Mitocondrial pyruvate metabolism

Mitocondrial pyruvate metabolism(MPM) is an enzyme that generates ATP form pyruvate.

Chemical reaction

$Pyruvate + 13ADP + 13Pi \rightarrow 13ATP$

Rate equation

• Chemical reactions proceed to equilibrium within closed systems. For a simple reaction $A \rightarrow B$ it is defined as $K_{eq} = \frac{[B]_{eq}}{[A]_{eq}}$ where forward and reverse rates are equal.
• Equilibrium is not reached in open system due to influx and outflux. Mass action ratio $\tau$ for $A \rightarrow B$ reaction is defined as $\tau = \frac{[B]_{ob}}{[A]_{ob}}$ where subscript ob represents observable at a given point.
• Deviation from equilibrium is measured with Disequilibrium constant $\rho$ as $\rho = \frac{\tau}{K_{eq}}$
• Given the simple uni molecular reaction $A \leftrightarrow B$ the mass action equation can be modified as

$v=K_1A-K_2B$
$v=K_1A \left(1-\frac{K_2B}{K_1A} \right)$

Considering $K_{eq} = \frac{K_1}{K_2}$ and $\tau = \frac{P_1P_2 \ldots}{S_1S_2 \ldots}$ we have,

$v=K_1A \left(1-\frac{\tau}{K_{eq}} \right)$

• The generalized arbitrary mass action ratio gives us

$v = K_1A^{n_1}B^{n_2} \ldots \left(1-\frac{\tau}{K_{eq}} \right)$ Or,
$v = K_1A^{n_1}B^{n_2} \ldots (1 - \rho)$

For eg. for the reaction $2A + B \leftrightarrow C + 2D$, the rate law would be $K_1A^2B \left(1-\rho\right)$

• This equation demonstrates how a rate expression can be divided into parts that include both kinetics and thermodynamic properties .

• Given the net rate of reaction $v = v_f \left( 1 - \frac{v_r}{v_f} \right)$, we have

$v = v_f \left(1 - \rho \right)$

In this model

• The rate law is defined as $v = K_1[Pyruvate][ADP]^{13}[Pi]^{13}\left(1-\frac{\frac{[ATP]^{13}}{[Pyruvate][ADP]^{13}[Pi]^{13}}}{K_{eq}}\right)$
• The $K_{eq}$ value for the reactions that converts pyruvate has been defined as Failed to parse (Cannot store math image on filesystem.): 3.32e^5 in
• The flux value at steady state is $v = 1 \times 10^{-4}$ .
• The steady state concentrations for substrates and products are $ATP=8.7 \pm 3 (5)$, $ADP = 2.7 \pm 1.3$, $Pyruvate = 8.5 \pm 3.6$ and $Pi = 7.5$.
• The $K_1$ value calculated from the above mentioned values are

Parameter values

Parameter	Value	Organism	Remarks
$V$	$1 \times 10^{-4}$	HeLa cell line	Constant flux