Rob D. Coalson

A Lattice Relaxation Algorithm for Three-Dimensional Poisson-Nernst-Planck Theory with Application to Ion Transport through the Gramicidin A Channel

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.

Molecular Basis for Cation Selectivity in Claudin-2―based Paracellular Pores: Identification of an Electrostatic Interaction Site

Paracellular ion transport in epithelia is mediated by pores formed by members of the claudin family. The degree of selectivity and the molecular mechanism of ion permeation through claudin pores are poorly understood. By expressing a high-conductance claudin isoform, claudin-2, in high-resistance Madin-Darby canine kidney cells under the control of an inducible promoter, we were able to quantitate claudin pore permeability. Claudin-2 pores were found to be narrow, fluid filled, and cation selective. Charge selectivity was mediated by the electrostatic interaction of partially dehydrated permeating cations with a negatively charged site within the pore that is formed by the side chain carboxyl group of aspartate-65. Thus, paracellular pores use intrapore electrostatic binding sites to achieve a high conductance with a high degree of charge selectivity.

Partial averaging approach to Fourier coefficient path integration

The recently introduced method of partial averaging is developed into a general formalism for computing simple Cartesian path integrals. Examples of its application to both harmonic and anharmonic systems are given. For harmonic systems, where analytical results can be derived, both imaginary and complex time evolution is discussed. For two representative anharmonic systems, Monte Carlo path integral simulations of the imaginary time propagator (statistical density matrix) are presented. Connections with other Cartesian path integral techniques are stressed.

A nonequilibrium golden rule formula for electronic state populations in nonadiabatically coupled systems

A formula for computing approximate leakage of population from an initially prepared electronic state with a nonequilibrium nuclear distribution to a second nonadiabatically coupled electronic state is derived and applied. The formula is a nonequilibrium generalization of the familiar golden rule, which applies when the initial nuclear state is a rovibrational eigenstate of the potential energy surface associated with the initially populated electronic state. Here, more general initial nuclear states are considered. The resultant prescription, termed the nonequilibrium golden rule formula, can be evaluated via semiclassical procedures and hence applied to multidimensional, e.g., condensed phase systems. To illustrate its accuracy, application is made to a spin–boson model of ‘‘inner sphere’’ electron transfer. This model, introduced by Garg et al. [J. Chem. Phys. 83, 4491 (1985)] for the nonadiabatic transition out of a thermal distribution of states in the initial (donor) electronic level, is extended to...

Extended wave packet dynamics; exact solution for collinear atom, diatomic molecule scattering☆

Abstract The semiclassical wave packet dynamics method of Heller is extended to provide a formally exact theory of quantum mechanical motion for multidimensional anharmonic systems by introducing a complete, orthonormal, time-dependent basis of generalized oscillator functions. The exact wavefunction is expressed in terms of this basis and the expansions are shown to develop according to linear, coupled first-order differential equations. Application to collinear inelastic atom-diatomic molecule scattering demonstrates the feasibility and convergence of the new method.

On the connection between Fourier coefficient and Discretized Cartesian path integration

The relationship between so‐called Discretized and Fourier coefficient formulations of Cartesian path integration is examined. In particular, an intimate connection between the two is established by rewriting the Discretized formulation in a manifestly Fourier‐like way. This leads to improved understanding of both the limit behavior and the convergence properties of computational prescriptions based on the two formalisms. The performance of various prescriptions is compared with regard to calculation of on‐diagonal statistical density matrix elements for a number of prototypical 1‐d potentials. A consistent convergence order among these prescriptions is established.

The Role of the Dielectric Barrier in Narrow Biological Channels: A Novel Composite Approach to Modeling Single-Channel Currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory.

Poisson-Nernst-Planck theory approach to the calculation of current through biological ion channels

The Poisson-Nernst-Planck (PNP) theory of electro-diffusion is reviewed. Techniques for numerical solution of the three-dimensional PNP equations are summarized, and several illustrative applications to ion transport through protein channels are presented. Strengths and weaknesses of the theory are discussed, as well as attempts to improve it via increasingly realistic evaluation of the force acting on each ion due to the protein/membrane environment.

Three-dimensional dynamic Monte Carlo simulations of driven polymer transport through a hole in a wall

Three-dimensional dynamic Monte Carlo simulations of polymer translocation through a cylindrical hole in a planar slab under the influence of an external driving force are performed. The driving force is intended to emulate the effect of a static electric field applied in an electrolytic solution containing charged monomer particles, as is relevant to the translocation of certain biopolymers through protein channel pores embedded in cell membranes. The time evolution of the probability distribution of the translocation coordinate (the number of monomers that have passed through the pore) is extracted from three-dimensional (3-D) simulations over a range of polymer chain lengths. These distributions are compared to the predictions of a 1-D Smoluchowski equation model of the translocation coordinate dynamics. Good agreement is found, with the effective diffusion constant for the 1-D Smoluchowski model being nearly independent of chain length.

Multidimensional variational Gaussian wave packet dynamics with application to photodissociation spectroscopy

The McLachlan variational principle for the time‐dependent Schrodinger equation is utilized in conjunction with extant localized Guassian wave packet technology to deduce equations of motion for general multidimensional Gaussians. These equations of motion are characterized by the same simplicity as the local quadratic expansion results of Heller [J. Chem. Phys. 62, 1544 (1975)]. However, the resultant variational wave packet evolution is shown to be an improvement over its local quadratic analog as a tool for computing certain photodissociation spectra. Numerical examples drawn from the Beswick–Jortner model of ICN photodissociation [Chem. Phys. 24, 1 (1977)] are presented.