Analysis of a genetic-metabolic oscillator with piecewise linear models - Chaves, Madalena; Oyarzún, Diego A.; Gouzé, Jean-Luc (Journal of theoretical biology, 2019)
•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.