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 $132 \pm 8.48$.

• 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 reported other value std. dev. from other Keq values are considered which is Failed to parse (Cannot store math image on filesystem.): \approx 30% . So the Keq value would be Failed to parse (Cannot store math image on filesystem.): 1 \pm 0.3

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
$K_{eq}$	Failed to parse (Cannot store math image on filesystem.): 1 \pm .3	Dimensionless