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PubMed1977

Random walk analysis of potassium fluxes associated with nerve impulses.

We present a novel recursion method for obtaining theoretical expressions for unidirectional single-file fluxes of ions through narrow membrane channels containing an arbitrary number of ion sites. The theory is applied to experimental tracer fluxes associated with nerve impulses from cephalopod giant axon membranes at various temperatures between 7 degrees and 27 degrees. The comparison between the theoretical and experimental one-way fluxes suggests that the potassium channel in nerve membrane contains three ion sites, which is consistent with the deduction by Hodgkin and Keynes that the potassium channel contains two or three sites on the basis of the ratio of tracer influx to tracer efflux. The analytical results in this paper provide a further test of the single-file model for nerve and other membrane preparations.

Action Potentials↗
PubMed1979

Self-avoiding random walks on lattice strips.

A self-avoiding walk on an infinitely long lattice strip of finite width will asymptotically exhibit an end-to-end separation proportional to the number of steps. A proof of this proposition is presented together with comments concerning an earlier attempt to deal with the matter. In addition, some unproved, yet "obvious," conjectures concerning self-avoiding walks are cited as basic propositions requiring study.

Journal Article↗
PubMed1993

Application of a random walk model to geographic distributions of animal mitochondrial DNA variation.

In rapidly evolving molecules, such as animal mitochondrial DNA, mutations that delineate specific lineages may not be dispersed at sufficient rates to attain an equilibrium between genetic drift and gene flow. Here we predict conditions that lead to nonequilibrium geographic distributions of mtDNA lineages, test the robustness of these predictions and examine mtDNA data sets for consistency with our model. Under a simple isolation by distance model, the variance of an mtDNA lineage's geographic distribution is expected be proportional to its age. Simulation results indicated that this relationship is fairly robust. Analysis of mtDNA data from natural populations revealed three qualitative distributional patterns: (1) significant departure of lineage structure from equilibrium geographic distributions, a pattern exhibited in three rodent species with limited dispersal; (2) nonsignificant departure from equilibrium expectations, exhibited by two avian and two marine fish species with potentials for relatively long-distance dispersal; and (3) a progression from nonequilibrium distributions for younger lineages to equilibrium distributions for older lineages, a condition displayed by one surveyed avian species. These results demonstrate the advantages of considering mutation and genealogy in the interpretation of mtDNA geographic variation.

Animals↗