Characterization and merger of oscillatory mechanisms in an artificial genetic regulatory network

Regulatory molecular networks have numerous pharmacological and medical applications. The oscillatory mechanisms and the role of oscillations in these regulatory networks are not fully understood. In this paper, we explore two oscillatory mechanisms: the hysteresis-based relaxation oscillator and the repressilator. We combine these mechanisms into one regulatory network so that only two parameters, the strength of an additional regulatory connection and the timescale separation for one of the variables, control the transition from one mechanism to the other. Our data support a qualitative difference between the oscillatory mechanisms, but in the parameter space, we found a single oscillatory region, suggesting that the two mechanisms support each other. We examine interactions in a basic population: that is, a pair of the composite oscillators. We found that the relaxation oscillation mechanism is much more resistant to oscillatory death as the cells are diffusively coupled in a population. Additionally, stationary pattern formation has been found to accompany the relaxation oscillation but not the repressilator mechanism. These properties may guide the identification of oscillatory mechanisms in complex natural regulatory networks.