The substrate-depletion error on the multiple Michaelis-Menten equation with and without an added term linearly dependent on the substrate concentration.

Saturation curves for substrate interaction with an acceptor (enzyme, binding or carrier protein) are often analysed on the assumption that the amount of acceptor-bound substrate is negligible compared to its total amount. Analytical criteria permitting one to decide whether the assumption is justified or not for systems described by a single Michaelis-Menten equation have been derived previously. For more complicated systems, error formulae often cannot be obtained in closed form, and, if obtainable, are unwieldy. How this more complicated problem can be tackled is shown for mixtures of acceptor sites described by a sum of several Michaelis-Menten terms, without or with an additional term for 'non-specific' uptake or binding. In particular, it is shown that the maximum error, for which simple analytical expressions are obtained, provides a valid criterion for assessing whether substrate depletion is negligible or not.