Area per molecule in a DPPC-Cholesterol bilayers depends non-linearly on the cholesterol concentration. Using flexible strings model of lipid membranes we calculate area per molecule in DPPC-Cholesterol mixtures in the biologically relevant concentra
tions range. Few parameters of the model are optimized for a perfect agreement with the area per lipid data available from molecular dynamics simulations. Lateral pressure at the hydrophilic interface, {gamma}, is taken to be proportional to the cholesterol concentration. Non-linearity arises as a consequence of the non-linear dependence of thermodynamical equilibrium area of molecules on {gamma}. DPPC lipid is modeled as flexible string of finite thickness and a given bending rigidity, while cholesterol molecule is modeled as rigid rod with finite thickness and infinite rigidity. Using parameters fitted to reproduce area per molecule dependence on cholesterol concentration, we had further calculated our model predictions for the NMR order parameter of DPPC lipid chains and coefficient of thermal area expansion. The microscopic nature of the model allows to consider a broad range of thermodynamic phenomena.
Critical lateral pressure for a pore formation and phase diagram of porous membrane are derived analytically as functions of the microscopic parameters of the lipid chains. The derivation exploits path-integral calculation of the free energy of the e
nsembles of semi-flexible strings and rigid rods that mimic the hydrophobic tails of lipids in the lipid bilayers and bolalipid membranes respectively. Analytical expressions for the area stretch/compressibility moduli of the membranes are derived in both models.
