Generating Concentration Gradients across Membranes for Molecular Dynamics Simulations of Periodic Systems

Abstract

The plasma membrane forms the boundary between a living entity and its environment and acts as a barrier to permeation and flow of substances. Several computational means of calculating permeability have been implemented for molecular dynamics (MD) simulations-based approaches. Except for double bilayer systems, most permeability studies have been performed under equilibrium conditions, in large part due to the challenges associated with creating concentration gradients in simulations utilizing periodic boundary conditions. To enhance the scientific understanding of permeation and complement the existing computational means of characterizing membrane permeability, we developed a non-equilibrium method that enables the generation and maintenance of steady-state gradients in MD simulations. We utilize PBCs advantageously by imposing a directional bias to the motion of permeants so that their crossing of the boundary replenishes the gradient, like a previous study on ions. Under these conditions, a net flow of permeants across membranes may be observed to determine bulk permeability by a direct application of (Formula presented.). In the present study, we explore the results of its application to an exemplary (Formula presented.) and POPC bilayer system, demonstrating accurate and precise permeability measurements. In addition, we illustrate the impact of permeant concentration and the choice of thermostat on the permeability. Moreover, we demonstrate that energetics of permeation can be closely examined by the dissipation of the gradient across the membrane to gain nuanced insights into the thermodynamics of permeability.