Thermodynamical Fluxes for the Modeling of Cardiac Mitochondrial Calcium Handling

Bachar Tarraf1, Michael Leguèbe2, Yves Coudière3
1Ph.D. student, 2Junior research scientist, 3University professor


Calcium handling is essential in cardiac excitation-contraction coupling. Cytoplasmic Calcium concentration is regulated by membrane fluxes, and fluxes between cytoplasm and various intracellular compartments, like sarcoplasmic reticulum, myofibrils, mitochondria.

Besides energy production through oxidative phosphorylation, cardiac mitochondria significantly participate in the intracellular Calcium cycle. Therefore abnormal mitochondrial activity may be linked to cardiac arrhythmia. In order to explore this question, we plan to develop mathematical models of the cardiac mitochondria, that address specifically Calcium handling.

There exists an extensive literature concerning mitochondrial models, though they are designed in a bottom-up, and iterative modeling approach. Consequently, they have in general a high level of complexity in terms of the number of parameters, and therefore their calibration is difficult and may be mathematically unfeasible. Additionally, the use of complex analytical expressions of mitochondrial flux led some authors to commit transcription errors when copying the expressions between papers.

Bertram et al. (J Theor Biol 2006) proposed to simplify the expressions by reducing the number of parameters, so as to describe the same dynamics with a minimal number of parameters. However, they made some biological assumptions that are not relevant to our context.

We revisited the flux expressions by resuming to the original work of Hill (1977), which has been the base of most mitochondrial models, tracking down transcription errors, and simplifying the final expressions by surface fitting to simpler analytical expressions.

In addition, we adopted an original modeling approach that consists in writing the model in terms of thermodynamics variables instead of concentrations.

The final model has around 30 parameters, compared to more than 100 for usual models. This is important since we plan to calibrate the model to experimental data on isolated mitochondria. Subsequently, the model may be introduced into ionic membrane models, as part of the Calcium cycle.