A generalized model of the repressilator

Abstract

Abstract:The repressilator is a regulatory cycle of n genes where each gene represses its successor in the cycle: 1 ⊣ 2 ⊣ . . . ⊣ n ⊣ 1. The system is modelled by ODEs for an arbitrary number of identical genes and arbitrarily strong repressor binding. A detailed mathematical analysis of the dynamical behavior is provided for two model systems: (i) a repressilator with leaky transcription and single-step cooperative repressor binding, and (ii) a repressilator with auto-activation and cooperative regulator binding. Genes are assumed to be present in constant amounts, transcription and translation are modelled by single-step kinetics, and mRNAs as well as proteins are assumed to be degraded by first order reactions. Several dynamical patterns are observed: Multiple steady states, periodic and aperiodic oscillations corresponding to limit cycles and heteroclinic cycles, respectively. The results of computer simulations are complemented by a detailed and complete stability analysis of all equilibria and of the heteroclinic cycle.

Entrainment and Control of Bacterial Populations: An in Silico Study over a Spatially Extended Agent Based Model

“…In the experimental work of Danino et al [22] a GRN comprised of three genes was introduced into bacterial cells and allowed for oscillations to exist due to the presence of activation-inhibition feedback loops part of the GRN [21,[24][25][26][27][28][29]. As shown in figure 1 these genes are, luxI, aiiA and yemGFP and all are under the influence of the same promoter, li-P [22].…”

“…In the experimental work [22], a synthetic genetic regulatory network (GRN) based on a quorum sensing (QS) architecture [23] was introduced into E.coli cells found within a microfluidic chamber. This GRN had activation-inhibition feedback loops, which lead to oscillatory behaviour [24][25][26][27][28][29], and also allowed for the production of a small hormone molecule referred to as an autoinducer that was freely exchanged between cells and their environment leading to an all-to-all coupling across members of the population. The result was synchronised population-wide oscillations in the metabolic states of cells, witnessed with the help of green fluorescent protein (GFP) whose induction relied on the GRN dynamics.…”

Stability Analysis of a Dynamical Model Representing Gene Regulatory Networks

“…For the analysis of system considered here we will use properties of Schwarzian derivatives, that are commonly employed in analysis of these types of cyclic nonlinear feedback systems, see e.g. Müller et al (2006). Let a function f be defined from R + to R + .…”

Self-regulation in a minimal model of chemical self-replication

“…Like others, i.e., [12,19] and [38,39], we consider a simple functional form to model either repression or activation of gene transcription characterized by the values (m,n). Since genetic repression is more often observed in biochemical systems, the repression case (0,2) has been widely studied in the literature [40][41][42][43][44][45], while the activation case has been seldom used [9][10][11][12][13]. Although repression tends to stabilize a dynamical system, activation coupled with degradation can show oscillatory behavior or even complex oscillations.…”

“…In the case of genetic regulation, we consider parameter values previously determined by several experimental groups [15,19,20,32,33,44]. In particular, we follow Widder's [32] parameter selection.…”