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- M F Schumaker, R Pomès, B Roux
- Biophysical journal
- 2000

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)

- P McGill, M F Schumaker
- Biophysical journal
- 1996

We have constructed a theory for diffusion through the pore of a single-ion channel by taking a limit of a random walk around a cycle of states. Similar to Levitt's theory of single-ion diffusion, one obtains boundary conditions for the Nernst-Planck equation that guarantee that the pore is occupied by at most one ion. Two of the terms in the boundary… (More)

- M F Schumaker, R Pomès, B Roux
- Biophysical journal
- 2001

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)

This article constructs trajectories associated with various boundary conditions for the Smoluchowski equation on an interval. Single-particle diffusion processes are first constructed by taking the diffusion limits of random walks. The diffusion limit gives both boundary conditions which enforce the single-particle constraint and properties of underlying… (More)

- Joseph A Gowen, Jeffrey C Markham, +4 authors Mark F Schumaker
- Biophysical journal
- 2002

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)

- M F Schumaker, C J Kentler
- Biophysical journal
- 1998

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)

- M F Schumaker, R MacKinnon
- Biophysical journal
- 1990

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)

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)

- Mark F Schumaker, David S Watkins
- The Journal of chemical physics
- 2004

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)

- Vitaly A. Selivanov, Marta Cascante, Mark Friedman, Mark F. Schumaker, Massimo Trucco, Tatyana V. Votyakova
- PLoS Computational Biology
- 2012

The mitochondrial electron transport chain transforms energy satisfying cellular demand and generates reactive oxygen species (ROS) that act as metabolic signals or destructive factors. Therefore, knowledge of the possible modes and bifurcations of electron transport that affect ROS signaling provides insight into the interrelationship of mitochondrial… (More)