Theoretical Study of Ion Transport in the Gramicidin a Channel

Modern techniques are used to study the permeation process of ions through the gramicidin A channel. The conformation of the gramicidin molecule is investigated experimentally in dimethylsulfoxide/acetone using the techniques of two-dimensional NMR spectroscopy. An empirical energy function is developed from ab initio calculations to represent the interaction of Li^{+}, Na^{+} and K^ {+} ions with the backbone of polypeptides; the parameters are tested in dense systems with free energy simulations. The dynamics of the gramicidin A channel dimer in the absence of water and ions is studied in the harmonic approximation by a vibrational analysis of the atomic motions relative to their equilibrium positions. The behavior of the water molecules in the channel is studied with a molecular dynamics simulation of a fully solvated Gramicidin A dimer embedded in a model membrane. the potential of mean force and the mobility of Na^{+ }, K^{+} and water are calculated in the interior of a gramicidin-like periodic poly (L,D)-alanine beta -helix. The potential of mean force of Na^ {+} ion along the axis of the gramicidin A channel is calculated with a molecular dynamics simulation of a fully solvated Gramicidin A dimer embedded in a model membrane; the gramicidin channel is modeled as a right -handed head-to-head beta-helix dimer. Binding sites are found at the extremities of the channel; no large activation energy barrier is caused by the dehydration process at the entrance of the channel. In the appendices, Statistical Mechanical theories are used to investigate the equilibrium and dynamical properties of the liquid state. A theory of aqueous solutions is used to provide an interpretation for the Born model of ion hydration at the molecular level; the Born radius of hydration is interpreted in terms of the first peak in the solute-solvent radial distribution function. We show that some proposed closures for the RISM equation of Chandler and Andersen possess no solution because they fail to satisfy the compressibility theorm; a new closure consistent with the compressibility theorm is suggested. The properties of the charge density at the membrane interface between two ionic solutions are examined using the Poisson-Boltzmann theory. Statistical mechanical theory is used to examine the microscopic aspects of the Nernst-Planck diffusion equation for ion channels. Molecular dynamics simulations are used to determine the time-dependent friction for pair diffusion in an isotropic Lennard-Jones fluid as a function of the separation between two diffusing particles.