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.

$K_{a} = \frac{1}{K_{d}}$

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 mM, 0.12 mM, 0.33 mM in Boyer et. al. (1969) . However, he also cited papers that describe the Ki value between 3.5 mM and 1.0 mM. Hernandez et. al. reported a value of 2.5 mM. Considering all these factors we consider the vlaue to lie in between 3.5mM and 1.0 mM. Taking these three values of 1.0, 2.5, 3.5 we have the Mean and Std. Dev. as $2.33 \pm 1.25$.

• 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.

• Four values for $Km_{PYR}$ found in the literature are 0.025,0.055 for Sparus aurata liver, 0.48 for Selenomonas ruminantium and 10 . The mean and std. dev. from these 4 values are 2.64 and 4.9.

• Two values of $Km_{ATP}$ have been reported in the literature. 0.35 for Sparus aurata liver and 0.86 . The uncertainty is then $0.60 \pm 0.36$.

• Two values of Serine activation for Pyruvate Kinase constant have been reported; 2 and 5 . Taking mean and Std. Dev. for this two value gives $3.5 \pm 2.12$.

• Del valle (1986) determined the Allosteric Constant $L$ with the effect of L-alanine and Furctose1,6BP. For L-alanine the value of $L$ is reported to be $3200 \pm 275$ whereas in the presence of $100 \mu M$ Fru1,6BP the value is reported as $2.3$. As in our model we do not consider the affect of L-alaine but consder only the effect of Fru1,6BP we took this value of $2.3$. But there is no uncertainty reported with this value. So we took the same proportion of uncertainty as that of L-alaine for this value. This gives the value as $2.3 \pm 0.184$

• The $K_{eq}$ values found in the literature are ΔGº´ = -23.0 | -31.4 | -24.98 | -26.815 kJ/mol, =>Keq = 10753.64 | 318061.48 | 16190 | 32995

• Hernandez reported the value of $Km_{PEP}$ as 0.014 in . But there is not Std. Dev. mentioned with the data. So we calculate the Std. Dev. based on the same maximum ratio of other kinetic parameters Std. Dev. which is for parameter $Km_{PYR}$. Considering this ratio of error the value for $Km_{PEP}$ is $0.014 \pm 0.0262$.

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	$3 \pm 1.3 (4)$ $195 \pm 84.5$	$U\cdot(\text{mg protein})^{-1}$ $mM\cdot(min)^{-1}$	HeLa cell line
$K_{eq}$	$117558.7 \pm 173764.13$
$Km_{PEP}$	$0.014 \pm 0.0262$	mM
$Km_{ADP}$	$0.24 \pm 0.03$	mM
$Km_{PYR}$	$2.64 \pm 4.9$	mM
$Km_{ATP}$	$0.60 \pm 0.36$	mM
$Ka_{F1,6BP}$	$0.00023 \pm 0.000085$	mM
$Ki_{ATP}$	$2.33 \pm 1.25$	mM
$L$	$2.3 \pm 0.184$	Dimensionless
$Ka_{SER}$	$3.5 \pm 2.12$	mM

Equilibrium constant

Equilibrium constant	Conditions	Source
318061.48	pH=7, T=25°C	Lehninger, (2008) p 553: $\Delta G' = -31.4\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{31400}{8.31*298.15}) \approx 318061.48$
10753.64	pH=7, T=25°C	$\Delta G' = -23.0\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{23000}{8.31*298.15}) \approx 10753.64$
23860.98	pH=7, T=25°C	$\Delta G' = -24.98\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{23000}{8.31*298.15}) \approx 23860.98$

• Averaging these values gives $117558.7 \pm 173764.13$