Hexokinase

The enzyme hexokinase phosphorylates (adds a phosphate group to) glucose in the cell's cytoplasm. In the process, a phosphate group from Adenosine triphosphate (ATP) is transferred to glucose producing glucose 6-phosphate (Glc6P).

Chemical equation

$Glucose_{in} + ATP \rightleftharpoons Glc6P + ADP$

Rate equation

Without inhibition

Random Bi-Bi Michaelis Menten is used.

$v = \frac{\frac{V_{mf}}{Km_{Glucose_{in}}K_{ATP}}\Big( [Glucose_{in}][ATP] - \frac{[Glc6P][ADP]}{K_{eq}} \Big)}{1 + \frac{[Glucose_{in}]}{Km_{Glucose_{in}}} + \frac{[ATP]}{K_{ATP}} + \frac{[Glucose_{in}][ATP]}{Km_{Glucose_{in}}K_{ATP}} + \frac{[Glc6P]}{K_{Glc6P}} + \frac{[ADP]}{K_{ADP}} +\frac{[Glc6P][ADP]}{K_{Glc6P}K_{ADP}} + \frac{[Glucose_{in}][ADP]}{K_{Glucose_{in}}K_{ADP}} +\frac{[Glc6P][ATP]}{K_{Glc6P}K_{ATP}} }$

With allosteric inhibition

Hexokinase is allosterically inhibited by Glc6P . The rate law taking into account this inhibition is

$\frac{V_{mf}* \frac{[Glucose]*[ATP]}{Km_{Glucose}*Km_{ATP}} }{ \left(1 + \frac{[Glc6P]}{Ki_{Glc6P}} \right)* \left( 1 + \frac{[Glucose]}{Km_{Glucose}} \right) + \frac{[ATP]}{Km_{ATP}} + \frac{[Glucose]*[ATP]}{Km_{Glucose}*Km_{ATP}} }$

Parameters

Without inhibition

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	0.04	$mM \times min^{-1}$	HeLa cell line
$K_{eq}$	651
$Km_{Glucose}$	0.1	mM
$Km_{ATP}$	1.1	mM
$Km_{Glc6P}$	$2e^{-002}$	mM
$Km_{ADP}$	3.5	mM

With inhibition

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	0.04	$mM \times min^{-1}$	HeLa cell line
$Km_{Glucose}$	0.1	mM
$Km_{ATP}$	1.1	mM
$Ki_{Glc6P}$	$0.02$	mM

Parameters with uncertainty

Hexokinase isoenzyme has been reported to vary in different developmental and metabolic status of the cell. In mammalian tissues four isoenzymes of Hexokinase is present . Hexokinase-II has been found to be overexpressed in several first growith cancer cells . Therefore in our model we have considered only the Hexokinase-II kinetic parameter values.

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	Failed to parse (Cannot store math image on filesystem.): 0.02 \pm 0.006 (n=4)	$U\cdot(\text{mg protein})^{-1}$	HeLA cell line
$Km_{Glucose}$	$0.37 \pm 0.003$ (n=5)	mM	SNU449 cell (Human Liver Tissue)
$Km_{ATP}$	$0.81 \pm 0.11$ (n=5)	mM
$Ki_{Glc6P}$	$0.24 \pm 0.06$ (n=5)	mM

Equilibrium constant

Equilibrium constant	Conditions	Source
4908	pH=7, T=25°C	Voet et al. from Newshole et al. (1973) : $\Delta G' = - 20.9\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{20900}{8.31*298.15}) \approx 4908$
846	pH=7, T=25°C	Lehninger, (1975) p 553: $\Delta G' = - 16.7\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{16700}{8.31*298.15}) \approx 845.8$
890	pH=7, T=25°C	Lehninger, (1975) p 396

Calculating average from these equlibrium constant gives the value of $2214.66 \pm 2332.60$