ROBERT A. ALBERTY 



Here the enzyme exists in two isomeric forms which are not 

 rapidly interconvertible, and only E is catalytically active. 

 Although mechanisms (2), (4), and (5) cannot be distinguished 

 by steady-state kinetic studies at high substrate concentrations, 

 they could be differentiated readily by transient-state studies. 



In the derivation of a rate equation for a particular mecha- 

 nism it is implicitly assumed that the individual rate constants 

 remain constant while the substrate concentration is varied. 

 If the substrate concentration is very low in comparison with that 

 of the buffer which maintains a constant pH and ionic environ- 

 ment, this ideal condition may be closely approached. However, 

 as the substrate concentration is increased the individual rate 

 constants may be affected because of changes in the ionic environ- 

 ment. Thus deviations from the Michaelis equation at high 

 substrate concentration may result from changes in individual 

 rate constants. Such deviations may also be a consequence of 

 the binding of substrate molecules or ions by the enzyme in such 

 a way as to alter the properties of the enzymatic site. The fact 

 that the rate may be either increased or decreased may be 

 represented by the addition of the following steps to mechanism 



(2). 



E -f S , SE (6) 



SE + S . SES > SE + P 



Here S is written to the left of E to represent its combination at 

 a neighboring site and to the right of E to represent combi- 

 nation at the enzymatic site. The steady-state treatment of 

 mechanism (2) plus mechanism (6) leads to the following rate 

 equation. 



^ V2 + ViK^/jl - Vi/V2)iS) , . 



"^ 1 -f ^2/(1 - ri/F2)(S) + K,K2/{\ - Fi/F2)(S)2 ^'^ 



In this equation Ki, K2, Vi, and V2 are constants. It may be 

 seen that at low substrate concentrations this equation reduces 

 to the Michaelis equation with maximum initial velocity Vi and 

 Michaelis constant Ki. Equation (7) represents the substrate 

 activation which occurs in the case of fumarase (2). 



570 



