Why substrate depletion has apparent first-order kinetics in enzymatic digestion

A number of enzyme digestion assays show apparent first-order kinetics of reactant depletion. There are four possible explanations of this phenomenon: (i) the reaction is dominated by a first-order limiting step, (ii) the digestion follows a pseudo-first-order kinetics under the excess of a reactant species, (iii) the first-order kinetics is only applicable to the slow transient of the reaction, or (iv) the aggregate behavior of the reaction pathway produces behavior indistinguishable from the first-order kinetics. In this paper, we investigate the kinetics for protein digestion by formulating rate equations for two proposed mechanisms, namely the one-by-one mechanism and the zipper mechanism. Our analysis shows that the kinetics of protein digestion follows apparent first-order kinetics irrespective of the mechanism for low initial substrate concentration compared to the initial enzyme concentration. Also, our results provide an explanation for experimental observations and suggest a new experimental protocol that could reveal information on the mechanism of digestion.