A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional volumes. Calculations of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with experimental measurements is obtained. Strengths and weaknesses of the PNP approach are discussed.

A dynamic lattice Monte Carlo (DLMC) simulation approach to the description of ion transport in dielectric environments is presented. Conventional approaches using periodic boundary conditions are inefficient for nonequilibrium situations in inhomogeneous systems. Instead, the simulated system is embedded in a bigger system that determines the average electrostatic potential and the ionic concentrations at its boundaries. Two issues are of special importance: implementing the given boundary conditions in the treatment of dynamical processes at and near the boundaries, and efficient evaluation of ion-ion interaction in the heterogeneous dielectric medium during the Monte Carlo simulation. The performance of the method is checked by comparing numerical results to exact solutions for simple geometries, and to mean field (Poisson-Nernst-Planck, PNP) theory in a system where the latter should provide a reasonable description. Other examples in which the PNP theory fails in various degrees are shown and discussed. In particular, PNP results deviate considerably from the DLMC dynamics for ion transport through rigid narrow membrane channels with large disparity between the dielectric constants of the protein and the water environments.

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 Å) studied.

Nitric oxide (NO) acts as a signal molecule in the nervous system, as a defense against infections, as a regulator of blood pressure, and as a gate keeper of blood flow to different organs. In vivo, it is thought to have a lifetime of a few seconds. Therefore, its direct detection at low concentrations is difficult. We report on a new type of hybrid, organic-semiconductor, electronic sensor that makes detection of nitric oxide in physiological solution possible. The mode of action of the device is described to explain how its electrical resistivity changes as a result of NO binding to a layer of native hemin molecules. These molecules are self-assembled on a GaAs surface to which they are attached through a carboxylate binding group. The new sensor provides a fast and simple method for directly detecting NO at concentrations down to 1 microM in physiological aqueous (pH=7.4) solution at room temperature.