Inducing concentration gradients across the membrane in molecular dynamics simulations to investigate membrane permeability.

Abstract

Membranes compartmentalize cells and their intracellular components, endowing cells with control over the local concentrations of metabolites. As a matter of fact, most ions and substrates maintain an electrochemical gradient across the membranes. Replicating such gradients in molecular dynamic (MD) simulations, which very often use periodic boundary conditions (PBC), is challenging. Here we introduce a novel, non-equilibrium technique for MD simulations which enables one to generate a sustained concentration gradient across the membrane and directly calculate permeability using the relation derived from Fick's first law, J=P(Δ;C). We generate concentration gradients by unidirectionally biasing targeted permeants near the periodic boundaries forcing them into the next periodic image without directly influencing permeants in the vicinity of the membrane. We used O2 to evaluate the method with a thorough statistical treatment through block averaging. We validated our technique on an exemplary POPC membrane, with calculated O2 permeabilities in agreement with published experimental and computational values. Our method yielded a permeability of P = 13.32 ± 2.22 cm/s for a system with a solution-phase concentration of [O2] = 19.2 mM using the CSVR thermostat over the course of a microsecond simulation. We found that the permeant concentration significantly alters the calculated permeability (P = 6.35 ± 4.86 cm/s for [O2] = 174 µM versus P = 23.8 ± 2.71 cm/s for [O2] = 153 mM). The thermostat choice also affected the permeability with the Langevin thermostat reducing permeability (P = 11.38 ± 2.78 cm/s; [O2] = 20.0 mM) as it fails to conserve momentum. By using its fundamental definition, we can robustly determine bulk permeability of membranes using our concentration gradient method, even those containing proteins which we intend to study in future work.