VALIDITY OF THE MICHAELIS-MENTEN THEORY 21 



should K„, be used in this connection when its interpretation is uncertain. 

 With regard to the subscript numbers on the rate constants (l\. A-.j. and 

 k2 instead of the more commonly used k^, A',, and k^). enzyme kinetics 

 will be more and more concerned with longer multistep sequences and the 

 use of the same number for a step, with a negative subscript referring to 

 the reverse reaction, is clearer. For example, when one sees k_3 it is imme- 

 diately evident that it refers to the reverse reaction of the third step in the 

 sequence. 



The Michaelis constant iiC,,; is unquestionably an important and useful 

 constant characterizing an enzyme even though its physical meaning is 

 not known, since it specifies the quantitative dependence of the rate on the 

 substrate concentration. Within the past few years, many enzymes have 

 been subjected to exhaustive analysis to interpret K^^ and each of the three 

 situations above has been observed; thus for tryx)sin and chymotrypsin, 

 K„^ = Kg and Michaelis-Menten kinetics are followed, whereas for carboxy- 

 peptidase, peroxidase, alcohol dehydrogenase, and glucose oxidase. ^,„ 

 is a kinetic constairfr The protease ficin is in the category where K,,^ in- 

 volves all the rate constants. The deviation of K,,^ from K^ increases as 

 k2 or F„; increases in situations where A'j can be varied by altering the con- 

 ditions of the experiment (Slater and Bonner. 1952) since: 



Kr„ = K, + -^ (2-12) 



It is thus possible that the K^^^ for a single enzyme may require different 

 interpretations depending on the experimental conditions. Peroxidase un- 

 der ordinary circumstances gives a K,,^ that is essentially k.y k^ but when 

 the concentration of hydrogen donor (leucomalachite green) is reduced 

 sufficiently k.2 can become comparable to k_i or even less (Chance, 1943). 

 A similar situation holds for succinic dehydrogenase, where under the usual 

 conditions ^,„ is more likely to be a complex function that a dissociation 

 constant (Slater and Bonner, 1952). 



With regard to the relative values of the rate constants, it is illustrative 

 to conceive of the course of an enzymic reaction in terms of the free ener- 

 gies of the molecular species and complexes. Several such energy contours 

 are plotted in Fig. 2-4 for various possibilities in the relative values of the 

 rate constants. Theoretically any of these pathways, or intermediate ones, 

 might be followed by an enzyme reaction. However, in situations D, E, 

 and F the ES complex is less stable than the reactants {K^ > 1 M) 

 and this is seldom observed in enzyme reactions. Situation A represents the 

 classic Michaelis formulation (/i,„ = K, = A'_i Z.'^) and B the case where Kj,^ 

 is a kinetic constant (A',„ = koki); intermediate between the.se would be 

 the situations where K„^ is a function of all three rate constants. In reaction 

 C the rate would not be determined by the breakdown of the ES complex 



