Minimal kinetic mechanism and general equation for deuterium isotope effects on enzymic reactions: uncertainty of detecting a rate-limiting step

A general equation is proposed for representing the kinetic functions which govern the expression of an isotope effect on the maximal velocity of an enzyme-catalyzed reaction. The origin and form of the functions are illustrated by examining a series of enzymatic mechanisms of progressively increasing complexity. The number of functions similarly increase, reaching a limit of three, with differing thermodynamic and kinetic properties. Further expansion of mechanisms causes an orderly and predictable algebraic expansion of each function, making it possible to write out, by simple inspection, the kinetic equation describing an isotope effect expressed on the maximal velocity for any enzymatic mechanism in which the isotope perturbs a single reactive step. The functions are interactive and allow for the possibility that an isotope effect on Vmax may be independent of the rate of a second, isotopically insensitive step, be it infinitely fast or slow. This allowance leads to an uncertainty of the ability of an isotope effect to detect a rate-limiting step, and the unequal distribution of kinetic and thermodynamic properties among three functions leads to an inadequacy of the singular concept of a rate-limiting step to serve as a basis for interpreting isotope effects on enzyme-catalyzed reactions. A minimal mechanism for consideration of isotope effects is proposed in order to embrace all three functions. It consists of a single catalytic step which is isotopically sensitive and reversible, two reversible precatalytic steps, and one reversible postcatalytic step, plus steps for binding and release of substrates and products.