Diffusive flux in a model of stochastically gated oxygen transport in insect respiration.

TitleDiffusive flux in a model of stochastically gated oxygen transport in insect respiration.
Publication TypeJournal Article
Year of Publication2016
AuthorsBerezhkovskii, AM, Shvartsman, SY
JournalJ Chem Phys
Volume144
Issue20
Pagination204101
Date Published2016 May 28
ISSN1089-7690
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.

DOI10.1063/1.4950769
Alternate JournalJ Chem Phys
PubMed ID27250273
PubMed Central IDPMC4884186
Grant ListR01 GM107103 / GM / NIGMS NIH HHS / United States