Graph theory approaches for molecular dynamics simulations.

Graph theory, a branch of mathematics that focuses on the study of graphs (networks of nodes and edges), provides a robust framework for analysing the structural and functional properties of biomolecules. By leveraging molecular dynamics (MD) simulations, atoms or groups of atoms can be represented as nodes, while their dynamic interactions are depicted as edges. This network-based approach facilitates the characterization of properties such as connectivity, centrality, and modularity, which are essential for understanding the behaviour of molecular systems. This review details the application and development of graph theory-based models in studying biomolecular systems. We introduce key concepts in graph theory and demonstrate their practical applications, illustrating how innovative graph theory approaches can be employed to design biomolecular systems with enhanced functionality. Specifically, we explore the integration of graph theoretical methods with MD simulations to gain deeper insights into complex biological phenomena, such as allosteric regulation, conformational dynamics, and catalytic functions. Ultimately, graph theory has proven to be a powerful tool in the field of molecular dynamics, offering valuable insights into the structural properties, dynamics, and interactions of molecular systems. This review establishes a foundation for using graph theory in molecular design and engineering, highlighting its potential to transform the field and drive advancements in the understanding and manipulation of biomolecular systems.