Bifurcation Analysis and Probabilistic Energy Landscapes of Two-Component Genetic Network

Genetic oscillators play an important role in cell physiology. In this paper, we investigate the global kinetics of an activator-repressor genetic oscillator through the bifurcation analysis and probabilistic energy landscape. The results reveal that the bifurcation can induce the rich dynamics with the variation of the parameters, including monostable state, oscillations, and bistable state. These dynamics are further investigated by the probabilistic energy landscapes in which the force from the negative gradient of the energy landscapes attract the system down to the oscillation path, and the flux is the driving force of the oscillations. Besides, the probabilistic energy landscapes show that the dynamics exhibit distinct transition features when the system is close to the critical points of the oscillation region. Based on the theory of energy landscape, we also explore how the system parameters and noise affect the stability of the activator-repressor oscillations through the physical methods of barrier heights and energy dissipation. The simulation results show that the system parameters and noise intensity have a negative relation with the stability of the oscillations, and the control parameter can play a positive role in maintaining the stability of oscillations. Our methods are quite general and can be utilized to explore the potential global dynamics of more complicated gene regulatory systems.