The interpretation of multiple-step transient-state kinetic isotope effects

In contrast to steady-state kinetic isotope effects (KIEs), transient-state tKIEs are both time and signal dependent and therefore require a very different form of theory for their interpretation. We have previously provided such a theory for the case of single-step isotopic substitutions. No such properly derived theory applicable to the analysis of multiple-step isotopic substitutions required by transient-state solvent isotope effect studies has been available up to this time. Here, we set forth a more general form of that theory which is applicable to multiple-step substituted cases. We prove three theorems: 1. the observed transient-state KIE for any given reactive component in the reaction sequence evaluated at zero time (tKIE(0)) is in fact the arithmetic product of the intrinsic KIEs of all the steps that precede the formation of that component. 2. The observed tKIE(0) is completely independent of the intrinsic KIEs of any reverse step in the reaction. 3. The intrinsic KIE of any step may be obtained by dividing the value of the tKIE(0) for that step by the value of the tKIE(0) of the immediately preceding step in the reaction sequence.