The lateral stress profile of fluid lipid membranes as revealed by the diffuse interface approach

The distribution of lateral stress within a lipid bilayer is of fundamental biological interest as it regulates membrane-protein interactions, with a particular impact on mechanosensitive channels. At the same time, the lateral stress profile is thermodynamically related to the elastic constants governing the macroscopic behavior of membrane vesicles. Therefore, it is tempting to try to understand how macroscopic elastic constants affect stresses within the membrane, and vice versa. It has recently been shown that a diffuse interface description of the membrane captures key features of both the macroscopic scale and the few-nanometer scale of the bilayer thickness. The approach provides the lateral stress profile as a function of the macroscopic elastic constants, whereas, usually, the reverse procedure is used in molecular dynamics simulations to extract the constants from the measured profile. Here, the complete expression of the lateral stress profile of the diffuse interface is derived, also taking into account the case of membranes under tension. The profile turns out to be the superposition of several contributions that depend on the various elastic constants. We show that tension affects the Gaussian modulus of the bilayer, in agreement with independent arguments. The approach provides a correction to the second moment of the lateral stress comparable to that based on the monolayer-bilayer consistency relation. Finally, we discuss changes in the lateral stress profile due to the insertion of molecules within the membrane. Such changes play a crucial role in membrane-protein interactions, as they influence part of the work required to gate channels.