Journal of Statistical Physics

, Volume 121, Issue 5, pp 969–994

Chaotic Dynamics in an Electronic Model of a Genetic Network

  • Leon Glass
  • Theodore J. Perkins
  • Jonathan Mason
  • Hava T. Siegelmann
  • Roderick Edwards
Article

DOI: 10.1007/s10955-005-7009-y

Cite this article as:
Glass, L., Perkins, T.J., Mason, J. et al. J Stat Phys (2005) 121: 969. doi:10.1007/s10955-005-7009-y

Abstract

We consider dynamics in a class of piecewise-linear ordinary differential equations and in an electronic circuit that model genetic networks. In these models, gene activity varies continuously in time. However, as in Boolean or discrete-time switching networks, gene activity is driven high or low based only on whether the activities of the regulating genes are high or low (i.e., above or below certain thresholds). Depending on the “regulatory logic”, these models can exhibit simple dynamics, like stable fixed points or oscillation, or chaotic dynamics. The observed qualitative and quantitative differences between the dynamics in the idealized equations and the dynamics in the electronic circuit lead us to focus attention on the analysis of the dynamics as a function of parameter values. We propose new techniques for solving the inverse problem – the problem of inferring the regulatory logic and parameters from time series data. We also give new symbolic and statistical methods for characterizing dynamics in these networks.

Keywords

genetic networks symbolic dynamics chaos limit cycle oscillation inverse problem 

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Leon Glass
    • 1
  • Theodore J. Perkins
    • 2
  • Jonathan Mason
    • 3
  • Hava T. Siegelmann
    • 4
  • Roderick Edwards
    • 5
  1. 1.Centre for Nonlinear Dynamics in Physiology and Medicine, Department of PhysiologyMcGill UniversityMontrealCanada
  2. 2.McGill Centre for BioinformaticsMcGill UniversityMontrealCanada
  3. 3.The Krasnow Institute for Advanced StudyGeorge Mason UniversityFairfaxUSA
  4. 4.Computer Science BuildingUniversity of MassachusettsAmherstUSA
  5. 5.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaV8W 3P4

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