A quenched oscillator network for pattern formation in gene expression

Biologists have long searched for reaction net works that can spontaneously generate spatial patterns in the presence of diffusion. The studies so far closely follow Alan Turing\´s "activator-inhibitor" model, where diffusion destabilizes a spatially homogeneous steady state. In this paper, we propose a new type of Turing system based on an oscillator that destabilizes a spatially homogeneous steady state towards a spatio-temporal pattern. We develop a model based on current experimentally-viable systems and study its benefits and limitations.