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

Alexander M. Berezhkovskii, Stanislav Y. Shvartsman

Research output: Contribution to journalArticle

6 Scopus citations

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.

Original languageEnglish (US)
Article number204101
JournalJournal of Chemical Physics
Volume144
Issue number20
DOIs
StatePublished - May 28 2016

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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