Analysis of biochemical reactions models with delays

  • Bodnar M
  • Foryś U
  • Poleszczuk J
  • 8

    Readers

    Mendeley users who have this article in their library.
  • 18

    Citations

    Citations of this article.

Abstract

Deterministic descriptions of three biochemical reaction channels formerly considered by Bratsun et al. (2005) [19] are studied. These descriptions are based on the mass action law and for the simple protein production with delayed degradation differ from that proposed by Bratsun et al. An explicit solution to this model is calculated. For the model of reaction with negative feedback and delayed production, global stability of a unique positive steady state is proved. According to the models of these two reaction channels considered in the present paper there cannot appear delayed induced oscillations. For the model of reaction with negative feedback, dimerisation and delayed protein production, local stability for a unique positive steady state is shown for some range of parameters. It is also proved that for some range of parameters the destabilisation due to the increasing delay can occur and delayed induced oscillations may appear. © 2010 Elsevier Inc.

Author-supplied keywords

  • Asymptotic analysis
  • Biochemical reaction
  • Delay differential equations
  • Hopf bifurcation
  • Local and global stability

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free