πŸ“’ Bazil 2010

Modeling mitochondrial bioenergetics with integrated volume dynamics1



  • Current experimental techniques limit the ability to resolve details of the mitochondrial bioenergetic processes in vivo


Model Development
Model schematics

  • 73 state system of differential-algebraic equations (DAEs) that consists of 65 non-linear ordinary differential equations (ODEs)
  • derived from heart tissue of either bovine, porcine or rat with some data obtained from liver tissue
  • ANT: Metelkin model (two distinct adenine nucleotide binding sites )
  • mitochondrial calcium dynamics similar to Nguyen et al. [2], Cortassa et al. [3] and Dash and Beard
  • β€˜futile’ K+-cycle plays a major role in mitochondrial volume homeostasis

Parameter Estimation

  • our independent data sets consisting of 32 data curves were used from Bose et al. [8], LaNoue et al. [9], Wan et al. [10] and Kowaltowski et al.
  • For each data set, the model was initialized from a condensed, fully oxidized and de-energized state via initialization simulations that replicated the experimental incubation conditions
  • TCA cycle intermediate dynamics of the model were fitted to the data set presented by LaNoue et al
  • Mitochondrial Ξ”Οˆ, NAD/NADH redox state, myocardial oxygen consumption (MVO2), cytochrome c3+/c2+ redox state and matrix pH were reported as the extra-mitochondrial Pi was progressively increased from 0 to 10 mM.
  • The volume dynamics were fitted to the transient mitochondrial matrix swelling data published by Kowalowski et al

Corroborating the Model through Simulation

  • robustness of the model to local parameter perturbations
  • qualitative agreement of predicted trends with experimental observations
  • the ability of the model to reproduce experimental data that was not used in fitting its parameters.
  • absolute-value normalized local sensitivity coefficients (LSC) were computed
  • on average that a perturbation of 1% for a given parameter results in less than a 0.738 +/βˆ’ 0.118% change in the state dynamics of the model for the experiments considered
  • The model was also able to reproduce the well known mitochondrial shrinkage/swelling dynamics in the presence of Pi and ADP: extra-mitochondrial Pi-titration was increased, mitochondrial matrix water volume increased with the state 3 volume being lower than the state 2 volume


  • The model presented in this manuscript is based on previous models [1]–[4] and includes integrated calcium dynamics and a detailed description of the K+-cycle and its effect on mitochondrial bioenergetics and matrix volume regulation
  • The IMS volume is partly responsible for this regulation by having a direct effect on the cellular bioenergetics in vivo
  • During mitochondrial swelling, the increase in matrix volume causes a reciprocal decrease in IMS volume that enables creatine kinase (mtCK) to bind to the voltage-dependent anion channel (VDAC) thus reducing the adenine nucleotide outer membrane permeability
  • The hypothesized volume-dependent mKHE by Garid was incorporated into the model. This volume dependence is necessary to maintain sufficient potassium efflux at high Ξ”Οˆ during mKATP opening
  • Mitochondria from specific tissue types are phenotypically different and contain various amounts of electron transport proteins, matrix proteins and lipid types optimized to support their designated function.
  • heart mitochondria possess much higher electron transport activity relative to liver mitochondria
  • During the model development, it is important to consider any artifacts in the experimental data that may have been inadvertently generated during the mitochondrial isolation.
  • To simulate the precise experimental conditions during model development, a few explicit assumptions were necessary
  • All mathematical models are abstractions of the underlying process; the level of detail included in the model is dependent upon the application. This is particularly true for the calcium dynamics associated with mitochondrial bioenergetics
    • The mitochondrial Na+/Ca2+ dynamics were simulated using a simplified Na+/Ca2+ cycling mechanisms with only the CaUNI, mNCE and mNHE processes represented.
    • omission of the rapid mode of calcium uptake (RAM)
    • The Na+ independent calcium efflux mechanism is not included in the model formulation since the underlying process is uncertain


  1. Bazil JN, Buzzard GT, Rundell AE. Modeling mitochondrial bioenergetics with integrated volume dynamics. PLoS Comput. Biol. 2010;6(1):e1000632. doi:10.1371/journal.pcbi.1000632. PMC2793388 ↩︎