Declarative modeling of a neurulation-like process

Abstract

MGS is an experimental programming language dedicated to the modeling and the simulation of a special kind of discrete dy- namical systems. Dynamical systems with a dynamical structure (or (DS) 2) arise when the state space is not fixed a priori but is jointly computed with the current state during the simulation. In this case the evolution function is often given through local rules that drive the interaction between some system components. MGS offers a new kind of data structure, topological collections, to describe the state of a dynamical system, and a new kind of control structure, transformations, to express local and discrete evolution laws. These two notions permit an easy specification of (DS) 2. We propose in this paper a presentation of the MGS language and its main contributions. We show that various topological collections can be unified using concepts developed in combinatorial algebraic topology: cellular complexes and topological chains. Then we apply the notions brought by MGS to model and simulate the first step towards the simulation of the neurulation process in developmental biology where a sheet of cells evolves to a neural tube. It is a direct description of the modification of the topology of an arbitrary structure expressed in terms of local discrete evolution laws.