Bilayer permeability during phase transition as an Erlang flow of hydrophilic pores resulting from diffusion in the radius space

Abstract

The formation of hydrophilic pores in a lipid bilayer during phase transition is described using the Smoluchowski equation with an additional term of the hydrophobic pore source. This term is added to account for defects in lipid packing during phase transition. We assume that the temporal sequence of the pores is a stochastic process, a non-stationary second-order Erlang flow. Flow characteristics depend on the equation solution and determine the formation times of the hydrophilic pores. The calculated distribution of the durations of intervals between hydrophilic pores is in a good agreement with experimental data published before. In the context of this model we describe the influence of poly(ethylene glycol) on the pore formation frequency.