Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface of the PM plays an important role in governing their heterogeneous surface distribution. However, the stability behavior of the surface distribution of protein aggregates remains poorly understood. Therefore, understanding the spatial patterns that can emerge on the PM solely through protein-protein interaction, lateral diffusion, and feedback is an important step towards a complete description of the mechanisms behind protein clustering on the cell surface. In this work, we investigate the pattern formation of a reaction-diffusion model that describes the dynamics of a system of ligand-receptor complexes. The purely diffusive ligand in the cytosol can bind receptors in the PM, and the resultant ligand-receptor complexes not only diffuse laterally but can also form clusters resulting in different oligomers. Finally, the largest oligomers recruit ligands from the cytosol in a positive feedback. From a methodological viewpoint, we provide theoretical estimates for diffusion-driven instabilities of the protein aggregates based on the Turing mechanism. Our main result is a threshold phenomenon, in which a sufficiently high recruitment of ligands promotes the input of new monomeric components and consequently drives the formation of a single-patch spatially heterogeneous steady-state.
The adhesion of biomembranes is mediated by the binding of membrane-anchored receptor and ligand proteins. The proteins can only bind if the separation between apposing membranes is sufficiently close to the length of the protein complexes, which leads to an interplay between protein binding and membrane shape. In this article, we review current models of biomembrane adhesion and novel insights obtained from the models. Theory and simulations with elastic-membrane and coarse-grained molecular models of biomembrane adhesion indicate that the binding of proteins in membrane adhesion strongly dep…
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…
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…
Though membrane trafficking of cell junction proteins has been studied extensively for more than two decades, the accumulated knowledge remains fragmentary. The goal of this review is to synthesize published studies on the membrane trafficking of the five major junction transmembrane proteins: claudins, occludin, and junction adhesion molecules (JAMs) in tight junctions; cadherins and nectins in adherens junctions; to identify underlying common mechanisms; to highlight their functional consequences on barrier function; and to identify knowledge gaps. Clathrin-mediated endocytosis appears to be…
It has recently been proposed that proteins embedded in lipidic bio-membranes can spontaneously self-organize into stable small clusters, or membrane nano-domains, due to the competition between short-range attractive and longer-range repulsive forces between proteins, specific to these systems. In this paper, we carry on our investigation, by Monte Carlo simulations, of different aspects of cluster phases of proteins in bio-membranes. First, we compare different long-range potentials (including notably three-body terms) to demonstrate that the existence of cluster phases should be quite gener…
Motivated by single-molecule experiments on synaptic membrane protein domains, we use a stochastic lattice model to study protein reaction and diffusion processes in crowded membranes. We find that the stochastic reaction-diffusion dynamics of synaptic proteins provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the single-molecule trajectories observed for synaptic proteins, and spatially inhomogeneous protein lifetimes at the cell membrane. Our results suggest that central aspects of the sin…
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…
Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation, and is strongly affected by membrane composition.
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…
We study the effect of membrane proteins on the shape, composition and thermodynamic stability of the surrounding membrane. When the coupling between membrane composition and curvature is strong enough the nearby composition and shape both undergo a transition from over-damped to under-damped spatial variation, well before the membrane becomes unstable in the bulk. This transition is associated with a change in the sign of the thermodynamic energy and hence has the unusual features that it can favour the early stages of coat assembly necessary for vesiculation (budding), while suppressing the …
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…
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…
The adhesion of biological membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. Central questions are how the binding kinetics of these proteins is affected by the membranes and by the membrane anchoring of the proteins. In this article, we (i) present detailed data for the binding of membrane-anchored proteins from coarse-grained molecular dynamics simulations, and (ii) provide a theory that describes how the binding kinetics depends on the average separation and thermal roughness of the adhering membranes, and on the anchoring, lengths, and length variation…
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…
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 discuss a realistic scenario, accounting for the existence of sub-micrometric protein domains in cell membranes. At the biological level, such membrane domains have been shown to be specialized, in order to perform a determined biological task, in the sense that they gather one or a few protein species out of the hundreds of different ones that a cell membrane may contain. By analyzing the balance between mixing entropy and protein affinities, we propose that such protein sorting in distinct domains can be explained without appealing to pre-existing lipidic micro-phase separations, as in th…
Lipid bilayers forming biological membranes are known to behave as viscous 2D fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it has been shown [Proc. Nat. Acad. Sci. USA 112, E3639 (2015)] that such active proteins should in- duce non-thermal fluctuating lipid flows leading to diffusion enhancement and chemotaxis-like drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid …
Clathrin-mediated endocytosis (CME) is a key pathway for transporting cargo into cells via membrane vesicles. It plays an integral role in nutrient import, signal transduction, neurotransmission and cellular entry of pathogens and drug-carrying nanoparticles. As CME entails substantial local remodeling of the plasma membrane, the presence of membrane tension offers resistance to bending and hence, vesicle formation. Experiments show that in such high tension conditions, actin dynamics is required to carry out CME successfully. In this study, we build upon these pioneering experimental studies …
The intricate shapes of biological membranes such as tubules and membrane stacks are induced by proteins. In this article, we systematically investigate the membrane shapes induced by arc-shaped scaffolds such as proteins and protein complexes with coarse-grained modeling and simulations. We find that arc-shaped scaffolds induce membrane tubules at membrane coverages larger than a threshold of about 40%, irrespective of their arc angle. The membrane morphologies at intermediate coverages below this tubulation threshold, in contrast, strongly depend on the arc angle. Scaffolds with arc angles o…
Min-protein oscillations in Escherichia coli with spontaneous formation of two-stranded filaments in a three-dimensional stochastic reaction-diffusion model
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and …
Lipid phase heterogeneity in the plasma membrane is thought to be crucial for many aspects of cell signaling, but the physical basis of participating membrane domains such as "lipid rafts" remains controversial. Here we consider a lattice model yielding a phase diagram that includes several states proposed to be relevant for the cell membrane, including microemulsion - which can be related to membrane curvature - and Ising critical behavior. Using a neural network-based machine learning approach, we compute the full phase diagram of this lattice model. We analyze selected regions of this phase…
The cellular basis for the adaptive immune response during antigen recognition relies on a specialized protein interface known as the immunological synapse (IS). Understanding the biophysical basis for protein patterning by deciphering the quantitative rules for their formation and motion is an important aspect of characterizing immune cell recognition and thence the rules for immune system activation. We propose a minimal mathematical model for the physical basis of membrane protein patterning in the IS, which encompass membrane mechanics, protein binding kinetics and motion, and fluid flow i…
We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic…
The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant K2D and the on- and off-rate constants of anchored receptors and ligands in their 'two-dimensional' (2D) membrane environment strongly depend on the membra…
Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor proteins, by polymerization of the cytoskeleton, or due to the interactions between membrane proteins binding onto the membrane. The numerous experimental observations of tube formation have been amply supported by mathematical modeling of the associated membrane mechanics and have provided insights into the force-displacement relationships of membrane tubes. R…
Many of the processes that underly neural computation are carried out by ion channels embedded in the plasma membrane, a two-dimensional liquid that surrounds all cells. Recent experiments have demonstrated that this membrane is poised close to a liquid-liquid critical point in the Ising universality class. Here we use both exact and stochastic techniques on the lattice Ising model to explore the ramifications of proximity to criticality for proteins that are allosterically coupled to Ising composition modes. Owing to diverging generalized susceptibilities, such a protein's activity becomes st…
Collective behavior of proteins on biomembranes is usually studied within the spontaneous curvature model. Here we consider an alternative phenomenological approach, which accounts consistently for partial ordering of proteins as well as the anchoring forces exerted on a membrane by layer of proteins. We show analytically that such anisotropic interactions can drive membrane bending, resulting in non-trivial equilibrium morphologies. The predicted instabilities can advance our conceptual understanding of physical mechanisms behind collective phenomena in biological systems, in particular those…
