A Hybrid Approach for Highly Coarse-grained Lipid Bilayer Models

SMARTINI3 parametrization of multi-scale membrane models via unsupervised learning methods

In this study, we utilize genetic algorithms to develop a realistic implicit solvent ultra-coarse-grained (ultra-CG) membrane model comprising only three interaction sites. The key philosophy of the ultra-CG membrane model SMARTINI3 is its compatibility with realistic membrane proteins, for example, modeled within the Martini coarse-grained (CG) model, as well as with the widely used GROMACS software for molecular simulations. Our objective is to parameterize this ultra-CG model to accurately reproduce the experimentally observed structural and thermodynamic properties of Phosphatidylcholine (PC) membranes in real units, including properties such as area per lipid, area compressibility, bending modulus, line tension, phase transition temperature, density profile, and radial distribution function. In our example, we specifically focus on the properties of a POPC membrane, although the developed membrane model could be perceived as a generic model of lipid membranes. To optimize the performance of the model (the fitness), we conduct a series of evolutionary runs with diverse random initial population sizes (ranging from 96 to 384). We demonstrate that the ultra-CG membrane model we developed exhibits authentic lipid membrane behaviors, including self-assembly into bilayers, vesicle formation, membrane fusion, and gel phase formation. Moreover, we demonstrate compatibility with the Martini coarse-grained model by successfully reproducing the behavior of a transmembrane domain embedded within a lipid bilayer. This facilitates the simulation of realistic membrane proteins within an ultra-CG bilayer membrane, enhancing the accuracy and applicability of our model in biophysical studies.

Computational modeling of membrane trafficking processes: From large molecular assemblies to chemical specificity

In the last decade, molecular dynamics (MD) simulations have become an essential tool to investigate the molecular properties of membrane trafficking processes, often in conjunction with experimental approaches. The combination of MD simulations with recent developments in structural biology, such as cryo-electron microscopy and artificial intelligence-based structure determination, opens new, exciting possibilities for future investigations. However, the full potential of MD simulations to provide a molecular view of the complex and dynamic processes involving membrane trafficking can only be realized if certain limitations are addressed, and especially those concerning the quality of coarse-grain models, which, despite recent successes in describing large-scale systems, still suffer from far-from-ideal chemical accuracy. In this review, we will highlight recent success stories of MD simulations in the investigation of membrane trafficking processes, their implications for future research, and the challenges that lie ahead in this specific research domain.

Utilizing Machine Learning to Greatly Expand the Range and Accuracy of Bottom-Up Coarse-Grained Models through Virtual Particles

Coarse-grained (CG) models parametrized using atomistic reference data, i.e., "bottom up" CG models, have proven useful in the study of biomolecules and other soft matter. However, the construction of highly accurate, low resolution CG models of biomolecules remains challenging. We demonstrate in this work how virtual particles, CG sites with no atomistic correspondence, can be incorporated into CG models within the context of relative entropy minimization (REM) as latent variables. The methodology presented, variational derivative relative entropy minimization (VD-REM), enables optimization of virtual particle interactions through a gradient descent algorithm aided by machine learning. We apply this methodology to the challenging case of a solvent-free CG model of a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer and demonstrate that introduction of virtual particles captures solvent-mediated behavior and higher-order correlations which REM alone cannot capture in a more standard CG model based only on the mapping of collections of atoms to the CG sites.

Machine Learning-Driven Multiscale Modeling: Bridging the Scales with a Next-Generation Simulation Infrastructure

Interdependence across time and length scales is common in biology, where atomic interactions can impact larger-scale phenomenon. Such dependence is especially true for a well-known cancer signaling pathway, where the membrane-bound RAS protein binds an effector protein called RAF. To capture the driving forces that bring RAS and RAF (represented as two domains, RBD and CRD) together on the plasma membrane, simulations with the ability to calculate atomic detail while having long time and large length- scales are needed. The Multiscale Machine-Learned Modeling Infrastructure (MuMMI) is able to resolve RAS/RAF protein-membrane interactions that identify specific lipid-protein fingerprints that enhance protein orientations viable for effector binding. MuMMI is a fully automated, ensemble-based multiscale approach connecting three resolution scales: (1) the coarsest scale is a continuum model able to simulate milliseconds of time for a 1 μm2 membrane, (2) the middle scale is a coarse-grained (CG) Martini bead model to explore protein-lipid interactions, and (3) the finest scale is an all-atom (AA) model capturing specific interactions between lipids and proteins. MuMMI dynamically couples adjacent scales in a pairwise manner using machine learning (ML). The dynamic coupling allows for better sampling of the refined scale from the adjacent coarse scale (forward) and on-the-fly feedback to improve the fidelity of the coarser scale from the adjacent refined scale (backward). MuMMI operates efficiently at any scale, from a few compute nodes to the largest supercomputers in the world, and is generalizable to simulate different systems. As computing resources continue to increase and multiscale methods continue to advance, fully automated multiscale simulations (like MuMMI) will be commonly used to address complex science questions.

A Core-Shell Approach for Systematically Coarsening Nanoparticle-Membrane Interactions: Application to Silver Nanoparticles

The continuous release of engineered nanomaterial (ENM) into the environment may bring about health concerns following human exposure. One important source of ENMs are silver nanoparticles (NPs) that are extensively used as anti-bacterial additives. The introduction of ENMs into the human body can occur via ingestion, skin uptake or the respiratory system. Therefore, evaluating how NPs translocate over bio-membranes is essential in assessing their primary toxicity. Unfortunately, data regarding membrane-NP interaction is still scarce, as is theoretical and in silico insight into what governs adhesion and translocation for the most relevant NPs and membranes. Coarse-grained (CG) molecular descriptions have the potential to alleviate this situation, but are hampered by the absence of a direct link to NP materials and membrane adhesion mechanisms. Here, we interrogate the relationship between the most common NP representation at the CG level and the adhesion characteristics of a model lung membrane. We find that this representation for silver NPs is non-transferable, meaning that a proper CG representation for one size is not suited for other sizes. We also identify two basic types of primary adhesion-(partial) NPs wrapping by the membrane and NP insertion into the membrane-that closely relate to the overall NP hydrophobicity and significantly differ in terms of lipid coatings. The proven non-transferability of the standard CG representation with size forms an inspiration for introducing a core-shell model even for bare NPs that are uniform in composition. Using existing all-atom molecular dynamics (MD) data as a reference, we show that this extension does allow us to reproduce size-dependent NP adhesion properties and lipid responses to NP binding at the CG level. The subsequent CGMD evaluation for 10 nm Ag NPs provides new insight into membrane binding for relevant NP sizes and into the role of water in trapping NPs into defected mixed monolayer-bilayer states. This development will be instrumental for simulating NP-membrane adhesion towards more experimentally relevant length and time scales for particular NP materials.

A Data-Driven Dimensionality Reduction Approach to Compare and Classify Lipid Force Fields

Molecular dynamics simulations of all-atom and coarse-grained lipid bilayer models are increasingly used to obtain useful insights for understanding the structural dynamics of these assemblies. In this context, one crucial point concerns the comparison of the performance and accuracy of classical force fields (FFs), which sometimes remains elusive. To date, the assessments performed on different classical potentials are mostly based on the comparison with experimental observables, which typically regard average properties. However, local differences of the structure and dynamics, which are poorly captured by average measurements, can make a difference, but these are nontrivial to catch. Here, we propose an agnostic way to compare different FFs at different resolutions (atomistic, united-atom, and coarse-grained), by means of a high-dimensional similarity metrics built on the framework of Smooth Overlap of Atomic Position (SOAP). We compare and classify a set of 13 FFs, modeling 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers. Our SOAP kernel-based metrics allows us to compare, discriminate, and correlate different FFs at different model resolutions in an unbiased, high-dimensional way. This also captures differences between FFs in modeling nonaverage events (originating from local transitions), for example, the liquid-to-gel phase transition in dipalmitoylphosphatidylcholine (DPPC) bilayers, for which our metrics allows us to identify nucleation centers for the phase transition, highlighting some intrinsic resolution limitations in implicit versus explicit solvent FFs.

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.

Swarm-CG: Automatic Parametrization of Bonded Terms in MARTINI-Based Coarse-Grained Models of Simple to Complex Molecules via Fuzzy Self-Tuning Particle Swarm Optimization

We present Swarm-CG, a versatile software for the automatic iterative parametrization of bonded parameters in coarse-grained (CG) models, ideal in combination with popular CG force fields such as MARTINI. By coupling fuzzy self-tuning particle swarm optimization to Boltzmann inversion, Swarm-CG performs accurate bottom-up parametrization of bonded terms in CG models composed of up to 200 pseudo atoms within 4-24 h on standard desktop machines, using default settings. The software benefits from a user-friendly interface and two different usage modes (default and advanced). We particularly expect Swarm-CG to support and facilitate the development of new CG models for the study of complex molecular systems interesting for bio- and nanotechnology. Excellent performances are demonstrated using a benchmark of 9 molecules of diverse nature, structural complexity, and size. Swarm-CG is available with all its dependencies via the Python Package Index (PIP package: swarm-cg). Demonstration data are available at: www.github.com/GMPavanLab/SwarmCG.

Coarse-grained implicit solvent lipid force field with a compatible resolution to the Cα protein representation

Biological membranes have been prominent targets for coarse-grained (CG) molecular dynamics simulations. While minimal CG lipid models with three beads per lipid and quantitative CG lipid models with >10 beads per lipid have been well studied, in between them, CG lipid models with a compatible resolution to residue-level CG protein models are much less developed. Here, we extended a previously developed three-bead lipid model into a five-bead model and parameterized it for two phospholipids, POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine). The developed model, iSoLF, reproduced the area per lipid, hydrophobic thickness, and phase behaviors of the target phospholipid bilayer membranes at the physiological temperature. The model POPC and DPPC membranes were in liquid and gel phases, respectively, in accordance with experiments. We further examined the spontaneous formation of a membrane bilayer, the temperature dependence of physical properties, the vesicle dynamics, and the POPC/DPPC two-component membrane dynamics of the CG lipid model, showing some promise. Once combined with standard Cα protein models, the iSoLF model will be a powerful tool to simulate large biological membrane systems made of lipids and proteins.

Quantification of spatio-temporal scales of dynamical heterogeneity of water near lipid membranes above supercooling

A hydrated 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) lipid membrane is investigated using an all atom molecular dynamics simulation at 308 K to determine the physical sources of universal slow relaxations of hydration layers and length-scale of the spatially heterogeneous dynamics. Continuously residing interface water (IW) molecules hydrogen bonded to different moieties of lipid heads in the membrane are identified. The non-Gaussian parameters of all classes of IW molecules show a cross-over from cage vibration to translational diffusion. A significant non-Gaussianity is observed for the IW molecules exhibiting large length correlations in translational van Hove functions. Two time-scales for the ballistic motions and hopping transitions are obtained from the self intermediate scattering functions of the IW molecules with an additional long relaxation, which disappears for bulk water. The long relaxation time-scales for the IW molecules obtained from the self intermediate scattering functions are in good accordance with the hydrogen bond relaxation time-scales irrespective of the nature of the chemical confinement and the confinement lifetime. Employing a block analysis approach, the length-scale of dynamical heterogeneities is captured from a transition from non-Gaussianity to Gaussianity in van Hove correlation functions of the IW molecules. The heterogeneity length-scale is comparable to the wave-length of the small and weak undulations of the membrane calculated by Fourier transforms of lipid tilts. This opens up a new avenue towards a possible correlation between heterogeneity length-scale and membrane curvature more significant for rippled membranes. Thus, our analyses provide a measure towards the spatio-temporal scale of dynamical heterogeneity of confined water near membranes.

Curvature induction and sensing of the F-BAR protein Pacsin1 on lipid membranes via molecular dynamics simulations

F-Bin/Amphiphysin/Rvs (F-BAR) domain proteins play essential roles in biological processes that involve membrane remodelling, such as endocytosis and exocytosis. It has been shown that such proteins transform the lipid membrane into tubes. Notably, Pacsin1 from the Pacsin/Syndapin subfamily has the ability to transform the membrane into various morphologies: striated tubes, featureless wide and thin tubes, and pearling vesicles. The molecular mechanism of this interesting ability remains elusive. In this study, we performed all-atom (AA) and coarse-grained (CG) molecular dynamics simulations to investigate the curvature induction and sensing mechanisms of Pacsin1 on a membrane. From AA simulations, we show that Pacsin1 has internal structural flexibility. In CG simulations with parameters tuned from the AA simulations, spontaneous assembly of two Pacsin1 dimers through lateral interaction is observed. Based on the complex structure, we show that the regularly assembled Pacsin1 dimers bend a tensionless membrane. We also show that a single Pacsin1 dimer senses the membrane curvature, binding to a buckled membrane with a preferred curvature. These results provide molecular insights into polymorphic membrane remodelling.

Adversarial-residual-coarse-graining: Applying machine learning theory to systematic molecular coarse-graining

We utilize connections between molecular coarse-graining (CG) approaches and implicit generative models in machine learning 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.

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 form 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 low surface concentration that add insight into how I-BAR domain proteins may contribute to certain aspects of membrane remodeling in cells.

Systematic Coarse-Grained Lipid Force Fields with Semiexplicit Solvation via Virtual Sites

Despite the central role of lipids in many biophysical functions, the molecular mechanisms that dictate macroscopic lipid behavior remain elusive to both experimental and computational approaches. As such, there has been much interest in the development of low-resolution, implicit-solvent coarse-grained (CG) models to dynamically simulate biologically relevant spatiotemporal scales with molecular fidelity. However, in the absence of solvent, a key challenge for CG models is to faithfully emulate solvent-mediated forces, which include both hydrophilic and hydrophobic interactions that drive lipid aggregation and self-assembly. In this work, we provide a new methodological framework to incorporate semiexplicit solvent effects through the use of virtual CG particles, which represent structural features of the solvent-lipid interface. To do so, we leverage two systematic coarse-graining approaches, multiscale coarse-graining (MS-CG) and relative entropy minimization (REM), in a hybrid fashion to construct our virtual-site CG (VCG) models. As a proof-of-concept, we focus our efforts on two lipid species, 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoyl- sn-glycero-3-phosphocholine (DPPC), which adopt a liquid-disordered and gel phase, respectively, at room temperature. Through our analysis, we also present, to our knowledge, the first direct comparison between the MS-CG and REM methods for a complex biomolecule and highlight each of their strengths and weaknesses. We further demonstrate that VCG models recapitulate the rich biophysics of lipids, which enable self-assembly, morphological diversity, and multiple phases. Our findings suggest that the VCG framework is a powerful approach for investigation into macromolecular biophysics.

Simulation Best Practices for Lipid Membranes [Article v1.0]

We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.

Flexible lipid nanomaterials studied by NMR spectroscopy

Advances in solid-state nuclear magnetic resonance spectroscopy inform the emergence of material properties from atomistic-level interactions in membrane lipid nanostructures.

ATP-dependent membrane remodeling links EHD1 functions to endocytic recycling

Endocytic and recycling pathways generate cargo-laden transport carriers by membrane fission. Classical dynamins, which generate transport carriers during endocytosis, constrict and cause fission of membrane tubes in response to GTP hydrolysis. Relatively, less is known about the ATP-binding Eps15-homology domain-containing protein1 (EHD1), a dynamin family member that functions at the endocytic-recycling compartment. Here, we show using cross complementation assays in C. elegans that EHD1's membrane binding and ATP hydrolysis activities are necessary for endocytic recycling. Further, we show that ATP-bound EHD1 forms membrane-active scaffolds that bulge tubular model membranes. ATP hydrolysis promotes scaffold self-assembly, causing the bulge to extend and thin down intermediate regions on the tube. On tubes below 25 nm in radius, such thinning leads to scission. Molecular dynamics simulations corroborate this scission pathway. Deletion of N-terminal residues causes defects in stable scaffolding, scission and endocytic recycling. Thus, ATP hydrolysis-dependent membrane remodeling links EHD1 functions to endocytic recycling.

Organizing membrane-curving proteins: the emerging dynamical picture

Lipid membranes play key roles in cells, such as in trafficking, division, infection, remodeling of organelles, among others. The key step in all these processes is creating membrane curvature, typically under the control of many anchored, adhered or included proteins. However, it has become clear that the membrane itself can mediate the interactions among proteins to produce highly ordered assemblies. Computer simulations are ideally suited to investigate protein organization and the dynamics of membrane remodeling at near-micron scales, something that is extremely challenging to tackle experimentally. We review recent computational efforts in modeling protein-caused membrane deformation mechanisms, specifically focusing on coarse-grained simulations. We highlight work that exposed the membrane-mediated ordering of proteins into lines, meshwork, spirals and other assemblies, in what seems to be a very generic mechanism driven by a combination of short and long-ranged forces. Modulating the mechanical properties of membranes is an underexplored signaling mechanism in various processes deserving of more attention in the near future.

Solvent Hydrodynamics Enhances the Collective Diffusion of Membrane Lipids

The collective motion of membrane lipids over hundreds of nanometers and nanoseconds plays an essential role in the formation of submicron complexes of lipids and proteins in the cell membrane. These dynamics are difficult to access experimentally and are currently poorly understood. One of the conclusions of the celebrated Saffman-Debrück (SD) theory is that lipid disturbances smaller than the Saffman length (microns) are not affected by the hydrodynamics of the embedding solvent. Using molecular dynamics and coarse-grained models with implicit hydrodynamics we show that this is not true. Hydrodynamic interactions between the membrane and the solvent strongly enhance the short-time collective diffusion of lipids at all scales. The momentum transferred between the membrane and the solvent in the normal direction (not considered by the SD theory) propagates tangentially over the membrane inducing long-ranged repulsive forces amongst lipids. As a consequence, the lipid collective diffusion coefficient increases proportionally to the disturbance wavelength. We find quantitative agreement with the predicted anomalous diffusion in quasi-two-dimensional dynamics, observed in colloids confined to a plane but embedded in a three-dimensional solvent.

Biophysics of membrane curvature remodeling at molecular and mesoscopic lengthscales

At the micron scale, where cell organelles display an amazing complexity in their shape and organization, the physical properties of a biological membrane can be better-understood using continuum models subject to thermal (stochastic) undulations. Yet, the chief orchestrators of these complex and intriguing shapes are a specialized class of membrane associating often peripheral proteins called curvature remodeling proteins (CRPs) that operate at the molecular level through specific protein-lipid interactions. We review multiscale methodologies to model these systems at the molecular as well as at the mesoscopic and cellular scales, and also present a free energy perspective of membrane remodeling through the organization and assembly of CRPs. We discuss the morphological space of nearly planar to highly curved membranes, methods to include thermal fluctuations, and review studies that model such proteins as curvature fields to describe the emergent curved morphologies. We also discuss several mesoscale models applied to a variety of cellular processes, where the phenomenological parameters (such as curvature field strength) are often mapped to models of real systems based on molecular simulations. Much insight can be gained from the calculation of free energies of membranes states with protein fields, which enable accurate mapping of the state and parameter values at which the membrane undergoes morphological transformations such as vesiculation or tubulation. By tuning the strength, anisotropy, and spatial organization of the curvature-field, one can generate a rich array of membrane morphologies that are highly relevant to shapes of several cellular organelles. We review applications of these models to budding of vesicles commonly seen in cellular signaling and trafficking processes such as clathrin mediated endocytosis, sorting by the ESCRT protein complexes, and cellular exocytosis regulated by the exocyst complex. We discuss future prospects where such models can be combined with other models for cytoskeletal assembly, and discuss their role in understanding the effects of cell membrane tension and the mechanics of the extracellular microenvironment on cellular processes.

Entropic elasticity based coarse-grained model of lipid membranes

Various models for lipid bilayer membranes have been presented to investigate their morphologies. Among them, the aggressive coarse-grained models, where the membrane is represented by a single layer of particles, are computationally efficient and of practical importance for simulating membrane dynamics at the microscopic scale. In these models, soft potentials between particle pairs are used to maintain the fluidity of membranes, but the underlying mechanism of the softening requires further clarification. We have analyzed the membrane area decrease due to thermal fluctuations, and the results demonstrate that the intraparticle part of entropic elasticity is responsible for the softening of the potential. Based on the stretching response of the membrane, a bottom-up model is developed with an entropic effect explicitly involved. The model reproduces several essential properties of the lipid membrane, including the fluid state and a plateau in the stretching curve. In addition, the area compressibility modulus, bending rigidity, and spontaneous curvature display linear dependence on model parameters. As a demonstration, we have investigated the closure and morphology evolution of membrane systems driven by spontaneous curvature, and vesicle shapes observed experimentally are faithfully reproduced.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

Long-Range Organization of Membrane-Curving Proteins

Biological membranes have a central role in mediating the organization of membrane-curving proteins, a dynamic process that has proven to be challenging to probe experimentally. Using atomic force microscopy, we capture the hierarchically organized assemblies of Bin/amphiphysin/Rvs (BAR) proteins on supported lipid membranes. Their structure reveals distinct long linear aggregates of proteins, regularly spaced by up to 300 nm. Employing accurate free-energy calculations from large-scale coarse-grained computer simulations, we found that the membrane mediates the interaction among protein filaments as a combination of short- and long-ranged interactions. The long-ranged component acts at strikingly long distances, giving rise to a variety of micron-sized ordered patterns. This mechanism may contribute to the long-ranged spatiotemporal control of membrane remodeling by proteins in the cell.

Self-Assembly of Lecithin and Bile Salt in the Presence of Inorganic Salt in Water: Mesoscale Computer Simulation

The influence of inorganic salt on the structure of lecithin/bile salt mixtures in aqueous solution is studied by means of dissipative particle dynamics simulations. We propose a coarse-grained model of phosphatidylcholine and two types of bile salts (sodium cholate and sodium deoxycholate) and also take into account the presence of low molecular weight salt. This model allows us to study the system on rather large time and length scales (up to about ∼20 μs and 50 nm) and to reveal mechanisms of experimentally observed increasing viscosity upon increasing the low molecular weight salt concentration in this system. We show that increasing the low molecular weight salt concentration induces the growth of cylinder-like micelles formed in lecithin/bile salt mixtures in water. These wormlike micelles can entangle into transient networks displaying perceptible viscoelastic properties. Computer simulation results are in good qualitative agreement with experimental observations.

The mesoscopic membrane with proteins (MesM-P) model

We present the Mesoscopic Membrane with Proteins (MesM-P) model, an extension of a previously developed elastic membrane model for mesoscale simulations of lipid membranes. MesM-P employs a discrete mesoscopic quasi-particle approach to model protein-facilitated shape and topology changes of the lipid membrane on length and time scales inaccessible to all-atom and quasimolecular coarse-grained molecular dynamics simulations. We investigate the ability of MesM-P to model the behavior of large lipid vesicles as a function of bound protein density. We find four distinct mechanisms for protein aggregation on the surface of the membrane, depending on membrane stiffness and protein spontaneous curvature. We also establish a connection between MesM-P and the results of higher resolution coarse-grained molecular dynamics simulations.

Suppressing membrane height fluctuations leads to a membrane-mediated interaction among proteins

Membrane-induced interactions can play a significant role in the spatial distribution of membrane-bound proteins. We develop a model that combines a continuum description of lipid bilayers with a discrete particle model of proteins to probe the emerging structure of the combined membrane-protein system. Our model takes into account the membrane's elastic behavior, the steric repulsion between proteins, and the quenching of membrane shape fluctuations due to the presence of the proteins. We employ coupled Langevin equations to describe the dynamics of the system. We show that coupling to the membrane induces an attractive interaction among proteins, which may contribute to the clustering of proteins in biological membranes. We investigate the lateral protein diffusion and find that it is reduced due to transient fluctuations in membrane shape.

How curvature-generating proteins build scaffolds on membrane nanotubes

Bin/Amphiphysin/Rvs (BAR) domain proteins control the curvature of lipid membranes in endocytosis, trafficking, cell motility, the formation of complex subcellular structures, and many other cellular phenomena. They form 3D assemblies that act as molecular scaffolds to reshape the membrane and alter its mechanical properties. It is unknown, however, how a protein scaffold forms and how BAR domains interact in these assemblies at protein densities relevant for a cell. In this work, we use various experimental, theoretical, and simulation approaches to explore how BAR proteins organize to form a scaffold on a membrane nanotube. By combining quantitative microscopy with analytical modeling, we demonstrate that a highly curving BAR protein endophilin nucleates its scaffolds at the ends of a membrane tube, contrary to a weaker curving protein centaurin, which binds evenly along the tube's length. Our work implies that the nature of local protein-membrane interactions can affect the specific localization of proteins on membrane-remodeling sites. Furthermore, we show that amphipathic helices are dispensable in forming protein scaffolds. Finally, we explore a possible molecular structure of a BAR-domain scaffold using coarse-grained molecular dynamics simulations. Together with fluorescence microscopy, the simulations show that proteins need only to cover 30-40% of a tube's surface to form a rigid assembly. Our work provides mechanical and structural insights into the way BAR proteins may sculpt the membrane as a high-order cooperative assembly in important biological processes.

Multiscale simulations of protein-facilitated membrane remodeling

Protein-facilitated shape and topology changes of cell membranes are crucial for many biological processes, such as cell division, protein trafficking, and cell signaling. However, the inherently multiscale nature of membrane remodeling presents a considerable challenge for understanding the mechanisms and physics that drive this process. To address this problem, a multiscale approach that makes use of a diverse set of computational and experimental techniques is required. The atomistic simulations provide high-resolution information on protein-membrane interactions. Experimental techniques, like electron microscopy, on the other hand, resolve high-order organization of proteins on the membrane. Coarse-grained (CG) and mesoscale computational techniques provide the intermediate link between the two scales and can give new insights into the underlying mechanisms. In this Review, we present the recent advances in multiscale computational approaches established in our group. We discuss various CG and mesoscale approaches in studying the protein-mediated large-scale membrane remodeling.

The multiscale coarse-graining method. XI. Accurate interactions based on the centers of charge of coarse-grained sites

It is essential to be able to systematically construct coarse-grained (CG) models that can efficiently and accurately reproduce key properties of higher-resolution models such as all-atom. To fulfill this goal, a mapping operator is needed to transform the higher-resolution configuration to a CG configuration. Certain mapping operators, however, may lose information related to the underlying electrostatic properties. In this paper, a new mapping operator based on the centers of charge of CG sites is proposed to address this issue. Four example systems are chosen to demonstrate this concept. Within the multiscale coarse-graining framework, CG models that use this mapping operator are found to better reproduce the structural correlations of atomistic models. The present work also demonstrates the flexibility of the mapping operator and the robustness of the force matching method. For instance, important functional groups can be isolated and emphasized in the CG model.

Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence

Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that the method provides realistic dynamical CG models that have non-Markovian or close to Markovian behavior that is consistent with the actual dynamical behavior of the all-atom system used to construct the CG model. Both the construction and the simulation of such a dynamic CG model have computational requirements that are similar to those of the corresponding MS-CG model and are good candidates for CG modeling of very large systems.

Biomembranes in atomistic and coarse-grained simulations

The architecture of biological membranes is tightly coupled to the localization, organization, and function of membrane proteins. The organelle-specific distribution of lipids allows for the formation of functional microdomains (also called rafts) that facilitate the segregation and aggregation of membrane proteins and thus shape their function. Molecular dynamics simulations enable to directly access the formation, structure, and dynamics of membrane microdomains at the molecular scale and the specific interactions among lipids and proteins on timescales from picoseconds to microseconds. This review focuses on the latest developments of biomembrane force fields for both atomistic and coarse-grained molecular dynamics (MD) simulations, and the different levels of coarsening of biomolecular structures. It also briefly introduces scale-bridging methods applicable to biomembrane studies, and highlights selected recent applications.

Membrane tension controls the assembly of curvature-generating proteins

Proteins containing a Bin/Amphiphysin/Rvs (BAR) domain regulate membrane curvature in the cell. Recent simulations have revealed that BAR proteins assemble into linear aggregates, strongly affecting membrane curvature and its in-plane stress profile. Here, we explore the opposite question: do mechanical properties of the membrane impact protein association? By using coarse-grained molecular dynamics simulations, we show that increased surface tension significantly impacts the dynamics of protein assembly. While tensionless membranes promote a rapid formation of long-living linear aggregates of N-BAR proteins, increase in tension alters the geometry of protein association. At high tension, protein interactions are strongly inhibited. Increasing surface density of proteins leads to a wider range of protein association geometries, promoting the formation of meshes, which can be broken apart with membrane tension. Our work indicates that surface tension may play a key role in recruiting proteins to membrane-remodelling sites in the cell.

BAR domain proteins are known to reshape cell membranes. Using coarse-grained molecular dynamics simulations, Simunovic and Voth demonstrate that membrane tension strongly affects the association of BAR proteins, in turn controlling their recruitment to membrane-remodelling sites.

Seeing the Forest in Lieu of the Trees: Continuum Simulations of Cell Membranes at Large Length Scales

Biological membranes exhibit long-range spatial structure in both chemical composition and geometric shape, which gives rise to remarkable physical phenomena and important biological functions. Continuum models that describe these effects play an important role in our understanding of membrane biophysics at large length scales. We review the mathematical framework used to describe both composition and shape degrees of freedom, and present best practices to implement such models in a computer simulation. We discuss in detail two applications of continuum models of cell membranes: the formation of microemulsion and modulated phases, and the effect of membrane-mediated interactions on the assembly of membrane proteins.

Solvent-Free, Highly Coarse-Grained Models for Charged Lipid Systems

We present a methodology to develop coarse-grained lipid models such that electrostatic interactions between the coarse-grained sites can be derived accurately from an all-atom molecular dynamics trajectory and expressed as an effective pairwise electrostatic potential with appropriate screening functions. The reference nonbonded forces from the all-atom trajectory are decomposed into separate electrostatic and van der Waals (vdW) forces, based on the multiscale coarse-graining method. The coarse-grained electrostatic potential is assumed to be a general function of unknown variables and the final site–site interactions are obtained variationally, where the residual of the electrostatic forces from the assumed field is minimized. The resulting electrostatic interactions are fitted to screened electrostatics functions, with a special treatment for distance-dependent dielectrics and screened dipole–dipole interactions. The vdW interactions are derived separately. The resulting charged hybrid coarse-graining method is applied to various solvent-free three-site models of anionic lipid systems.

LipidWrapper: an algorithm for generating large-scale membrane models of arbitrary geometry

As ever larger and more complex biological systems are modeled in silico, approximating physiological lipid bilayers with simple planar models becomes increasingly unrealistic. In order to build accurate large-scale models of subcellular environments, models of lipid membranes with carefully considered, biologically relevant curvature will be essential. In the current work, we present a multi-scale utility called LipidWrapper capable of creating curved membrane models with geometries derived from various sources, both experimental and theoretical. To demonstrate its utility, we use LipidWrapper to examine an important mechanism of influenza virulence. A copy of the program can be downloaded free of charge under the terms of the open-source FreeBSD License from http://nbcr.ucsd.edu/lipidwrapper. LipidWrapper has been tested on all major computer operating systems.

α-Synuclein-induced membrane remodeling is driven by binding affinity, partition depth, and interleaflet order asymmetry

We have investigated the membrane remodeling capacity of the N-terminal membrane-binding domain of α-synuclein (α-Syn₁₀₀). Using fluorescence correlation spectroscopy and vesicle clearance assays, we show that α-Syn₁₀₀ fully tubulates POPG vesicles, the first demonstration that the amphipathic helix on its own is capable of this effect. We also show that at equal density of membrane-bound protein, α-Syn has dramatically reduced affinity for, and does not tubulate, vesicles composed of a 1:1 POPG:POPC mixture. Coarse-grained molecular dynamics simulations suggested that the difference between the pure POPG and mixture results may be attributed to differences in the protein’s partition depth, the membrane’s hydrophobic thickness, and disruption of acyl chain order. To explore the importance of these attributes compared with the role of the reduced binding energy, we created an α-Syn₁₀₀ variant in which we removed the hydrophobic core of the non-amyloid component (NAC) domain and tested its impact on pure POPG vesicles. We observed a substantial reduction in binding affinity and tubulation, and simulations of the NAC-null protein suggested that the reduced binding energy increases the protein mobility on the bilayer surface, likely impacting the protein’s ability to assemble into organized pretubule structures. We also used simulations to explore a potential role for interleaflet coupling as an additional driving force for tubulation. We conclude that symmetry across the leaflets in the tubulated state maximizes the interaction energy of the two leaflets and relieves the strain induced by the hydrophobic void beneath the amphipathic helix.

The power of coarse graining in biomolecular simulations

Computational modeling of biological systems is challenging because of the multitude of spatial and temporal scales involved. Replacing atomistic detail with lower resolution, coarse grained (CG), beads has opened the way to simulate large-scale biomolecular processes on time scales inaccessible to all-atom models. We provide an overview of some of the more popular CG models used in biomolecular applications to date, focusing on models that retain chemical specificity. A few state-of-the-art examples of protein folding, membrane protein gating and self-assembly, DNA hybridization, and modeling of carbohydrate fibers are used to illustrate the power and diversity of current CG modeling.

Protein-mediated transformation of lipid vesicles into tubular networks

Key cellular processes are frequently accompanied by protein-facilitated shape changes in the plasma membrane. N-BAR-domain protein modules generate curvature by means of complex interactions with the membrane surface. The way they assemble and the mechanism by which they operate are largely dependent on their binding density. Although the mechanism at lower densities has recently begun to emerge, how membrane scaffolds form at high densities remains unclear. By combining electron microscopy and multiscale simulations, we show that N-BAR proteins at high densities can transform a lipid vesicle into a 3D tubular network. We show that this process is a consequence of excess adhesive energy combined with the local stiffening of the membrane, which occurs in a narrow range of mechanical properties of both the membrane and the protein. We show that lipid diffusion is significantly reduced by protein binding at this density regime and even more in areas of high Gaussian curvature, indicating a potential effect on molecular transport in cells. Finally, we reveal that the breaking of the bilayer topology is accompanied by the nematic arrangement of the protein on the surface, a structural motif that likely drives the formation of reticular structures in living cells.

Linear aggregation of proteins on the membrane as a prelude to membrane remodeling

Adhesion and insertion of curvature-mediating proteins can induce dramatic structural changes in cell membranes, allowing them to participate in several key cellular tasks. The way proteins interact to generate curvature remains largely unclear, especially at early stages of membrane remodeling. Using a coarse-grained model of Bin/amphiphysin/Rvs domain with an N-terminal helix (N-BAR) interacting with flat membranes and vesicles, we demonstrate that at low protein surface densities, binding of N-BAR domain proteins to the membrane is followed by a linear aggregation and the formation of meshes on the surface. In this process, the proteins assemble at the base of emerging membrane buds. Our work shows that beyond a more straightforward scaffolding mechanism at high bound densities, the interplay of anisotropic interactions and the local stress imposed by the N-BAR proteins results in deep invaginations and endocytic vesicular bud-like deformations, an order of magnitude larger than the size of the individual protein. Our results imply that by virtue of this mechanism, cell membranes may achieve rapid local increases in protein concentration.

Simulation study of the structure and phase behavior of ceramide bilayers and the role of lipid head group chemistry

Ceramides are known to be a key component of the stratum corneum, the outermost protective layer of the skin that controls barrier function. In this work, molecular dynamics simulations are used to examine the behavior of ceramide bilayers, focusing on non-hydroxy sphingosine (NS) and non-hydroxy phytosphingosine (NP) ceramides. Here, we propose a modified version of the CHARMM force field for ceramide simulation, which is directly compared to the more commonly used GROMOS-based force field of Berger (Biophys. J. 1997, 72); while both force fields are shown to closely match experiment from a structural standpoint at the physiological temperature of skin, the modified CHARMM force field is better able to capture the thermotropic phase transitions observed in experiment. The role of ceramide chemistry and its impact on structural ordering is examined by comparing ceramide NS to NP, using the validated CHARMM-based force field. These simulations demonstrate that changing from ceramide NS to NP results in changes to the orientation of the OH groups in the lipid headgroups. The arrangement of OH groups perpendicular to the bilayer normal for ceramide NP, verse parallel for NS, results in the formation of a distinct hydrogen bonding network, that is ultimately responsible for shifting the gel-to-liquid phase transition to higher temperature, in direct agreement with experiment.