3-phosphoglycerate mutase

Phosphoglycerate mutase (PGAM) is an enzyme that catalyzes the internal transfer of a phosphate group from C-3 to C-2 which results in the conversion of 3-phosphoglycerate (3PG) to 2-phosphoglycerate (2PG).

Chemical equation

$3PG \rightleftharpoons 2PG$

Rate equation

Mono-substrate reversible Michaelis-Menten equation is used.

$\frac{V_{mf}\frac{[3PG]}{Km_{3PG}}-V_{mr}\frac{[2PG]}{Km_{2PG}}}{1 + \frac{[3PG]}{Km_{3PG}} + \frac{[2PG]}{Km_{2PG}}}$

Modified rate law to take Thermodynamic constraint into consideration

$\frac{V_{mf}\frac{[3PG]}{Km_{3PG}} \left( 1 -\frac{[2PG]}{K_{eq}[3PG]} \right)}{1 + \frac{[3PG]}{Km_{3PG}} + \frac{[2PG]}{Km_{2PG}}}$

Parameter values

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	0.94	$\text{mM min}^{-1}$	HeLa cell line
$V_{mr}$	0.36	$\text{mM min}^{-1}$
$Km_{3PG}$	0.19	mM
$Km_{2PG}$	0.12	mM

Parameters with uncertainty

• Three reported values of $Km_{3PG}$ are considered. 0.19 , 0.5 and 0.4.

• Two values of $Km_{3PG}$ are found for Human cells. They are reported as 0.28 and 0.12. Averaging them gives mean value of 0.2 and 0.08

• As the value of the $K_{eq}$ does not depend on the organism, the mean and std. dev. of the distribution can be calculated from the various values reported in the literature.
• $V_{mr}$ can be sampled based on Haldane equation
  $K_{eq} = \frac{V_{forward}*K_{product}}{V_{reverse}*K_{substrate}}$ or Alternatively, same percentage of error mentioned for $V_{mf}$ considering the value for $V_{mf}$ reported in the model file of Hernandez (2011). This gives the value of $V_{mr} = 0.36 \pm 0.25$

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	$1.4 \pm 1$	$\text{mM min}^{-1}$	HeLa cell line
$V_{mr}$	Sampled based on Haldane equation $K_{eq} = \frac{V_{forward}*K_{product}}{V_{reverse}*K_{substrate}}$	$\text{mM min}^{-1}$
$Km_{3PG}$	$0.36 \pm 0.12$	mM	Multiple tissue of Human cell
$Km_{2PG}$	$0.2 \pm 0.08$	mM	Multiple tissue of Human cell

Equilibrium constant

Equilibrium constant	Conditions	Source
0.15	pH=7, T=25°C	Voet et al. from Newshole et al. (1973) p 97: $\Delta G' = 4.7\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-4700}{8.31*298.15}) \approx 0.15$
0.17	pH=7, T=25°C	Lehninger, (2008) p 553: $\Delta G' = 4.4\ kJ.mol^{-1}$, $Keq = exp(-\frac{\Delta G'}{RT}) = exp(\frac{-4400}{8.31*298.15}) \approx 0.17$
0.167	pH=7, T=297.15 K	From Meyerhof et al. 1949 (NIST database [49MEY/OES_1388])
0.19	pH=7.2, T=25°C	From Chiba et al. 1959 (NIST database [59CHI/SUG_1391])
0.20	pH=6, T=25°C	From Grisolia et al. 1975 (NIST database [75GRI/CAR_1396])

Averaging all those values gives $K_{eq} = 0.17 \pm 0.019$