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- Mark F Schumaker
- 2002

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, Sara E Morrison, Timothy A Cross, David D Busath, Eric J Mapes +1 other
- 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)

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)

A framework model of single-proton conduction through gramicidin was previously designed to incorporate potentials of mean force and diffusion coefficients computed by the molecular dynamics simulations of Pom s and Roux (1). The resulting diffusion model was solved analytically using the lumped state approximation (LSA), allowing a detailed comparison to… (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)

- Mark F Schumaker, David M Kramer
- Bulletin of mathematical biology
- 2011

We have programmed a Monte Carlo simulation of the Q-cycle model of electron transport in cytochrome b(6)f complex, an enzyme in the photosynthetic pathway that converts sunlight into biologically useful forms of chemical energy. Results were compared with published experiments of Kramer and Crofts (Biochim. Biophys. Acta 1183:72-84, 1993). Rates for the… (More)

The number of substrate molecules that can bind to the active site of an enzyme at one time is constrained. This paper develops boundary conditions that correspond to the constraint of single-occupancy binding. Two simple models of substrate molecules diffusing to a single-occupancy site are considered. In the interval model, a fixed number of substrate… (More)

- Eric J Mapes, Mark F Schumaker
- Bulletin of mathematical biology
- 2006

A modern approach to studying the detailed dynamics of biomolecules is to simulate them on computers. Framework models have been developed to incorporate information from these simulations in order to calculate properties of the biomolecules on much longer time scales than can be achieved by the simulations. They also provide a simple way to think about the… (More)

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