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

Abstract 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.