📒 Wei 2011

Mitochondrial energetics, pH regulation, and ion dynamics: a computational-experimental approach1



  • Ion regulation (H+, Na+, Ca2+, Pi) are incorporated into the guinea pig heart mitochondria model.
    • equilibrium constants and multiple acid-base equilibria of metabolites with H+
    • associations with Mg2+
    • dependence of IDH and MDH on pH
    • SDH as part of the ETC
    • parameters were either obtained directly from the literature or optimized by minimizing the differences between the model simulation and experimental data
    • Ionic fluxes was tested under steady-state and time-dependent situations
    • state 4 to state 3 transition: a highly energized (i.e., high ΔΨm) and reduced redox status of low respiration and ATP synthesis to high respiratory and ATP synthesis fluxes.
  • Tested the model at the steady state by studying the dependence of respiratory and ATP synthesis fluxes on their driving forces (i.e., Δp, redox, and phosphorylation potentials)


Steady-state behavior

  • As ADPi increases, it is taken up into the matrix, raising the ADPm steady-state level. Higher ADPm decreases the phosphorylation potential, leading to an increase in ATP synthesis, dissipattion of the proton motive force, Δp, NADH consumption and a drop of its redox potential.
  • E/F: substrate deprivation

Calcium uniporter, NHE, and PiC fluxes in relation to pmf

  • the flux through PiC decreases with Δp subsequent to the Pi demand for phosphorylation by the ATP synthase
  • The range of flux values is rather narrow, but it agrees well with the range of Ca2+ uptake fluxes determined experimentally in isolated heart mitochondria

Time-dependent behavior

  • The apparent incomplete collapse of ΔΨm seen in the experimental data may be due to the dynamic range of the ΔΨm probe, TMRM, which is sensitive within the range of 130–210 mV under our experimental conditions

Transition from state 4 to state 3

  • simulated RCR of ∼2.5, similar to experiments.
  • reversal of the H+ pumping direction upon uncoupling, as expected
  • P/O ratio: 1.67 to 2.02 in Fig2. 0.5 in state 4 to 1.25 in state 3. negative upon uncoupling.

Mitochondrial pH and Pi responses during energetic transitions

  • EXP: Addition of 2.0 mM Pi => increase of ΔΨm and a higher reduction of NADH
  • MODEL: change in ΔΨm, but the level of NADH remained constant
  • PiC: Pi/OH antiport, Pi uptake triggers intramitochondrial acidification, resulting in a decrease of the ΔpH component of Δp.
  • large buffering capacity of H+ => pH_mito barly changes


  • This model involves interactions between energetics (i.e., TCA cycle, respiration, and ATP synthesis fluxes) and the dynamics of several ions, including Ca2+, Na+, Pi, and H+
  • The Δp is used for the import of respiratory substrates and Pi (driven by ΔpH), ADP in exchange for ATP through the ANT (driven by ΔΨm), volume regulation (K+, Na+, and anions), energetic signaling (Ca2+), and heat production (H+)
  • Na+ levels increased (∼10%) during energization of the membrane after substrate addition, and decreased (∼13%) in state 3 after ADP addition. Na+ is also known to increase in cardiac mitochondria after episodes of ischemia/reperfusion. Mitochondrial NHE activity also appears to be required for steady-state Ca2+ cycling in energized mitochondria.
  • The model does not account for direct activation of TCA cycle dehydrogenases by Pi, partly explain the lack of increase in NADH observed in the simulations after a pulse of Pi
  • The addition of cyanide shows a close agreement for changes in ΔΨm, i.e., 10 mV (from ∼180 mV to ∼170 mV) as compared with 5 mV (from 165 mV to 160 mV) observed in the experiments

Validation tests

  • respiratory (VO2) and ATP synthesis (VATPsynthase) fluxes to the driving forces (Δp, AF1, Ares)
  • simulation of experimental profiles of ΔΨm and NADH during the transition between states 2/4 and 3, hypoxia (mimicked by CN− addition), and uncoupling by DNP
  • simulation of the increase in VO2 and VATPsynthase upon addition of ADP, decrease under hypoxia and reversal of the ATP synthase during uncoupling
  • reproduction of changes in ΔΨm after Pi addition during state 2/4 respiration
  • interconversion between ΔpH and ΔΨm after addition of Pi

Strengths and limitations of the mitochondrial model

  • optimized the model parameters by adjusting the kinetic constants to reproduce experimental measurements of state variables:

    • TCA cycle intermediates
    • H+ concentration (pH_mito > pH_cyto)
    • Na+ concentration in the matrix (close to the extramitochondrial)
    • steady-state levels of ΔΨm and NADH in state 4
    • fluxes of uniporter (Vuni) and respiratory rates (VO2)
  • Differences: fast relaxation of the state variables observed in the experiments. Some processes are omitted, such as transport of K+ and its associated effect on mitochondrial matrix volume, and the metabolism of ROS. These processes consume Δp and redox potential (e.g., through transhydrogenase activity), resulting in an increase in respiration and a faster NADH consumption rate.

Comparison with previous models of mitochondrial energetics

  • Beard also presented a detailed model that encompassed ion transport, including Pi, K+, and H+. But oxidative phosphorylation rate expressions assume linear flow-force, not S-shaped. And it does not account for Na+ or Ca2+ transport or its effects on energy metabolism.

  • The model exhibits an exponential relationship between mitochondrial and extramitochondrial Ca2+ concentrations, and also accounts for H+ dynamics, the acid-base equilibria of metabolites, and the pH dependence of thermodynamic constants.

Acid-base equilibria and binding polynomials

For both cytoplasmic and mitochondrial compartments.1 $$ \begin{aligned} P_{ATP} &= 1 + \frac{[H^+]}{K_{a}^{ATP}} + \frac{[Mg^{2+}]}{K_{Mg}^{ATP}} \cr P_{ADP} &= 1 + \frac{[H^+]}{K_{a}^{ADP}} + \frac{[Mg^{2+}]}{K_{Mg}^{ADP}} \cr P_{Pi} &= 1 + \frac{[H^+]}{K_{a}^{Pi}} \cr P_{SUC} &= 1 + \frac{[H^+]}{K_{a}^{SUC}} \cr P_{H_2O} &= 1 + \frac{[H^+]}{K_w} \cr [OH^-] &= K_{A}^{H_2O} / [H^+] \cr [ATP^{4-}] &= \Sigma ATP / P_{ATP} \cr [ADP^{3-}] &= \Sigma ADP / P_{ADP} \cr [HPO_4^{2-}] &= \Sigma Pi / P_{Pi} \cr [HATP^{3-}] &= [ATP^{4-}] \frac{[H^+]}{K_{a}^{ATP}} \cr [HADP^{2-}] &= [ADP^{3-}] \frac{[H^+]}{K_{a}^{ADP}} \cr [H_2 PO_4^-] &= [HPO_4^{2-}] \frac{[H^+]}{K_{a}^{Pi}} \cr [MgATP^{2-}] &= [ATP^{4-}] \frac{[Mg^{2+}]}{K_{Mg}^{ATP}} \cr [MgADP^-] &= [ADP^{3-}] \frac{[Mg^{2+}]}{K_{Mg}^{ADP}} \cr \end{aligned} $$

$\delta_H$1E-5-mitochondria $[H^+]$ buffering capacity
$pK_{a}^{ATP}$6.48-pK of ATP acid dissociation constant
$pK_{a}^{ADP}$6.38-pK of ADP acid dissociation constant
$pK_{a}^{Pi}$6.75-pKa of phosphate acid dissociation constant
$pK_{Mg}^{ATP}$4.19-pK of ATP magnesium dissociation constant
$pK_{Mg}^{ADP}$3.25-pK of ADP magnesium dissociation constant
$pK_{a}^{SUC}$5.2-pK of succinic acid dissociation constant
$pKw$14pK of water acid dissociation constant

Citrate synthase (CS)

$$ \begin{aligned} J_{CS} &= \frac{k_{cat} E_T AB}{(1+A)(1+B)} \cr A &= \ce{[AcCoA]} / K_m^{AcCoA} \cr B &= \ce{[OAA]} / K_m^{OAA} \end{aligned} $$

$k_{cat}$0.23523HzCatalytic constant
$E_T$400μMEnzyme concentration of CS
$K_m^{AcCoA}$12.6μMMichaelis constant for AcCoA
$K_m^{OAA}$0.64μMMichaelis constant for OAA
$\ce{[AcCoA]}$1000μMAcetyl CoA concentration
$k_{cat}$ (cell)0.15891HzCatalytic constant (cellular model)

Aconitase (ACO)

$$ \begin{aligned} J_{ACO} &= k_f ([CIT] - [ISOC] / K_{eq}) \cr \ce{[CIT]} &= \Sigma_{CAC} - [ISOC] - [\alpha KG]-[SCoA] - [SUC] - [FUM] - [MAL] - [OAA] \end{aligned} $$

$k_f$0.11688HzForward rate constant of ACO
$K_{eq}$2.22-Equilibrium constant of ACO
$\Sigma_{CAC}$1300μMSum of TCA cycle intermediates
$k_f$ (cell)0.078959HzForward rate constant (cellular model)

Isocitrate dehydrogenase, NADH-producing (IDH3)

$$ \begin{aligned} J_{IDH3} &= \frac{k_{cat} E_T AB}{f_H AB + f_i B + f_a A + f_a f_i} \cr f_H & = 1 + \frac{[H^+]_m}{K_{H1}} + \frac{K_{H2}}{[H^+]_m} \cr A &= [NAD] / K_{NAD} \cr B &= ([ISOC] / K_{ISOC})^n \cr f_a &= \frac{K_A}{K_A + [ADP]_m} \frac{K_{CA}}{K_{CA} + [Ca^{2+}]_m} \cr f_i &= 1 + \frac{[NADH]}{K_{NADH}} \cr \end{aligned} $$

$k_{cat}$11.88kHzRate constant of IDH3
$E_T$109μMConcentration of IDH3
$K_{H1}$1E-9MIonization constant of IDH3
$K_{H2}$9E-7MIonization constant of IDH3
$K_{NAD}$923μMMichaelis constant for NAD
$K_{ISOC}$1520μMMichaelis constant for isocitrate
$n$2-Cooperativity for isocitrate
$K_A$620μMActivation constant by ADP
$K_{CA}$0.5μMActivation constant for calcium
$K_{NADH}$190μMInhibition constant by NADH
$k_{cat}$ (cell)535HzRate constant (cellular model)

Alpha-ketoglutarate dehydrogenase (KGDH)

$$ \begin{aligned} J_{KGDH} &= \frac{k_{cat} E_T AB}{f_H AB + f_a (A + B)} \cr f_H & = 1 + \frac{[H^+]_m}{K_{H1}} + \frac{K_{H2}}{[H^+]_m} \cr A &= [NAD] / K_{NAD} \cr B &= ([\alpha KG] / K_{AKG})^n \cr f_a &= \frac{K_{MG}}{K_{MG} + [Mg^{2+}]_m} \frac{K_{CA}}{K_{CA} + [Ca^{2+}]_m} \cr \end{aligned} $$

$k_{cat}$13.2HzRate constant of KGDH
$E_T$500μMConcentration of KGDH
$K_{H1}$4E-8MIonization constant of KGDH
$K_{H2}$7E-8MIonization constant of KGDH
$K_{NAD}$38700μMMichaelis constant for NAD
$K_{AKG}$30000μMMichaelis constant for αKG
$n$1.2-Hill coefficient for αKG
$K_{MG}$30.8μMActivation constant for Mg
$K_{CA}$0.15μMActivation constant for Ca
$k_{cat}$ (cell)17.9HzRate constant (cellular model)

Succinate-CoA ligase (SL)

$$ \begin{aligned} J_{SL} &= k_f ([SCoA][ADP]_m[Pi]_m - [SUC][ATP]_m[CoA]/K_{eq}^{app}) \cr K_{eq}^{app} &= K_{eq} \frac{P_{SUC}P_{ATP}}{P_{Pi}P_{ADP}} \end{aligned} $$

$k_f$0.028μM * HzForward rate constant of SL
$K_{eq}$3.115-Equilibrium constant of SL
[CoA]20μMCoenzyme A concentration
$k_f$ (cell)0.0284μM * HzForward rate constant (cellular model)

Succinate dehydrogenase (SDH)

See electron transport chain.

Fumarate hydratase (FH)

$$ J_{FH} = k_f ([FUM] - [MAL] / K_{eq}) $$

$k_f$8.3HzForward rate constant
$K_{eq}$1.0-Equilibrium constant
$k_f$ (cell)8.4HzForward rate constant (cellular model)

Malate dehydrogenase (MDH)

$$ \begin{aligned} J_{MDH} &= \frac{k_{cat} E_T AB f_a f_i}{(1+A)(1+B)} \cr A &= \frac{[MAL]}{K_{MAL}}\frac{K_{OAA}}{K_{OAA} + [OAA]} \cr B &= [NAD] / K_{NAD} \cr f_a &= k_{offset} + \left( 1 + \frac{[H^+]_m}{K_{H1}} (1 + \frac{[H^+]_m}{K_{H2}}) \right)^{-1} \cr f_i &= \left( 1 + \frac{K_{H3}}{[H^+]_m} (1 + \frac{K_{H4}}{[H^+]_m}) \right)^{2} \cr \end{aligned} $$

$k_{cat}$124.2HzRate constant
$K_{H1}$1.131E-8MIonization constant
$K_{H2}$2.67E-2MIonization constant
$K_{H3}$6.68E-12MIonization constant
$K_{H4}$5.62E-9MIonization constant
$k_{offset}$0.0399Offset of MDH pH activation factor
$K_{NAD}$224.4μMMichaelis constant for NAD
$K_{MAL}$1493μMMichaelis constant for malate
$K_{OAA}$31μMInhibition constant for oxaloacetate
$k_{cat}$ (cell)125.9HzRate constant for cellular model

Aspartate aminotransferase (AAT)

$$ J_{AAT} = k_f [OAA][GLU] \frac{k_{ASP}K_{eq}}{k_{ASP}K_{eq} + k_f[\alpha KG]} $$

$k_f$21.4HzForward rate constant
$k_{ASP}$0.0015HzRate constant of aspartate consumption
$K_{eq}$6.6Equilibrium constant
[GLU]30000μMGlutamate concentration
$k_f$ (cell)21.7HzForward rate constant (cellular model)

  1. Wei AC, Aon MA, O’Rourke B, Winslow RL, Cortassa S. Mitochondrial energetics, pH regulation, and ion dynamics: a computational-experimental approach. Biophys J. 2011;100(12):2894-903. PMC3123977 ↩︎