Analysis of a negative feedback biochemical oscillator

In this paper we describe and analyze a biochemical network that admits oscillatory solutions. Such network simplifies and generalizes the chemical reaction structure of a recently published synthetic in vitro oscillator [1]. We analytically demonstrate that this system admits oscillatory solutions, using simple linearization techniques. Numerical simulations suggest that the oscillatory domain of the system is a closed region, which can be expanded when additional reactions are present. We are devising a structural analysis of the system to derive explicit design criteria to achieve oscillations.