Control design for sustained oscillation in a two-gene regulatory network |
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Authors: | Email author" target="_blank">Roderick?EdwardsEmail author Sehjeong?Kim P?van den?Driessche |
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Institution: | (1) ICREA-Complex Systems Lab, Universitat Pompeu Fabra (PRBB-GRIB), Dr Aiguader 88, 08003 Barcelona, Spain;(2) EMBL-CRG Systems Biology Research Unit, Centre for Genomic Regulation (CRG), UPF, Dr Aiguader 88, 08003 Barcelona, Spain;(3) Santa Fe Institute, 1399 Hyde Park Road, 87501 Santa Fe NM, USA |
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Abstract: | Control strategies for gene regulatory networks have begun to be explored, both experimentally and theoretically, with implications
for control of disease as well as for synthetic biology. Recent work has focussed on controls designed to achieve desired
stationary states. Another useful objective, however, is the initiation of sustained oscillations in systems where oscillations
are normally damped, or even not present. Alternatively, it may be desired to suppress (by damping) oscillations that naturally
occur in an uncontrolled network. Here we address these questions in the context of piecewise-affine models of gene regulatory
networks with affine controls that match the qualitative nature of the model. In the case of two genes with a single relevant
protein concentration threshold per gene, we find that control of production terms (constant control) is effective in generating
or suppressing sustained oscillations, while control of decay terms (linear control) is not effective. We derive an easily
calculated condition to determine an effective constant control. As an example, we apply our analysis to a model of the carbon
response network in Escherichia coli, reduced to the two genes that are essential in understanding its behavior. |
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