Thermodynamically consistent stochastic models for active transmembrane transport processes.

Abstract

Simulating the full transport cycle of an active transporter driven an ionic electrochemical transmembrane gradient with atomistic detail has been challenging because full cycle completions occur on typical time scales ranging from milliseconds to seconds, out of reach of typical molecular dynamic (MD) simulations. Instead, multiscaling approaches have been developed that break the cycle into elementary steps for which kinetic and equilibrium parameters can be obtained from MD. These parameters are combined in a stochastic kinetic model whose master equation is solved under varying external conditions such as ion concentrations and membrane potential. We developed two improvements for this well-known approach: (1) We introduce the multibind algorithm to derive thermodynamically consistent state free energies and rates from input free energy differences and rates; without such a step, a kinetic model is not guaranteed to obey the laws of thermodynamics and may produce nonsensical results. We also show how the resulting model can be used for parameter inference of microscopic parameters from macroscopic experimental measurements. (2) As an alternative to the numerical solution of the steady state problem, one can exactly solve it using Hill's diagrammatic approach. Our Kinetic Diagram Analysis (KDA) implementation of Hill's method yields symbolic rational expressions for arbitrary kinetic graphs that can be analytically manipulated and directly evaluated. We demonstrate the kinetic graph multiscale approach for sodium/proton antiporters.