Nonequilibrium patterns in phase-separating ternary membranes

A Rationale for Mesoscopic Domain Formation in Biomembranes

Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also be observed in vitro on model systems such as supported membranes or lipid vesicles. Lipid mixtures separating in liquid-ordered and liquid-disordered phases below a demixing temperature play a pivotal role in this context. Protein-protein and protein-lipid interactions also contribute to membrane shaping by promoting small domains or clusters. Such phase separations displaying characteristic length-scales falling in-between the nanoscopic, molecular scale on the one hand and the macroscopic scale on the other hand, are named mesophases in soft condensed matter physics. In this review, we propose a classification of the diverse mechanisms leading to mesophase separation in biomembranes. We distinguish between mechanisms relying upon equilibrium thermodynamics and those involving out-of-equilibrium mechanisms, notably active membrane recycling. In equilibrium, we especially focus on the many mechanisms that dwell on an up-down symmetry breaking between the upper and lower bilayer leaflets. Symmetry breaking is an ubiquitous mechanism in condensed matter physics at the heart of several important phenomena. In the present case, it can be either spontaneous (domain buckling) or explicit, i.e., due to an external cause (global or local vesicle bending properties). Whenever possible, theoretical predictions and simulation results are confronted to experiments on model systems or living cells, which enables us to identify the most realistic mechanisms from a biological perspective.

Nanodomains in Biomembranes with Recycling

Cell membranes are out of thermodynamic equilibrium notably because of membrane recycling, i.e., active exchange of material with the cytosol. We propose an analytically tractable model of biomembrane predicting the effects of recycling on the size of protein nanodomains also called protein clusters. The model includes a short-range attraction between proteins and a weaker long-range repulsion which ensures the existence of so-called cluster phases in equilibrium, where monomeric proteins coexist with finite-size domains. Our main finding is that, when taking recycling into account, the typical cluster size at steady state increases logarithmically with the recycling rate at fixed protein concentration. Using physically realistic model parameters, the predicted 2-fold increase due to recycling in living cells is most likely experimentally measurable with the help of super-resolution microscopy.

Alteration of interleaflet coupling due to compounds displaying rapid translocation in lipid membranes

The spatial coincidence of lipid domains at both layers of the cell membrane is expected to play an important role in many cellular functions. Competition between the surface interleaflet tension and a line hydrophobic mismatch penalty are conjectured to determine the transversal behavior of laterally heterogeneous lipid membranes. Here, by a combination of molecular dynamics simulations, a continuum field theory and kinetic equations, I demonstrate that the presence of small, rapidly translocating molecules residing in the lipid bilayer may alter its transversal behavior by favoring the spatial coincidence of similar lipid phases.

Equilibrium microphase separation in the two-leaflet model of lipid membranes

Because of the coupling between local lipid composition and the thickness of the membrane, microphase separation in two-component lipid membranes can take place; such effects may underlie the formation of equilibrium nanoscale rafts. Using a kinetic description, this phenomenon is analytically and numerically investigated. The phase diagram is constructed through the stability analysis for linearized kinetic equations, and conditions for microphase separation are discussed. Simulations of the full kinetic model reveal the development of equilibrium membrane nanostructures with various morphologies from the initial uniform state.

Where Biology Meets Physics--A Converging View on Membrane Microdomain Dynamics

For several decades, the phenomenon of membrane component segregation into microdomains has been a well-known and highly debated subject, and varying concepts including the raft hypothesis, the fence-and-picket model, hydrophobic-mismatch, and specific protein-protein interactions have been offered as explanations. Here, we review the level of insight into the molecular architecture of membrane domains one is capable of obtaining through biological experimentation. Using SNARE proteins as a paradigm, comprehensive data suggest that several dozens of molecules crowd together into almost circular spots smaller than 100 nm. Such clusters are highly dynamical as they constantly capture and lose molecules. The organization has a strong influence on the functional availability of proteins and likely provides a molecular scaffold for more complex protein networks. Despite this high level of insight, fundamental open questions remain, applying not only to SNARE protein domains but more generally to all types of membrane domains. In this context, we explain the view of physical models and how they are beneficial in advancing our concept of micropatterning. While biological models generally remain qualitative and descriptive, physics aims towards making them quantitative and providing reproducible numbers, in order to discriminate between different mechanisms which have been proposed to account for experimental observations. Despite the fundamental differences in biological and physical approaches as far as cell membrane microdomains are concerned, we are able to show that convergence on common points of views is in reach.

Fluctuating hydrodynamics of multicomponent membranes with embedded proteins

A simulation method for the dynamics of inhomogeneous lipid bilayer membranes is presented. The membrane is treated using stochastic Saffman-Delbrück hydrodynamics, coupled to a phase-field description of lipid composition and discrete membrane proteins. Multiple applications are considered to validate and parameterize the model. The dynamics of membrane composition fluctuations above the critical point and phase separation dynamics below the critical point are studied in some detail, including the effects of adding proteins to the mixture.

Modeling the interplay between protein and lipid aggregation in supported membranes

We present a theoretical model that deals with the complex interplay between lipid segregation and the self-aggregation of lipid-attached proteins. The model, in contrast to previous ones that consider proteins only as passive elements affecting the lipid distribution, describes the system including three terms: the dynamic interactions between protein monomers, the interactions between lipid components, and a mixed term considering protein-lipid interactions. It is used to explain experimental results performed on a well-defined system in which a self-aggregating soluble bacterial cytoskeletal protein polymerizes on a lipid bilayer containing two lipid components. All the elements considered in a previously described protein model, including torsion of the monomers within the filament, are needed to account for the observed filament shapes. The model also points out that lipid segregation can affect the length and curvature of the filaments and that the dynamic behavior of the lipids and proteins can have different time scales, giving rise to memory effects. This simple model that considers a dynamic protein assembly on a fluid and active lipid surface can be easily extended to other biologically relevant situations in which the interplay between protein and lipid aggregation is needed to fully describe the system.

Physical aspects of heterogeneities in multi-component lipid membranes

Ever since the raft model for biomembranes has been proposed, the traditional view of biomembranes based on the fluid-mosaic model has been altered. In the raft model, dynamical heterogeneities in multi-component lipid bilayers play an essential role. Focusing on the lateral phase separation of biomembranes and vesicles, we review some of the most relevant research conducted over the last decade. We mainly refer to those experimental works that are based on physical chemistry approach, and to theoretical explanations given in terms of soft matter physics. In the first part, we describe the phase behavior and the conformation of multi-component lipid bilayers. After formulating the hydrodynamics of fluid membranes in the presence of the surrounding solvent, we discuss the domain growth-law and decay rate of concentration fluctuations. Finally, we review several attempts to describe membrane rafts as two-dimensional microemulsion.

Phases and fluctuations in a model for asymmetric inhomogeneous fluid membranes

We propose and analyze a model for phase transitions in an inhomogeneous fluid membrane, that couples local composition with curvature nonlinearly. For asymmetric membranes, our model shows generic non-Ising behavior and the ensuing phase diagram displays either a first- or a second-order phase transition through a critical point (CP) or a tricritical point (TP), depending upon the bending modulus. It predicts generic nontrivial enhancement in fluctuations of asymmetric membranes that scales with system size in a power-law fashion at the CP and TP in two dimensions, not observed in symmetric membranes. It also yields two-dimensional Ising universality class for symmetric membranes, in agreement with experimental results.

Concentration fluctuations and phase transitions in coupled modulated bilayers

We consider the formation of finite-size domains in lipid bilayers consisting of saturated and hybrid lipids. First, we describe a monolayer model that includes a coupling between a compositional scalar field and a two-dimensional vectorial order parameter. Such a coupling yields an effective two-dimensional microemulsion free energy for the lipid monolayer, and its characteristic length of compositional modulations can be considered as the origin of finite-size domains in biological membranes. Next, we consider a coupled bilayer composed of two modulated monolayers and discuss the static and dynamic properties of concentration fluctuations above the transition temperature. We also investigate the micro-phase separation below the transition temperature and compare the micro-phase separated structures with statics and dynamics of concentration fluctuations above the transition.

Monodisperse domains by proteolytic control of the coarsening instability

The coarsening instability typically disrupts steady-state cluster-size distributions. We show that degradation coupled to the cluster size, such as arising from biological proteolysis, leads to a fixed-point cluster size. Stochastic evaporative and condensative fluxes determine the width of the fixed-point size distribution. At the fixed point, we show how the peak size and width depend on number, interactions, and proteolytic rate. This proteolytic size-control mechanism is consistent with the phenomenology of pseudopilus length control in the general secretion pathway of bacteria.

Nanodomain stabilization dynamics in plasma membranes of biological cells

We discover that a synergistically amplifying role of stabilizing membrane proteins and continuous lipid recycling can explain the physics governing the stability, polydispersity, and dynamics of lipid raft domains in plasma membranes of biological cells. We establish the conjecture using a generalized order parameter based on theoretical formalism, endorsed by detailed scaling arguments and domain mapping. Quantitative agreements with morphological distributions of raft complexes, as obtained from Förster resonance energy transfer based visualization, support the present theoretical conjecture.

Effect of integral proteins in the phase stability of a lipid bilayer: application to raft formation in cell membranes

The existence of lipid rafts is a controversial issue. The affinity of cholesterol for saturated lipids is manifested in macroscopic phase separation in model membranes, and is believed to be the thermodynamic driving force for raft formation. However, there is no clear reason to explain the small (nanometric) size of raft domains in cell membranes. In a recent paper Yethiraj and Weisshaar [Biophys. J. 93, 3113 (2007)] proposed that the effect of neutral integral membrane proteins may prevent from the formation of large lipid domains. In this paper we extend this approach by studying the effect of the protein size, as well as the lipid-protein interaction. Depending on these factors, two different mechanisms for nanodomain stabilization are shown to be possible for static proteins. The application of these results to a biological context is discussed.

Lipid microdomains: structural correlations, fluctuations, and formation mechanisms

Compositional lipid microdomains ("lipid rafts") in mammalian plasma membranes are believed to facilitate many important cellular processes. While several physically distinct scenarios predicting the presence of finite-sized microdomains in vivo have been proposed in the past, direct experimental verification or falsification of model predictions has remained elusive. Herein, we demonstrate that the combination of the spatial correlation and temporal fluctuation spectra of the lipid domains can be employed to unambiguously differentiate between the existing theoretical scenarios. Furthermore, the differentiation of the raft formation mechanisms using this methodology can be achieved by collecting data at physiologically relevant conditions without the need to tune control parameters.

Influence of nonequilibrium lipid transport, membrane compartmentalization, and membrane proteins on the lateral organization of the plasma membrane

Compositional lipid domains (lipid rafts) in plasma membranes are believed to be important components of many cellular processes. The mechanisms by which cells regulate the sizes, lifetimes, and spatial localization of these domains are rather poorly understood at the moment. We propose a robust mechanism for the formation of finite-sized lipid raft domains in plasma membranes, the competition between phase separation in an immiscible lipid system and active cellular lipid transport processes naturally leads to the formation of such domains. Simulations of a continuum model reveal that the raft size distribution is broad and the average raft size is strongly dependent on the rates of cellular and interlayer lipid transport processes. We demonstrate that spatiotemporal variations in the recycling may enable the cell to localize larger raft aggregates at specific parts along the membrane. Moreover, we show that membrane compartmentalization may further facilitate spatial localization of the raft domains. Finally, we demonstrate that local interactions with immobile membrane proteins can spatially localize the rafts and lead to further clustering.

Formation and regulation of lipid microdomains in cell membranes: theory, modeling, and speculation

Compositional lipid microdomains ("lipid rafts") in plasma membranes are believed to be important components of many cellular processes. The biophysical mechanisms by which cells regulate the size, lifetime, and spatial localization of these domains are rather poorly understood at the moment. Over the years, experimental studies of raft formation have inspired several phenomenological theories and speculations incorporating a wide variety of thermodynamic assumptions regarding lipid-lipid and lipid-protein interactions, and the potential role of active cellular processes on membrane structure. Here we critically review and discuss these theories, models, and speculations, and present our view on future directions.