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

Membrane curvature sensing and symmetry breaking of the M2 proton channel from Influenza A

The M2 proton channel aids in the exit of mature influenza viral particles from the host plasma membrane through its ability to stabilize regions of high negative Gaussian curvature (NGC) that occur at the neck of budding virions. The channels are homo-tetramers that contain a cytoplasm-facing amphipathic helix (AH) that is necessary and sufficient for NGC generation; however, constructs containing the transmembrane spanning helix, which facilitates tetramerization, exhibit enhanced curvature generation. Here, we used all-atom molecular dynamics (MD) simulations to explore the conformational dynamics of M2 channels in lipid bilayers revealing that the AH is dynamic, quickly breaking the fourfold symmetry observed in most structures. Next, we carried out MD simulations with the protein restrained in four- and twofold symmetric conformations to determine the impact on the membrane shape. While each pattern was distinct, all configurations induced pronounced curvature in the outer leaflet, while conversely, the inner leaflets showed minimal curvature and significant lipid tilt around the AHs. The MD-generated profiles at the protein-membrane interface were then extracted and used as boundary conditions in a continuum elastic membrane model to calculate the membrane-bending energy of each conformation embedded in different membrane surfaces characteristic of a budding virus. The calculations show that all three M2 conformations are stabilized in inward-budding, concave spherical caps and destabilized in outward-budding, convex spherical caps, the latter reminiscent of a budding virus. One of the C2-broken symmetry conformations is stabilized by 4 kT in NGC surfaces with the minimum energy conformation occurring at a curvature corresponding to 33 nm radii. In total, our work provides atomistic insight into the curvature sensing capabilities of M2 channels and how enrichment in the nascent viral particle depends on protein shape and membrane geometry.

Mesoscopic elasticity controls dynamin-driven fission of lipid tubules

Mesoscale physics bridges the gap between the microscopic degrees of freedom of a system and its large-scale continuous behavior and highlights the role of a few key quantities in complex and multiscale phenomena, like dynamin-driven fission of lipid membranes. The dynamin protein wraps the neck formed during clathrin-mediated endocytosis, for instance, and constricts it until severing occurs. Although ubiquitous and fundamental for life, the cooperation between the GTP-consuming conformational changes within the protein and the full-scale response of the underlying lipid substrate is yet to be unraveled. In this work, we build an effective mesoscopic model from constriction to fission of lipid tubules based on continuum membrane elasticity and implicitly accounting for ratchet-like power strokes of dynamins. Localization of the fission event, the overall geometry, and the energy expenditure we predict comply with the major experimental findings. This bolsters the idea that a continuous picture emerges soon enough to relate dynamin polymerization length and membrane rigidity and tension with the optimal pathway to fission. We therefore suggest that dynamins found in in vivo processes may optimize their structure accordingly. Ultimately, we shed light on real-time conductance measurements available in literature and predict the fission time dependency on elastic parameters.

Atomistic Insight into the Lipid Nanodomains of Synaptic Vesicles

Membrane curvature, once regarded as a passive consequence of membrane composition and cellular architecture, has been shown to actively modulate various properties of the cellular membrane. These changes could also lead to segregation of the constituents of the membrane, generating nanodomains with precise biological properties. Proteins often linked with neurodegeneration (e.g., tau, alpha-synuclein) exhibit an unintuitive affinity for synaptic vesicles in neurons, which are reported to lack distinct, ordered nanodomains based on their composition. In this study, all-atom molecular dynamics simulations are used to study a full-scale synaptic vesicle of realistic Gaussian curvature and its effect on the membrane dynamics and lipid nanodomain organization. Compelling indicators of nanodomain formation, from the perspective of composition, surface areas per lipid, order parameter, and domain lifetime, are identified in the vesicle membrane, which are absent in a flat bilayer of the same lipid composition. Therefore, our study supports the idea that curvature may induce phase separation in an otherwise fluid, disordered membrane.

The local variation of the Gaussian modulus enables different pathways for fluid lipid vesicle fusion

Viral infections, fertilization, neurotransmission, and many other fundamental biological processes rely on membrane fusion. Straightforward calculations based on the celebrated Canham-Helfrich elastic model predict a large topological energy barrier that prevents the fusion process from being thermally activated. While such high energy is in accordance with the physical barrier function of lipid membranes, it is difficult to reconcile with the biological mechanisms involved in fusion processes. In this work, we use a Ginzburg-Landau type of free energy that recovers the Canham-Helfrich model in the limit of small width-to-vesicle-extension ratio, with the additional ability to handle topological transitions. We show that a local modification of the Gaussian modulus in the merging region both dramatically lowers the elastic energy barrier and substantially changes the minimal energy pathway for fusion, in accordance with experimental evidence. Therefore, we discuss biological examples in which such a modification might play a crucial role.

Nonuniversal impact of cholesterol on membranes mobility, curvature sensing and elasticity

Biological membranes, composed mainly of phospholipids and cholesterol, play a vital role as cellular barriers. They undergo localized reshaping in response to environmental cues and protein interactions, with the energetics of deformations crucial for exerting biological functions. This study investigates the non-universal role of cholesterol on the structure and elasticity of saturated and unsaturated lipid membranes. Our study uncovers a highly cooperative relationship between thermal membrane bending and local cholesterol redistribution, with cholesterol showing a strong preference for the compressed membrane leaflet. Remarkably, in unsaturated membranes, increased cholesterol mobility enhances cooperativity, resulting in membrane softening despite membrane thickening and lipid compression caused by cholesterol. These findings elucidate the intricate interplay between thermodynamic forces and local molecular interactions that govern collective properties of membranes.

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.

Mesoscale simulations: An indispensable approach to understand biomembranes

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

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.

State-specific morphological deformations of the lipid bilayer explain mechanosensitive gating of MscS ion channels

The force-from-lipids hypothesis of cellular mechanosensation posits that membrane channels open and close in response to changes in the physical state of the lipid bilayer, induced for example by lateral tension. Here, we investigate the molecular basis for this transduction mechanism by studying the mechanosensitive ion channel MscS from Escherichia coli and its eukaryotic homolog MSL1 from Arabidopsis thaliana. First, we use single-particle cryo-electron microscopy to determine the structure of a novel open conformation of wild-type MscS, stabilized in a thinned lipid nanodisc. Compared with the closed state, the structure shows a reconfiguration of helices TM1, TM2, and TM3a, and widening of the central pore. Based on these structures, we examined how the morphology of the membrane is altered upon gating, using molecular dynamics simulations. The simulations reveal that closed-state MscS causes drastic protrusions in the inner leaflet of the lipid bilayer, both in the absence and presence of lateral tension, and for different lipid compositions. These deformations arise to provide adequate solvation to hydrophobic crevices under the TM1-TM2 hairpin, and clearly reflect a high-energy conformation for the membrane, particularly under tension. Strikingly, these protrusions are largely eradicated upon channel opening. An analogous computational study of open and closed MSL1 recapitulates these findings. The gating equilibrium of MscS channels thus appears to be dictated by opposing conformational preferences, namely those of the lipid membrane and of the protein structure. We propose a membrane deformation model of mechanosensation, which posits that tension shifts the gating equilibrium towards the conductive state not because it alters the mode in which channel and lipids interact, but because it increases the energetic cost of the morphological perturbations in the membrane required by the closed state.

LongBondEliminator: A Molecular Simulation Tool to Remove Ring Penetrations in Biomolecular Simulation Systems

We develop a workflow, implemented as a plugin to the molecular visualization program VMD, that can fix ring penetrations with minimal user input. LongBondEliminator, detects ring piercing artifacts by the long, strained bonds that are the local minimum energy conformation during minimization for some assembled simulation system. The LongBondEliminator tool then automatically treats regions near these long bonds using multiple biases applied through NAMD. By combining biases implemented through the collective variables module, density-based forces, and alchemical techniques in NAMD, LongBondEliminator will iteratively alleviate long bonds found within molecular simulation systems. Through three concrete examples with increasing complexity, a lignin polymer, an viral capsid assembly, and a large, highly glycosylated protein aggrecan, we demonstrate the utility for this method in eliminating ring penetrations from classical MD simulation systems. The tool is available via gitlab as a VMD plugin, and has been developed to be generically useful across a variety of biomolecular simulations.

Determination of Elastic Parameters of Lipid Membranes with Molecular Dynamics: A Review of Approaches and Theoretical Aspects

Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the development of molecular dynamics (MD), a variety of in silico methods have been proposed for the determination of elastic parameters of simulated lipid membranes. These MD methods allow for the consideration of details unattainable in experimental techniques and represent a distinct scientific field, which is rapidly developing. This work provides a review of these MD approaches with a focus on theoretical aspects. Two main challenges are identified: (i) the ambiguity in the transition from the continuum description of elastic theories to the discrete representation of MD simulations, and (ii) the determination of intrinsic elastic parameters of lipid mixtures, which is complicated due to the composition-curvature coupling effect.

Activation energy and force fields during topological transitions of fluid lipid vesicles

Topological transitions of fluid lipid membranes are fundamental processes for cell life. For example, they are required for endo- and exocytosis or to enable neurotransmitters to cross the neural synapses. Here, inspired by the idea that fusion and fission proteins could have evolved in Nature in order to carry out a minimal work expenditure, we evaluate the minimal free energy pathway for the transition between two spherical large unilamellar vesicles and a dumbbell-shaped one. To address the problem, we propose and successfully use a Ginzburg-Landau type of free energy, which allows us to uniquely describe without interruption the whole, full-scale topological change. We also compute the force fields needed to overcome the involved energy barriers. The obtained forces are in excellent agreement, in terms of intensity, scale, and spatial localization with experimental data on typical fission protein systems, whereas they suggest the presence of additional features in fusion proteins.

Molecular Dynamics Simulations of Curved Lipid Membranes

Eukaryotic cells contain membranes with various curvatures, from the near-plane plasma membrane to the highly curved membranes of organelles, vesicles, and membrane protrusions. These curvatures are generated and sustained by curvature-inducing proteins, peptides, and lipids, and describing these mechanisms is an important scientific challenge. In addition to that, some molecules can sense membrane curvature and thereby be trafficked to specific locations. The description of curvature sensing is another fundamental challenge. Curved lipid membranes and their interplay with membrane-associated proteins can be investigated with molecular dynamics (MD) simulations. Various methods for simulating curved membranes with MD are discussed here, including tools for setting up simulation of vesicles and methods for sustaining membrane curvature. The latter are divided into methods that exploit scaffolding virtual beads, methods that use curvature-inducing molecules, and methods applying virtual forces. The variety of simulation tools allow researcher to closely match the conditions of experimental studies of membrane curvatures.

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.

Cholesterol Hinders the Passive Uptake of Amphiphilic Nanoparticles into Fluid Lipid Membranes

Plasma membranes represent pharmacokinetic barriers for the passive transport of site-specific drugs within cells. When engineered nanoparticles (NPs) are considered as transmembrane drug carriers, the plasma membrane composition can affect passive NP internalization in many ways. Among these, cholesterol-regulated membrane fluidity is probably one of the most biologically relevant. Herein, we consider small (2-5 nm in core diameter) amphiphilic gold NPs capable of spontaneously and nondisruptively entering the lipid bilayer of plasma membranes. We study their incorporation into model 1,2-dioleoyl-sn-glycero-3-phosphocholine membranes with increasing cholesterol content. We combine dissipative quartz crystal microbalance experiments, atomic force microscopy, and molecular dynamics simulations to show that membrane cholesterol, at biologically relevant concentrations, hinders the molecular mechanism for passive NP penetration within fluid bilayers, resulting in a dramatic reduction in the amount of NP incorporated.

The Role of the Membrane in Transporter Folding and Activity

The synthesis, folding, and function of membrane transport proteins are critical factors for defining cellular physiology. Since the stability of these proteins evolved amidst the lipid bilayer, it is no surprise that we are finding that many of these membrane proteins demonstrate coupling of their structure or activity in some way to the membrane. More and more transporter structures are being determined with some information about the surrounding membrane, and computational modeling is providing further molecular details about these solvation structures. Thus, the field is moving towards identifying which molecular mechanisms - lipid interactions, membrane perturbations, differential solvation, and bulk membrane effects - are involved in linking membrane energetics to transporter stability and function. In this review, we present an overview of these mechanisms and the growing evidence that the lipid bilayer is a major determinant of the fold, form, and function of membrane transport proteins in membranes.

Simulating realistic membrane shapes

Biological membranes exhibit diversity in their shapes and complexity in chemical compositions that are linked to many cellular functions. These two central features of biomembranes have been the subject of numerous simulation studies, using a diverse range of computational techniques. Currently, the field is able to capture this complexity at increasing levels of realism and connect the microscopic view on protein-lipid interactions to cellular morphologies at the level of entire organelles. Here we highlight recent advances in this topic, identify current bottlenecks, and sketch possible ways ahead.

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.

How cholesterol stiffens unsaturated lipid membranes

Cholesterol is an integral component of eukaryotic cell membranes and a key molecule in controlling membrane fluidity, organization, and other physicochemical parameters. It also plays a regulatory function in antibiotic drug resistance and the immune response of cells against viruses, by stabilizing the membrane against structural damage. While it is well understood that, structurally, cholesterol exhibits a densification effect on fluid lipid membranes, its effects on membrane bending rigidity are assumed to be nonuniversal; i.e., cholesterol stiffens saturated lipid membranes, but has no stiffening effect on membranes populated by unsaturated lipids, such as 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). This observation presents a clear challenge to structure-property relationships and to our understanding of cholesterol-mediated biological functions. Here, using a comprehensive approach-combining neutron spin-echo (NSE) spectroscopy, solid-state deuterium NMR (²H NMR) spectroscopy, and molecular dynamics (MD) simulations-we report that cholesterol locally increases the bending rigidity of DOPC membranes, similar to saturated membranes, by increasing the bilayer's packing density. All three techniques, inherently sensitive to mesoscale bending fluctuations, show up to a threefold increase in effective bending rigidity with increasing cholesterol content approaching a mole fraction of 50%. Our observations are in good agreement with the known effects of cholesterol on the area-compressibility modulus and membrane structure, reaffirming membrane structure-property relationships. The current findings point to a scale-dependent manifestation of membrane properties, highlighting the need to reassess cholesterol's role in controlling membrane bending rigidity over mesoscopic length and time scales of important biological functions, such as viral budding and lipid-protein interactions.

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.

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 Glt_Ph, 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.