Solvent-free simulations of heterogeneous lipid bilayers

Two molecular implicit solvent models for fluid lipid bilayers are presented. The first represents lipids by rigid, asymmetric, soft spherocylinders. The three parameter potential between pairs of lipids gives rise to micelles, fluid bilayers, and gel-like bilayers. Fluid bilayers have compressibility moduli in agreement with experimental systems but display bending moduli at least three times larger than typical biological membranes without cholesterol. The second three parameter model represents lipids by flexible chains of beads; the hydrophobic effect is mimicked through a soft pair potential localized at the interface between hydrophobic and hydrophilic beads. Fluid bilayers composed of these molecules have both compressibility moduli and elastic moduli in agreement with experimental systems, as well as realistic interfacial tensions and stress profiles. Monte Carlo simulations are used to demonstrate self-assembly for both models.; Phase behavior is studied for bilayers composed of the rigid model. Regions of solid, "hexatic", and fluid bilayer behavior are established by identification of phase boundaries. The main melting transition is found to be density driven; the melting temperature scales inversely with lipid length since thermal expansion increases with lipid aspect ratio. A plausible sub-transition is identified for longer molecules. The dependence of membrane elasticity on bilayer thickness is obtained by adjusting the length of the rigid molecules at constant temperature and surface tension. The bending modulus scales with the square of the membrane thickness, as expected, but the proportionality constant is an order of magnitude smaller than expected using continuum elastic theories or measured by experiments. The proportionality constant is found to be non-monotonic for bilayers composed of multiple lipid species; the thinnest membranes are not the most flexible. This is shown to be quantitatively consistent with the random quadratic mixing behavior of the model lipids.; We present an elastic Hamiltonian for membrane energetics that captures bilayer undulation and peristaltic deformations over all wavelengths, including the short wavelength protrusion regime. The model implies continuous functional forms for thermal undulation and peristaltic amplitudes as a function of wavelength and predicts previously overlooked relationships between these curves. Undulation and peristaltic spectra display excellent agreement with data from both atomistic and coarse-grained models over all simulated length scales. Additionally, the model accurately predicts the bilayer's response to a range of both positively and negatively mismatched cylindrical "protein" inclusions as observed in coarse-grained simulation. This elastic response provides an explanation for gramicidin ion channel lifetime vs. membrane thickness data that requires no fit constants. The physical parameters inherent to this picture may be expressed in terms of familiar material properties associated with lipid monolayers. Inclusion of a finite monolayer spontaneous curvature, a finite monolayer Gaussian curvature modulus, and accounting for lipid volume changes on the boundary of the inclusion are essential to obtain fully consistent agreement between theory and the full range of available simulation/experimental data.