Dynamical properties of the repressilator model

Abstract

Oscillatory regulatory networks have been discovered in many regulatory pathways. Due to their enormous complexity, it is necessary to study their dynamics by means of highly simplified models. These models have received particular value because artificial regulatory networks can be engineered experimentally. In this paper, we study dynamical properties of an artificial regulatory oscillator called repressilator. We have shown that oscillations arise from the existence of an absorbing toruslike region in the phase space of the model. This geometric structure requires monotonic repression at all promoters and the absence of any regulatory connections apart from a cyclic repression loop. We show that oscillations collapse as only weak extra connections are introduced if there is imbalance between the attended concentrations and those sufficient for saturation of the promoters. We found that a pair of diffusively coupled repressilators displays synchronization properties similar to those of relaxation oscillators if the regulatory connections in the cyclic repression loop are strong. Thus, the role of strengthening these connections can be viewed as introducing time scale separation among variables. This may explain controversial synchronization properties reported for repressilators in earlier studies.

Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation

“…One example of such oscillating system is a repressilator (a type of synthetic biological oscillator [49][50][51][52][53][54]) of the form…”

Equilibrium switching in nonlinear interaction networks with concurrent antagonism

“…Example 2. One example of such oscillating system is a repressilator (a type of synthetic biological oscillator [52,53,54,55,56,57]) of the form…”

Hopf bifurcation in the full repressilator equations

“…It just gives an indication about its existence. Here, in this work, we consider the full system in dimension six, and we extend the results of [9,10] on the supercritical Hopf bifurcation to the six-dimensional differential system (2). Our main result is the following one.…”

“…In the papers [9,10], the authors consider a reduced system of dimension three. The reduction assumes that the three excluded variables, that is, m i , evolve an order of magnitude faster than the other three.…”