Hexose-6-phosphate isomerase

The enzyme Hexose-6-phosphate isomerase converts Glucose 6-phosphate (Glc6P) into its isomer Fructose 6-phosphate (Fru6P). Isomers have the same molecular formula, but the atoms of each molecule are arranged differently.

Chemical reaction

$Glc6P \rightleftharpoons Fru6P$

Rate equation

Reversible competitive inhibition with Ery4P, 6PG and FBP.

$v=\frac{V_{mf}\frac{[Glc6P]}{Km_{Glc6P}} - V_{mr} \frac{[Fru6P]}{Km_{Fru6P}} }{ 1 + \frac{[Glc6P]}{Km_{Glc6P}} + \frac{[Fru6P]}{Km_{Fru6P}} + \frac{[ERY4P]}{Ki_{ERY4P}} + \frac{[6PG]}{Ki_{6PG}} + \frac{[Fru1,6BP]}{Ki_{Fru1,6BP}} }$

Substituting with Haldane equation to ensure thermodynamic consistency we have

$v= \frac{V_{mf}\frac{[Glc6P]}{Km_{Glc6P}}\left(1 - \frac{[Fru6P]}{K_{eq}[Glc6P]} \right)}{ 1 + \frac{[Glc6P]}{Km_{Glc6P}} + \frac{[Fru6P]}{Km_{Fru6P}} + \frac{[ERY4P]}{Ki_{ERY4P}} + \frac{[6PG]}{Ki_{6PG}} + \frac{[Fru1,6BP]}{Ki_{Fru1,6BP}} }$

Parameter values

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	0.4	$mM \times min^{-1}$	HeLa cell line	3 cell assays
$V_{mr}$	0.9	$mM \times min^{-1}$		1 cell assay
$Km_{Glc6P}$	0.4 $\pm$ 0.03 mM	mM		3 cell assays
$Km_{Fru6P}$	0.05	mM		2 cell assays
$Ki_{ERY4P}$	0.001	mM		Adjusted in the interval based on activity
$Ki_{Fru1,6BP}$	0.06	mM		Adjusted in the interval based on activity
$Ki_{6PG}$	0.015	mM		Adjusted in the interval based on activity

Parameters with uncertainty

• The V is measured in the reverse order for the enzyme ($V_{mr}$) in as $3 \pm 1.7$$U\cdot(\text{mg protein})^{-1}$. The $V_{mf}$ is calculated based on Haldane equation. The same relative percent error for $V_{mr}$ is used to define the uncertainty of this parameter. The value is $0.17 \pm 0.09$ $U\cdot(\text{mg protein})^{-1}$.

• The uncertainty of $Km_{Fru6P}$ for HeLa cell line are calculated based on the same proportion of uncertainty for AS-30D cell reported in the paper Marín-Hernández et. al., Modeling cancer glycolysis .

• The value of $Ki_{Ery4P}$, $Ki_{Fru1,6BP}$ and $Ki_{6PG}$ are the averaged from the forward and reverse reaction value listed in Table S6 .

• The uncertainty for $Ki_{Ery4P}$ in HeLa cell line is mentioned in the forward reaction as $1 \pm 0.07 \mu M$ and in the reverse direction as $0.86 \mu M$. The mean value is calcualated as $\frac{1 + 0.86}{2} \mu M$ and the standard deviation is calculated based on the same ratio mentioned in forward reaction which comes as $0.00093 \pm 0.000063$ in mM.

• Same principle is used for $Ki_{6PG}$. The mean value is $\frac{0.0176+0.0155}{2} = 0.017$ and the standard deviation is calculted based on the same ratio of reverse reaction for HeLa cell line; 0.0043

• There are two reported value for $Ki_{Fru1,6BP}$; 0.1, 0.06. The mean and standard deviation are calcualted from these two values.

Parameter	Value	Units
$V_{mf}$	$0.17 \pm 0.09$	Failed to parse (Cannot store math image on filesystem.): U\cdot(\text{mg protein})^{-1}
$V_{mr}$	$3 \pm 1.7$	$U\cdot(\text{mg protein})^{-1}$
$Km_{Glc6P}$	$0.4 \pm 0.03$ mM	mM
$Km_{Fru6P}$	$0.05 \pm 0.0214$	mM
$Ki_{ERY4P}$	$0.0009 \pm 0.000063$	mM
$Ki_{Fru1,6BP}$	$0.08 \pm 0.02$	mM
$Ki_{6PG}$	$0.017 \pm 0.0043$	mM

Equilibrium constant

Equilibrium constant	Conditions	Source
0.50	pH=7, T=25°C	Lehninger, (2008) p 553: $\Delta G' = 1.7\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-1700}{8.31*298.15}) \approx 0.50$
0.51	pH=7, T=25°C	Lehninger, (1975) p 396: Keq(reverse)=1.97 => Keq(forward)=1/1.97=0.51.
0.41	pH=7, T=25°C	Voet et al. from Newshole et al. (1973) p 97: $\Delta G' = 2.2\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-2200}{8.31*298.15}) \approx 0.41$

• Averaging these values gives $0.47 \pm 0.05$