Theory of slow-motion EPR lineshapes for studies of membrane curvature

Abstract

The direct calculation method of slow-motion EPR spectra is presented based on the stochastic Liouville equation in the Langevin form, using the trajectories of Brownian dynamics (BD) simulations. We have developed a model of EPR slow-motion lineshapes describing a probe molecule residing in a curved bilayer system. Two dynamic processes are active: one is local reorientation motion of the lipid chain, and the second is the lateral diffusion of the spin probe along the curved lipid bilayer surface. The trajectories of two independent BD simulations are combined in order to describe the stochastic fluctuation of the electron spin–lattice Hamiltonian. The method of obtaining the Langevin equation describing lateral diffusion from the diffusion equation is discussed in detail. We solve the stochastic Liouville–von Neumann equation in the semiclassical approximation. EPR slow-motion lineshapes are obtained together with electron spin correlation functions. The synthesis of classical simulation methods and the lineshape model is illustrated by calculating a number of curvature dependent EPR lineshapes. Two curved model surfaces are considered namely the rippled z=a sin(bx) surface and the so called “Baltic Sea” z=a[sin(bx)+sin(by)].