Automated Techniques for Stability Analysis of Delta-Notch Lateral Inhibition Mechanism

We describe, in detail, the modeling and automatic analysis of the Delta-Notch lateral inhibition mechanism using a hybrid systems framework. Inhibitory lateral signaling between adjacent cells is one of the central processes responsible for cell-differentiation in a cluster of identical cells. The basic modeling unit used in this paper is a hybrid automata and more complex models are built using compositions over hybrid automata. Analysis of the resulting model is done by creating a finite-state discrete abstract transition system for the hybrid model and model-checking this abstraction against the properties of interest. The abstraction technique, which is completely automated, uses suitable support from decision procedures and theorem-provers. The automated abstraction of continuous models of biological systems onto discrete transition systems enables new kinds of analysis on problems of biological interest.