9 Scopus citations


We consider a dynamic framework frequently used to model gene regulatory and signal transduction networks: monotonic ODEs that are composed of Hill functions. We derive conditions under which activity or inactivity in one system variable induces and sustains activity or inactivity in another. Cycles of such influences correspond to positive feedback loops that are self-sustaining and control-robust, in the sense that these feedback loops “trap” the system in a region of state space from which it cannot exit, even if the other system variables are externally controlled. To demonstrate the utility of this result, we consider prototypical examples of bistability and hysteresis in gene regulatory networks, and analyze a T-cell signal transduction ODE model from the literature.

Original languageEnglish (US)
Pages (from-to)36-44
Number of pages9
JournalJournal of Theoretical Biology
StatePublished - Dec 14 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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