Thermodynamics of nanocluster phases: a unifying theory

Role of the membrane anchor in the regulation of Lck activity

Theoretical work suggests that collective spatiotemporal behavior of integral membrane proteins should be modulated by boundary lipids sheathing their membrane anchors. Here, we show evidence for this prediction while investigating the mechanism for maintaining a steady amount of the active form of integral membrane protein Lck kinase (LckA) by Lck trans-autophosphorylation regulated by the phosphatase CD45. We used super-resolution microscopy, flow cytometry, and pharmacological and genetic perturbation to gain insight into the spatiotemporal context of this process. We found that LckA is generated exclusively at the plasma membrane, where CD45 maintains it in a ceaseless dynamic equilibrium with its unphosphorylated precursor. Steady LckA shows linear dependence, after an initial threshold, over a considerable range of Lck expression levels. This behavior fits a phenomenological model of trans-autophosphorylation that becomes more efficient with increasing LckA. We then challenged steady LckA formation by genetically swapping the Lck membrane anchor with structurally divergent ones, such as that of Src or the transmembrane domains of LAT, CD4, palmitoylation-defective CD4 and CD45 that were expected to drastically modify Lck boundary lipids. We observed small but significant changes in LckA generation, except for the CD45 transmembrane domain that drastically reduced LckA due to its excessive lateral proximity to CD45. Comprehensively, LckA formation and maintenance can be best explained by lipid bilayer critical density fluctuations rather than liquid-ordered phase-separated nanodomains, as previously thought, with "like/unlike" boundary lipids driving dynamical proximity and remoteness of Lck with itself and with CD45.

Domain formation in bicomponent vesicles induced by composition-curvature coupling

Lipid vesicles composed of a mixture of two types of lipids are studied by intensive Monte Carlo numerical simulations. The coupling between the local composition and the membrane shape is induced by two different spontaneous curvatures of the components. We explore the various morphologies of these biphasic vesicles coupled to the observed patterns such as nano-domains or labyrinthine mesophases. The effect of the difference in curvatures, the surface tension, and the interaction parameter between components is thoroughly explored. Our numerical results quantitatively agree with the previous analytical results obtained by Gueguen et al. [Eur. Phys. J. E 37, 76 (2014)] in the disordered (high temperature) phase. Numerical simulations allow us to explore the full parameter space, especially close to and below the critical temperature, where analytical results are not accessible. Phase diagrams are constructed and domain morphologies are quantitatively studied by computing the structure factor and the domain size distribution. This mechanism likely explains the existence of nano-domains in cell membranes as observed by super-resolution fluorescence microscopy.

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.

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.

The extracellular δ-domain is essential for the formation of CD81 tetraspanin webs

CD81 is a ubiquitously expressed member of the tetraspanin family. It forms large molecular platforms, so-called tetraspanin webs that play physiological roles in a variety of cellular functions and are involved in viral and parasite infections. We have investigated which part of the CD81 molecule is required for the formation of domains in the cell membranes of T-cells and hepatocytes. Surprisingly, we find that large CD81 platforms assemble via the short extracellular δ-domain, independent from a strong primary partner binding and from weak interactions mediated by palmitoylation. The δ-domain is also essential for the platforms to function during viral entry. We propose that, instead of stable binary interactions, CD81 interactions via the small δ-domain, possibly involving a dimerization step, play the key role in organizing CD81 into large tetraspanin webs and controlling its function.

Modeling curvature-dependent subcellular localization of the small sporulation protein SpoVM in Bacillus subtilis

Recent in vivo experiments suggest that in the bacterium, Bacillus subtilis, the cue for the localization of the small sporulation protein, SpoVM, an essential factor in spore coat formation, is curvature of the bacterial plasma membrane. In vitro measurements of SpoVM adsorption to vesicles of varying sizes also find high sensitivity of adsorption to vesicle radius. This curvature-dependent adsorption is puzzling given the orders of magnitude difference in length scale between an individual protein and the radius of curvature of the cell or vesicle, suggesting protein clustering on the membrane. Here we develop a minimal model to study the relationship between curvature-dependent membrane adsorption and clustering of SpoVM. Based on our analysis, we hypothesize that the radius dependence of SpoVM adsorption observed in vitro is governed primarily by membrane tension, while for in-vivo localization of SpoVM, we propose a highly sensitive mechanism for curvature sensing based on the formation of macroscopic protein clusters on the membrane.

Aggregation on a membrane of particles undergoing active exchange with a reservoir

We investigate the dynamics of clusters made of aggregating particles on a membrane which exchanges particles with a reservoir. Exchanges are driven by chemical reactions which supply energy to the system, leading to the establishment of a non-equilibrium steady state. We predict the distribution of cluster size at steady state. We show in particular that in a regime, that cannot exist at equilibrium, the distribution is bimodal: the membrane is mainly populated of single particles and finite-size clusters. This work is motivated by the observations that have revealed the existence of submicrometric clusters of proteins in biological membranes.

Clusters of proteins in biomembranes: insights into the roles of interaction potential shapes and of protein diversity

It has recently been proposed that proteins embedded in lipidic biomembranes can spontaneously self-organize into stable small clusters, or membrane nanodomains, 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 biomembranes. First, we compare different long-range potentials (including notably three-body terms) to demonstrate that the existence of cluster phases should be quite generic. Furthermore, a real membrane contains hundreds of different protein species that are far from being randomly distributed in these nanodomains. We take this protein diversity into account by modulating protein-protein interaction potentials both at short and longer range. We confirm theoretical predictions in terms of biological cluster specialization by deciphering how clusters recruit only a few protein species. In this respect, we highlight that cluster phases can turn out to be an advantage at the biological level, for example by enhancing the cell response to external stimuli.

The thermodynamics of simple biomembrane mimetic systems

Insight into the forces governing a system is essential for understanding its behavior and function. Thermodynamic investigations provide a wealth of information that is not, or is hardly, available from other methods. This article reviews thermodynamic approaches and assays to measure collective properties such as heat adsorption / emission and volume variations. These methods can be successfully applied to the study of lipid vesicles (liposomes) and biological membranes. With respect to instrumentation, differential scanning calorimetry, pressure perturbation calorimetry, isothermal titration calorimetry, dilatometry, and acoustic techniques aimed at measuring the isothermal and adiabatic processes, two- and three-dimensional compressibilities are considered. Applications of these techniques to lipid systems include the measurement of different thermodynamic parameters and a detailed characterization of thermotropic, barotropic, and lyotropic phase behavior. The membrane binding and / or partitioning of solutes (proteins, peptides, drugs, surfactants, ions, etc.) can also be quantified and modeled. Many thermodynamic assays are available for studying the effect of proteins and other additives on membranes, characterizing non-ideal mixing, domain formation, bilayer stability, curvature strain, permeability, solubilization, and fusion. Studies of membrane proteins in lipid environments elucidate lipid-protein interactions in membranes. Finally, a plethora of relaxation phenomena toward equilibrium thermodynamic structures can be also investigated. The systems are described in terms of enthalpic and entropic forces, equilibrium constants, heat capacities, partial volume changes, volume and area compressibility, and so on, also shedding light on the stability of the structures and the molecular origin and mechanism of the structural changes.

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.