ABSTRACT
Passive or unassisted ion permeation through lipid bilayers involves a type of rare events by which cells regulate their salt concentrations and pH. It is important to understand its mechanism in order to develop technologies of, for example, delivering or maintaining small drug-like molecules inside cells. In earlier simulations of passive ion permeations, the commonly used sampling methods usually define the positions of ions relative to the membrane as a measure of permeation, i.e., the collective variable, ignoring the active participations of other particles. Newly defined collective variables involving the movements of ions, lipids, and water molecules allow us to identify the transition paths on the free energy landscape using the 2D umbrella sampling techniques. In this work, this technique was used to study the permeation processes of some well-known ions, sodium, potassium, and chloride. It is found permeations of sodium and potassium are assisted by important lipid bilayer deformations and massive water solvation, while chloride may not. Chloride may have two different possible pathways, in which the energetic favorable one is similar to the solubility-diffusion model. The free energy barriers for the permeation of these ions are in semiquantitative agreement with experiments. Further analyses on the distributions of oxygens and interaction energies suggest the electrostatic interactions between ions and polar headgroups of lipids may greatly influence membrane deformation as well as the water wire and furthermore the free energy barriers of waterwire mediated pathways. For chloride, the nonwaterwire pathway may be energetically favorable.
