Ivan Chang, Margit Heiske, Thierry Letellier, Douglas Wallace, Pierre Baldi

Mitochondrial bioenergetic processes are central to the production of cellular energy, and a decrease in the expression or activity of enzyme complexes responsible for these processes can result in energetic deficit that correlates with many metabolic diseases and aging. Unfortunately, existing computational models of mitochondrial bioenergetics either lack relevant kinetic descriptions of the enzyme complexes, or incorporate mechanisms too specific to a particular mitochondrial system and are thus incapable of capturing the heterogeneity associated with these complexes across different systems and system states.

Here we introduce a new composable rate equation, the chemiosmotic rate law, that expresses the flux of a prototypical energy transduction complex as a function of: the saturation kinetics of the electron donor and acceptor substrates; the redox transfer potential between the complex and the substrates; and the steady-state thermodynamic force-to-flux relationship of the overall electro-chemical reaction.

Modeling of bioenergetics with this rate law has several advantages:

1. it minimizes the use of arbitrary free parameters while featuring biochemically relevant parameters that can be obtained through progress curves of common enzyme kinetics protocols;
2. it is modular and can adapt to various enzyme complex arrangements for both in vivo and in vitro systems via transformation of its rate and equilibrium constants;
3. it provides a clear association between the sensitivity of the parameters of the individual complexes and the sensitivity of the system’s steady-state.

To validate our approach, we conduct in vitro measurements of ETC complex I, III, and IV activities using rat heart homogenates, and construct an estimation procedure for the parameter values directly from these measurements. In addition, we show the theoretical connections of our approach to the existing models, and compare the predictive accuracy of the rate law with our experimentally fitted parameters to those of existing models.

Finally, we present a complete perturbation study of these parameters to reveal how they can significantly and differentially influence global flux and operational thresholds, suggesting that this modeling approach could help enable the comparative analysis of mitochondria from different systems and pathological states.

Documents for Download

The two notebook files demonstrate the use of a new reaction rate law specifically derived for the electron transport chain (ETC) complexes of the Mitochondria’s oxidative phosphorylation pathway.
Standard Form.nb shows how the rate law is defined, how to estimate (fit) its parameters from data, and how to obtain simulation output.
Standard Form

In Vitro ETC Chain Threshold.nb demonstrates the application of the rate law on a simplified electron transport chain consisting of three of its main complexes, mimicking in vitro experimental conditions. The demonstration shows how the variations/perturbations of the rate law parameters on the individual complexes affect the threshold of the flux of the overall ETC pathway.
In Vitro ETC Chain Threshold

Raw enzyme kinetics data of Complex I from spectrophotometer measurement of NADH absorption. Please unzip the folder “ComplexI_121207” to the same directory as the notebook files.
ComplexI_121207

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