Journal of Mathematical Biology

, Volume 20, Issue 1, pp 39–57

Models of genetic control by repression with time delays and spatial effects

  • J. M. Mahaffy
  • C. V. Pao

DOI: 10.1007/BF00275860

Cite this article as:
Mahaffy, J.M. & Pao, C.V. J. Math. Biology (1984) 20: 39. doi:10.1007/BF00275860


Two models for cellular control by repression are developed in this paper. The models use standard theory from compartmental analysis and biochemical kinetics. The models include time delays to account for the processes of transcription and translation and diffusion to account for spatial effects in the cell. This consideration leads to a coupled system of reactiondiffusion equations with time delays. An analysis of the steady-state problem is given. Some results on the existence and uniqueness of a global solution and stability of the steady-state problem are summarized, and numerical simulations showing stability and periodicity are presented. A Hopf bifurcation result and a theorem on asymptotic stability are given for the limiting case of the models without diffusion.

Key words

Genetic control models reaction diffusion equations with delays 

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • J. M. Mahaffy
    • 1
  • C. V. Pao
    • 1
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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