Mark F. Schumaker

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We develop a model for proton conduction through gramicidin based on the molecular dynamics simulations of Pomès and Roux (Biophys. J. 72:A246, 1997). The transport of a single proton through the gramicidin pore is described by a potential of mean force and diffusion coefficient obtained from the molecular dynamics. In addition, the model incorporates the(More)
This paper describes a framework model for proton conduction through gramicidin; a model designed to incorporate information from molecular dynamics and use this to predict conductance properties. The state diagram describes both motion of an excess proton within the pore as well as the reorientation of waters within the pore in the absence of an excess(More)
We present an extensive set of measurements of proton conduction through gramicidin A (gA), B (gB), and M (gM) homodimer channels which have 4, 3, or 0 Trp residues at each end of the channel, respectively. In gA we find a shoulder separating two domains of conductance increasing with concentration, confirming the results of Eisenman, G., B. Enos, J.(More)
Recent experimental evidence suggests that certain membrane channels operate in a nearly ion-saturated state. We therefore consider a "single-vacancy" model of ion permeation: if a channel has n conducting sites, it will contain either n or n-1 ions. Simple analytical expressions for the current, conductance, and reversal potential under bi-ionic conditions(More)
We present a far-field analysis of ion diffusion toward a channel embedded in a membrane with a fixed charge density. The Smoluchowski equation, which represents the 3D problem, is approximated by a system of coupled three- and two-dimensional diffusions. The 2D diffusion models the quasi-two-dimensional diffusion of ions in a boundary layer in which the(More)
We present a simple two-parameter model for surface charge directly associated with ion channels. A spherically symmetric "charged shell" models a distribution of surface charge arrayed about the channel entrance, with a corresponding set of image charges behind the plane of the membrane. The transition between a regime of buffered conductance and a regime(More)
The lumped state approximation ͑LSA͒ is a method for handling boundary conditions for diffusion on an interval which simplifies the description of transitions into and out of the interval. It was originally motivated by the problem of proton conduction through the ion channel gramicidin. This paper discusses the mean first passage time of a diffuser(More)
The general form of the Smoluchowski equation in two reaction coordinates is obtained as the diffusion limit of a random walk on an infinite square grid using transition probabilities that satisfy detailed balance at thermodynamic equilibrium. The diffusion limit is then used to construct a generalization of the single-particle model to two reaction(More)