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

• The dissociation constant is commonly used to describe the affinity between a ligand (L) (such as a drug) and a protein (P) i.e. how tightly a ligand binds to a particular protein. In the specific case of antibodies (Ab) binding to antigen (Ag), usually the affinity constant is used. It is the inverted dissociation constant.

Failed to parse (Cannot store math image on filesystem.): K_{a} = = \frac{1}{K_{d}}

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. The range rule tells that the mean of a sample is the average of the maximum and the minimum value and standard deviation is approximately equal to one fourth of the range of the data ie. s = (Maximum – Minimum)/4. So the mean is (0.0004 + 0.00006)/2= 0.00023 and std. dev. = 0.000085.

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
$Ka_{F1,6BP}$	$0.00023 \pm 0.000085$	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 $k_d = 0.2 mM$