Monocarboxylate (Lactate) transporter

Monocarboxylate transporters, or MCTs, constitute a family of proton-linked plasma membrane transporters that carry molecules having one carboxylate group (monocarboxylates), such as lactate and pyruvate.

Chemical equation

$Lactate_{in} \rightleftharpoons Lactate_{out}$

Rate equation

Reversible Michaelis-Menten rate law is used

$\frac{V_{mf} \times \frac{[Lactate_{in}]}{Km_{Lactate_{in}}} - Vmr \times \frac{[Lactate_{out}]}{Km_{Lactate_{out}}}}{1 + \frac{[Lactate_{in}]}{Km_{Lactate_{in}}} + \frac{[Lactate_{out}]}{Km_{Lactate_{out}}}}$

Modified rate law to take Thermodynamic constraint into consideration

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

Parameter values

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	2.5	$\text{mM min}^{-1}$	Human tumor cells
$V_{mr}$	2.4	$\text{mM min}^{-1}$	Rat liver cells
$Km_{Lactate_{in}}$	4.5	mM	Rat liver cell
$Km_{Lactate_{out}}$	4.54	mM	Human tumor cells

Parameters with uncertainty

• Among different isoforms the MCT1 in Tumour cells are considered in this model. The $Km_{Lactate_{in}}$ is defined as $4.38 \pm 1.81$ and $V_{mf} = 2.5 \pm 0.48$ with 6 experiments.

• In the legend of Table-1 of it states that the Km and Vmax values for monocarboxylate transport are from mouse Ehrlich Lettre ́ tumor cells. We also consider these values for $Km_{Lactate_{out}}$ and $V_{mr}$. In the publication the values are given in $mean \pm S.E.$ with 7 experiments. Calculating Std. Dev. from S.E gives, $4.54 \pm 1.93$ for $Km_{Lactate_{out}}$ and $0.0207 \pm 0.003$ for $V_{mr}$.

Parameter	Value	Units	Organism	Remarks
$V_{mf}$	$2.5 \pm 0.48$	$\text{mM min}^{-1}$	Human tumor cells
$V_{mr}$	$0.0207 \pm 0.003$	$\text{mM min}^{-1}$	Human Tumor cell
$Km_{Lactate_{in}}$	$4.38 \pm 1.81$	mM	Human tumour cell
$Km_{Lactate_{out}}$	$4.54 \pm 1.93$	mM	Human tumor cells

Equilibrium constant

• The $K_{eq}$ value of the transporters are reported to be 1.00. As the $K_{eq}$ is directly related to $K_{m}$ values of substrate and product, the uncertainty would also be dependent. The highest uncertainty is mentioned for $K_{Glucose_{out}}$ which is $70%$ of the actual value. The same percentage of error is assumed for $K_{eq}$; $0.70$.
  
• Alternative-2: In order to ensure that the uncertainty does not affect the model equilibrium a small uncertainty of 5% can be considered for transporter. In our model we have applied this approach. So $K_{eq} = 1 \pm 0.05$