Network design principle for robust oscillatory behaviors with respect to biological noise

Abstract

Oscillatory behaviors, which are ubiquitous in transcriptional regulatory networks, are often subject to inevitable biological noise. Thus a natural question is how transcriptional regulatory networks can robustly achieve accurate oscillation in the presence of biological noise. Here, we search all two- and three-node transcriptional regulatory network topologies for those robustly capable of accurate oscillation against the parameter variability (extrinsic noise) or stochasticity of chemical reactions (intrinsic noise). We find that, no matter what source of the noise is applied, the topologies containing the repressilator with positive auto-regulation show higher robustness of accurate oscillation than those containing the activator-inhibitor oscillator, and additional positive auto-regulation enhances the robustness against noise. Nevertheless, the attenuation of different sources of noise is governed by distinct mechanisms: the parameter variability is buffered by the long period, while the stochasticity of chemical reactions is filtered by the high amplitude. Furthermore, we analyze the noise of a synthetic human nuclear factor κB (NF-κB) signaling network by varying three different topologies, and verify that the addition of a repressilator to the activator-inhibitor oscillator, which leads to the emergence of high-robustness motif—the repressilator with positive auto-regulation, improves the oscillation accuracy in comparison to the topology with only an activator-inhibitor oscillator. These design principles may be applicable to other oscillatory circuits.

Modelling genetic stability in engineered cell populations

“…As with the toggle switch, this idea has not been experimentally tested, however some studies examine the robustness of repressilator dynamics through other means. Potvin et al, for example, experimentally show that decreasing sources of noise in their repressilator designs improved the regularity of oscillations [44], while Qiao et al [45] show that oscillation-inducing network designs improve robustness when they contain positive autoregulation. As a result, while our analysis suggests one source of irregularity in oscillations (i.e.…”

Spatially coordinated collective phosphorylation filters spatiotemporal noises for precise circadian timekeeping

“…We calculated several features (e.g., period, amplitude, correlation time) from the oscillatory time series. First, in Figure 2G, we calculated the correlation time 55,56 and the relative amplitude 31 , as done in previous studies. Specifically, to calculate the correlation time, we estimated parameters τ C and P by fitting to the autocorrelation function where x ( t ) is the R n time series obtained from the simulation.…”

“…To quantify the accuracy and the strength of the simulated oscillations, we calculated the correlation time and the relative amplitude of the time series of 𝑅 $ (see STAR Methods). The correlation time describes how fast the autocorrelation function of the oscillatory time series decays 55,56 . If the time series exhibits a noisy oscillation, autocorrelation will decay rapidly, resulting in a short correlation time.…”

“…We calculated several features (e.g., period, amplitude, correlation time) from the oscillatory time series. First, in Figure 2G, we calculated the correlation time 55,56 where 𝑥(𝑡) is the 𝑅 $ time series obtained from the simulation. Then, the correlation time is defined as 𝜏 E , and it describes how fast the autocorrelation decays over time.…”

When synthetic biology fails: a modular framework for predicting genetic stability in engineered cell populations

“…for example, experimentally show that decreasing sources of noise in their repressilator designs improved the regularity of oscillations [44], while Qiao et al [45] show that oscillation-inducing network designs improve robustness when they contain positive autoregulation. As a result, while our analysis suggests one source of irregularity in oscillations (i.e.…”