Period Doubling Bifurcations in a Forced Cell-Free Genetic Oscillator

Complex non-linear dynamics such as period doubling and chaos have been previously found in computational models of the oscillatory gene networks of biological circadian clocks, but their experimental study is difficult. Here, we present experimental evidence of period doubling in a forced synthetic genetic oscillator operated in a cell-free gene expression system. To this end, an oscillatory negative feedback gene circuit is established in a microfluidic reactor, which allows continuous operation of the system over extended periods of time. We first thoroughly characterize the unperturbed oscillator and find good agreement with a four-species ODE model of the system. Guided by simulations, microfluidics is then used to periodically perturb the system by modulating the concentration of one of the oscillator components with a given amplitude and frequency. When the ratio of the external `zeitgeber' period and the intrinisic period is close to 1, we experimentally find period doubling and quadrupling in the oscillator dynamics, whereas for longer zeitgeber periods, we find stable entrainment. Our theoretical model suggests favorable conditions for which the oscillator can be utilized as an externally synchronized clock, but also demonstrates that related systems could, in principle, display chaotic dynamics.

Reaction-Diffusion Model for the Arrest of Oscillations in the Somitogenesis Segmentation Clock

The clock and wavefront model is one of the most accepted models for explaining the embryonic process of somitogenesis. According to this model, somitogenesis is based upon the interaction between a genetic oscillator, known as segmentation clock, and a moving wavefront, which provides the positional information indicating where each pair of somites is formed. Recently, Cotterell et al. (2015) reported a conceptually different mathematical model for somitogenesis. The authors called it a progressive oscillatory reaction-diffusion (PORD) model. In this model, somitogenesis is driven by short-range interactions and the posterior movement of the front is a local, emergent phenomenon, which is not controlled by global positional information. With the PORD model, it was possible to explain some experimental observations that are incompatible with the clock and wavefront model. However the PORD model has the disadvantage of being quite sensitive to fluctuations. In this work, we propose a modified version of the PORD model in order to overcome this and others inconveniences. By means of numerical simulations and a numerical stability analysis, we demonstrate that the modified PORD model achieves the robustness characteristic of somitogenesis, when the effect of the wavefront is included.

Theory of genetic oscillations with external noisy regulation

We present a general theory of noisy genetic oscillators with externally regulated production rate. The observables that characterize the genetic oscillator are discussed, and it is shown how their statistics depend on the statistics of the external regulator. We show that these observables have generic features that are observed in two different experimental systems: the expression of the circadian clock genes in fibroblasts, and in the transient and oscillatory dynamics of the segmentation clock genes observed in cells disassociated from zebrafish embryos. Our work shows that genetic oscillations with diverse biological contexts can be understood in a common framework based on delayed negative feedback system, and slow regulator dynamics.

Bacterial variability in the mammalian gut captured by a single-cell synthetic oscillator

Synthetic gene oscillators have the potential to control timed functions and periodic gene expression in engineered cells. Such oscillators have been refined in bacteria in vitro, however, these systems have lacked the robustness and precision necessary for applications in complex in vivo environments, such as the mammalian gut. Here, we demonstrate the implementation of a synthetic oscillator capable of keeping robust time in the mouse gut over periods of days. The oscillations provide a marker of bacterial growth at a single-cell level enabling quantification of bacterial dynamics in response to inflammation and underlying variations in the gut microbiota. Our work directly detects increased bacterial growth heterogeneity during disease and differences between spatial niches in the gut, demonstrating the deployment of a precise engineered genetic oscillator in real-life settings.