First moment of lateral pressure in lipid membrane: theoretical calculation

Analytical expression for the first moment of lateral pressure in a flat and bent membrane has been represented in this study. The calculation was carried out within the microscopic model of lipid bilayer. Macroscopic parameters of lipid membrane in this model (partial function, free energy, bending modulus, lateral pressure and so on) may be expressed through the microscopic parameters of the lipid chain (area per chain, length, bending rigidity of lipid). Lateral pressure profile in a lipid bilayer is a distribution of the entropic repulsion between neighboring lipid chains by membrane thickness. Lateral pressure in a bent bilayer is a very important characteristic of lipid membrane because it influences on membrane elastic constants. And although bending modulus is a well-known feature, little is known about the position of neutral surface (non-expanded surface). Moreover, analytical expression for lateral pressure in the bent bilayer is connected to the expression of mixed deformation modulus (bending with stretching). Its zero value indicates the case of pure bending and relaxation of neutral surface. In contradistinction to membrane with curvature the first moment of lateral pressure in a flat membrane (so named spontaneous bending moment) is significantly affected on membrane protein activity because it is related with macroscopic characteristic - inter-facial surface tension. So, the microscopic theory represented in this article enables calculation of bending modulus for lipid bilayer, bending modulus for lipid monolayer, area stretching modulus, bending-stretching modulus, spontaneous bending moment for lipid monolayer and also defining the position of neutral surface.