Analysis of a genetic-metabolic oscillator with piecewise linear models

• Published in: Journal of theoretical biology Vol. 462; pp. 259 - 269
• Main Authors: Chaves, Madalena, Oyarzún, Diego A., Gouzé, Jean-Luc
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 07.02.2019; Elsevier
• Subjects: Automatic Control Engineering; Biological Clocks; Computer Science; Feedback; Gene Regulatory Networks; Linear Models; Metabolic engineering; Metabolic Networks and Pathways; Metabolic pathways; Models, Genetic; Periodic orbits; Piecewise affine systems; Synthetic biology; Metabolic engineering; Gene regulatory networks; Periodic orbits; Metabolic pathways; Synthetic biology; Piecewise affine systems; synthetic biology; gene regulatory networks; metabolic engineering; periodic orbits; piecewise affine systems
• ISSN: 0022-5193; 1095-8541; 1095-8541
• DOI: 10.1016/j.jtbi.2018.10.026

•Analysis of the emergent dynamics in genetic-metabolic networks, using piecewise linear models.•An alternative mathematical model for the synthetic metabolator network is proposed.•This new model allows the co-existence of two types of oscillatory behavior, in agreement with experimental observations: a periodic orbit and damped oscillations towards a fixed point. Interactions between gene regulatory networks and metabolism produce a diversity of dynamics, including multistability and oscillations. Here, we characterize a regulatory mechanism that drives the emergence of periodic oscillations in metabolic networks subject to genetic feedback regulation by pathway intermediates. We employ a qualitative formalism based on piecewise linear models to systematically analyze the behavior of gene-regulated metabolic pathways. For a pathway with two metabolites and three enzymes, we prove the existence of two co-existing oscillatory behaviors: damped oscillations towards a fixed point or sustained oscillations along a periodic orbit. We show that this mechanism closely resembles the “metabolator”, a genetic-metabolic circuit engineered to produce autonomous oscillations in vivo.