Thermodynamical Fluxes for the Modeling of Cardiac Mitochondrial Calcium Handling

Abstract

It is known that mitochondria play a crucial role in the handling of calcium by cardiac cells during the excitationcontraction cycle. However, the precise characterization of this role is still under debate.With this intent, a collection of mathematical models have been developed, but they generally show a level of complexity that is not compatible with inverse problem techniques required for calibration with experimental data. Their large number of equations and parameters can also lead to transcription mistakes that can be found in the literature. In this paper we apply a similar methodology as Bertram et al.in [1] to propose a simple model that is derived from the base equations that constitute the origin of most mitochondrial models [2].Our model describes the main features of the mitochondrial activity with 6 equations and ∼30 parameters, which we will eventually reduce in a forthcoming sensitivity analysis.

Global Sensitivity Analysis for Uncertain Parameters Applied to a Cardiac Mitochondrial Model

“…In this work, we firstly carried out a global sensitivity analysis on the model proposed in [1]. It was completed in two steps, the analysis on the internal mitochondrial flux functions outputs, and the analysis on the state variables of the model along a typical trajectory.…”

“…For this reason, developping cardiac models that take into account the activ-ity of the mitochondria is important. In our previous paper [1], we introduced a mathematical model that describes key mechanisms of the cardiac mitochondria, specifically dioxygen consumption, calcium (Ca 2+ ) regulation through the uniporter and the Na + /Ca 2+ exchanger, and the ATP synthesis. The model consists of six state variables that describe the activity of the mitochondria through ion fluxes (Fig.…”

“…These source terms allow us to mimic an experimental condition, for instance an addition of cytoplasmic ADP. The biological meaning of the fluxes V j and the derivation of their expressions can be found in [1]. Even though our model is considered simple (34 parameters overall) in comparison with models in the literature, it is still impossible to calibrate it to fit experimental data.…”

“…Mathematical models are useful to better understand the complexity of mitochondrial dynamics within a cardiac cell, and we are specifically interested in the dynamics of calcium. Litterature models reflect this complexity, especially in terms of number of equations and parameters, which makes them impossible to calibrate to experimental data.In this paper, we apply a global sensitivity analysis on our previously discussed simple mitochondria model [1], in order to quantify the uncertainty of the parameters. This analysis is done in two steps.…”

“…In this paper, we apply a global sensitivity analysis on our previously discussed simple mitochondria model [1], in order to quantify the uncertainty of the parameters. This analysis is done in two steps.…”