Equilibrium properties of E. coli lactose permease symport-A random-walk model approach

The symport of lactose and H+ is an important physiological process in E. coli, for it is closely related to cellular energy supply. In this paper, we review, extend and analyse a newly proposed cotransport model that takes the "leakage" phenomenon (uncoupled particle translocation) into account and also satisfies the static head equilibrium condition. Then, we use the model to study the equilibrium properties, including equilibrium solution and the time required to reach equilibrium, of the symport process of E. coli LacY protein, when varying the parameters of the initial state of cotransport system. It can be found that in our extended model, H+ and lactose will reach their equilibrium state separately, and when "leakage" exists, it linearly affects the equilibrium solution, which is a useful property that the original model does not have. We later investigated the effect of the volume of periplasm and cytoplasm on the equilibrium properties. For a certain E. coli cell, as it continues to lose water and contract, the time for cytoplasm pH to be stabilized by symport increases monotonically when the cell survives. Finally, we reproduce the experimental data from a literature to verify the validity of the extension in this symport process. The above phenomena and other findings in this paper may help us to not only further validate or improve the model, but also deepen our understanding of the cotransport process of E. coli LacY protein.