Coexistence of Hopf-born rotation and heteroclinic cycling in a time-delayed three-gene auto-regulated and mutually-repressed core genetic regulation network. (21st October 2021) - Yang, Lei; Sun, Weigang; Turcotte, Marc
Highlights: Computational and Analytical Investigation of a Time-Delayed Core Gene Regulation Network. Study of the coexistence of Hopf born Rotation and Heteroclinic Rotation. Numerical and Analytical Investigation of the Concomitant New Phenotypes. Investigation of the Impact of these Concomitant Phenotypes on Evolutionary Selection. Abstract: In this work, we study the behavior of a time-delayed mutually repressive auto-activating three-gene system. Delays are introduced to account for the location difference between DNA transcription that leads to production of messenger RNA and its translation that result in protein synthesis. We study the dynamics of the system using numerical simulations, computational bifurcation analysis and mathematical analysis. We find Hopf bifurcations leading to stable and unstable rotation in the system, and we study the rotational behavior as a function of cyclic mutual repression parameter asymmetry between each gene pair in the network. We focus on how rotation co-exists with a stable heteroclinic flow linking the three saddles in the system. We find that this coexistence allows for a transition between two markedly different types of rotation leading to strikingly different phenotypes. One type of rotation belongs to Hopf-induced rotation while the other type, belongs to heteroclinic cycling between three saddle nodes in the system. We discuss the evolutionary and biological implications of our findings.