Period Doubling Bifurcations in a Forced Cell-Free Genetic Oscillator

Abstract

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.