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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Transient dynamics around unstable periodic orbits in the generalized repressilator model
Natalja Strelkowa1, Mauricio Barahona
1Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom. natalja.strelkowa06@imperial.ac.uk
Chaos (Woodbury, N.Y.)
|July 5, 2011
Summary
We analyzed gene networks, finding unstable orbits that create long-lasting oscillations. These dynamics are crucial for understanding biological systems in confined environments and for synthetic biology applications.
Area of Science:
- Systems Biology
- Theoretical Biology
- Bioengineering
Background:
- The generalized repressilator is a gene network with a ring topology.
- Understanding temporal dynamics is key for confined, noisy biological systems like bacterial cells.
Purpose of the Study:
- To analyze the temporal dynamics of the generalized repressilator.
- To identify conditions for long-lived oscillating transients relevant to bioengineering and synthetic biology.
Main Methods:
- Analytical conditions for unstable periodic orbits.
- Analysis of spatial symmetries and traveling wave solutions.
- Characterization of two-kink configurations.
Main Results:
- Identified a sequence of unstable periodic orbits leading to long-lived oscillating transients.
- Demonstrated that these orbits exhibit spatial symmetries and relate to topological defects.
- Showed that long-lived transients correspond to propagating quasistable two-kink configurations.
Conclusions:
- The generalized repressilator exhibits complex temporal dynamics driven by unstable orbits.
- These dynamics are relevant for understanding biological functions in confined environments.
- The model shares similarities with experimental electronic systems like magnetic flux gates.
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