Switchable genetic oscillator operating in quasi-stable mode

Abstract

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behaviour in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.

Transient dynamics around unstable periodic orbits in the generalized repressilator model

“…This is precisely the case in even-numbered repressilator rings: although their steady state is typically bistable, with two attracting fixed points, 21 the attractor is approached through long-lived oscillating transients that dominate the observable dynamics. 24 In a recent paper, we showed that this transient behavior could be exploited to produce switchable oscillations by using feedback to operate the system around these unstable oscillations. 24 In this paper, we show that the observed long-lived transients have their origin in the existence of UPOs that attract initial conditions to their vicinity, thus funneling the dynamics into a lower-dimensional oscillatory subspace from which it is difficult to escape.…”

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.…”

Online model selection for synthetic gene networks

“…An eight species generalised repressilator [14] is considered, where each of the species represses another species in a ring topology. The corresponding dynamic Choose a regularisation parameter λ s ;…”

“…10: end procedure 11: Update: 12: procedure UPDATE(Ŝ trials) 13: Update candidate functions as stated in the introduction to Section IV; 14 end if 24: end procedure equations that we would like to identify from time series data are as follows:…”