Bulletin of Mathematical Biology

, Volume 73, Issue 9, pp 2132–2151 | Cite as

Dynamic Stabilization in the PU1-GATA1 Circuit Using a Model with Time-Dependent Kinetic Change

  • Jay L. Michaels
  • Vincent Naudot
  • Larry S. Liebovitch
Open Access
Original Article

Abstract

The PU.1 and GATA1 genes play an important role in the differentiation of blood stem cells. The protein levels expressed by these genes are thought to be regulated by a self-excitatory feedback loop for each gene and a cross-inhibitory feedback loop between the two genes. A mathematical model that captures the dynamical interaction between these two genes reveals that constant levels of self-excitation and cross-inhibition allow the most self-exciting or cross-inhibiting gene to dominate the system. However, since biological systems rarely exist in an unchanging equilibrium, we modeled this gene circuit using discrete time-dependent changes in the parameters in lieu of steady state parameters. These time-dependent parameters lead to new phenomena, including the development of new limit cycles and basins of attraction. These phenomena are not present in models using constant parameter values. Our findings suggest that even small perturbations in the PU.1 and GATA1 feedback loops may substantially alter the gene expression and therefore the cell phenotype. These time-dependent parameter models may also have implications for other gene systems and provide new ways to understand the mechanisms of cellular differentiation.

Keywords

Computational biology of gene regulatory networks Blood stem cell fate commitment 

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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Jay L. Michaels
    • 1
  • Vincent Naudot
    • 2
  • Larry S. Liebovitch
    • 3
  1. 1.Department of PsychologyFlorida Atlantic UniversityBoca RatonUSA
  2. 2.Department of Mathematical ScienceFlorida Atlantic UniversityBoca RatonUSA
  3. 3.Division of Mathematics and Natural Sciences, Queens CollegeCity University of New YorkFlushingUSA

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