Hierarchical Bond Graph Modelling of Biochemical Networks

TL;DR

This paper introduces a hierarchical bond graph modeling approach for biochemical networks, enabling modular, thermodynamically compliant, and reusable models that can be constructed from simpler components and applied to complex biological processes.

Contribution

It extends bond graph modeling to hierarchical, modular biochemical networks with thermodynamic compliance and provides methods to derive parameters from literature data.

Findings

Successfully modeled glycogenolysis in skeletal muscle

Ensured thermodynamic compliance independent of parameter precision

Provided formulas relating free-energy and equilibrium constants

Abstract

The bond graph approach to modelling biochemical networks is extended to allow hierarchical construction of complex models from simpler components. This is made possible by representing the simpler components as thermodynamically open systems exchanging mass and energy via ports. A key feature of this approach is that the resultant models are robustly thermodynamically compliant: the thermodynamic compliance is not dependent on precise numerical values of parameters. Moreover, the models are reusable due to the well-defined interface provided by the energy ports. To extract bond graph model parameters from parameters found in the literature, general and compact formulae are developed to relate free-energy constants and equilibrium constants. The existence and uniqueness of solutions is considered in terms of fundamental properties of stoichiometric matrices. The approach is illustrated by building a hierarchical bond graph model of glycogenolysis in skeletal muscle.