Declarative modeling of a neurulation-like process.

Area of Science:

• Computer Science
• Computational Biology
• Mathematical Modeling

Background:

• Dynamical systems often have fixed state spaces, limiting their application to systems with evolving structures.
• Modeling systems with dynamically changing structures requires specialized approaches.

Purpose of the Study:

• Introduce MGS, an experimental programming language for modeling and simulating dynamical systems with dynamical structures ((DS)(2)).
• Present the core concepts of MGS: topological collections and transformations.
• Demonstrate MGS's utility in simulating biological processes, specifically early neurulation.

Main Methods:

• Developed MGS with unique data structures (topological collections) and control structures (transformations).
• Unified topological collections using concepts from combinatorial algebraic topology (cellular complexes, topological chains).
• Applied MGS to model the initial stages of neurulation, a key developmental biology process.

Main Results:

• MGS facilitates the easy specification of (DS)(2).
• The language effectively models the topological changes in structures governed by local, discrete evolution laws.
• Successfully simulated the first step of neurulation, demonstrating MGS's capability in complex biological modeling.

Conclusions:

• MGS provides a powerful framework for simulating systems with dynamically changing structures.
• The language's approach, rooted in topological concepts, is well-suited for modeling biological morphogenesis.
• MGS offers a direct method for describing topological modifications using local interaction rules.