| [1] |
P. Gawthrop.
Computing biomolecular system steady-states.
IEEE Transactions on NanoBioscience, 17(1):36--43, March 2018.
Published online 25th December 2017.
[ bib |
DOI ]
A new approach to compute the equilibria and the steady-states of biomolecular systems modeled by bond graphs is presented. The approach is illustrated using a model of a biomolecular cycle representing a membrane transporter and a model of the mitochondrial electron transport chain. Keywords: Biological system modeling;Chemicals;Electric potential;Kinetic theory;Mathematical model;Nanobioscience;Steady-state;Biological system modeling;computational systems biology;systems biology |
| [2] |
Peter J. Gawthrop and Edmund J. Crampin.
Biomolecular system energetics.
In Proceedings of the 13th International Conference on Bond
Graph Modeling (ICBGM'18), Bordeaux, 2018. Society for Computer
Simulation.
Available at arXiv:1803.09231.
[ bib |
arXiv ]
Efficient energy transduction is one driver of evolution; and thus understanding biomolecular energy transduction is crucial to understanding living organisms. As an energy-orientated modelling methodology, bond graphs provide a useful approach to describing and modelling the efficiency of living systems. This paper gives some new results on the efficiency of metabolism based on bond graph models of the key metabolic processes: glycolysis. |
| [3] |
P. Gawthrop and E. J. Crampin.
Bond graph representation of chemical reaction networks.
IEEE Transactions on NanoBioscience, 17(4):449--455, October
2018.
Available at arXiv:1809.00449.
[ bib |
DOI |
arXiv ]
The Bond Graph approach and the Chemical Reaction Network approach to modelling biomolecular systems developed independently. This paper brings together the two approaches by providing a bond graph interpretation of the chemical reaction network concept of complexes. Both closed and open systems are discussed. The method is illustrated using a simple enzyme-catalysed reaction and a trans-membrane transporter. Keywords: Chemicals;Junctions;Substrates;Standards;Nanobioscience;Biological system modeling;Open systems |
| [4] |
Michael Pan, Peter J. Gawthrop, Kenneth Tran, Joseph Cursons, and Edmund J.
Crampin.
Bond graph modelling of the cardiac action potential: implications
for drift and non-unique steady states.
Proceedings of the Royal Society of London A: Mathematical,
Physical and Engineering Sciences, 474(2214), 2018.
Available at arXiv:1802.04548.
[ bib |
DOI |
arXiv ]
Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a extquoteleftconserved moietyextquoteright. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems. |
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