Mean lifetime and first-passage time of the enzyme species involved in an enzyme reaction. Application to unstable enzyme systems

Taking as starting point the complete analysis of mean residence times in linear compartmental systems performed by Garcia-Meseguer et al. (Bull. Math. Biol. 65:279-308, 2003) as well as the fact that enzyme systems, in which the interconversions between the different enzyme species involved are of first or pseudofirst order, act as linear compartmental systems, we hereby carry out a complete analysis of the mean lifetime that the enzyme molecules spend as part of the enzyme species, forms, or groups involved in an enzyme reaction mechanism. The formulas to evaluate these times are given as a function of the individual rate constants and the initial concentrations of the involved species at the onset of the reaction. We apply the results to unstable enzyme systems and support the results by using a concrete example of such systems. The practicality of obtaining the mean times and their possible application in a kinetic data analysis is discussed.