Analytical Calculation of the Bending Modulus in a Lipid Membrane: Revisiting Existing Theory

Abstract: This work analytically calculates the first moment of lateral pressure in a bent bilayer using a model that treats lipid molecules as flexible elastic chains. The key point is that lateral pressure in a curved lipid membrane influences membrane elastic constants, particularly the bending modulus, which is related to lateral pressure through its first moment. Although the bending modulus is well known, little is known about its theoretical estimate. The microscopic model presented here enables calculation of the bending modulus for the lipid bilayer, the bending modulus for the lipid monolayer, an area-stretching modulus, a bending-stretching modulus, the spontaneous bending moment for the lipid monolayer, and the position of the neutral surface (non-expanded surface). We obtain these theoretical estimates from an analytical expression for the first correction to the lateral pressure profile in the bent lipid membrane, calculated using a well-known condensed-matter-physics method: perturbation theory in the small parameter L0J, where L0 is the unperturbed monolayer thickness, and J is the curvature. The results are compared with available data and fall within the range of experimental values and molecular dynamics data.