A genetic timer through noise-induced stabilization of an unstable state

Abstract

Stochastic fluctuations affect the dynamics of biological systems. Typically, such noise causes perturbations that can permit genetic circuits to escape stable states, triggering, for example, phenotypic switching. In contrast, studies have shown that noise can surprisingly also generate new states, which exist solely in the presence of fluctuations. In those instances noise is supplied externally to the dynamical system. Here, we present a mechanism in which noise intrinsic to a simple genetic circuit effectively stabilizes a deterministically unstable state. Furthermore, this noise-induced stabilization represents a unique mechanism for a genetic timer. Specifically, we analyzed the effect of noise intrinsic to a prototypical two-component gene-circuit architecture composed of interacting positive and negative feedback loops. Genetic circuits with this topology are common in biology and typically regulate cell cycles and circadian clocks. These systems can undergo a variety of bifurcations in response to parameter changes. Simulations show that near one such bifurcation, noise induces oscillations around an unstable spiral point and thus effectively stabilizes this unstable fixed point. Because of the periodicity of these oscillations, the lifetime of the noise-dependent stabilization exhibits a polymodal distribution with multiple, well defined, and regularly spaced peaks. Therefore, the noise-induced stabilization presented here constitutes a minimal mechanism for a genetic circuit to function as a timer that could be used in the engineering of synthetic circuits.bifurcation ͉ dynamics ͉ circuit ͉ stochastic ͉ quantized cycle S tochastic fluctuations in gene expression and protein concentrations are a natural by-product of biochemical reactions in cells. Properties of this biochemical noise within genetic circuits, such as their amplitude, distribution, and propagation, have been extensively characterized (1-9). Additionally, theoretical and experimental studies have established that such noise can induce stochastic switching between distinct and stable phenotypic states (5, 10-23). Noise within genetic circuits is therefore thought to contribute to phenotypic heterogeneity in genetically identical cellular populations. It has also recently been shown experimentally that noise can trigger cellular differentiation in fruit flies and bacteria (14,17,18,24). Together, these studies establish that noise can play an active functional role in cellular processes by effectively destabilizing and thus inducing escape from stable phenotypic states.Besides its common role in destabilizing stable states, noise can also have the more counterintuitive effect of generating new stable states that do not exist in the absence of fluctuations (25). In particular, noise-induced bistability has been reported theoretically (26, 27) and experimentally (2). In those situations, one of the two stable solution branches is usually present irrespective of fluctuations, whereas the second one is purely induced by noise (28). The appeara...

Optimizing periodicity and polymodality in noise-induced genetic oscillators

“…In addition, the noise-induced stabilization of the unstable state emerges close to a Hopf bifurcation [13] beyond which the system becomes bistable. Despite these constraints in the parameter values, the activator-repressor system presented here is robust to parameter changes, as shown in Fig.…”

“…2(a)]. This leads to the trajectory getting trapped orbiting around the unstable fixed point for an integer number of cycles, thus generating a polymodal distribution of pulse durations [13].…”

“…To that end we consider one of the most basic oscillator architectures, namely a two-component activatorinhibitor system operating in an excitable regime (close to the oscillatory region) and subject to noise. We recently showed that such a model system exhibits noise-induced stabilization of an unstable spiral state [13]. Due to its excitable character, this model system displays noise-triggered excursions away from the stable (rest) state, during which the cell passes through a region near the unstable spiral.…”

Parameter asymmetry and time‐scale separation in core genetic commitment circuits

“…In recent years, we have learned that biochemical fluctuations (i.e., "noise") are an integral part of how living systems not only mechanistically work, but also why Evolution picked certain regulation schemes over others [5][6][7][8][9][10][11][12]. Therefore, it is not only continuous nonlinear dynamics that is relevant, but it is also stochasticity induced by the paucity of some key molecular regulator(s) in the system.…”

Stochastic oscillatory dynamics of generalized repressilators

“…Several systems are known in which stochastic fluctuations excite oscillating behavior in genetic circuits [5,6,7] by either effectively stabilizing unstable periodic orbits [7,6] or leading to coherence resonance in the monostable system [5].…”