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
$V_{mf}$	1.9	$\text{mM min}^{-1}$	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 $k_d = 0.2 mM$

Parameters with uncertainty

• Three values of $Ki_{ATP}$ have been reported as 0.14, 0.12, 0.33 in Boyer et. al. (1969) . The Mean and Std. Dev. is Failed to parse (Cannot store math image on filesystem.): 0.19 \pm 0.09 .

• Four isoforms of PYK exists. Among those four, three isoforms (R, L and M2) exhibits cooperative kinetics activated by Fru1,6BP (Ka = 0.00006 - 0.0004). For calculating the mean and standard deviation we consider max = 0.0004 and min = 0.00006. Consdiering Failed to parse (Cannot store math image on filesystem.): \bar{x} we have Failed to parse (Cannot store math image on filesystem.): max \approx \bar{x} + 6*\sigma.

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	$3 \pm 1.3 (4)$	$\text{mM min}^{-1}$	HeLa cell line
$K_{eq}$	195172			Recalculated from the ΔGº´ = - 31.4 KJ mol-1.
$Km_{PEP}$	Failed to parse (Cannot store math image on filesystem.): 0.17 \pm 0.01	mM
$Km_{ADP}$	$0.24 \pm 0.03$	mM
$Km_{PYR}$	10	mM
$Km_{ATP}$	0.86	mM
$Ka_{F1,6BP}$	$4\times 10^{-4}$	mM
$Ki_{ATP}$	Failed to parse (Cannot store math image on filesystem.): 0.19 \pm 0.09	mM
$L$	$3200 \pm 275$	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 $k_d = 0.2 mM$