Dynamics in high-dimensional model gene networks

Authors:
K. Kappler;R. Edwards;L. Glass
Affiliations:
Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, STN CSC, Victoria, BC, Canada V8W 3P4;Department of Mathematics and Statistics, University of Victoria, BC, Canada and Centre for Nonlinear Dynamics in Physiology and Medicine, Department of Physiology, McIntyre Medical Sciences Build ...;Centre for Nonlinear Dynamics in Physiology and Medicine, Department of Physiology, McIntyre Medical Sciences Building, McGill University, Montréal, Qué., Canada
Venue:
Signal Processing - Special issue: Genomic signal processing
Year:
2003

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Abstract

We consider dynamics in a class of ordinary differential equations representing a simplified model of a genetic network. In this network, the model genes control the production rates of products of other genes by a logical function. Thus, the concentration of a particular gene's product is driven either up or down depending on the particular combination of activity states (active or inactive, i.e., gene product above or below threshold) of a set of relevant 'input' genes. The interactions are based on binary functions but the evolution of gene product concentrations is continuous in time, unlike the discrete-time Boolean networks of Kauffman and others. Numerical methods allow rapid and accurate integration of the model equations. Also, theory now allows analytic confirmation of numerically observed attractors. This enables us to determine changes in the distribution of dynamical properties (attractor types) of random networks as the size of the networks increase and as the number of inputs to each gene increases.