Pyruvate kinase

Pyruvate kinase is a transferase enzyme that catalyzes the transfer of a phosphate group from phosphoenolpyruvate (PEP) to ADP, yielding one molecule of pyruvate and one molecule of ATP.

Chemical reaction

$PEP + ADP \rightleftharpoons Pyrvate + ATP$

Rate equation

The rate equation is represented by the allosteric regualation model of Monod, Wyman and Changeux (MWS). Fru1,6BP and Serine are activators and ATP is inhibiting. Simple Micahelis-Menten kinetics (Briggs Haldane) is used for ADP and reverse reaction

$v=V_m \left( \left(\frac{\frac{[ADP]}{K_{ADP}}}{1+\frac{[ADP]}{K_{ADP}}}\right) \left( \frac{\frac{[PEP]}{Km_{PEP}}\left( 1+\frac{[PEP]}{Km_{PEP}} \right)^3 }{ \frac{L \left( 1 + \frac{[ATP]}{Ki_{ATP}} \right)^4 }{ \left( 1 + \frac{[SER]}{Ka_{SER}} \right)^4 \left( 1 + \frac{F1,6BP}{Ka_{F1,6BP}} \right)^4 } + \left( 1 + \frac{[PEP]}{Km_{PEP}} \right)^4} \right) - \left( \frac{\frac{[ATP][PYR]}{K_{ATP} \times K_{PYR} \times K_{eq}}}{1 +\frac{[ATP]}{K_{ATP}} + \frac{[PYR]}{K_{PYR}} + \frac{[ATP][PYR]}{K_{ATP} \times K_{PYR} }} \right) \right)$

Parameter values

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	195	$\text{mM min}^{-1}$	HeLa cell line
$K_{eq}$	195172			Recalculated from the ΔGº´ = - 31.4 KJ mol-1.
$Km_{PEP}$	0.014	mM
$Km_{ADP}$	0.4	mM
$Km_{PYR}$	10	mM
$Km_{ATP}$	0.86	mM
$Ka_{F1,6BP}$	$4\times 10^{-4}$	mM
$Ki_{ATP}$	2.5	mM
$L$	1	Dimensionless
$Ka_{SER}$	5	mM		For allosteric regulation the affinity constant is used. It is the inverted dissociation constant. so $Ka_{SER} = \frac{1}{K_d}$ where $k_d = 0.2 mM$