20 2. THE KINETICS OF ENZYME REACTIONS 



than the dissociation of the complex into the enzyme and original substrate. 

 A more general treatment was developed by Briggs and Haldane (1925) 

 based on steady-state kinetics wherein the rates of formation and break- 

 down of the complex are assumed to be equal and the concentration of the 

 complex remains constant during the experimental period. Assuming the 

 same reaction sequence of Eq. 2-1: 



'^^^^^ ■■ ^■:(E)(S) — ^-_i(ES) — UE8) = (2-9) 



dt 



Proceeding in the same manner as previously, the steady-state concentra- 

 tion of the complex is found to be: 



ki{8) + A;_i -I- ki 



and the rate equation is identical in form to Eq. 2-7: 



(S) .. (S) 



(S) + [(A:_i + k,)lk^] "" (S) + K, 



(2-11) 



except that the Michaelis constant is no longer the simple dissociation 

 constant of the complex, k_Jki, but also involves k^. Three general situa- 

 tions may be visualized. 



(a) k_i = ki Km = [k-i + k2)lki General Michaelis constant 



(6) k_i > ^'2 K,n = Ks = k^Jki Substrate dissociation constant 



(c) k_i <^ ki K,„ == kijki Kinetic constant 



The constants derived from kinetic data may thus have different meanings 

 and one must determine the values of the rate constants A;_i and k^ in order 

 to be certain of the correct interpretation. 



It is important to comment at this point on the symbolism chosen for 

 the constants in the rate equation. The choice of K„^ to indicate the Mi- 

 chaelis constant as determined from kinetic data by graphical analysis, 

 where the physical meaning is unknown, and of K, to represent the true 

 dissociation constant of the ES complex or substrate constant is basically 

 in agreement with Dixon and Webb (1958). In many of the rate equations 

 throughout this volume, this constant will be written as K^. because the de- 

 rivations of the equations will assume equilibrium conditions, but in most 

 cases Kf. may be replaced with K„^, where K^,,, may be expressed in terms of 

 the various rate constants from a steady-state treatment. In comparing 

 affinities of enzymes for substrates and inhibitors, it is appropriate to use 

 K^ and K. (the dissociation constant of the EI complex), but in no case 



