A statistical approach reveals designs for the most robust stochastic gene oscillators

Abstract

The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed? Can we make genetic oscillators arbitrarily robust? These questions are technically challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and concentrate on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the number of interactions, the presence of autoregulation, and degradation of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding additional feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biology. KEYWORDS: oscillations, robustness, circuit topology, stochastic processes, sequential Monte Carlo A major challenge facing the progress of synthetic biology is the design and implementation of systems that function in the face of fluctuating cellular environments. While it is widely accepted within the field that the task of constructing and rewiring pathways is tractable, predicting in silico how an implemented system will behave in vivo under different cellular conditions remains a huge challenge. 1 Robust systems perform their function over a wide range of parameters and external influences. If we could design and build synthetic systems that are robust, then not only would the systems have a higher probability of functioning, but we would also enhance their predictability. Robustness in the context of biological systems has been intensively studied for almost two decades. 2−6 Approaches to studying this in biological systems often utilize the frameworks of feedback and robust control. 7 It is wellknown that feedback mechanisms can increase the robustness of a biological system, 8,9 and there are trade-offs between robustness and performance, fragility, and efficiency. 10,11 Although som...

A computational method for the investigation of multistable systems and its application to genetic switches

“…We find that the parameters representing the rates of degradation of the transcription factors in the system (k x ,k y ) must both be large in relation to the prior range, and approximately equal, for bistability to occur. Protein degradation rates have been shown to be important for many system behaviours including oscillations [7,56,57]. We also find that the steady states of the LU-CS model are symmetric: the values for the dominant and repressed species are equivalent in both steady states.…”

Multiobjective Identification of a Feedback Synthetic Gene Circuit

“…Note that, we used the lumped propensity functions derived from the reduced model, like the f (n i 3 , t) Hill-like function associated with LuxI repression. This approach has already been used in [53]. We validated it for our model (see Appendix I) by simulating the pseudoreaction associated with f (n i 3 , t) using the CLE approach and comparing the result with the one obtained by simulating the expanded set of corresponding original reactions using the Gillespie's direct method Stochastic Simulation Algorithm (SSA).…”

“…Following an approach used in [53], we validated the use of a high-order propensity function by simulating the pseudoreaction associated with f (n 3 , t) using the CLE approach and then comparing this result with the one obtained by simulating the set of corresponding original reactions using the Gillespie's direct method SSA.…”

High-resolution mapping of the period landscape reveals polymorphism in cell cycle frequency tuning

“…Theoretical studies on the topological designs of biological oscillators (Tsai et al, 2008;Woods et al, 2016) have suggested that the positive feedback loops may play an important role in the robustness and great tunability of an oscillator. Modeling of the cell cycle network has also highlighted the essential role of Cdk1/Wee1/Cdc25 positive feedback in the cell cycle behavior as a relaxation oscillator, which provided an explanation why the cell cycle is highly tunable in frequency (Tsai et al, 2008;Gérard et al, 2012).…”