Let's assume a situation where a molecule, S, is transported out of the cell by membrane transporter T. For simplicity we do not consider any other synthesis or production processes. Furthermore, we assume Michaelis-Menten (but another enzyme mechanism would lead to the same question, I think).

Mass balance concentration: $\frac{d [S]}{dt} = - [T] \; kcat \; \frac{[S]}{[S] + Km} $

Mass balance amount (moles): $\frac{d S}{dt} = - T \; kcat \; \frac{[S]}{[S] + Km} $

In both mass-balances the square brackets [.] indicate concentration.

In order for the units to match, the first mass balance equation expresses the transporter term as concentration (i.e. $\frac{T}{Volume_{cell}}$). Does that make sense? After all, these transporters are stuck in the membrane and not 'floating around' in the cell like the S molecules. Expressing T as concentration assumes that the transporter molecules are equally distributed across the volume, which is not the case. Does this not lead to an overestimation of the reaction rate?

Or did I make a mistake somewhere?


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