Analysing and simulating energy-based models in biology using BondGraphTools

Abstract

Like all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

A semantics, energy-based approach to automate biomodel composition

“…The biochemical species are defined using the component C e , given by the constitutive relation u = RT ln( K q q ) ( Boltzmann’s formula), where R (J mol −1 K −1 ) is the ideal gas constant, T (K) is the absolute temperature, q (mol m −3 ) is the molar concentration of the species, and K q (mol −1 ) is the species thermodynamic constant [ 34 ]. K q is related to the kinetic free energy of species to participate in reactions and is defined as where V c is the volume of the compartment, q ref is the reference concentration (normally 1 mol), and is the standard free energy formation of the species [ 25 ];…”

“…The task of automated model composition requires bond graph software that readily supports automation. For this purpose, we have selected BondGraphTools—an open-source Python library for bond graph modelling—created and developed by Cudmore et al [ 25 ], accessible from https://github.com/BondGraphTools/BondGraphTools . BondGraphTools supports modularisation and automation in model building.…”

“…Because bond graph models assign a chemical potential to each species, they automatically adhere to detailed balance constraints. Hence, parameters can be modified without violating thermodynamic consistency [ 25 ]. This ensures that model composition respects the constraints on thermodynamics for biochemical systems.…”

“…This platform allows us to automatically construct a composed model from annotated CellML files treated as modules. Because the CellML files do not contain the bond graph structure, a separate bond graph library in Python (BondGraphTools [ 25 ]) automatically deals with any required changes in the conservation laws. The annotated parameters from the CellML models are then extracted and their values assigned to their equivalent bond graph parameters.…”

Network Thermodynamics of Biological Systems: A Bond Graph Approach

“…Edmund Crampin [1] made seminal contributions to Systems Biology which will remain influential in the field. One of his many research areas was the energy-based analysis of biological systems using the bond graph approach and he coauthored an number of papers [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and directly influenced others [18][19][20][21][22][23]. This paper brings together and summarises this work, illustrates the approach using photosynthesis as an example and suggests future research directions.…”