📒 Metelkin 2009

Modeling of ATP–ADP steady‐state exchange rate mediated by the adenine nucleotide translocase in isolated mitochondria1


Introduction of Adenine nucleotide translocase (ANT)

  • Catalyzes the reversible exchange of ADP for ATP with a 1:1 stoichiometry across the inner mitochondrial membrane (IMM).
  • Rate depends on mitochondrial membrane potential (ΔΨm) and ATP/ADP ratio of both sides
  • A kinetic model of mitochondrial phosphorylation
    • the model of adenine nucleotide exchange across the mitochondrial membrane by Metelkin et AL.
    • the model of F0/F1‐ATPase developed previously by Demin et al.
    • simple steady‐state model of the phosphate carrier
    • validated using data obtained from intact isolated rat liver mitochondria


  • The rate of appearance of ATP in the medium following addition of ADP to energized mitochondria is calculated from the measured rate of change in free extramitochondrial magnesium


  • The synthesis of ATP occurs at a potential from −100 mV or higher. At membrane potential values from 0 mV to −100 mV, the rate of ATP production by mitochondria is close to zero.
  • Within the physiological range, ATP production is controlled by ΔΨm
  • Two paramaters, cSYN and cANT have been chosen in such a way as to provide minimal deviation between experimental data (circles)

Nigericin decreases the ATP–ADP steady‐state exchange rate mediated by ANT

  • Nigericin is an ionophore that mediates the electrically neutral exchange of otassium ions for protons, eliminating the pH gradient across the mitochondrial membrane and causing a compensatory increase in ΔΨm.
  • decreased the ATP–ADP steady‐state exchange rate mediated by ANT significantly, even though it hyperpolarized mitochondria by 15 mV. Predicted by the model.
  • decrease in Pi flux through the inner mitochondrial membrane, due to the collapse of ΔpH caused by nigericin, reducing ATP synthase activity, then ATP export

matrix ATP and ADP values and the dependence of Pi on ΔpH

  • State3 (high ADPi, lower ΔΨ) -> state4 (low ADPi, higher ΔΨ)
  • Measured matrix ATP and ADP concentrations from mitochondrial matrix extracts by HPLC
  • At 0 mV, rat liver mitochondria: 3.64 ± 0.34 mm AMP, 8.23 ± 0.65 mm ADP, and 0.51 ± 0.05 mm ATP
  • At -170 mV, rat liver mitochondria: 2.57 ± 0.67 mm AMP, 2.98 ± 0.41 mm ADP (predicted 2.2 mm), and 7.11 ± 1.55 mm ATP (predicted 9.8 mm)
  • Other experiments report that a wide range of matrix ATP/ADP ratios during state 3, ranging from 0.01 to 4.5 or even in the 8–12 range. For mitochondria in situ or in vivo, most investigators agree with the 1–3 ratio range
  • A great proportion of the matrix adenine nucleotides is bound to proteins. The relationship between the measured total ATP/ADP ratio and free intramitochondrial ATP/ADP ratio is difficult to predict.
  • In the model, concentration of matrix Pi can be increased substantially, owing to an increase in ΔpH

Predictions of the direct‐reverse profile of ADP–ATP exchange by ANT as a function of ΔΨm

  • ANT reverses, bringing ATP into the matrix in exchange for ADP, driven by a ΔΨm less negative than approximately −100 mV
  • The directionality of ANT is thermodynamically governed by the concentrations of free nucleotides (ATP4− and ADP3−) across the IMM. Free nucleotides:

Kinetic behavior of the model resulting from consecutive addition of uncoupler and ADP

Model descriptors

Adenine nucleotide translocase (ANT)

$$ \begin{aligned} V_{ANT} &= \frac{E_{ANT}}{\Delta}(k_2 \cdot q \cdot [ATP^{4-}]_m \cdot \phi_D - k_3 \cdot [ADP^{3-}]_m \cdot \phi_T) \cr \phi_D &= [ADP^{3-}]_i / K_D^{ADP} \cr \phi_T &= [ATP^{4-}]_i / K_D^{ATP} \cr q &= \frac{k_3K_D^{ADP}}{k_2K_D^{ATP}} \cdot V_N^{-1}(\Delta\Psi) \cr K_D^{ADP} &= K_{D0}^{ADP} \cdot V_N^{-1}(3 \delta_D \Delta\Psi) \cr K_D^{ATP} &= K_{D0}^{ATP} \cdot V_N^{-1}(4 \delta_T \Delta\Psi) \cr k_2 &= k_2^0 \cdot V_N^{-1}((-3 \alpha_1 - 4 \alpha_2 + \alpha_3)\Delta\Psi) \cr k_3 &= k_3^0 \cdot V_N^{-1}((-4 \alpha_1 - 3 \alpha_2 + \alpha_3)\Delta\Psi) \cr \Delta &= (1 + \phi_D + \phi_T) ([ADP^{3-}]_m + q \cdot [ATP^{4-}]_m) \end{aligned} $$

Complex V (ATP synthase)

$$ \begin{aligned} V_{ATPase} &= V_{max}^{C5} \left( \frac{H_o}{K_{H_o}}E_{N}^{-1}(X\Delta\Psi) \right)^n \frac{N}{D} \cr N &= \phi_{MgADP} \phi_{Pi} - \phi_{MgATP} K_{eq}^{\prime} \left( \frac{H_o}{H_i}E_{N}^{-1}(\Delta\Psi) \right) \cr D &= 1 + \phi_{MgADP} \phi_{Pi} \phi_{H_o} + \phi_{MgATP} \phi_{H_i} \cr K_{eq}^{\prime} &= \frac{K_{MgT}^{C5}K_{eq}^{C5}K_{Mg}^{ATP}}{K_{MgD}^{C5} K_{Pi}^{C5}K_{Mg}^{ADP}} \cdot \frac{10^{-4}}{10^{-4} + K_{a}^{Pi}} \cr \phi_{MgADP} &= [MgADP] / K_{MgD}^{C5} \cr \phi_{MgATP} &= [MgATP] / K_{MgT}^{C5} \cr \phi_{Pi} &= [Pi] / K_{Pi}^{C5} \cr \phi_{H_o} &= H_o / K_{H_o}^{C5} \cr \phi_{H_i} &= H_i / (K_{H_i}^{C5} E_{N}^{-1}((1-X)\Delta\Psi)) \cr \end{aligned} $$


$F$$96485$$C/mol$Faraday constant
$T$$310$$K$Absolute temperature
$R$$8.314$$J/molK$Universal gas constant
$pH_o$$7.25$pH in experimental volume
$pH_i$$7.30$pH in matrix under phosphorylating conditions
$C_{mito}$$7.8 \cdot 10^{-6}$$F/mg$Capacitance of inner mitochondrial membrane
$\Sigma[Mg^{2+}]_o$$1$$mM$Total magnesium concentration in experimental volume
$[Mg^{2+}]_i$$0.35$$mM$Buffered magnesium concentration in the matrix
$\Sigma[Pi]_o$$10$$mM$Total inorganic phosphate concentration in experimental volume
$V_o$$2$$mL$Experimental volume
$\Sigma[A]_i$$12$$mM$Total concentration of adenylates (ATP + ADP) in the matrix (may vary considerably in the range 2.7–22 mM
$K_a^{Pi}$$6.13 \cdot 10^{-5}$$mM$Dissociation constant for H+ and phosphate (pKa = 7.2)
$K_{Mg}^{T}$$0.114$$mM$Dissociation constant for magnesium and ATP
$K_{Mg}^{D}$$0.906$$mM$Dissociation constant for magnesium and ADP
$K_{hyd}^{F1}$$2.23 \cdot 10^{8}$$mM$Equilibrium constant of ATP hydrolysis. ΔG0′ = −30.5 kJ/mol
$c^{F1}$$22$Correction factor characterizing activity of ATP synthase in a particular mitochondrial preparation
$n^{F1}$$3$H+/ATP ratio
$X^{F1}$$0.9$Parameter of H+‐ATP synthase electrostatic profile
$X_n^{F1}$$1 - X^{F1}$Parameter of H+‐ATP synthase electrostatic profile
$V_{max}^{F1}$$1.2 \cdot 10^{-4}$$nmol/(min·mg)$Maximal reaction rate of F1Fo ATPase
$K_{Ho}^{F1}$$3 \cdot 10^{-5}$$mM$Dissociation constant for extramitochondrial proton of F1Fo ATPase
$K_{Hi}^{F1}$$1 \cdot 10^{-6}$$mM$Dissociation constant for matrix proton of F1Fo ATPase
$K_{MgD}^{F1}$$5.56 \cdot 10^{-3}$$mM$Dissociation constant for MgADP of F1Fo ATPase
$K_{MgT}^{F1}$$0.926$$mM$Dissociation constant for MgATP of F1Fo ATPase
$K_{Pi}^{F1}$$0.355$$mM$Dissociation constant for phosphate of F1Fo ATPase
$c_{ANT}$$48$$mmol/mg$Effective coefficient (characterizes the amount of ANT dimer per mg of total mitochondrial protein)
$k_2^{ANT,0}$$0.18$$Hz$Constant of direct ANT exchange
$K_{To}^{ANT,0}$$0.057$$mM$Constant of reverse ANT exchange
$K_{Do}^{ANT,0}$$0.051$$mM$Constant of reverse ANT exchange
$\alpha_1$$0.268$Parameters of ANT electrostatic profile
$\alpha_2$$-0.205$Parameters of ANT electrostatic profile
$\alpha_3$$0.187$Parameters of ANT electrostatic profile
$\delta_T$$0.07$Parameters of ANT electrostatic profile
$\delta_D$$0.005$Parameters of ANT electrostatic profile
$k_{O_2}$$0.005$The empirical coefficients of membrane potential generation
$K_{O_2}$$1.45 \cdot 10^{-12}$
$k_{leak}$$0.438$$nmol/ (min·mg)$The empirical coefficients of membrane leakage description
$\beta_{leak}$$1.05$The empirical coefficients of membrane leakage description

  1. Metelkin E, Demin O, Kovács Z, Chinopoulos C. Modeling of ATP-ADP steady-state exchange rate mediated by the adenine nucleotide translocase in isolated mitochondria. FEBS J. 2009;276(23):6942-6955. doi:10.1111/j.1742-4658.2009.07394.x. ↩︎