Modular dynamic biomolecular modelling with bond graphs: the unification of stoichiometry, thermodynamics, kinetics and data

Abstract

Renewed interest in dynamic simulation models of biomolecular systems has arisen from advances in genome-wide measurement and applications of such models in biotechnology and synthetic biology. In particular, genome-scale models of cellular metabolism beyond the steady state are required in order to represent transient and dynamic regulatory properties of the system. Development of such whole-cell models requires new modelling approaches. Here, we propose the energy-based bond graph methodology, which integrates stoichiometric models with thermodynamic principles and kinetic modelling. We demonstrate how the bond graph approach intrinsically enforces thermodynamic constraints, provides a modular approach to modelling, and gives a basis for estimation of model parameters leading to dynamic models of biomolecular systems. The approach is illustrated using a well-established stoichiometric model of Escherichia coli and published experimental data.

Modular assembly of dynamic models in systems biology

“…However, in many cases, these rate laws are not thermodynamically consistent. The bond graph approach builds on existing work by using thermodynamically independent parameters to ensure that rate laws are thermodynamically consistent [ 15 , 44 , 48 ]. In this section, we use glycolysis as an example to demonstrate the ability of bond graphs to swap out rate laws for one another and to benchmark the performance of alternative rate laws.…”

“…One can create a model of glycolysis by using the stoichiometry to define a high-level reaction structure with swappable modules for each enzyme, and then choose an appropriate rate law for each enzyme, depending on the fit to data ( Fig 7 ). Indeed, this approach was taken by Gawthrop et al [ 48 ].…”

“…Embedding bond graphs within a programmatic environment enables the construction of models using higher-level descriptions, allowing modellers define models using a relatively parsimonious set of commands. Previous work has shown that bond graphs can be constructed from a stoichiometric matrix [48] and a series of reactions [31]. Nonetheless, further work is needed to help automate model construction, in particular making use of rule-based approaches for constructing models of highly complex interactions between proteins, ligands and receptors [77,78].…”

“…Thus, a bond graph approach allows alternative rate laws to be easily swapped for one another while retaining thermodynamic consistency. It is worth noting that the Michaelis-Menten rate law can be derived as a simplification of a more complex mass action model [ 47 , 48 ].…”

A semantics, energy-based approach to automate biomodel composition

“…In this step, a function checks the mergeability of the identically annotated entities. If they are not mergeable, the function ignores the entities [ 53 ]. Otherwise, it passes them to the next step.…”