Engineering principles of synthetic biochemical oscillators with negative cyclic feedback

This paper analyzes oscillatory dynamics of a class of cyclic gene regulatory networks and provides engineering principles for the synthesis of biochemical oscillators. We first review previous results that the oscillatory parameter regime of the gene regulatory circuits can be rigorously explored by the local stability analysis of a unique equilibrium. The local stability analysis then leads to the first engineering principle that the circuit components, or genes, should be chosen so that the kinetic profiles of the circuit components are similar to each other. Using a homogeneous oscillator model, we further discuss design strategies to reduce the cell-to-cell variability of the oscillators that is caused by intrinsic noise.