Comparison of dynamic lattice Monte Carlo simulations and the dielectric self-energy Poisson-Nernst-Planck continuum theory for model ion channels

Simulations of ion permeation through narrow model cylindrical channels are carried out using a dynamic lattice Monte Carlo (DLMC) algorithm (equivalent to high friction Langevin dynamics) for the time evolution of the ions in the system on the basis of a careful evaluation of the electrostatic forces acting upon each particle. To mimic the process of ion transport through protein channels, the cylindrical channel is embedded in a dielectric slab (representing a lipid bilayer membrane). The protein/membrane structure is taken to be rigid, and the water solvent is treated as a dielectric continuum. Results of these simulations are compared to corresponding results obtained via Poisson-Nernst-Planck (PNP) theory. In the PNP approach, the mobile ions are treated as a continuous charge density, and the electrostatic force on each ion is treated in an approximate fashion. Significant differences between DLMC and PNP results are found, with the degree of discrepancy increasing as the radius of the ion channel is reduced. A major source of error is traced to the neglect in the effective PNP potential of the dielectric self-energy (DSE), which is due to the interaction of each permeant ion with the dielectrically inhomogeneous environment provided by the water/channel/membrane system. When this static single-particle potential is precalculated and added to the effective potential used in PNP theory, substantial improvement in the quality of the results for current-voltage curves and steady-state concentrations is obtained. In fact, the results obtained by this approach, termed dielectric self-energy Poisson-Nernst-Planck (DSEPNP) theory, agree nearly quantitatively with DLMC simulation results over the entire range of channel radii (4-12 Angstrom) studied.