Diffusion in an age-structured randomly switching environment. (19th June 2018)

• Record Type: Journal Article
• Authors: Bressloff, Paul C; Lawley, Sean D; Murphy, Patrick
• Is Part Of: Journal of physics. Volume 51:Number 31(2018)
• Publication Date: 2018-06-19
• Subjects: age-structured -- diffusion -- stochastic gating -- random environment -- characteristics; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aaca7c
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Age-structured processes are well-established in population biology, where birth and death rates often depend on the age of the underlying populations. Recently, however, different examples of age-structured processes have been considered in the context of cell motility or certain types of stochastically gated ion channels, where the state of the system is determined by a switching process with age-dependent transition rates. In this paper we consider the particular problem of diffusion on a finite interval, with randomly switching boundary conditions due to the presence of an age-structured stochastic gate at one end of the interval. When the gate is closed the particles are reflected, whereas when it is open the domain is in contact with a particle bath. We use a moments method to derive a partial differential equation for the expectations of the stochastic concentration, conditioned on the state of the gate. We then use transform methods to eliminate the residence time of the age-structured switching, resulting in non-Markovian equations for the expectations, and determine the effective steady-state concentration gradient. Our analytical results are shown to match those obtained using Monte Carlo simulations.