Lateral pressure profile in lipid membranes with curvature: Analytical calculation

An analytical expression is obtained for the lateral pressure profile in the hydrophobic part of a lipid bilayer of finite curvature. Calculations are carried out within a microscopic model of a lipid bilayer, according to which the energy of a lipid chain represents the energy of a flexible string of finite thickness and the interaction between lipid chains is considered as a steric (entropic) repulsion. This microscopic model allows one to obtain an expression for the distribution of lateral pressure in membranes with given curvature if one considers the bending of a membrane as a small deviation from a flat conformation and applies perturbation theory in the small parameter L ₀ J, where L ₀ is the hydrophobic thickness of a monolayer and J is the mean curvature of the lipid bilayer. The resulting pressure profile depends on the microscopic parameters of the lipid chain: the bending modulus of the lipid chain, incompressible area per lipid chain, and the thickness of a flat monolayer. The coefficient of entropic repulsion between lipids is calculated self-consistently. The analytical results obtained for the lateral pressure distribution are in qualitative agreement with molecular dynamic simulations.