# 📒 Metelkin 2009

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

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## 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

## Methods

- 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

## Results

- 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)

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

## Parameters

Symbol | Value | Units | Description |
---|---|---|---|

$F$ | $96485$ | $C/mol$ | 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 | |

$K_{O_2}$ | $1.45 \cdot 10^{-12}$ | ||

$\beta_{O_2}$ | $0.36$ | ||

$k_{leak}$ | $0.438$ | $nmol/ (min·mg)$ | The empirical coefficients of membrane leakage description |

$\beta_{leak}$ | $1.05$ | The empirical coefficients of membrane leakage description |

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. https://febs.onlinelibrary.wiley.com/doi/full/10.1111/j.1742-4658.2009.07394.x ↩︎