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M F Schumaker

Publications and source records attributed to M F Schumaker.

12 recordsLinked to original sources
PubMed2001

Framework model for single proton conduction through gramicidin.

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 proton. The model is constructed as the diffusion limit of a random walk, allowing control over the boundary behavior of trajectories. Simple assumptions about the boundary behavior are made, which allow an analytical solution for the proton current and conductance. This is compared with corresponding expressions from statistical mechanics. The random walk construction allows diffusing trajectories underlying the model to be simulated in a simple way. Details of the numerical algorithm are described.

Algorithms↗
PubMed2000

A combined molecular dynamics and diffusion model of single proton conduction through gramicidin.

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 dynamics of a defect in the hydrogen bonding structure of pore waters without an excess proton. Proton entrance and exit were not simulated by the molecular dynamics. The single proton conduction model includes a simple representation of these processes that involves three free parameters. A reasonable value can be chosen for one of these, and the other two can be optimized to yield a good fit to the proton conductance data of, Ann. N.Y. Acad. Sci. 339:8-20) for pH > or = 1.7. A sensitivity analysis shows the significance of this fit.

Biophysics↗
PubMed1998

Far-field analysis of coupled bulk and boundary layer diffusion toward an ion channel entrance.

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 electrical potential interaction with the membrane surface charge is important. The 3D diffusion models ion transport in the bulk region outside the boundary layer. Analytical expressions for concentration and flux are developed that are accurate far from the channel entrance. These provide boundary conditions for a numerical solution of the problem. Our results are used to calculate far-field ion flows corresponding to experiments of Bell and Miller (Biophys. J. 45:279, 1984).

Biophysics↗
PubMed1996

Boundary conditions for- single-ion diffusion.

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 conditions are identical to those given by Levitt. However, the construction gives rise to a third term not found in Levitt's theory. With this term, the channel spends exponentially distributed intervals in the empty state. Ion sample paths have been simulated to help visualize trajectories near the channel entrances, with and without the new term. We use the modified Levitt theory to fit several potential profiles to the conductance data of Russell et al. In particular, we have analyzed the profile for Na+ in gramicidin calculated by Roux and Karplus. The peak-to-peak amplitude of their result must be reduced to at most 35% of its original value to fit the data. But with this reduction, excellent fits are obtained.

Computer Simulation↗
PubMed1995

Orientation independence of single-vacancy and single-ion permeability ratios.

Single-vacancy models have been proposed as open channel permeation mechanisms for K+ channels. Single-ion models have been used to describe permeation through Na+ channels. This paper demonstrates that these models have a distinctive symmetry property. Their permeability ratios, measured under biionic conditions, are independent of channel orientation when the reversal potential is zero. This symmetry is a property of general m-site single-vacancy channels, m-site shaking-stack channels, as well as m-site single-ion channels. An experimental finding that the permeability ratios of a channel did not have this symmetry would provide evidence that a single-vacancy or single-ion model is an incorrect or incomplete description of permeation.

Animals↗
PubMed1994

Functional multiplicity of motor molecules revealed by a simple kinetic analysis.

We present a simple analytical solution for a kinetic model of motor molecule function with multiple arms. This model has a rate of motion proportional to the probability that all arms in a complex are detached from the cytoskeleton and, therefore, we refer to it as obligate cooperativity. The model has the form: v = Vmax/(1 + q/S)n, where Vmax is the maximum velocity, the product nq is the effective Michaelis constant at high [ATP], and n is the number of arms. Values of n = 2 and n = 1 give good fits to the heavy meromyosin and myosin S1 sliding velocity data, respectively, consistent with the number of active sites. Despite the complexity of the eukaryotic axoneme, beat frequency data from Chlamydomonas wild-type and oda mutants are also fit by this model.

Animals↗
PubMed1994

A simple model for surface charge on ion channel proteins.

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 of rapidly falling conductance at very low ionic strength is found to depend on the magnitude of the surface charge as well as the separation between the charge and the channel entrance. This resolves an apparent discrepancy between the experimental findings of Naranjo and Latorre (1993. Biophys. J. 64:1038-1050) and previous theoretical computations. The charged-shell model is used in a comparative study of the toad skeletal muscle conductance data of Naranjo and Latorre, the rat skeletal muscle conductances of Ravindran et al. (1992. Biophys. J. 61:494-508), and a second set of rat muscle conductances presented in this paper.

Animals↗
PubMed1992

Shaking stack model of ion conduction through the Ca(2+)-activated K+ channel.

Motivated by the results of Neyton and Miller (1988. J. Gen. Physiol. 92:549-586), suggesting that the Ca(2+)-activated K+ channel has four high affinity ion binding sites, we propose a physically attractive variant of the single-vacancy conduction mechanism for this channel. Simple analytical expressions for conductance, current, flux ratio exponent, and reversal potential under bi-ionic conditions are found. A set of conductance data are analyzed to determine a realistic range of parameter values. Using these, we find qualitative agreement with a variety of experimental results previously reported in the literature. The exquisite selectivity of the Ca(2+)-activated K+ channel may be explained as a consequence of the concerted motion of the "stack" in the proposed mechanism.

Animals↗
PubMed1990

A simple model for multi-ion permeation. Single-vacancy conduction in a simple pore model.

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 are derived. The results are compared with those of single ion models and recent experiments on Ca2(+)-activated K+ channels.

Biophysical Phenomena↗
PubMed1978

A program which automatically quantitates gel electrophoretic autoradiograms.

The use of a computer-coupled film scanner to measure and analyze autoradiograms of gel electropherograms is described. A program has been written which fits Gaussian curves to the complex band pattern that constitutes a density profile without the need for estimated parameters in the input. The great majority of the fits are satisfactory. This program, which is written in FORTRAN, runs on a small, inexpensive computer. Another program which approximates a Gaussian least squares fit has been run for comparison; this procedure can also be used to refine occasional unsatisfactory fits. Finally, a program has been written which sums the density profile within specified limits, so that the integrated intensities of bands due to isolated protein components may be found.

Algorithms↗