The purpose of this project is to investigate the physical mechanisms by which the lipid membrane influences the protein functions that underlie most biological processes. A typical project in the lab identifies a hypothesis for a particular mechanism in conceptual terms, forms a mathematical or physical model for the process, then tests and refines the model using a molecular simulation. Next the project is developed to make predictions that can be tested in the laboratory. The projects use the NIH Biowulf computing cluster to run the simulations and models. Molecular dynamics software (such as NAMD and CHARMM) are used to conduct molecular simulations. In-house software development for public distribution is a key element of the lab. A number of projects have been developed this year. 1) In this first project, we justify a new hypothesis for how cholesterol partitions between the outer and inner leaflets of the plasma membrane. We consider the plasma membrane that contains a cholesterol molar fraction of 0.4 and ask how that cholesterol is distributed between the two leaves. Because of the rapid flip-flop of cholesterol between leaves, we assume that its distribution is determined by the equality of its chemical potentials in the two leaves. When we consider only the contributions of entropy and interactions to the cholesterol chemical potential in our model system, we find, not surprisingly, that the cholesterol is mostly in the outer leaf because of the strong attraction between cholesterol and sphingomyelin (SM), which is predominantly in that leaf. We find 72% there. We then include the contribution from the bending energy in each leaf that must be overcome to join the leaves in a flat bilayer. The product of bending modulus and spontaneous curvature is obtained from simulation. We find that the addition of cholesterol to the outer leaf reduces the spontaneous curvature, which is initially positive, until it passes through zero when the molar fraction of cholesterol in the outer leaf is 0.28. Additional cholesterol is driven toward the inner leaf by the sphingomyelin phosphatidylcholine mixture. This is resisted by the bending energy contribution to the inner leaf. We find, again by simulation, that the addition of cholesterol monotonically increases the magnitude of the spontaneous curvature of the inner leaf, which is negative. This increases its bending energy. We conclude that as a result of these competing effects, the percentage of cholesterol in the outer leaf is reduced to ca. 63%. 2) In this project, in collaboration with Prof. Margaret Johnson of Johns Hopkins University, we developed a new software method for simulating lipids on continuum surfaces. This project included contributions from the summer intern program. Localization of proteins to a membrane is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion methods offer a powerful tool for capturing lipid-specific binding to membrane surfaces by treating lipids explicitly as individual diffusible binding sites. However, modeling lipid particle populations is expensive. Here we present an algorithm for reversible binding of proteins to continuum surfaces with implicit lipids, providing dramatic speed-ups to many body simulations. Our algorithm can be readily integrated into most reaction-diffusion software packages. We characterize changes to kinetics that emerge from explicit versus implicit lipids as well as surface adsorption models, showing excellent agreement between our method and the full explicit lipid model. Compared to models of surface adsorption, which couple together binding affinity and lipid concentration, our implicit lipid model decouples them to provide more flexibility for controlling surface binding properties and lipid inhomogeneity, and thus reproducing binding kinetics and equilibria. Crucially, we demonstrate our methods application to membranes of arbitrary curvature and topology, modeled via a subdivision limit surface, again showing excellent agreement with explicit lipid simulations. Unlike adsorption models, our method retains the ability to bind lipids after proteins are localized to the surface (through e.g. a protein-protein interaction), which can greatly increase stability of multi-protein complexes on the surface. Our method will enable efficient cell-scale simulations involving proteins localizing to realistic membrane models, which is a critical step for predictive modeling and quantification of in vitro and in vivo dynamics. 3) In this third project we tackled a challenging problem in membrane-regulated protein diffusion: How to propagate surface-bound particles in a way that is consistent with their mechanism of attachment to the membrane. We described two methods for propagating coupled membrane and embedded particle dynamics with ensembles valid to second order in the deformation of the membrane. Proteins and functional lipids associate with cellular membranes, and their attachments influence membrane physical and dynamical properties. Therefore it is necessary to accurately model the coupled dynamics of the membrane and any associated material of interest. We have developed two methods for coupling membrane and particle dynamics that differ in the binding mechanism of the particle to the surface. The on-surface mechanism should be used for particles that slide along the membrane; this description leads to an effective reduction of the membrane surface tension. The in-surface mechanism treats the particles as tightly bound to the lipidic binding sites; the method avoids double counting lateral entropy of implicitly modeled lipids. We emphasize the differences between these two mechanisms, when it is appropriate to use them, and how the methods differ from previously used dynamic methods.
