A general thermodynamic approach for model reduction of enzyme cycles and electrogenic transporters

Mathematical models of enzyme cycles form the basis of quantifying key features of metabolism and membrane transport. These models are often integrated into more comprehensive models such as whole-cell models to understand emergent behaviours between interacting components. However, it is currently computationally infeasible to simulate the full dynamical behaviour of every enzyme at a network scale. Model reduction is frequently used to improve computational efficiency, but in general, these approaches do not preserve physical and thermodynamic consistency. Here, we outline a general method for simplifying enzyme kinetics models while retaining mass, charge and energy balance. We base our approach on the bond graph, which is a general methodology for modelling biological systems from fundamental physical laws. This approach ensures that key physical constraints are enforced in every model, regardless of their complexity. Our thermodynamic model reduction framework is readily extended to electrogenic transporters through the coupling of chemical and electrical processes. Through the application of our approach to both hypothetical enzyme cycles and real data from the Na+/K+ ATPase, we show that it can rapidly screen for plausible network structures in circumstances where enzyme catalytic mechanisms may not be fully characterised, facilitating biological discovery and drug development.