Design and Analysis of a Tunable Recombinase-Based Oscillator

Oscillations are fundamental for autonomous operation in many biological systems, from individual cells to entire organisms such as cell division, muscle contraction, circadian rhythm and neuron firing. Furthermore, understanding the underlying design principles of oscillators by analyzing natural systems and building synthetic biomolecular oscillators are of crucial importance to identify minimal requirements for periodic behavior. As revealed by the various experimental and theoretical synthetic oscillators proposed to date, any oscillator structure consists of negative feedback with a time delay. Despite the simplicity of these principles, it is still unclear how to tune and predict the period in a rational manner that is comparable to electronic oscillators. The nonlinearity of the systems makes it challenging to find closed-form solution of its dynamics. In this work, we address this challenge by the design of a recombinase-based relaxation oscillator that delivers a tunable and predictable period. We take inspiration from the architecture of an electronic multivibrator, and we propose to build a biomolecular multivibrator oscillator by combining positive feedback with negative feedback. This circuit can be realized using different biomolecular components for eukaryote or prokaryote cells. Modeling and numerical simulations show that our approximation of the period as a function of the parameters of the proposed recombinase-based oscillator estimate the period rationally. Stochastic simulations of a single- copy circuit suggest that the oscillations are robust at a low and high number of molecules.