Dynamical Principles of Two-Component Genetic Oscillators

Abstract

Genetic oscillators based on the interaction of a small set of molecular components have been shown to be involved in the regulation of the cell cycle, the circadian rhythms, or the response of several signaling pathways. Uncovering the functional properties of such oscillators then becomes important for the understanding of these cellular processes and for the characterization of fundamental properties of more complex clocks. Here, we show how the dynamics of a minimal two-component oscillator is drastically affected by its genetic implementation. We consider a repressor and activator element combined in a simple logical motif. While activation is always exerted at the transcriptional level, repression is alternatively operating at the transcriptional (Design I) or post-translational (Design II) level. These designs display differences on basic oscillatory features and on their behavior with respect to molecular noise or entrainment by periodic signals. In particular, Design I induces oscillations with large activator amplitudes and arbitrarily small frequencies, and acts as an “integrator” of external stimuli, while Design II shows emergence of oscillations with finite, and less variable, frequencies and smaller amplitudes, and detects better frequency-encoded signals (“resonator”). Similar types of stimulus response are observed in neurons, and thus this work enables us to connect very different biological contexts. These dynamical principles are relevant for the characterization of the physiological roles of simple oscillator motifs, the understanding of core machineries of complex clocks, and the bio-engineering of synthetic oscillatory circuits.

Deterministic characterization of stochastic genetic circuits

“…Each simulation run generates a collection of interspike times from which the mean ͳTʹ and the variance ͳ(ͳTʹ Ϫ T) 2 ʹ 1/2 can be calculated. Following Steuer et al (13), the quality of the noise-induced oscillations is measured by using the noise-to-signal ratio T ϭ ͳ(ͳTʹ Ϫ T) 2 ʹ 1/2 /ͳTʹ, and the system is said to exhibit regular oscillations where T is small (13,38). The dependence of T on the repressor degradation rate is shown in Fig.…”

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

“…In this way, we have a self-activating bistable unit which is coupled to a negative feedback loop. The simplest, idealized implementation of this unit has been analyzed on a deterministic level, with protein concentrations as the only dynamical variables, and it is known to produce oscillations in a certain range of model parameters [8,9]. In particular, the model studied in Ref.…”

Caveats in modeling a common motif in genetic circuits

“…Since we are interested in the fate of the regular oscillations in case of slow and ultra-slow genes, it is important not to need a finetuning for seeing oscillations for fast genes. Furthermore, we would like to compare our equations (28,29) with the deterministic equations as they were derived for "design I" in [9]. In common with those equations of [9] is the limit of fast genes and the realization of the repression operating on the transcriptional level.…”

“…Furthermore, we would like to compare our equations (28,29) with the deterministic equations as they were derived for "design I" in [9]. In common with those equations of [9] is the limit of fast genes and the realization of the repression operating on the transcriptional level. The main differences between both sets of equations are firstly the power one of Φ A in Eq.…”

“…In principle a number of intermediate steps may be included in these loops, and these intermediate steps need not be on the same level in case of a hierarchical organization. They could amount to reactions between genes leading to production rates on the level of proteins, or on the same level, just to reactions between proteins, and it may make a big difference if protein A is repressed via the binding of a transcription factor of type B to gene b (design I), or via a direct repression of protein A via B (design II), as it was emphasized in [9]. There it was shown that the distinct set of equations, corresponding to the two designs, lead to different oscillatory features and different behavior with respect to noise and external periodic signals, so that the motif in the first design acts as an "integrator" of external stimuli, in the second design as a "resonator".…”