Triosephosphate isomerase

This enzyme rapidly inter-converts the molecules Dihydroxyacetone phosphate (DHAP) and Glyceraldehyde 3-phosphate (Gly3P). Gly3P is removed as soon as it is formed to be used in the next step of glycolysis.

Chemical equation

$DHAP \rightleftharpoons Gly3P$

Rate equation

Reversible Michaelis-Menten is used

$v = \frac{ V_{mf}\frac{[DHAP]}{K_{DHAP}} - V_{mr}\frac{[Gly3P]}{K_{Gly3P}} }{1 + \frac{[DHAP]}{K_{DHAP}} + \frac{[Gly3P]}{K_{Gly3P}} }$

Modified rate law considering thermodynamic constant is

$v = \frac{ V_{mf}\frac{[DHAP]}{K_{DHAP}}\left(1 - \frac{[Gly3P]}{K_{eq}[DHAP]} \right)}{1 + \frac{[DHAP]}{K_{DHAP}} + \frac{[Gly3P]}{K_{Gly3P}} }$

Paramters

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	5	$mM \times min^{-1}$	Hela cell line
$V_{mr}$	42	$mM \times min^{-1}$
$Km_{Gly3P}$	0.51	mM
$Km_{DHAP}$	1.6	mM

Parameters with uncertainty

• The activity is measured in Activity in the reverse reaction in Hernandez (2006) et. al. $V_{mf}$ is sampled based on Haldane equation $K_{eq} = \frac{V_{forward}*K_{product}}{V_{reverse}*K_{substrate}}$ using the value Failed to parse (Cannot store math image on filesystem.): K_{eq} = 20.9 \pm 3.1 , $Km_{Gly3P}$ and $Km_{DHAP}$.
  

Alternative-1 the reported fixed point value can be considered with the standard deviation calculated based on the same ratio of $V_{mf}$ which is $\approx 31%$. This gives the value Failed to parse (Cannot store math image on filesystem.): V_{mf}=5 \pm 1.55 $U\cdot(\text{mg protein})^{-1}$
Alternative-2 Calculating $V_{mf}$ from $V_{mr}$ based on Haldane equation which gives the value of 2.911 and with the same percent of erro Std. Dev. is 0.90.

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	Sampled based on the Haldane equation. Alternative: Failed to parse (Cannot store math image on filesystem.): 5 \pm 1.55 or $2.911 \pm 0.90$ conversion gives Failed to parse (Cannot store math image on filesystem.): 325 \pm 100.48	$U\cdot(\text{mg protein})^{-1}$ $mM \times min^{-1}$
$V_{mr}$	$42 \pm 13 (3)$	$mM \times min^{-1}$
$Km_{Gly3P}$	$0.40 \pm 0.03 (4)$	mM	Human liver
$Km_{DHAP}$	$0.59 \pm 0.01 (4)$	mM	Human liver
$K_{eq}$	$0.047 \pm 0.00697 (4)$	mM	$K_{eq}(reverse) = 20.9, and so K_{eq}(forward) = \frac{1}{20.9} = 0.047$

Equilibrium constant

Equilibrium constant	Conditions	Source
0.045	pH=8, T=25°C	Bergmeyer Methods of enzymatic analysis page 515
0.041	pH=7, T=25°C	Voet et al. from Newshole et al. (1973) p 97: $\Delta G' = 7.9\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-7900}{8.31*298.15}) \approx 0.041$
0.048	pH=7, T=25°C	Lehninger, (1975) p 408: $\Delta G' = 7.5\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-7500}{8.31*298.15}) \approx 0.048$
0.0475	pH=7, T=25°C	Lehninger, (1975) p 396.

• Taking average of all those values give $0.0457 \pm 0.002863$