Synchronization of fractional-order repressilatory genetic oscillators with time delay

Abstract

Genetic oscillators have been widely used in modeling key processes of biological systems, especially cell cycles and circadian rhythms. In particular, repressilatory genetic oscillators have been employed in modeling the dynamics of mRNA and protein interactions with transcriptional and translational feedback loops at the molecular level. In addition, synchronization of these oscillators is crucial for understanding the underlying mechanisms of the associated biological processes. In this paper, models of fractional-order genetic oscillators and their coupling are established, where the aspects of time delay, coupling strength, noise, and stability are all taken into consideration. Communication in the proposed coupling model is based on quorum sensing. The synchronization of the fractional-order repressilator model has been examined through simulations which show three main findings. Firstly, the synchronization of the fractional-order repressilator model can be optimized through coupling weight selection. Secondly, the synchronization can be enhanced by increasing the fractional order and decreasing the time delay and the noise intensity. Finally, transitions between the states of the fractional-order repressilatory oscillator can be achieved through varying the fractional order. The simulation results verify the biological relevance of the genetic oscillator models, and their potential for explaining the underlying mechanisms of the associated biological processes.