How to synchronize Biological Clocks

Clocklike rhythms are found in every organism, from bacteria to humans and need to be perfectly synchronized in order to regulate the basic mechanisms for life. Biological oscillators can synchronize even in noisy environments and despite differences between the biochemical parameters of the clocks. Even if this intrinsic robustness has stimulated several attempts to explain the emergence synchronization phenomena, a systematic theoretical framework for its study is still lacking. This paper is concerned with a novel algorithm to study networks of biological clocks. A new set of conditions is established that can be used to verify whether an existing network synchronizes or to give guidelines to construct a new synthetic network of biological oscillators that synchronize. The methodology uses the so-called contraction theory from dynamical system theory and Gershgorin disk theorem. The main features of our algorithm is that it explicitly takes into account the presence of noise and parameter mismatches and provides simple algebraic constraints on the parameters of the oscillator. The strategy is validated on two examples: a model of glycolisis in yeast cells and a synthetic network of Repressilators that synchronizes.