Condition for Sustained Oscillations in Repressilator Based on a Hybrid Modeling of Gene Regulatory Networks

Honglu Sun, Jean-Paul Comet, Maxime Folschette, Morgan Magnin

2023

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; then, 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.

Paper Citation

in Harvard Style

Sun H., Comet J., Folschette M. and Magnin M. (2023). Condition for Sustained Oscillations in Repressilator Based on a Hybrid Modeling of Gene Regulatory Networks. In Proceedings of the 16th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2023) - Volume 3: BIOINFORMATICS; ISBN 978-989-758-631-6, SciTePress, pages 29-40. DOI: 10.5220/0011614300003414

in Bibtex Style

@conference{bioinformatics23,
author={Honglu Sun and Jean-Paul Comet and Maxime Folschette and Morgan Magnin},
title={Condition for Sustained Oscillations in Repressilator Based on a Hybrid Modeling of Gene Regulatory Networks},
booktitle={Proceedings of the 16th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2023) - Volume 3: BIOINFORMATICS},
year={2023},
pages={29-40},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011614300003414},
isbn={978-989-758-631-6},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2023) - Volume 3: BIOINFORMATICS
TI - Condition for Sustained Oscillations in Repressilator Based on a Hybrid Modeling of Gene Regulatory Networks
SN - 978-989-758-631-6
AU - Sun H.
AU - Comet J.
AU - Folschette M.
AU - Magnin M.
PY - 2023
SP - 29
EP - 40
DO - 10.5220/0011614300003414
PB - SciTePress