Dynamics of coupled repressilators: The role of mRNA kinetics and transcription cooperativity

Abstract

Oscillatory regulatory networks have been discovered in many cellular pathways. An especially challenging area is studying dynamics of cellular oscillators interacting with one another in a population. Synchronization is only one of and the simplest outcome of such interaction. It is suggested that the outcome depends on the structure of the network. Phase-attractive (synchronizing) and phase-repulsive coupling structures were distinguished for regulatory oscillators. In this paper, we question this separation. We study an example of two interacting repressilators (artificial regulatory oscillators based on cyclic repression). We show that changing the cooperativity of transcription repression (Hill coefficient) and reaction timescales dramatically alter synchronization properties. The network becomes birhythmic-it chooses between the in-phase and antiphase synchronization. Thus, the type of synchronization is not characteristic for the network structure. However, we conclude that the specific scenario of emergence and stabilization of synchronous solutions is much more characteristic.

Electronic Implementation of a Repressilator with Quorum Sensing Feedback

“…One of the important discoveries, in this direction, is the design of an artificial genetic network known as a repressilator [4] which consists of a ring of three genes inhibiting each other in cyclic order that shows oscillatory behaviors. Theoretical studies of the single deterministic, stochastic, and even electronic repressilator have attracted attention of many investigators [8]–[17].…”

Networks of coupled circuits: From a versatile toggle switch to collective coherent behavior

“…We should remark that the bifurcation diagram and the synchronization properties may alter if one of these parameters would change. For a system of two coupled repressilators it was shown [11] that the very Hill coefficients and reaction time scales (in our case also implicitly kept fixed) can dramatically influence the type of synchronization, so that it is not the mere network topology of activating or repressing couplings that determines the synchronization. Therefore our conclusions should be understood to hold for given fixed values of these parameters.…”

Coherence and stochastic resonance in a birhythmic van der Pol system

“…To characterize the birhythmic system one can analyze the dynamics of the radius A of the oscillations, as per equation (4). A principal question is: does the quasi-potential The quasi-potential energy of a bistable system and an illustration of the escape process.…”

“…a stable orbit in the phase space. More rarely, one encounters birhythmicity, or the contemporary presence of two stable orbits (limit cycles) for the same set of parameters, as in some biochemical systems [1] or circadian oscillations [2], cell populations [3,4], neuronal dynamics [5], protein dynamics [6]. To model the oscillations, one of the first, and still nowadays prototypal system, is the van der Pol oscillator [7], that has been employed for biological modelling [8] and other oscillations [9][10][11].…”