Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays.

Yoko Suzuki,José N Onuchic,Eshel Ben-Jacob,Mingyang Lu

doi:10.1038/srep21037

Abstract

Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer.

Highlights

One of the challenges in molecular cell biology is to understand how cells fulfill their functions through specific gene regulations[1]
We present a concise description of the circuit motifs and their possible dynamical behaviors. We show that these circuits give rise to a rich variety of dynamical modes-periodic (P), quasi-periodic (QP), weak chaotic (WC) and strong chaotic (SC) dynamics
As is mentioned in the previous section, a self-inhibitory single gene element with time delay (Fig. 3a) has nearly the same dynamics as a classical repressilator composed of three identical genes

Summary

Introduction

One of the challenges in molecular cell biology is to understand how cells fulfill their functions through specific gene regulations[1]. Different from previous studies of chaotic dynamics in gene circuits, we include the effects of time delays in the self and cross regulations. In Supplementary section SI1, we show that the dynamics of a repressilator is comparable to that of a self-inhibitory single gene element (Fig. 1a) with time delay.

Results

Conclusion