title: Kernel representations for flux and concentration in ion channel models with time-varying concentrations.
abstract: This paper explores stochastic models for the study of ion transport in biological cells. It considers one-dimensional models with time-varying concentrations at the boundaries. The average concentration and flux in the channel are obtained as kernel representations, where the kernel functions have a probabilistic interpretation which contributes to a better understanding of the models. In particular, the kernel representation is given for the flux at a boundary point, providing a correct version of a representation found in the literature. This requires special attention because one of the kernel functions exhibits a singularity. This kernel representation is feasible due to the linearity of the system that arises from the assumed independence between ions.
authors.affiliation: Department of Mathematics and Statistics, University of Saskatchewan, 142 McLean Hall, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, Canada. jalvarezv@ieee.org
authors.forename: Juan
authors.initials: J
authors.lastname: Alvarez
authors.forename: Bruce
authors.initials: B
authors.lastname: Hajek
mesh_terms: D004058:Diffusion; D007473:Ion Channels / Q000737:chemistry*; D007477:Ions / Q000737:chemistry; D008954:Models, Biological
chemical_list: D007473:Ion Channels; D007477:Ions