Stability of a model for cell metabolism
type: Item
instance of: scholarly article
title: Stability of a model for cell metabolism
zbMATH Open document ID: 0881.92014
DOI: 10.1016/S0895-7177(96)00170-7
author: H. Khanina
author: Aleksey D. Drozdov
published in: Mathematical and Computer Modelling
publication date: 1998-02-17T00:00:00Z
review text: The paper is concerned with explicit stability conditions for a stationary solution of equations describing the cell metabolism. A cell is modeled as a hereditary dynamic system with a specific time delay. As is common practice, a time delay in functional-differential equations is assumed to be given. The stability problem consists in imposing restrictions on coefficients of these equations which would ensure the Lyapunov stability of a fixed solution. The system behavior obeys functional-differential equations of the standard nature, i.e., either ordinary integro-differential equations, or partial integro-differential equations. Mass transfer through a cell is described by parabolic partial differential equations in a domain occupied by the cell with specific differential relationships on a boundary (membrane) of this domain. By excluding mass transport across the protoplasm from the membrane to the nucleus from our consideration, we reduce the initial problem to an ordinary integro-differential equation on the boundary with an integral operator dependent essentially on the molecular diffusion inside the cell. To develop stability conditions we linearize the problem and employ a method of integral inequalities. It is shown that a large number of coefficients determining the mass transport is reduced to three basic dimensionless parameters, one of which characterizes the cell geometry, another characterizes a stationary process of transport, and the third characterizes feedback control in cell metabolism. We derive a stability condition formulated explicitly as an inequality dependent on the above parameters. The dependence of the ultimate parameter of the feedback control on the two others is studied analytically and numerically.
Mathematics Subject Classification ID: 92C30
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45M10
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 1042766
zbMATH Keywords: nutrition transport
zbMATH Keywords: cell metabolism
zbMATH Keywords: time delay
MaRDI profile type: Publication
cites work: Volterra integral and differential equations
cites work: Q3997912
cites work: Introduction to functional differential equations
cites work: Q4692887
cites work: Q4698533
cites work: Q4003237
cites work: Q4152381
cites work: Permanence and the dynamics of biological systems
cites work: Q3137926
cites work: Q3994920
cites work: Interaction of spatial diffusion and delays in models of genetic control by repression
cites work: Stability results for a model of repression with external control
cites work: Models of genetic control by repression with time delays and spatial effects
cites work: The qualitative dynamics of a class of biochemical control circuits
cites work: Q3895289
full work available at URL: s0895-7177(96)00170-7
OpenAlex ID: W1992669345
description: scientific article; zbMATH DE number 1042766