Abstract
Genetic networks play a fundamental role in the regulation and control of the development and function of organisms. A simple model of gene networks assumes that a gene can be switched on or off as regulatory inputs to the gene cross critical thresholds. In studies of dynamics of such networks, we found unusual dynamical behavior in which phase plane trajectories display irregular dynamics that shrink over long times. This observation leads us to identify a type of dynamics, that can be described as collapsing chaos, in which the Lyapunov exponent is positive, but points on the trajectory approach the origin in the long time limit.
Highlights
One of the idealizations of genetic regulatory networks is that gene expression is regulated in a combinatorial fashion
As discussed in prior work, these piecewise linear equations can exhibit a large number of different dynamical properties including stable steady states, stable limit cycles, chaotic dynamics, and multiple attractors [4, 5]
We focus attention on one unusual aspect of the dynamics observed in this example: an apparently shrinking or collapsing chaotic attractor
Summary
One of the idealizations of genetic regulatory networks is that gene expression is regulated in a combinatorial fashion. Modern research in genetic control has focused on the network wiring diagrams for regulatory control [6]. In work going back to the 1970s [8, 9], our group has proposed a mathematical formulation that develops piecewise linear models for this type of regulatory control. As discussed in prior work, these piecewise linear equations can exhibit a large number of different dynamical properties including stable steady states, stable limit cycles, chaotic dynamics, and multiple attractors [4, 5]. A variety of modifications of the original equations is possible to include the effects of continuous rather than switching control, ot to include multiple thresholds for the control. We have been working to develop techniques to predict possible nonlinear dynamical behaviors of a given network based on the wiring diagram of the network.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
