Erlang flow of hydrophilic pore formation and closure events in a lipid bilayer during phase transition resulting from diffusion in the radius space

The Smoluchowski equation with an energy profile of a special type and an assumed hydrophobic ("half") pore source term is used to describe the process of hydrophilic pore formation in a lipid bilayer at the gel-liquid phase transition. The source term reflects the occurrence of molecule packing defects in a lipid bilayer at phase transition. The time sequences of the pore formation and closure events are treated as non-stationary, second-order Erlang flows whose characteristics depend on the equation solution. The computed distributions of the time intervals between hydrophilic pores, and pore lifetimes agree with the previously published experimental interpulse interval and pulse duration histograms for the current fluctuations through planar bilayer membranes of DPPC immersed in a LiCl aqueous solution containing polyethylene glycol. Thus, the statistical analysis of pore formation and closure times leads us to conclude that firstly, the increased permeability of a lipid bilayer during the gel-liquid phase transition is accounted for by the emergence of additional hydrophobic defects in the heterogeneous structure of the bilayer and secondly, that the non-exponential distributions of the lipid channel closed and open times observed in experiments are evidence that the process of hydrophilic pore formation is not a one-step process but involves at least two dependent events.