title: Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.
abstract: Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.
authors.affiliation: Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
authors.forename: Alexander M
authors.initials: AM
authors.lastname: Berezhkovskii
authors.affiliation: Department of Chemical and Biological Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA.
authors.forename: Stanislav Y
authors.initials: SY
authors.lastname: Shvartsman
mesh_terms: D000818:Animals; D019069:Cell Respiration / Q000502:physiology; D004058:Diffusion; D007313:Insecta / Q000378:metabolism*; D008954:Models, Biological; D010100:Oxygen / Q000378:metabolism*
chemical_list: D010100:Oxygen