A bond graph approach to integrative biophysical modelling

© 2019 Michael PanA major goal of systems biology is to develop comprehensive, multi-scale mathematical models of physiological systems that integrate biological knowledge from the scale of molecules to the scale of tissues and organs. Models on this scale hold great potential in advancing our knowledge of biology and medicine, but they have yet to be achieved in complex biological systems. It is widely acknowledged that constructing large-scale models requires the reuse and integration of existing models; however, model integration is currently challenging because many existing models violate the conservation laws of physics, especially conservation of energy. It is therefore highly desirable to express models in a framework that respects the laws of physics and thermodynamics. Bond graphs are an energy-based modelling framework, initially developed for use in multi-physics engineering systems to help derive equations consistent with the laws of physics. More recently, bond graphs have been applied to the field of biology where they have helped in making models physically and thermodynamically consistent. While bond graphs provide several advantages for large-scale modelling such as thermodynamic consistency and hierarchical modelling, they have yet to be applied to large-scale dynamic models of biological systems. This thesis aims to develop methods based on the bond graph framework to facilitate model reuse and integration. These methods are demonstrated by applying them to biomolecular systems within the cardiac cell. Firstly, bond graphs are applied to membrane transporters, demonstrating that bond graphs can be used to correct thermodynamic inconsistencies within existing models. Secondly, independently developed models of ion channels and transporters are coupled into a model of cardiac electrophysiology, showing that bond graphs can be used to systematically explain the issues of drift and non-unique steady states that affect many existing models. Finally, a generalised method for simplifying models of enzyme kinetics is developed and used to facilitate the development of simple, thermodynamically consistent models of enzymes that are easily incorporated into larger models