2013/01/07 by Mikucki, Michael, Zhou, Y. C.
#35J #35Q #49S #82B #82D #92C #Analysis of PDEs (math.AP) #Biomolecules (q-bio.BM) #FOS: Biological sciences #FOS: Mathematics
paper · doi:10.48550/arxiv.1301.1104
Simulating protein-membrane interactions is an important and dynamic area of research. A proper definition of electrostatic forces on membrane surfaces is necessary for developing electromechanical models of protein-membrane interactions. Here we modeled the bilayer membrane as a continuum with general continuous distributions of lipids charges on membrane surfaces. A new electrostatic potential energy functional was then defined for this solvated protein-membrane system. We investigated the geometrical transformation properties of the membrane surfaces under a smooth velocity field. These properties allows us to apply the Hadamard-Zolesio structure theorem, and the electrostatic forces on membrane surfaces can be computed as the shape derivative of the electrostatic energy functional.