Nucleosid diphosphate kinase

Nucleoside-diphosphate kinases are enzymes that catalyze the exchange of phosphate groups between different nucleotides. The overall effect of NDKs is to transfer a phosphate group from a nucleoside triphosphate to a nucleoside diphosphate. Starting with ATP and UDP, the activity of NDK produces ADP and UTP.

Chemical equation

$ATP + UDP \leftrightarrow ADP + UTP$

Rate equation

Random order Bi-Bi rate law is used from

$\frac{ \frac{V_{max}}{K_m^{ATP}K_m^{UDP}}\left( [ATP][UDP] - \frac{[ADP][UTP]}{K_{eq}} \right) } { \left( 1 + \frac{[ATP]}{K_{m}^{ATP}} \right)\left( 1 + \frac{[UDP]}{K_{m}^{UDP}} \right) + \left( 1 + \frac{[ADP]}{K_{m}^{ADP}} \right)\left( 1 + \frac{[UTP]}{K_{m}^{UTP}} \right) -1 }$

Parameter values

• A mean body weight is defined as 75Kg in Konig et. al . The $V_{max}$ is calculated by multiplying the reported value with body weight.

Parameter	Value	Units	Organism	Remarks
$V_{max}$	$131.25$	$min^{-1}$	Human Liver
$K_{m}^{ATP}$	$1.33$	mM	Rat liver
$K_{m}^{ADP}$	$0.042$	mM	Rat liver
$K_{m}^{UTP}$	$16$	mM	Rat tissue
$K_{m}^{UDP}$	$0.19$	mM	Rat liver
$K_{eq}$	$1$	Dimensionless

Parameters with uncertainty

• In the paper by Walter (1980) et. al. two values of $K_{m}^{ADP}$, $K_{m}^{ATP}$ and $K_{m}^{UDP}$ have been reported; one for cytosolic kinase and the other for membrane-associated kinase. As in our model we are not differentiating between cytosolic and membrane-associated kinase, we would consider both those values and calculate the uncertainty from them.

• Similarly two values of $K_{m}^{UTP}$ has been reported in Fukuchi (1994) et. al. ; for $\alpha$ kinase and $\beta$ kinase. Taking average of those kinase gives a value of $21.5 \pm 7.77$

• Two values of $V_{max}$ is also reported in Fukuchi (1994) et. al. ; 126 (4.20 $\text{mmol min}^{-1}\text{ mg}^{-1}$ multiplied with 30 mg) and 138 (4.60 $\text{mmol min}^{-1}\text{ mg}^{-1}$ multiplied with 30 mg) $\text{mmol min}^{-1}$. Taking average gives $132 \pm 8.48$.

Note:

• Standard free energy $\Delta G^{o}{'}$ is reported to be zero kJ/mol. Therefore the value of Keq can be assumed to be constant. As there was no other value reported, Std. Dev. from transporter Keq values are considered which is $\approx 70%$. So the Keq value would be $1 \pm 0.7$

Parameter	Value	Units	Organism	Remarks
$V_{max}$	$132 \pm 8.48$	$min^{-1}$	Rat lever
$K_{m}^{ATP}$	$1.49 \pm 0.23$	mM
$K_{m}^{ADP}$	$0.0575 \pm 0.02$	mM
$K_{m}^{UTP}$	$21.5 \pm 7.77$	mM
$K_{m}^{UDP}$	$0.17 \pm 0.02$	mM
$K_{eq}$	$1 \pm 0.7$	Dimensionless