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Preparation of Liquid Crystal Networks for Macroscopic Oscillatory Motion Induced by Light

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Published on: September 20, 2017

Structural principles for periodic orbits in glass networks.

Linghong Lu¹, Roderick Edwards

¹Department of Mathematics and Statistics, University of Victoria, PO Box 3060, STN CSC, Victoria, BC, V8W 3R4, Canada.

Journal of Mathematical Biology

|May 26, 2009

Summary

Gene regulatory network structure dictates dynamic behaviors. This study shows that specific network cycles can lead to periodic orbits, extending previous findings on gene regulation dynamics.

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Area of Science:

Systems Biology
Computational Biology
Mathematical Biology

Background:

Piecewise-linear differential equation models, known as Glass networks, are used to analyze gene regulatory interactions.
Periodicity is a key dynamic behavior in these regulatory systems.

Purpose of the Study:

To establish new relationships between the structural properties of gene regulatory networks and their dynamic behaviors.
To explore the existence of periodic orbits within these networks based on their structural principles.

Main Methods:

Utilized the state space of gene regulatory networks, represented as a digraph on an n-cube for single-threshold models.
Investigated the connection between network structure, specifically cycles in the state space, and the existence of periodic orbits.

Main Results:

Demonstrated that for many classes of cycles in the state space, parameter values exist that support periodic orbits.
Showed that for certain network structures, stable periodic orbits can be achieved.

Conclusions:

Network structure significantly influences the potential for periodic dynamics in gene regulatory systems.
These findings expand upon earlier theoretical work on the dynamics of gene regulatory networks.