We extend the Saffman theory of membrane hydrodynamics to account for the correlated motion of membrane proteins, along with the effect of protein concentration on that correlation and on the response of the membrane to stresses. Expressions for the coupling diffusion coefficients of protein pairs and their concentration dependence are derived in the limit of small protein size relative to the inter-protein separation. The additional role of membrane viscosity as determining the characteristic length scale for membrane response leads to unusual concentration effects at large separation -- the transverse coupling increases with protein concentration, whereas the longitudinal one becomes concentration-independent.
We use coarse grained molecular dynamics simulations to investigate diffusion properties of sheared lipid membranes with embedded transmembrane proteins. In membranes without proteins, we find normal in-plane diffusion of lipids in all flow conditions. Protein embedded membranes behave quite differently: by imposing a simple shear flow and sliding the monolayers of the membrane over each other, the motion of protein clusters becomes strongly superdiffusive in the shear direction. In such a circumstance, subdiffusion regime is predominant perpendicular to the flow. We show that superdiffusion i…
Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors, and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus, there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins, and el…
The viscosity of lipid bilayer membranes plays an important role in determining the diffusion constant of embedded proteins and the dynamics of membrane deformations, yet it has historically proven very difficult to measure. Here we introduce a new method based on quantification of the large-scale circulation patterns induced inside vesicles adhered to a solid surface and subjected to simple shear flow in a microfluidic device. Particle Image Velocimetry based on spinning disk confocal imaging of tracer particles inside and outside of the vesicle, and tracking of phase-separated membrane domai…
We examine the interactions between actively rotating proteins moving in a membrane. Experimental evidence suggests that such rotor proteins, like the ATP synthases of the inner mitochondrial membrane, can arrange themselves into lattices. We show that crystallization is possible through a combination of hydrodynamic and repulsive interactions between the rotor proteins. In particular, hydrodynamic interactions induce rotational motion of the rotor protein assembly that, in the presence of repulsion, drives the system into a hexagonal lattice. The entire crystal rotates with an angular velocit…
Curvature-inducing proteins containing a Bin/Amphiphysin/Rvs domain often have intrinsically disordered domains. Recent experiments have shown that these disordered chains enhance curvature sensing and generation. Here, we report on the modification of protein-membrane interactions by disordered chains using meshless membrane simulations. The protein and bound membrane are modeled together as a chiral crescent protein rod with two excluded-volume chains. As the chain length increases, the repulsion between them reduces the cluster size of the proteins. It induces spindle-shaped vesicles and a …
Specific lipid environments are necessary for the establishment of protein signalling platforms in membranes, yet their origin has been highly debated. We present a continuum, exactly solvable model of protein induced local demixing of lipid membranes. The coupling between a local composition and a local thickness of the membrane induces lipid domains around inclusions with hydrophobic mismatch, even for temperatures above the miscibility critical point of the membrane. The model qualitatively explains the experimentally observed formation of lipid domains induced by anchoring of reconstituted…
Proteins often form chiral assembly structures on a biomembrane. However, the role of the chirality in the interaction with an achiral membrane is poorly understood. Here, the differential behavior between chiral and achiral crescent-shaped protein rods was investigated using meshless membrane simulations. The achiral rods deformed the membrane tube into an elliptical shape by stabilizing the edges of the ellipse. In contrast, the chiral rods formed a helical assembly that generated a cylindrical membrane tube with a constant radius in addition to the elliptical tube. This helical assembly cou…
In living cells, membrane morphology is regulated by various proteins. Many membrane reshaping proteins contain a Bin/Amphiphysin/Rvs (BAR) domain, which consists of a banana-shaped rod. The BAR domain bends the biomembrane along the rod axis and the features of this anisotropic bending have recently been studied. Here, we report on the role of the BAR protein rods in inducing membrane tubulation, using large-scale coarse-grained simulations. We reveal that a small spontaneous side curvature perpendicular to the rod can drastically alter the tubulation dynamics at high protein density, whereas…
We investigate membrane-mediated interactions between transmembrane proteins using coarse-grained models. We compare the effective potential of mean force (PMF) between two proteins, which are always aligned parallel to the z-axis of the simulation box, with those PMFs obtained for proteins with fluctuating orientations. The PMFs are dominated by an oscillatory packing-driven contribution and a smooth attractive hydrophobic mismatch contribution, which vanishes if the hydrophobic length of the protein matches the thickness of the membrane. If protein orientations are allowed to fluctuate, the …
Self-assembly of protein monomers into distinct membrane protein oligomers provides a general mechanism for diversity in the molecular architectures, and resulting biological functions, of membrane proteins. We develop a general physical framework describing the thermodynamic competition between different oligomeric states of membrane proteins. Using the mechanosensitive channel of large conductance as a model system, we show how the dominant oligomeric states of membrane proteins emerge from the interplay of protein concentration in the cell membrane, protein-induced lipid bilayer deformation…
Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic mechanisms underlying spatial organisation in cells. In this work, we use a continuum model of membrane and protein dynamics to study the behaviour of curvature-inducing proteins on membranes of spherical shape, such as living cells or lipid vesicles. We show that the interplay between curvature energy, entropic forces, and the geometric constraints on the memb…
Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembrane. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered using mean-field theory including an orientation-dependent excluded volume. The proteins exhibit a second-order or first-order nematic transition with increasing protein density depending on the radius of the membrane tube. The tube curvatures for the maximum protein binding and orientational order are different and varied by the protein density and rigidit…
BAR superfamily proteins have a banana-shaped domain that causes the local bending of lipid membranes. We study as to how such a local anisotropic curvature induces effective interaction between proteins and changes the global shape of vesicles and membrane tubes using meshless membrane simulations. The proteins are modeled as banana-shaped rods strongly adhered to the membrane. Our study reveals that the rods assemble via two continuous directional phase separations unlike a conventional two-dimensional phase separation. As the rod curvature increases, in the membrane tube the rods assemble a…
Hydrophobic thickness mismatch between integral membrane proteins and the surrounding lipid bilayer can produce lipid bilayer thickness deformations. Experiment and theory have shown that protein-induced lipid bilayer thickness deformations can yield energetically favorable bilayer-mediated interactions between integral membrane proteins, and large-scale organization of integral membrane proteins into protein clusters in cell membranes. Within the continuum elasticity theory of membranes, the energy cost of protein-induced bilayer thickness deformations can be captured by considering compressi…
While modern structural biology has provided us with a rich and diverse picture of membrane proteins, the biological function of membrane proteins is often influenced by the mechanical properties of the surrounding lipid bilayer. Here we explore the relation between the shape of membrane proteins and the cooperative function of membrane proteins induced by membrane-mediated elastic interactions. For the experimental model system of mechanosensitive ion channels we find that the sign and strength of elastic interactions depend on the protein shape, yielding distinct cooperative gating curves fo…
Central to understanding membrane bound cell signaling is to quantify how the membrane ultra-structure consisting of transient spatial domains modulates signaling and how the signaling influences this ultra-structure. Yet, measuring the association of membrane proteins with domains in living, intact cells poses considerable challenges. Here, we describe a non-destructive method to quantify protein-lipid domain and protein cytoskeleton interactions in single, intact cells enabling continuous monitoring of the protein domains interaction over time during signaling.
Adsorption of proteins onto membranes can alter the local membrane curvature. This phenomenon has been observed in biological processes such as endocytosis, tubulation and vesiculation. However, it is not clear how the local surface properties of the membrane, such as membrane tension, change in response to protein adsorption. In this paper, we show that the classical elastic model of lipid membranes cannot account for simultaneous changes in shape and membrane tension due to protein adsorption in a local region, and a viscous-elastic formulation is necessary to fully describe the system. Ther…
Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the membrane deformation induced by the excitable reaction-diffusion waves of curvature-inducing proteins and the alternation in the waves due to the deformation, using a coarse-grained simulation of tubular membranes with a modified FitzHugh--Nagumo model. Protein-propagating waves deform tubular membranes, and large deformations induce budding and erase waves…
In this perspective we describe the critical role membranes play in modulating the structures of the Amyloid Precursor Proteins to produce the peptides involved in the Alzheimer's disease. Some of the key concepts related to protein aggregation including the potential role of the excited states of monomers in initiating protein aggregation are described.
The membrane tubulation induced by banana-shaped protein rods is investigated by using coarse-grained meshless membrane simulations. It is found that the tubulation is promoted by laterally isotropic membrane inclusions that generate the same sign of spontaneous curvature as the adsorbed protein rods. The inclusions are concentrated in the tubules and reduce the bending energy of the tip of the tubules. On the other hand, the inclusions with an opposite curvature suppress the tubulation by percolated-network formation at a high protein-rod density while they induce a spherical membrane bud at …
The function of membrane-embedded proteins such as ion channels depends crucially on their conformation. We demonstrate how conformational changes in asymmetric membrane proteins may be inferred from measurements of their diffusion. Such proteins cause local deformations in the membrane, which induce an extra hydrodynamic drag on the protein. Using membrane tension to control the magnitude of the deformations and hence the drag, measurements of diffusivity can be used to infer--- via an elastic model of the protein--- how conformation is changed by tension. Motivated by recent experimental res…
The shape transformations of fluid membranes induced by curved protein rods are studied using meshless membrane simulations. The rod assembly at low rod density induces a flat membrane tube and oblate vesicle. It is found that the polyhedral shapes are stabilized at high rod densities. The discrete shape transition between triangular and buckled discoidal tubes is obtained and their curvature energies are analyzed by a simple geometric model. For vesicles, triangular hosohedron and elliptic-disk shapes are formed in equilibrium, whereas tetrahedral and triangular prism shapes are obtained as m…
We review the theoretical analyses and simulations of the interactions between curvature-inducing proteins and biomembranes. Laterally isotropic proteins induce spherical budding, whereas anisotropic proteins, such as Bin/Amphiphysin/Rvs (BAR) superfamily proteins, induce tabulation. Both types of proteins can sense the membrane curvature. We describe the theoretical analyses of various transitions of protein binding accompanied by a change in various properties, such as the number of buds, the radius of membrane tubes, and the nematic order of anisotropic proteins. Moreover, we explain the me…
Membrane deformation inside living cells is crucial for the proper shaping of various intracellular organelles and is necessary during the fission/fusion processes that allow membrane recycling and transport (e.g. endocytosis). Proteins that induce membrane curvature play a key role in such processes, mostly by adsorbing to the membrane and forming a scaffold that deforms the membrane according to the curvature of the proteins. In this paper we explore the possibility of membrane tube destabilisation through a pearling mechanism enabled by the combined effects of the adsorbed curved proteins a…
Experiments have revealed that membrane proteins can form two-dimensional clusters with regular translational and orientational protein arrangements, which may allow cells to modulate protein function. However, the physical mechanisms yielding supramolecular organization and collective function of membrane proteins remain largely unknown. Here we show that bilayer-mediated elastic interactions between membrane proteins can yield regular and distinctive lattice architectures of protein clusters, and may provide a link between lattice architecture and lattice function. Using the mechanosensitive…
Cell membranes interact with a myriad of curvature-active proteins that control membrane morphology and are responsible for mechanosensation and mechanotransduction. Some of these proteins, such as those containing BAR domains, are curved and elongated, and hence may adopt different states of orientational order, from isotropic to maximize entropy to nematic as a result of crowding or to adapt to the curvature of the underlying membrane. Here, extending the work of [Nascimento et. al, Phys. Rev. E, 2017, 96, 022704], we develop a mean-field density functional theory to predict the orientationa…
In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S.A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein arrangement and characteristic size. We develop a model of MPPN self-assembly in which the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects. With all model parameters determined directly from experiments, our model correctly predicts the …
In cell membranes, proteins and lipids are organized into sub-micrometric nanodomains of varying size, shape and composition, performing specific functions. Despite their biological importance, the detailed morphology of these nanodomains remains unknown. Not only can they hardly be observed by conventional microscopy due to their small size, but there is no full consensus on the theoretical models to describe their structuring and their shapes. Here, we use a combination of analytical calculations and Monte Carlo simulations based upon a model coupling membrane composition and shape to show t…
Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of ves…
Lipid rafts are heterogeneous dynamic lipid domains of the cell membranes that are involved in several biological processes, like protein and lipids specific transport and signaling. Our understanding of lipid raft formation is still limited, due to the transient and elusive nature of these domains {\it in vivo}, in contrast to the stable phase-separated domains observed in artificial membranes. Inspired by experimental findings highlighting the relevance of transmembrane proteins for lipid rafts, we investigate lipid domain nucleation by coarse-grained molecular dynamics and Ising model simul…
Continuum or hybrid modeling of bilayer membrane morphological dynamics induced by embedded proteins necessitates the identification of protein-membrane interfaces and coupling of deformations of two surfaces. In this article we developed (i) a minimal total geodesic curvature model to describe these interfaces, and (ii) a numerical one-one mapping between two surface through a conformal mapping of each surface to the common middle annulus. Our work provides the first computational tractable approach for determining the interfaces between bilayer and embedded proteins. The one-one mapping allo…
Proteins in photosynthetic membranes can organize into patterned arrays that span the membrane's lateral size. Attractions between proteins in different layers of a membrane stack can play a key role in this ordering, as was suggested by microscopy and fluorescence spectroscopy and demonstrated by computer simulations of a coarse-grained model. The architecture of thylakoid membranes, however, also provides opportunities for inter-layer interactions that instead disfavor the high protein densities of ordered arrangements. Here we explore the interplay between these opposing driving forces, and…
Protein-stabilised emulsions can be seen as mixtures of unadsorbed proteins and of protein-stabilised droplets. To identify the contributions of these two components to the overall viscosity of sodium caseinate o/w emulsions, the rheological behaviour of pure suspensions of proteins and droplets were characterised, and their properties used to model the behaviour of their mixtures. These materials are conveniently studied in the framework developed for soft colloids. Here, the use of viscosity models for the two types of pure suspensions facilitates the development of a semi-empirical model th…
The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio $λ$ (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate $\dotγ$ applied to the RBC. However, the membrane viscosity $μ_m$ plays a major role in a realistic description of RBC's dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity $μ_m$ on the TB-TT …
An interfacial regularized Stokeslet scheme is presented to predict the motion of solid bodies (e.g. proteins or gel-phase domains) embedded within flowing lipid bilayer membranes. The approach provides a numerical route to calculate velocities and angular velocities in complex flow fields that are not amenable to simple Faxén-like approximations. Additionally, when applied to shearing motions, the calculations yield predictions for the effective surface viscosity of dilute rigid body-laden membranes. In the case of cylindrical proteins, effective viscosity calculations are compared to two pri…
Biological membranes constitute boundaries of cells and cell organelles. Physico-chemical 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 appara…
Macromolecular complexation leading to coupling of two or more cellular membranes is a crucial step in a number of biological functions of the cell. While other mechanisms may also play a role, adhesion always involves the fluctuations of deformable membranes, the diffusion of proteins and the molecular binding and unbinding. Because these stochastic processes couple over a multitude of time and length scales, theoretical modeling of membrane adhesion has been a major challenge. Here we present an effective Monte Carlo scheme within which the effects of the membrane are integrated into local r…
The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and ves…
The mobility of membrane proteins controls many biological functions. The application of the model of Saffman and Delbrück to the diffusion of membrane proteins does not account for all the experimental measurements. These discrepancies have triggered a lot of studies on the role of the mechanical factors in the mobility. After a short review of the Saffman and Delbrück model and of some key experiments, we explore the various ways to incorporate the effects of the different mechanical factors. Our approach focuses on the coupling of the protein to the membrane, which is the central element in…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be attributed to interactions between proteins and membranes. These interactions include protein diffusion and formation of aggregates due to protein-protein interactions in the plane of the membrane. Recently, we developed a model that couples the in-plane flow of lipids and diffusion of proteins with the out-of-plane bending of the membrane. Building on this work,…
We propose an improved prediction method of the tertiary structures of $α$-helical membrane proteins based on the replica-exchange method by taking into account helix deformations. Our method allows wide applications because transmembrane helices of native membrane proteins are often distorted. In order to test the effectiveness of the present method, we applied it to the structure predictions of glycophorin A and phospholamban. The results were in accord with experiments.
Curvature-sensing and curvature-remodeling proteins are known to reshape cell membranes, and this remodeling event is essential for key biophysical processes such as tubulation, exocytosis, and endocytosis. Curvature-inducing proteins can act as curvature sensors as well as induce curvature in cell membranes to stabilize emergent high curvature, non-spherical, structures such as tubules, discs, and caveolae. A definitive understanding of the interplay between protein recruitment and migration, the evolution of membrane curvature, and membrane morphological transitions is emerging but remains i…
The curvature sensitive localization of proteins on membranes is vital for many cell biological processes. Coarse-grained models are routinely employed to study the curvature sensing phenomena and membrane morphology at the length scale of few micrometers. Two prevalent phenomenological models exist for modeling experimental observations of curvature sensing, (1) the spontaneous curvature model and (2) the curvature mismatch model, which differ in their treatment of the change in elastic energy due to the binding of proteins on the membrane. In this work, the prediction of sensing and generati…
We investigate the effect of mobile polymer brushes on proteins embedded in biological membranes by employing both Asakura-Oosawa type of theoretical model and coarse-grained molecular dynamics simulations. The brush polymer-induced depletion attraction between proteins changes non-monotonically with the size of brush. The depletion interaction, which is determined by the ratio of protein size to the grafting distance between brush polymers, increases linearly with brush size as long as the polymer brush height is shorter than the protein size. When the brush height exceeds the protein size, h…
Membrane proteins deform the surrounding lipid bilayer, which can lead to membrane-mediated interactions between neighboring proteins. Using the mechanosensitive channel of large conductance (MscL) as a model system, we demonstrate how the observed differences in protein structure can affect membrane-mediated interactions and cooperativity among membrane proteins. We find that distinct oligomeric states of MscL lead to distinct gateway states for the clustering of MscL, and predict signatures of MscL structure and spatial organization in the cooperative gating of MscL. Our modeling approach es…
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the membrane shape through its spontaneous curvature and bending rigidity. The lateral motion of the protein may be viewed as diffusion in an effective potential, hence, the effective mobility is always reduced compared to the case of free diffusion. Using a rigorous path-integral approach we derive an analytical expression for the effective diffusion coefficient for…
There are a great many proteins that localize to and collectively generate curvature in biological fluid membranes. We study changes in the topology of fluid membranes due to the presence of highly anisotropic, curvature-inducing proteins. Generically, we find a surprisingly rich phase diagram with phases of both positive and negative Gaussian curvature. As a concrete example modeled on experiments, we find that a lamellar phase in a negative Gaussian curvature regime exhibits a propensity to form screw dislocations of definite burgers scalar but of both chirality. The induced curvature depend…
Recent experiments by Y. Gambin et al. [PNAS 103, 2098 (2006)] have called into question the applicability of the Saffman-Delbruck diffusivity for proteins embedded in the lipid bilayers. We present a simple argument to account for this observation that should be generically valid for a large class of transmembrane and membrane bound proteins. Whenever the protein-lipid interactions locally deform the membrane, that deformation generates new hydrodynamic stresses on the protein-membrane complex leading to a suppression of its mobility. We show that this suppression depends on the protein size …
Integral membrane proteins deform the surrounding bilayer creating long-ranged forces that influence distant proteins. These forces can be attractive or repulsive, depending on the proteins' shape, height, contact angle with the bilayer, as well as the local membrane curvature. Although interaction energies are not pairwise additive, for sufficiently low protein density, thermodynamic properties depend only upon pair interactions. Here, we compute pair interaction potentials and entropic contributions to the two-dimensional osmotic pressure of a collection of noncircular proteins. In contrast …
Measurements of lateral diffusion of proteins in a membrane typically assume that the movement of the protein occurs in a flat plane. Real membranes, however, are subject to thermal fluctuations, leading to movement of an inclusion into the third dimension. We calculate the magnitude of this effect by projecting real three-dimensional diffusion onto an effective one on a flat plane. We consider both a protein that is free to diffuse in the membrane and one that also couples to the local curvature. For a freely diffusing inclusion the measured projected diffusion constant is up to 15% smaller t…
