Reconstructing protein remodeled membranes in molecular detail from mesoscopic models

There and back again: bridging meso- and nano-scales to understand lipid vesicle patterning

We describe a complete methodology to bridge the scales between nanoscale molecular dynamics and (micrometer) mesoscale Monte Carlo simulations in lipid membranes and vesicles undergoing phase separation, in which curving molecular species are furthermore embedded. To go from the molecular to the mesoscale, we notably appeal to physical renormalization arguments enabling us to rigorously infer the mesoscale interaction parameters from its molecular counterpart. We also explain how to deal with the physical timescales at stake at the mesoscale. Simulating the as-obtained mesoscale system enables us to equilibrate the long wavelengths of the vesicles of interest, up to the vesicle size. Conversely, we then backmap from the meso- to the nano-scale, which enables us to equilibrate in turn the short wavelengths down to the molecular length-scales. By applying our approach to the specific situation of patterning a vesicle membrane, we show that macroscopic membranes can thus be equilibrated at all length-scales in achievable computational time offering an original strategy to address the fundamental challenge of timescale in simulations of large bio-membrane systems.

Modeling membrane reshaping driven by dynamic protein assemblies

Remodeling of membranes in living systems is almost universally coupled to self-assembly of soluble proteins. Proteins assemble into semi-rigid shells that reshape attached membranes, and into filaments that protrude membranes. These assemblies are temporary, building from reversible protein and membrane interactions that must nucleate in the proper location. The interactions are strongly influenced by the nonequilibrium environment of the cell, such as gradients of components or active modifications by kinases. From a modeling perspective, understanding mechanisms and control thus requires 1. time-dependent approaches that ideally incorporate 2. macromolecular structure, 3. out-of-equilibrium processes, and 4. deformable membranes over microns and seconds. Realistically, tradeoffs must be made with these last three features. However, we see recent developments from the highly coarsened molecule-based scale, the continuum reaction-diffusion scale, and hybrid approaches as stimulating efforts in diverse applications. We discuss here methodological advances and progress towards simulating these processes as they occur physiologically.

Bottom-up Coarse-Graining: Principles and Perspectives

Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

Backmapping triangulated surfaces to coarse-grained membrane models

Many biological processes involve large-scale changes in membrane shape. Computer simulations of these processes are challenging since they occur across a wide range of spatiotemporal scales that cannot be investigated in full by any single current simulation technique. A potential solution is to combine different levels of resolution through a multiscale scheme. Here, we present a multiscale algorithm that backmaps a continuum membrane model represented as a dynamically triangulated surface (DTS) to its corresponding molecular model based on the coarse-grained (CG) Martini force field. Thus, we can use DTS simulations to equilibrate slow large-scale membrane conformational changes and then explore the local properties at CG resolution. We demonstrate the power of our method by backmapping a vesicular bud induced by binding of Shiga toxin and by transforming the membranes of an entire mitochondrion to near-atomic resolution. Our approach opens the way to whole cell simulations at molecular detail.

Computer simulations of large-scale changes in membrane shape are challenging since they occur across a wide range of spatiotemporal scales. Here, authors present a multiscale algorithm that backmaps a continuum membrane model represented as a dynamically triangulated surface to its corresponding molecular model based on the coarse-grained Martini force field.

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.

Systems biology of cellular membranes: a convergence with biophysics

Systems biology and systems medicine have played an important role in the last two decades in shaping our understanding of biological processes. While systems biology is synonymous with network maps and '-omics' approaches, it is not often associated with mechanical processes. Here, we make the case for considering the mechanical and geometrical aspects of biological membranes as a key step in pushing the frontiers of systems biology of cellular membranes forward. We begin by introducing the basic components of cellular membranes, and highlight their dynamical aspects. We then survey the functions of the plasma membrane and the endomembrane system in signaling, and discuss the role and origin of membrane curvature in these diverse cellular processes. We further give an overview of the experimental and modeling approaches to study membrane phenomena. We close with a perspective on the converging futures of systems biology and membrane biophysics, invoking the need to include physical variables such as location and geometry in the study of cellular membranes. WIREs Syst Biol Med 2017, 9:e1386. doi: 10.1002/wsbm.1386 For further resources related to this article, please visit the WIREs website.

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.

Sustainable Nanotechnology: Opportunities and Challenges for Theoretical/Computational Studies

For assistance in the design of the next generation of nanomaterials that are functional and have minimal health and safety concerns, it is imperative to establish causality, rather than correlations, in how properties of nanomaterials determine biological and environmental outcomes. Due to the vast design space available and the complexity of nano/bio interfaces, theoretical and computational studies are expected to play a major role in this context. In this minireview, we highlight opportunities and pressing challenges for theoretical and computational chemistry approaches to explore the relevant physicochemical processes that span broad length and time scales. We focus discussions on a bottom-up framework that relies on the determination of correct intermolecular forces, accurate molecular dynamics, and coarse-graining procedures to systematically bridge the scales, although top-down approaches are also effective at providing insights for many problems such as the effects of nanoparticles on biological membranes.

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.

Phenomenology based multiscale models as tools to understand cell membrane and organelle morphologies

An intriguing question in cell biology is "how do cells regulate their shape?" It is commonly believed that the observed cellular morphologies are a result of the complex interaction among the lipid molecules (constituting the cell membrane), and with a number of other macromolecules, such as proteins. It is also believed that the common biophysical processes essential for the functioning of a cell also play an important role in cellular morphogenesis. At the cellular scale-where typical dimensions are in the order of micrometers-the effects arising from the molecular scale can either be modeled as equilibrium or non-equilibrium processes. In this chapter, we discuss the dynamically triangulated Monte Carlo technique to model and simulate membrane morphologies at the cellular scale, which in turn can be used to investigate several questions related to shape regulation in cells. In particular, we focus on two specific problems within the framework of isotropic and anisotropic elasticity theories: namely, (i) the origin of complex, physiologically relevant, membrane shapes due to the interaction of the membrane with curvature remodeling proteins, and (ii) the genesis of steady state cellular shapes due to the action of non-equilibrium forces that are generated by the fission and fusion of transport vesicles and by the binding and unbinding of proteins from the parent membrane.

Nature's lessons in design: nanomachines to scaffold, remodel and shape membrane compartments

Our understanding of the membrane sculpting capabilities of proteins from experimental model systems could be used to construct functional compartmentalised architectures for the engineering of synthetic cells.

Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

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.

A comparison of coarse-grained and continuum models for membrane bending in lipid bilayer fusion pores

To establish the validity of continuum mechanics models quantitatively for the analysis of membrane remodeling processes, we compare the shape and energies of the membrane fusion pore predicted by coarse-grained (MARTINI) and continuum mechanics models. The results at these distinct levels of resolution give surprisingly consistent descriptions for the shape of the fusion pore, and the deviation between the continuum and coarse-grained models becomes notable only when the radius of curvature approaches the thickness of a monolayer. Although slow relaxation beyond microseconds is observed in different perturbative simulations, the key structural features (e.g., dimension and shape of the fusion pore near the pore center) are consistent among independent simulations. These observations provide solid support for the use of coarse-grained and continuum models in the analysis of membrane remodeling. The combined coarse-grained and continuum analysis confirms the recent prediction of continuum models that the fusion pore is a metastable structure and that its optimal shape is neither toroidal nor catenoidal. Moreover, our results help reveal a new, to our knowledge, bowing feature in which the bilayers close to the pore axis separate more from one another than those at greater distances from the pore axis; bowing helps reduce the curvature and therefore stabilizes the fusion pore structure. The spread of the bilayer deformations over distances of hundreds of nanometers and the substantial reduction in energy of fusion pore formation provided by this spread indicate that membrane fusion can be enhanced by allowing a larger area of membrane to participate and be deformed.

Understanding the role of amphipathic helices in N-BAR domain driven membrane remodeling

Endophilin N-BAR (N-terminal helix and Bin/amphiphysin/Rvs) domain tubulates and vesiculates lipid membranes in vitro via its crescent-shaped dimer and four amphipathic helices that penetrate into membranes as wedges. Like F-BAR domains, endophilin N-BAR also forms a scaffold on membrane tubes. Unlike F-BARs, endophilin N-BARs have N-terminal H0 amphipathic helices that are proposed to interact with other N-BARs in oligomer lattices. Recent cryo-electron microscopy reconstructions shed light on the organization of the N-BAR lattice coats on a nanometer scale. However, because of the resolution of the reconstructions, the precise positioning of the amphipathic helices is still ambiguous. In this work, we applied a coarse-grained model to study various membrane remodeling scenarios induced by endophilin N-BARs. We found that H0 helices of N-BARs prefer to align in an antiparallel manner at two ends of the protein to form a stable lattice. The deletion of H0 helices causes disruption of the lattice. In addition, we analyzed the persistence lengths of the protein-coated tubes and found that the stiffness of endophilin N-BAR-coated tubules qualitatively agrees with previous experimental work studying N-BAR-coated tubules. Large-scale simulations on membrane liposomes revealed a systematic relation between H0 helix density and local membrane curvature fluctuations. The data also suggest that the H0 helix is required for BARs to form organized structures on the liposome, further illustrating its important function.

Membrane sculpting by F-BAR domains studied by molecular dynamics simulations

Interplay between cellular membranes and their peripheral proteins drives many processes in eukaryotic cells. Proteins of the Bin/Amphiphysin/Rvs (BAR) domain family, in particular, play a role in cellular morphogenesis, for example curving planar membranes into tubular membranes. However, it is still unclear how F-BAR domain proteins act on membranes. Electron microscopy revealed that, in vitro, F-BAR proteins form regular lattices on cylindrically deformed membrane surfaces. Using all-atom and coarse-grained (CG) molecular dynamics simulations, we show that such lattices, indeed, induce tubes of observed radii. A 250 ns all-atom simulation reveals that F-BAR domain curves membranes via the so-called scaffolding mechanism. Plasticity of the F-BAR domain permits conformational change in response to membrane interaction, via partial unwinding of the domains 3-helix bundle structure. A CG simulation covering more than 350 µs provides a dynamic picture of membrane tubulation by lattices of F-BAR domains. A series of CG simulations identified the optimal lattice type for membrane sculpting, which matches closely the lattices seen through cryo-electron microscopy.

To generate organelles, eukaryotic cells sculpt their membranes into compartments, often employing proteins as chaperones, for example, F-BAR domains. The latter induce formation of tubular and vesicular membranes. Functional and structural studies suggest that F-BAR domains sculpt membranes through electrostatic interactions, driving the membrane to match the concave surface of the protein's banana-like shape. Cryo-electron microscopy (cryo-EM) studies provide an average static picture of how F-BAR domains form lattices on the surface of membranes to induce tube formation. Complementing the cryo-EM images, molecular dynamics simulations reported here offer a detailed, dynamic picture of membrane tubulation by a lattice of F-BAR domains and identified lattice types optimally attuned to producing high membrane curvature. The simulations reproduced also a process lasting 350 µs in which lattices of F-BAR domains form a complete tube out of an initially flat membrane. The molecular dynamics study offers, thereby, both a large-scale picture of membrane sculpting by F-BAR domain lattices as well as atomic-level dynamic information about the involvement of the individual F-BAR domain and its interactions with partner F-BAR domains and membrane in the sculpting process.

Curvature forces in membrane lipid-protein interactions

Membrane biochemists are becoming increasingly aware of the role of lipid-protein interactions in diverse cellular functions. This review describes how conformational changes in membrane proteins, involving folding, stability, and membrane shape transitions, potentially involve elastic remodeling of the lipid bilayer. Evidence suggests that membrane lipids affect proteins through interactions of a relatively long-range nature, extending beyond a single annulus of next-neighbor boundary lipids. It is assumed the distance scale of the forces is large compared to the molecular range of action. Application of the theory of elasticity to flexible soft surfaces derives from classical physics and explains the polymorphism of both detergents and membrane phospholipids. A flexible surface model (FSM) describes the balance of curvature and hydrophobic forces in lipid-protein interactions. Chemically nonspecific properties of the lipid bilayer modulate the conformational energetics of membrane proteins. The new biomembrane model challenges the standard model (the fluid mosaic model) found in biochemistry texts. The idea of a curvature force field based on data first introduced for rhodopsin gives a bridge between theory and experiment. Influences of bilayer thickness, nonlamellar-forming lipids, detergents, and osmotic stress are all explained by the FSM. An increased awareness of curvature forces suggests that research will accelerate as structural biology becomes more closely entwined with the physical chemistry of lipids in explaining membrane structure and function.

Membrane binding and self-association of the epsin N-terminal homology domain

Epsin possesses a conserved epsin N-terminal homology (ENTH) domain that acts as a phosphatidylinositol 4,5-bisphosphate‐lipid‐targeting and membrane‐curvature‐generating element. Upon binding phosphatidylinositol 4,5‐bisphosphate, the N-terminal helix (H₀) of the ENTH domain becomes structured and aids in the aggregation of ENTH domains, which results in extensive membrane remodeling. In this article, atomistic and coarse-grained (CG) molecular dynamics (MD) simulations are used to investigate the structure and the stability of ENTH domain aggregates on lipid bilayers. EPR experiments are also reported for systems composed of different ENTH-bound membrane morphologies, including membrane vesicles as well as preformed membrane tubules. The EPR data are used to help develop a molecular model of ENTH domain aggregates on preformed lipid tubules that are then studied by CG MD simulation. The combined computational and experimental approach suggests that ENTH domains exist predominantly as monomers on vesiculated structures, while ENTH domains self-associate into dimeric structures and even higher‐order oligomers on the membrane tubes. The results emphasize that the arrangement of ENTH domain aggregates depends strongly on whether the local membrane curvature is isotropic or anisotropic. The molecular mechanism of ENTH‐domain-induced membrane vesiculation and tubulation and the implications of the epsin's role in clathrin-mediated endocytosis resulting from the interplay between ENTH domain membrane binding and ENTH domain self-association are also discussed.

Structural basis of membrane bending by the N-BAR protein endophilin

Functioning as key players in cellular regulation of membrane curvature, BAR domain proteins bend bilayers and recruit interaction partners through poorly understood mechanisms. Using electron cryomicroscopy, we present reconstructions of full-length endophilin and its N-terminal N-BAR domain in their membrane-bound state. Endophilin lattices expose large areas of membrane surface and are held together by promiscuous interactions between endophilin's amphipathic N-terminal helices. Coarse-grained molecular dynamics simulations reveal that endophilin lattices are highly dynamic and that the N-terminal helices are required for formation of a stable and regular scaffold. Furthermore, endophilin accommodates different curvatures through a quantized addition or removal of endophilin dimers, which in some cases causes dimerization of endophilin's SH3 domains, suggesting that the spatial presentation of SH3 domains, rather than affinity, governs the recruitment of downstream interaction partners.