Session W45: Focus Session: Soft Matter Physics of Heterogeneous Membranes - Theory and Simulation

Hybrid Lipids as Line Active Molecules

The lipid raft hypothesis suggests that stable nanoscopic domains in cellular membranes play an important role in several biological processes. Model membranes composed of saturated lipids, unsaturated lipids, and cholesterol (SUC membranes) exhibit coexisting chain-ordered and -disordered domains. However, these domains are unstable and the positive line tension at the interfaces between these domains drives coarsening until their size reaches of the order of the system size. This motivates the search for physical mechanisms that may reduce the line tension to zero and thus stabilize nanoscopic domains in biological membranes. There is a theoretical suggestion that the positive line tension at the interfaces between domains in SUC membranes results from the chain packing incompatibility between the ordered chains of saturated lipids and the disordered chains of unsaturated lipids. Hybrid lipids that have one saturated and one unsaturated chains may reconcile this chain packing incompatibility. We have used a phenomenological model to predict that a small concentration of hybrid lipids added to SUC membranes can reduce the line tension between coexisting domains to zero. However, this tends to occur only at low temperatures that may not be experimentally accessible, because localizing the hybrid lipids to the interfaces costs mixing entropy and this strongly suppresses the reduction of the line tension. Indeed, hybrid lipids are major components of biological membranes; unsaturated lipids are rather minor and uncommon. We have used a liquid crystal model to analyze the phase separation and line tension between domains in model membranes composed of saturated lipids, hybrid lipids, and cholesterol (SHC membranes). This model predicts that the line tension is reduced to zero at relatively higher in SHC membranes because the hybrid lipids are already at the interface and the mixing entropy of localization is no longer relevant.   

Turing Patterns on Curved Surfaces

Surface curvature modifies the emergence of Turing patterns in reaction-diffusion systems on two-dimensional interfaces. We adapt operator perturbation theory, familiar in quantum mechanics, to determine how curvature affects diffusion. When these modifications are taken into account in Turing's stability analysis, we observe new phenomena that may be relevant to patterning on cell membranes, neuron synapses, and fluid interfaces with reactive surfactants. A cylinder with longitudinal ripples illustrates how Turing patterns can lock into phase with the ripples when the most unstable mode is nearly commensurate with the ripples. The framework we introduce also sheds light on diffusion constrained to a rippled sphere, a Gaussian bump, and other shapes. More generally, it is relevant to any model that involves the Laplacian on a curved manifold.   

2D Ising Model correlation function: Precise functional forms for comparison to membrane experiments

We find a precise form for the 2D Ising correlation function in the entire scaling regime as a function of external field $H$ and temperature $T$. It is surprising that there is no functional form available, perhaps explained by the surprising complexity of the universal scaling function compared to other statistical mechanics models (e.g. 2D free energy or 3D Ising correlation function). We can use these results to test the hypothesis that heterogeneities found in a wide variety of membrane systems are manifestations of an underlying Ising critical point. We fit Monte Carlo lattice simulations in the $(H,T)$-plane with a functional form in parametric coordinates, while matching analytical results at $H=0$ and $T=T_c$ to high accuracy. This functional form allows us to interpret FRET, NMR, or ESR data from membranes, where we can map experimentally controllable variables of composition and temperature onto the Ising axes of reduced temperature and magnetization.   

Fluctuating Lipid Bilayer Membranes With Diffusing Protein Inclusions: Hybrid Continuum-Particle Model

Many proteins through their geometry and specific interactions with lipids induce changes in local membrane material properties. This can manifest in local stiffness variations and locally induced curvatures that track protein location. To study such phenomena we introduce a new hybrid continuum-particle description for the membrane-protein system that incorporates protein interactions, hydrodynamic coupling, and thermal fluctuations. We investigate how protein curvature and membrane stiffness influences protein diffusion. We discuss how collective protein effects influence membrane mechanical properties, such as the spectrum of membrane bending fluctuations and the effective elastic bending modulus of the heterogeneous protein-lipid membrane. Finally, we discuss possible roles of the membrane fluctuations influencing the distribution of proteins within the membrane.   

Influence of chain rigidity on the conformation of model lipid membranes in the presence of cylindrical nanoparticle inclusions

We employ real-space self-consistent field theory to study the conformation of model lipid membranes in the presence of solvent and cylindrical nanoparticle inclusions (''peptides''). Whereas it is common to employ a polymeric Gaussian chain model for the lipids, here we model the lipids as persistent, worm-like chains. Our motivation is to develop a more realistic field theory to describe the action of pore-forming anti-microbial peptides that disrupt the bacterial cell membrane. We employ operator-splitting and a pseudo-spectral algorithm, using SpharmonicKit for the chain tangent degrees of freedom, to solve for the worm-like chain propagator. The peptides, modelled using a mask function, have a surface patterned with hydrophobic and hydrophillic patches, but no charge. We examine the role chain rigidity plays in the hydrophobic mismatch, the membrane-mediated interaction between two peptides, the size and structure of pores formed by peptide aggregates, and the free-energy barrier for peptide insertion into the membrane. Our results suggest that chain rigidity influences both the pore structure and the mechanism of pore formation.   

Mechanics, morphology, and mobility in stratum corneum membranes

The stratum corneum is the outermost layer of skin, and serves as a protective barrier against external agents, and to control moisture. It comprises keratin bodies (corneocytes) embedded in a matrix of lipid bilayers. Unlike the more widely studied phospholipid bilayers, the SC bilayers are typically in a gel-like state. Moreover, the SC membrane composition is radically different from more fluid counterparts: it comprises single tailed fatty acids, ceramides, and cholesterol; with many distinct ceramides possessing different lengths of tails, and always with two tails of different lengths. I will present insight from computer simulations into the morphology, mechanical properties, and diffusion (barrier) properties of these highly heterogeneous membranes. Our results provide some clue as to the design principles for the SC membrane, and is an excellent example of the use of wide polydispersity by natural systems.   

Curvature-driven domain formation in ternary lipid membranes

We model vesicles formed by three-component fluid membranes whose components have differing spontaneous curvatures. We use Monte Carlo simulated annealing to find low energy configurations for a range of component characteristics. A wide variety of ordered structures are found, including highly symmetric structures with elongated domains resembling faceted edges. We also observe an effective attraction between components of highest and lowest spontaneous curvature. We relate these effects to the interplay of spontaneous curvature and underlying geometric constraints. Our results suggest that the composition-shape coupling can be an important mechanism in the formation of highly ordered structures in many-component membranes.   

Entropy driven aggregation of adhesion sites of supported membranes

Supported lipid membranes are useful and important model systems for studying cell membrane properties and membrane mediated processes. One attractive application of supported membranes is the design of phantom cells exhibiting well defined adhesive properties and receptor densities. Adhesion of membranes may be achieved by specific and non-specific interactions, and typically requires the clustering of many adhesion bonds into ``adhesion zones''. One potential mediator of the early stages of the aggregation process is the Casimir-type forces between adhesion sites induced by the membrane thermal fluctuations. In the talk, I will present a theoretical analysis of fluctuation induced aggregation of adhesion sites in supported membranes. I will first discuss the influence of a single attachment point on the spectrum of membrane thermal fluctuations, from which the free energy cost of the attachment point will be deduced. I will then analyze the problem of a supported membrane with two adhesion points. Using scaling arguments and Monte Carlo simulations I will demonstrate that two adhesion points attract each other via an infinitely long range effective potential that grows logarithmically with the pair distance. Finally, I will discuss the many-body nature of the fluctuation induced interactions. I will show that while these interactions alone are not sufficient to allow the formation of aggregation clusters, they greatly reduce the strength of the residual interactions required to facilitate cluster formation. Specifically, for adhesion molecules interacting via a short range attractive potential, the strength of the direct interactions required for aggregation is reduced by about a factor of two to below the thermal energy kT.   

Membrane lateral structure: How immobilized particles can stabilize small domains

Membranes are two-dimensional fluid environments, consisting of lipids and proteins. In model membranes, macroscopic phase separation is routinely observed, but not so in biological membranes. Instead, the lateral structure of a biological membrane is characterized by small domains. This poses an interesting puzzle because a structure of small domains inevitably implies a large amount of interface, which is unfavorable because of line tension. In this contribution, it is shown that immobilized protein obstacles provide a mechanism to compensate the cost of line tension. The presence of such obstacles in biological membranes is known to occur (arising for instance from interactions with the underlying cytoskeleton). We present results from computer simulation, which indeed show that a structure of small domains becomes stable, already at a low concentrations of quenched obstacles. In addition, these results confirm a fundamental conjecture of de Gennes, stating that a fluid with quenched obstacles belongs to the universality class of the random-field Ising model.   

In-Plane Dynamics of Membranes with Immobile Inclusions

Cell membranes are anchored to the cytoskeleton via immobile inclusions. We investigate the effect of such anchors on the in-plane dynamics of a fluid membrane and mobile inclusions embedded in it. The immobile particles lead to a decreased diffusion coefficient of mobile ones and suppress the correlated diffusion of particle pairs. Due to the long-range, quasi-two-dimensional nature of membrane flows, these effects become significant at a low area fraction (below one percent) of immobile inclusions.   

Charge correlations in multicomponent ionic crystalline membranes

We investigate the dissociation state of a polyelectrolyte membrane with charged head groups in solution. This state depends on the salt concentration and pH of the solution, but spatial correlations also highly influence it. Spatial correlations are typically neglected in these systems, as they are difficult to treat analytically, but they can qualitatively alter the results. We numerically incorporate charge correlations on both flat and curved membranes by simulating a multicomponent system on a fluctuating network with electrostatic interactions, using the replica exchange Monte Carlo approach. The salt-induced screening effects are modeled within the Debye-Huckel theory. For weak enough screening, we find a strong suppression of dissociation regardless of pH, and the membrane may exhibit a reentrant structural phase transition as pH is varied.