Stochastic coherence in an oscillatory gene circuit model

Novel Tunable Spatio-Temporal Patterns From a Simple Genetic Oscillator Circuit

Multicellularity, the coordinated collective behavior of cell populations, gives rise to the emergence of self-organized phenomena at many different spatio-temporal scales. At the genetic scale, oscillators are ubiquitous in regulation of multicellular systems, including during their development and regeneration. Synthetic biologists have successfully created simple synthetic genetic circuits that produce oscillations in single cells. Studying and engineering synthetic oscillators in a multicellular chassis can therefore give us valuable insights into how simple genetic circuits can encode complex multicellular behaviors at different scales. Here we develop a study of the coupling between the repressilator synthetic genetic ring oscillator and constraints on cell growth in colonies. We show in silico how mechanical constraints generate characteristic patterns of growth rate inhomogeneity in growing cell colonies. Next, we develop a simple one-dimensional model which predicts that coupling the repressilator to this pattern of growth rate via protein dilution generates traveling waves of gene expression. We show that the dynamics of these spatio-temporal patterns are determined by two parameters; the protein degradation and maximum expression rates of the repressors. We derive simple relations between these parameters and the key characteristics of the traveling wave patterns: firstly, wave speed is determined by protein degradation and secondly, wavelength is determined by maximum gene expression rate. Our analytical predictions and numerical results were in close quantitative agreement with detailed individual based simulations of growing cell colonies. Confirming published experimental results we also found that static ring patterns occur when protein stability is high. Our results show that this pattern can be induced simply by growth rate dilution and does not require transition to stationary phase as previously suggested. Our method generalizes easily to other genetic circuit architectures thus providing a framework for multi-scale rational design of spatio-temporal patterns from genetic circuits. We use this method to generate testable predictions for the synthetic biology design-build-test-learn cycle.

Endogenous quasicycles and stochastic coherence in a closed endemic model

We study the role of demographic fluctuations in typical endemics as exemplified by the stochastic SIRS model. The birth-death master equation of the model is simulated using exact numerics and analyzed within the linear noise approximation. The endemic fixed point is unstable to internal demographic noise, and leads to sustained oscillations. This is ensured when the eigenvalues (λ) of the linearized drift matrix are complex, which in turn, is possible only if detailed balance is violated. In the oscillatory state, the phases decorrelate asymptotically, distinguishing such oscillations from those produced by external periodic forcing. These so-called quasicycles are of sufficient strength to be detected reliably only when the ratio |Im(λ)/Re(λ)| is of order unity. The coherence or regularity of these oscillations show a maximum as a function of population size, an effect known variously as stochastic coherence or coherence resonance. We find that stochastic coherence can be simply understood as resulting from a nonmonotonic variation of |Im(λ)/Re(λ)| with population size. Thus, within the linear noise approximation, stochastic coherence can be predicted from a purely deterministic analysis. The non-normality of the linearized drift matrix, associated with the violation of detailed balance, leads to enhanced fluctuations in the population amplitudes.

A comparative analysis of synthetic genetic oscillators

Synthetic biology is a rapidly expanding discipline at the interface between engineering and biology. Much research in this area has focused on gene regulatory networks that function as biological switches and oscillators. Here we review the state of the art in the design and construction of oscillators, comparing the features of each of the main networks published to date, the models used for in silico design and validation and, where available, relevant experimental data. Trends are apparent in the ways that network topology constrains oscillator characteristics and dynamics. Also, noise and time delay within the network can both have constructive and destructive roles in generating oscillations, and stochastic coherence is commonplace. This review can be used to inform future work to design and implement new types of synthetic oscillators or to incorporate existing oscillators into new designs.