lipid matrix, no molecular-resolution model describes the permeability of all chemical species simultaneously. Using molecular dynamics simulations of a model mixture of skin lipids, the self-assembly of the lipid matrix lamellae has been studied. At higher humidity, the resulting lamellar phase is maintained by partitioning excess water into isolated droplets of controlled size and spatial distribution. The droplets may fuse together to form intralamellar water channels, thereby providing a pathway for the permeation of hydrophilic species. These results reconcile competing data on the outer skin's structure and broaden the scope of molecular-based methods to improve the safety of topical products and to advance transdermal drug delivery.

Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics.

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this "Multi-Map" variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich-Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.

Large-scale state-dependent membrane remodeling by a transporter protein.

That channels and transporters can influence the membrane morphology is increasingly recognized. Less appreciated is that the extent and free-energy cost of these deformations likely varies among different functional states of a protein, and thus, that they might contribute significantly to defining its mechanism. We consider the trimeric Na+-aspartate symporter GltPh, a homolog of an important class of neurotransmitter transporters, whose mechanism entails one of the most drastic structural changes known. Molecular simulations indicate that when the protomers become inward-facing, they cause deep, long-ranged, and yet mutually-independent membrane deformations. Using a novel simulation methodology, we estimate that the free-energy cost of this membrane perturbation is in the order of 6-7 kcal/mol per protomer. Compensating free-energy contributions within the protein or its environment must thus stabilize this inward-facing conformation for the transporter to function. We discuss these striking results in the context of existing experimental observations for this and other transporters.

Structural Characterization of Biomolecules through Atomistic Simulations Guided by DEER Measurements.

Double electron-electron resonance (DEER) is a popular technique that exploits attached spin labels to probe the collective dynamics of biomolecules in a native environment. Like most spectroscopic approaches, DEER detects an ensemble of states accounting for biomolecular dynamics as well as the labels' intrinsic flexibility. Hence, the DEER data alone do not provide high-resolution structural information. To disentangle this variability, we introduce a minimally biased simulation method to sample a structural ensemble that reproduces multiple experimental signals within the uncertainty. In contrast to previous approaches, our method targets the raw data themselves, and thereby it brings forth an unbiased molecular interpretation of the experiments. After validation on the T4 lysozyme, we apply this technique to interpret recent DEER experiments on a membrane transporter binding protein (VcSiaP). The results highlight the large-scale conformational movement that occurs upon substrate binding and reveal that the unbound VcSiaP is more open in solution than the X-ray structure.

Mechanically Strong Polymer Sheets from Aligned Ultrahigh-Molecular-Weight Polyethylene Nanocomposites.

Ultrahigh-molecular-weight polyethylene (UHMWPE) is of great interest as a next-generation body armor material because of its superior mechanical properties. However, such unique properties depend critically on its microscopic structure characteristics, including the degree of crystallinity, chain alignment, and morphology. Here, we present a highly aligned UHMWPE and its composite sheets containing uniformly dispersed boron nitride (BN) nanosheets. The dispersion of BN nanosheets into the UHMWPE matrix increases its mechanical properties over a broad temperature range. Experiments and simulation confirm that the alignment of chain segments in the composite matrix increases with temperature, leading to an improvement in mechanical properties at high temperature. Together with the large thermal conductivity of UHMWPE and BN, our findings serve to expand the application spectrum of highly aligned polymer nanocomposite materials for ballistic panels and body armor over a broad range of temperatures.

Infrared and fluorescence assessment of the hydration status of the tryptophan gate in the influenza A M2 proton channel.

The M2 proton channel of the influenza A virus has been the subject of extensive studies because of its critical role in viral replication. As such, we now know a great deal about its mechanism of action, especially how it selects and conducts protons in an asymmetric fashion. The conductance of this channel is tuned to conduct protons at a relatively low biologically useful rate, which allows acidification of the viral interior of a virus entrapped within an endosome, but not so great as to cause toxicity to the infected host cell prior to packaging of the virus. The dynamic, structural and chemical features that give rise to this tuning are not fully understood. Herein, we use a tryptophan (Trp) analog, 5-cyanotryptophan, and various methods, including linear and nonlinear infrared spectroscopies, static and time-resolved fluorescence techniques, and molecular dynamics simulations, to site-specifically interrogate the structure and hydration dynamics of the Trp41 gate in the transmembrane domain of the M2 proton channel. Our results suggest that the Trp41 sidechain adopts the t90 rotamer, the χ2 dihedral angle of which undergoes an increase of approximately 35° upon changing the pH from 7.4 to 5.0. Furthermore, we find that Trp41 is situated in an environment lacking bulk-like water, and somewhat surprisingly, the water density and dynamics do not show a measurable difference between the high (7.4) and low (5.0) pH states. Since previous studies have shown that upon channel opening water flows into the cavity above the histidine tetrad (His37), the present finding thus provides evidence indicating that the lack of sufficient water molecules near Trp41 needed to establish a continuous hydrogen bonding network poses an additional energetic bottleneck for proton conduction.

High-resolution structures of the M2 channel from influenza A virus reveal dynamic pathways for proton stabilization and transduction.

The matrix 2 (M2) protein from influenza A virus is a proton channel that uses His37 as a selectivity filter. Here we report high-resolution (1.10 Å) cryogenic crystallographic structures of the transmembrane domain of M2 at low and high pH. These structures reveal that waters within the pore form hydrogen-bonded networks or "water wires" spanning 17 Å from the channel entrance to His37. Pore-lining carbonyl groups are well situated to stabilize hydronium via second-shell interactions involving bridging water molecules. In addition, room temperature crystallographic structures indicate that water becomes increasingly fluid with increasing temperature and decreasing pH, despite the higher electrostatic field. Complementary molecular dynamics simulations reveal a collective switch of hydrogen bond orientations that can contribute to the directionality of proton flux as His37 is dynamically protonated and deprotonated in the conduction cycle.

How Sensitive is the Amide†I Vibration of the Polypeptide Backbone to Electric Fields?

Site-selective isotopic labeling of amide carbonyls offers a nonperturbative means to introduce a localized infrared probe into proteins. Although this strategy has been widely used to investigate various biological questions, the dependence of the underlying amide I vibrational frequency on electric fields (or Stark tuning rate) has not been fully determined, which prevents it from being used in a quantitative manner in certain applications. Herein, through the use of experiments and molecular dynamics simulations, the Stark tuning rate of the amide I vibration of an isotopically labeled backbone carbonyl in a transmembrane α-helix is determined to be approximately 1.4 cm(-1) /(MV/cm). This result provides a quantitative basis for using this vibrational model to assess local electric fields in proteins, among other applications. For instance, by using this value, we are able to show that the backbone region of a dipeptide has a surprisingly low dielectric constant.

Structural Refinement of Proteins by Restrained Molecular Dynamics Simulations with Non-interacting Molecular Fragments.

The knowledge of multiple conformational states is a prerequisite to understand the function of membrane transport proteins. Unfortunately, the determination of detailed atomic structures for all these functionally important conformational states with conventional high-resolution approaches is often difficult and unsuccessful. In some cases, biophysical and biochemical approaches can provide important complementary structural information that can be exploited with the help of advanced computational methods to derive structural models of specific conformational states. In particular, functional and spectroscopic measurements in combination with site-directed mutations constitute one important source of information to obtain these mixed-resolution structural models. A very common problem with this strategy, however, is the difficulty to simultaneously integrate all the information from multiple independent experiments involving different mutations or chemical labels to derive a unique structural model consistent with the data. To resolve this issue, a novel restrained molecular dynamics structural refinement method is developed to simultaneously incorporate multiple experimentally determined constraints (e.g., engineered metal bridges or spin-labels), each treated as an individual molecular fragment with all atomic details. The internal structure of each of the molecular fragments is treated realistically, while there is no interaction between different molecular fragments to avoid unphysical steric clashes. The information from all the molecular fragments is exploited simultaneously to constrain the backbone to refine a three-dimensional model of the conformational state of the protein. The method is illustrated by refining the structure of the voltage-sensing domain (VSD) of the Kv1.2 potassium channel in the resting state and by exploring the distance histograms between spin-labels attached to T4 lysozyme. The resulting VSD structures are in good agreement with the consensus model of the resting state VSD and the spin-spin distance histograms from ESR/DEER experiments on T4 lysozyme are accurately reproduced.

Molecular dynamics simulations of cholesterol-rich membranes using a coarse-grained force field for cyclic alkanes.

The architecture of a biological membrane hinges upon the fundamental fact that its properties are determined by more than the sum of its individual components. Studies on model membranes have shown the need to characterize in molecular detail how properties such as thickness, fluidity, and macroscopic bending rigidity are regulated by the interactions between individual molecules in a non-trivial fashion. Simulation-based approaches are invaluable to this purpose but are typically limited to short sampling times and model systems that are often smaller than the required properties. To alleviate both limitations, the use of coarse-grained (CG) models is nowadays an established computational strategy. We here present a new CG force field for cholesterol, which was developed by using measured properties of small molecules, and can be used in combination with our previously developed force field for phospholipids. The new model performs with precision comparable to atomistic force fields in predicting the properties of cholesterol-rich phospholipid bilayers, including area per lipid, bilayer thickness, tail order parameter, increase in bending rigidity, and propensity to form liquid-ordered domains in ternary mixtures. We suggest the use of this model to quantify the impact of cholesterol on macroscopic properties and on microscopic phenomena involving localization and trafficking of lipids and proteins on cellular membranes.

Hydrogen-bonded water molecules in the M2 channel of the influenza A virus guide the binding preferences of ammonium-based inhibitors.

The tetrameric M2 proton channel of influenza A virus is an integral membrane protein responsible for the acidification of the viral interior. Drugs such as amantadine target the transmembrane region of wild type M2 by acting as pore blockers. However, a number of mutations affecting this domain confer drug resistance, prompting the need for alternative inhibitors. The availability of high-resolution structures of drug-bound M2, paired with computational investigations, revealed that inhibitors can bind at different sites, and provided useful insights in understanding the principles governing proton conduction. Here, we investigated by computation the energetic and geometric factors determining the relative stability of pore blockers at individual sites of different M2 strains. We found that local free energy minima along the translocation pathway of positively charged chemical species correspond to experimentally determined binding sites of inhibitors. Then, by examining the structure of water clusters hydrating each site, as well as of those displaced by binding of hydrophobic scaffolds, we predicted the binding preferences of M2 ligands. This information can be used to guide the identification of novel classes of inhibitors.

Dehydration of multilamellar fatty acid membranes: towards a computational model of the stratum corneum.

The level of hydration controls the cohesion between apposed lamellae of saturated free fatty acids found in the lipid matrix of stratum corneum, the outermost layer of mammalian skin. This multilamellar lipid matrix is highly impermeable to water and ions, so that the local hydration shell of its fatty acids may not always be in equilibrium with the acidity and relative humidity, which significantly change over a course of days during skin growth. The homeostasis of the stratum corneum at each moment of its growth likely requires a balance between two factors, which affect in opposite ways the diffusion of hydrophilic species through the stratum corneum: (i) an increase in water order as the lipid lamellae come in closer contact, and (ii) a decrease in water order as the fraction of charged fatty acids is lowered by pH. Herein molecular dynamics simulations are employed to estimate the impact of both effects on water molecules confined between lamellae of fatty acids. Under conditions where membrane undulations are energetically favorable, the charged fatty acids are able to sequester cations around points of contact between lamellae that are fully dehydrated, while essentially maintaining a multilamellar structure for the entire system. This observation suggests that the undulations of the fatty acid lamellae control the diffusion of hydrophilic species through the water phase by altering the positional and rotational order of water molecules in the embedded/occluded "droplets."