Authors:
Honglu Sun
1
;
Jean-Paul Comet
2
;
Maxime Folschette
3
and
Morgan Magnin
1
Affiliations:
1
Nantes Université,École Centrale Nantes, CNRS, LS2N, UMR 6004, F-44000 Nantes, France
;
2
University Côte d’Azur, I3S Laboratory, UMR CNRS 7271, CS 40121, 06903 Sophia Antipolis Cedex, France
;
3
Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France
Keyword(s):
Hybrid Modeling, Repressilator, Sustained Oscillation, Gene Regulatory Network, Synthetic Biology.
Abstract:
In this work, we study the existence of sustained oscillations in the “canonical” repressilator, a basic synthetic circuit of 3 genes leading to sustained oscillations. Previous works mostly used differential equations to study the repressilator. In our work, a pre-existing hybrid modeling framework of gene regulatory networks called HGRN is used to model this system. Compared to differential equations, dynamical properties of HGRNs are easier to prove theoretically due to its lower dynamical complexity. The objective of this work is to find conditions for the existence of sustained oscillations described by separable constraints on parameters. With such separable constraints, each parameter is constrained individually by an interval, which can provide useful information for the design of synthetic circuits. Our two major contributions are the following: firstly, we develop, by using the Poincaré map, a sufficient and necessary condition for the existence of sustained oscillations; t
hen, based on this condition, we give a method using the range enclosure property of Bernstein coefficients to compute compatible separable constraints. By applying this method, we successfully obtain sets of conditions for the existence of sustained oscillations described as separable constraints.
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