Stability of protein-decorated mixed lipid membranes: The interplay of lipid-lipid, lipid-protein, and protein-protein interactions

Regulation of phase boundaries and phase-segregated patterns in model membranes

Demixing of components has long been described in model membranes. It is a consequence of non-ideal lateral interactions between membrane components, and it causes the presence of segregated phases, forming patches (domains) of different properties, thus introducing heterogeneity into the membrane. In the present review we first describe the processes through which domains are generated, how they grow, and why they are rounded, striped or fractal-like, as well as why they get distributed forming defined patterns. Next, we focus on the effect of an additive on a lipid mixture, which usually induces shifts in demixing points, thus stabilizing or destabilizing the phase-segregated state. Results found for different model membranes are summarized, detailing the ways in which phase segregation and the generated patterns may be modulated. We focus on which are, from our viewpoint, the most relevant regulating factors affecting the surface texture observed in model membranes. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.

Spatial Rearrangement and Mobility Heterogeneity of an Anionic Lipid Monolayer Induced by the Anchoring of Cationic Semiflexible Polymer Chains

We use Monte Carlo simulations to investigate the interactions between cationic semiflexible polymer chains and a model fluid lipid monolayer composed of charge-neutral phosphatidyl-choline (PC), tetravalent anionic phosphatidylinositol 4,5-bisphosphate (PIP₂), and univalent anionic phosphatidylserine (PS) lipids. In particular, we explore how chain rigidity and polymer concentration influence the spatial rearrangement and mobility heterogeneity of the monolayer under the conditions where the cationic polymers anchor on the monolayer. We find that the anchored cationic polymers only sequester the tetravalent PIP₂ lipids at low polymer concentrations, where the interaction strength between the polymers and the monolayer exhibits a non-monotonic dependence on the degree of chain rigidity. Specifically, maximal anchoring occurs at low polymer concentrations, when the polymer chains have an intermediate degree of rigidity, for which the PIP₂ clustering becomes most enhanced and the mobility of the polymer/PIP₂ complexes becomes most reduced. On the other hand, at sufficiently high polymer concentrations, the anchoring strength decreases monotonically as the chains stiffen-a result that arises from the pronounced competitions among polymer chains. In this case, the flexible polymers can confine all PIP₂ lipids and further sequester the univalent PS lipids, whereas the stiffer polymers tend to partially dissociate from the monolayer and only sequester smaller PIP₂ clusters with greater mobilities. We further illustrate that the mobility gradient of the single PIP₂ lipids in the sequestered clusters is sensitively modulated by the cooperative effects between anchored segments of the polymers with different rigidities. Our work thus demonstrates that the rigidity and concentration of anchored polymers are both important parameters for tuning the regulation of anionic lipids.

Compositional redistribution and dynamic heterogeneity in mixed lipid membrane induced by polyelectrolyte adsorption: effects of chain rigidity

Monte Carlo simulation is employed to investigate the interaction between a polyelectrolyte and a fluid mixed membrane containing neutral (phosphatidyl-choline, PC), monovalent anionic (phosphatidylserine, PS), and multivalent anionic (phosphatidylinositol, PIP2) lipids. The effects of the intrinsic polyelectrolyte rigidity and solution ionic strength on the lateral rearrangement and dynamics of different anionic lipid species are systematically studied. Our results show that, the increase of polyelectrolyte chain rigidity reduces the loss of polyelectrolyte conformational entropy and the energy gains in electrostatic interaction, but raises the demixing entropy loss of the segregated anionic lipids. Therefore, the polyelectrolyte/membrane adsorption strength exhibits a non-monotonic dependence on the polyelectrolyte rigid parameter k ang, and there exists a certain optimal k ang for which the adsorption strength is maximal. Because the less loss of chain conformational entropy dominates the increase of the demixing entropy loss of the segregated anionic lipids and the decreases of the electrostatic energy gains, the semiflexible polyelectrolyte adsorbs onto the membrane more firmly than the flexible one. Whereas, for the adsorption of rigid polyelectrolyte, larger anionic lipid demixing entropy loss and less energy gain in the electrostatic interaction dominate over the decrease of the polyelectrolyte conformation entropy loss, leading to the desorption of the chain from the membrane. By decreasing the ionic concentration of the salt solution, the certain optimal k ang shifts to larger values. The cooperative effects of the adsorbing polyelectrolyte beads determine the concentration gradients and hierarchical mobility of the bound anionic lipids, as well as the polyelectrolyte dynamics.

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.

Dynamics and instabilities of lipid bilayer membrane shapes

Biological membranes undergo constant shape remodeling involving the formation of highly curved structures. The lipid bilayer represents the fundamental architecture of the cellular membrane with its shapes determined by the Helfrich curvature bending energy. However, the dynamics of bilayer shape transitions, especially their modulation by membrane proteins, and the resulting shape instabilities, are still not well understood. Here, we review in a unifying manner several theories that describe the fluctuations (i.e. undulations) of bilayer shapes as well as their local coupling with lipid or protein density variation. The coupling between local membrane curvature and lipid density gives rise to a 'slipping mode' in addition to the conventional 'bending mode' for damping the membrane fluctuation. This leads to a number of interesting experimental phenomena regarding bilayer shape dynamics. More importantly, curvature-inducing proteins can couple with membrane shape and eventually render the membrane unstable. A criterion for membrane shape instability is derived from a linear stability analysis. The instability criterion reemphasizes the importance of membrane tension in regulating the stability and dynamics of membrane geometry. Recent progresses in understanding the role of membrane tension in regulating dynamical cellular processes are also reviewed. Protein density is emphasized as a key factor in regulating membrane shape transitions: a threshold density of curvature coupling proteins is required for inducing membrane morphology transitions.

Monte Carlo simulation of protein-induced lipid demixing in a membrane with interactions derived from experiment

Lipid domain formation induced by annexin was investigated in mixtures of phosphatidylcholine (PC), phosphatidylserine (PS), and cholesterol (Chol), which were selected to mimic the inner leaflet of a eukaryotic plasma membrane. Annexins are ubiquitous and abundant cytoplasmic, peripheral proteins, which bind to membranes containing PS in the presence of calcium ions (Ca(2+)), but whose function is unknown. Prompted by indications of interplay between the presence of cholesterol in PS/PC mixtures and the binding of annexins, we used Monte Carlo simulations to investigate protein and lipid domain formation in these mixtures. The set of interaction parameters between lipids and proteins was assigned by matching experimental observables to corresponding variables in the calculations. In the case of monounsaturated phospholipids, the PS-PC and PC-Chol interactions are weakly repulsive. The interaction between protein and PS was determined based on experiments of annexin binding to PC/PS mixtures in the presence of Ca(2+). Based on the proposal that PS and cholesterol form a complex in model membranes, a favorable PS-Chol interaction was postulated. Finally, protein-protein favorable interactions were also included, which are consistent with observations of large, two-dimensional, regular arrays of annexins on membranes. Those net interactions between pairs of lipids, proteins and lipids, and between proteins are all small, of the order of the average kinetic energy. We found that annexin a5 can induce formation of large PS domains, coincident with protein domains, but only if cholesterol is present.

Multi-scale modeling in biology: how to bridge the gaps between scales?

Human physiological functions are regulated across many orders of magnitude in space and time. Integrating the information and dynamics from one scale to another is critical for the understanding of human physiology and the treatment of diseases. Multi-scale modeling, as a computational approach, has been widely adopted by researchers in computational and systems biology. A key unsolved issue is how to represent appropriately the dynamical behaviors of a high-dimensional model of a lower scale by a low-dimensional model of a higher scale, so that it can be used to investigate complex dynamical behaviors at even higher scales of integration. In the article, we first review the widely-used different modeling methodologies and their applications at different scales. We then discuss the gaps between different modeling methodologies and between scales, and discuss potential methods for bridging the gaps between scales.

Giant phospholipid/block copolymer hybrid vesicles: mixing behavior and domain formation

Lipids and block copolymers can be individually assembled into unsupported, spherical membranes (liposomes or polymersomes), each having their own particular benefits and limitations. Here we demonstrate the preparation of microscale, hybrid "lipopolymersomes" composed of the common lipid POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine) and the commercially available copolymer PBd-b-PEO (polybutadiene-b-poly(ethylene oxide)) with the goal of incorporating the advantageous qualities of the unitary systems into mixed-membrane capsules. We investigate the lipopolymersomes using confocal fluorescence microscopy and demonstrate that these hybrid membranes are well mixed on nanoscopic length scales within the permittable compositional windows for hybrid vesicle formation. We measure the intramembrane dynamics and mechanical properties of these hybrid membranes by fluorescence recovery after photobleaching (FRAP) and micropipet aspiration, respectively. For the first time, we demonstrate the demixing of lipid-rich and polymer-rich membrane domains within the same vesicle membrane. This is achieved by the biotinylation of one of the constituent species and cross linking with the protein NeutrAvidin. The resultant domain patterning is dependent upon which component carries the biotin functionality: cross linking of the copolymer species results in domains that ripen into a single, large, copolymer-rich island, and cross linking of the lipids yields many small, "spot-like", lipid-rich domains within a copolymer-rich matrix. We discuss these morphological differences in terms of the fluidity and mechanical properties of the membrane phases and the possible resultant interdomain interactions within the membrane. These heterogeneous hybrid lipopolymersomes could find applications in fields such as targeted delivery, controlled release, and environmental detection assays where these capsules possess the characteristics of biocompatible lipid membranes combined with enhanced mechanical strength and stability from the copolymer matrix.

Protein adsorption and desorption on lipid bilayers

The protein surface usually exhibits one or a few charged spots. If a lipid bilayer contains a significant amount of lipids with oppositely charged head groups, protein adsorption on a bilayer may be energetically favourable due to the protein-lipid electrostatic interaction. The specifics of this case are that the lipids are highly mobile and the protein adsorption is accompanied by the redistribution of lipids between the areas covered and not covered by protein. We present a kinetic model illustrating that this effect is especially interesting if the fraction of the surface covered by charged lipids is relatively low. In this situation, with increasing protein coverage, the protein desorption rate constant rapidly increases while the adsorption rate constant drops, so that there is critical fraction of the area covered by protein. Adsorption above this fraction is hindered both kinetically and thermodynamically.