Gene regulation models and evolution

M. Sami Fadali, M. Savageau

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


We examine the dynamics of gene regulation for a system with K environments with each environment favoring a different pattern of gene transcription and regulation in a prokaryotic organism. We recast the model of the system as discrete-time K-periodic. This allows us to exploit the well known properties of periodic systems to characterize the steady-state behavior of wild type versus mutant populations of the organism: We also obtain conditions on the parameters of the state matrix using the properties of positive linear systems. We examine in more detail the example of the lac operon of E. Coli which has two environments: a high demand environment H and a low demand environment L. The gene regulation system alternates between the two environments as the organism completes one life cycle. We derive conditions under which the system reaches steady growth alternating between a state xH and xL as each life cycle is completed. Our results show the dependence of the mutant to wild type ratio on the ratio of high demand to low demand duration.

Original languageEnglish (US)
Title of host publicationProceedings of the American Control Conference
Number of pages6
StatePublished - 2009
Event2009 American Control Conference, ACC 2009 - St. Louis, MO, United States
Duration: Jun 10 2009Jun 12 2009


Other2009 American Control Conference, ACC 2009
Country/TerritoryUnited States
CitySt. Louis, MO

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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