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 E. coli and published experimental data.

Modular assembly of dynamic models in systems biology

“…Embedding bond graphs within a programmatic environment allows models to be constructed using higher-level descriptions. Previous work has shown that bond graphs can be constructed from a series of reactions [41], and further work will focus on incorporating rule-based modelling for constructing models of highly complex interactions between proteins, ligands and receptors [61].…”

“…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 [40,41]. In some cases, the full dynamics of the enzymatic reaction need to be considered.…”

“…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 [33,37,41]. 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.…”

Dynamical models for metabolomics data integration

“…The choice of rate laws is a trade-off between "mechanisticness" on the one hand and model complexity and number of parameters on the other hand. Using a thermodynamics-based formalism [31,32] helps to create physically feasible models. Furthermore, such a parameterization can reduce the number of unknown parameters and simplify parameter estimation.…”

Energy-based advection modelling using bond graphs

“…The bond graph theory used in this paper was developed by Gawthrop and Crampin [9] and introductory material is available [21,22]. The bond graph modelling in this paper is based on the Python package [23] available at .…”