Turing-type instabilities in a mathematical model of notch and retinoic acid pathways

Abstract

In this paper we employ Turing Theory to study the effects of Notch and Retinoic Acid (RA) pathways on neuronal differentiation. A mathematical model consisting of two reaction-diffusion subsystems is presented such that each subsystem is compelled by the level of RA and activated Notch utilized in the experiment. We hypothesize an interaction between RA and Notch pathways. This interaction is reflected in the model by considering a perturbation to both subsystems. The conditions for the existence of Turing instabilities are established and compared for both cases where the two subsystems are either perturbed or unperturbed. For these two cases we present numerical simulations for Turing instabilities and Turing bifurcations. The study of Turing mechanism in interacting signaling pathways might bring some insight into the recent biological findings of neuronal differentiation.