ENZYME KINETICS 



E 



K, 



bE 



LaE 



EH, 



EF 



EM 



E 



LbEF 



K 



bEM 



K, 



bE 



F + EH , ^"' - EHF . ''' ' EHM , ^' ^ EH + M (14) 



^2 k\ k^ 



taEF 



iC, 



aEM 



K 



aE 



EHoF 



EHoM 



EH, 



Here the three forms of the catalytic site are represented by 

 EH2, EH, and E. The acid dissociation constants of the two 

 groups in the enzyme and in the enzyme-substrate complexes 

 are represented by K^^ and K^^. As indicated by the use of sub- 

 scripts, it is to be expected that the acid dissociation constants of 

 the groups will be different in the two types of enzyme-substrate 

 complexes and free enzyme. 



The steady-state treatment of this mechanism yields the 

 Michaelis-Menten equation for the steady-state velocities of 

 both the forward and reverse reactions, but the maximum initial 

 velocities and Michaelis constants are now functions of the pYi. 

 If the steps with rate constants k^ and ki are rate-determining, 

 the nature of this dependence is indicated by the equations for 

 the maximum initial velocity Fp and Michaelis constant K^ for 

 the forward reaction. 



kzkf>{E)o 



Fp = 



(^3 + ^4 + ki) 



1 + (H+)/A^aEF + ^bEK/(H+) 



(15) 



J. ^ Jk-A + k,k, + ^3^5) [1 + (H+)/A-aE + A-.e/(H+)] 



A-i(^3 + ^4 + k,) [1 + (H+)/A,ef + AbEF/(H+)] '^^^^ 



The acid dissociation constants of the enzyme-fumarate complex 

 -^aEF ^nd A'bEp are calculated from the variation of Vp with pH, 

 and the ionization constants of the free enzyme K^^ and K^^ are 

 obtained from the variation of Vp/Kp with pH. As required by 



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