A group theoretic approach to model comparison with simplicial representations

Area of Science:

• Computational Biology
• Mathematical Modeling
• Systems Biology

Background:

• Biological systems are complex, generating large datasets that require mathematical models for understanding.
• Existing models often use diverse mathematical formalisms, hindering direct comparison and unified descriptions.
• Comparing models based on conceptual structure is crucial for advancing biological systems research.

Purpose of the Study:

• To develop a rigorous and automatable methodology for comparing mathematical models of biological systems.
• To enhance the existing framework for model comparison using simplicial complexes.
• To introduce a group-theoretic approach for model comparison.

Main Methods:

• Representing models as labeled simplicial complexes to capture conceptual structure.
• Developing group actions on simplicial complexes to identify related model components (vertices).
• Providing an alternative framework representing models as groups for direct group-theoretic analysis.

Main Results:

• A rigorous and automatable method for determining model equivalence based on vertex symmetry in simplicial representations.
• Simplified and expedited comparison of mathematical models.
• A new group-theoretic framework enabling direct application of group theory to model comparison.

Conclusions:

• The developed methodology significantly advances the comparison of mathematical models in systems biology.
• Automated model equivalence determination using group actions on simplicial complexes enhances research efficiency.
• The group-theoretic framework offers a powerful alternative for unifying mathematical descriptions of biological systems.