Lactate dehydrogenase

A dehydrogenase is an enzyme that transfers a hydride from one molecule to another. Lactate dehydrogenase catalyzes the conversion of pyruvate to lactate and back, as it converts NADH to NAD⁺ and back.

Chemical reactions

$NADH + PYR \rightleftharpoons Lactate_{in} + NAD^+$

Rate equation

RAndom Bi-Bi reversible Michaelis-Menten equation is used.

$\frac{V_{mf}\frac{[NADH][PYR]}{Km_{NADH} K_{PYR}} - V_{mr}\frac{[Lactate_{in}][NAD]}{Km_{Lactate_{in}} K_{NAD}}}{1 + \frac{[NADH]}{Km_{NADH}} + \frac{[PYR]}{Km_{PYR}} + \frac{[NADH][PYR]}{Km_{NADH} Km_{PYR}} + \frac{[Lactate_{in}][NAD]}{Km_{Lactate_{in}} Km_{NAD}} + \frac{[Lactate_{in}]}{Km_{Lactate_{in}}} + \frac{[PYR]}{Km_{PYR}} }$

Modified rate law to take Thermodynamic constraint into consideration

$\frac{V_{mf}\frac{[NADH][PYR]}{Km_{NADH} K_{PYR}} \left(1 - \frac{[Lactate_{in}][NAD]}{K_{eq}[NADH][PYR]} \right)}{1 + \frac{[NADH]}{Km_{NADH}} + \frac{[PYR]}{Km_{PYR}} + \frac{[NADH][PYR]}{Km_{NADH} Km_{PYR}} + \frac{[Lactate_{in}][NAD]}{Km_{Lactate_{in}} Km_{NAD}} + \frac{[Lactate_{in}]}{Km_{Lactate_{in}}} + \frac{[PYR]}{Km_{PYR}} }$

Prameter values

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	3.4	$\text{mM min}^{-1}$	HeLa cell line
$V_{mr}$	0.54	$\text{mM min}^{-1}$	HeLa cell line
$Km_{PYR}$	0.1	mM	HeLa cell line
$Km_{LAC}$	4.7	mM	Rat AS-30D hepatoma
$Km_{NAD}$	0.07	mM	HeLa cell line
$Km_{NADH}$	0.002	mM	HeLa cell line

Parameters with uncertainty

• Mean and Std. Dev. for $V_{mf}$ has been reported in Table S3 for Marín-Hernández (2011) et. al. . The Std. Dev. for $V_{mr}$ is calculated based on the same ratio for $V_{mf}$.

• Reported values of $Km_{PYR}$ are 0.03 , 0.398 , 0.3 . The mean value with std. dev. is $0.24 \pm 0.19$.

• The value for $Km_{NAD}$ and $Km_{NADH}$ has been reported for Ovine (Sheep) as $Km_{NAD} = 3.96 \pm 0.17$ and $Km_{NADH} = 0.097 \pm 0.020$ . Due to lack of data in Human cells these two values are considered in our model.

• $Km_{LAC} = 4$ for LDH-1 and 2 isoforms and $Km_{LAC} = 7$ for LDH-4 and 5 isoforms are being reported in Marín-Hernández et. al. (2009). Mean and Std. Dev. from these two values are $5.5 \pm 2.12$

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	Failed to parse (Cannot store math image on filesystem.): 3.4 \pm 0.5 (3)	$\text{mM min}^{-1}$	HeLa cell line
$V_{mr}$	$0.54 \pm 0.073$	$\text{mM min}^{-1}$	HeLa cell line
$Km_{PYR}$	$0.24 \pm 0.19$	mM	HeLa cell line
$Km_{LAC}$	$5.5 \pm 2.12$	mM	Rat AS-30D hepatoma
$Km_{NAD}$	$3.96 \pm 0.17$	mM	Ovine (Sheep)
$Km_{NADH}$	$0.097 \pm 0.020$	mM	Ovine (Sheep)