The effect of time-dependent drive and delayed feedback loop in two-dimensional gene regulatory network

Recent advances in reprogramming a differentiated cell back to a pluripotent cell fate has rekindled interest in a quantitative understanding of the epigenetic landscape describing cellular differentiation. Reprogramming is a multistep process, involving multiple feedback loops. While the importance of feedback loops is well appreciated, most models assume instantaneous feedback, while biological feedback often involves a time delay between the signal and the response. In the present work, we propose a theoretical model based on a two-gene regulatory motif to investigate the role of time delay in the regulation of gene expression level. In particular, we focus on the interplay between time delayed feedback loops and time-dependent external chemical drive and their effect on dynamics. We observed that the concentration of the two transcription factors can undergo sustained oscillations and we speculate that this oscillatory state may provide an explanation of certain puzzling experiments on the reprogramming process. We also observe transdifferentiation-like behavior, where one differentiated state transitions to another without passing through an intermediate stem cell state.