On the catalytic activity of chemically modified enzymes involving two or more substrates and products

Catalytic activity of both native and chemically modified enzymes are numerically expressed in the literature with either kmax (= V/[ET]), or ke (=(V/[ET])/Km), if they refer to a one-substrate one-product reaction. Higher-order catalytic constants of the k'E type have not so far been calculated for enzyme reactions involving two or more substrates and products. a) It is shown here how such higher-order k'E-values can be calculated from easily obtainable experimental information; whatever the number of substrates and products, and even if binding of substrates and release of products follow a branched pathway. b) k'E-Values define the specific rate with which free substrates are converted by the enzyme into free products. Their dimensions (M-ns-1) are defined by the number of substrates (n). k'E-Values refer to the same process as the catalytic constants generally used in physical organic chemistry. c) The required experimental information is mainly based on steady state parameters of the V'- and K'm-types, supplemented with equilibrium and fast kinetic studies of straightforward substrate binding reactions. d) It is shown that higher-order k'E-values always involve the "Haldane problem" of the chemical reaction step. On the other hand, k'E-values are independent of the rate of release of all but the first product in the overall reaction. e) The so-called "Haldane relations" are shown to be determined by the way in which k'E-values can be calculated from V' and K'm-type experimental parameters. f) A number of theoretical considerations indicate that catalytic of the k'E-type are much more suitable for expressing the catalytic activity of chemically modified enzymes than maximal velocities are. This conclusion is demonstrated by a comparison of k'E- and k'max-values of some recently described modified forms of alcohol dehydrogenase.