66 3. KINETICS OF ENZYME INHIBITION 



INHIBITION KINETICS IN MUTUAL DEPLETION SYSTEMS 



The Michaelis-Menten treatment of enzyme kinetics and the formulation 

 of inhibition given above involve the assumption that the concentration of 

 enzyme is so small that combination of either substrate or inhibitor with 

 the enzyme does not appreciably reduce the concentrations of free substrate 

 and inhibitor. However, under certain experimental conditions and fre- 

 quently within the cell, the enzyme concentration may be sufficiently high 

 relative to substrate or inhibitor so that the equations presented are not 

 valid. In other situations the affinity of the enzyme for an inhibitor is so 

 high that the concentration of free inhibitor is reduced due to formation of 

 the EI complex, even though the enzyme concentration is low, for to obtain 

 inhibitions in the usual range correspondingly low inhibitor concentrations 

 must be used. The additional factor that must now be included in the ki- 

 netics is the reduction in substrate or inhibitor concentrations in systems 

 where the conditions lead to mutual depletion. These conditions are de- 

 termined principally by the value of the specific concentration of enzyme 

 (E/), since either a high enzyme concentration or a low dissociation constant 

 favors mutual depletion in free concentrations. 



Inasmuch as no general name has been given to enzyme systems of this 

 type, it is suggested that they be called " mutual depletion systems," be- 

 cause there is of necessity a mutual reduction in concentrations of free 

 enzyme and whatever components are involved. In situations where the 

 concentration of free inhibitor is decreased, it is evident that there must 

 also be a decrease in concentration of free enzyme if significant inhibition 

 occurs. It should also be clear that this extension of the simple theory may 

 apply to coenzymes and activators. In any system, composed of a number 

 of substances involved in the reaction, depletion may occur in one, any 

 number, or all of the components, depending on their relative dissociation 

 constants with respect to the complexes they form with the enzyme. The 

 specific concentration of the enzyme will usually be different with regard 

 to each of the components. The specific concentration of enzyme with re- 

 spect to substrate is (E,)/iC„ with respect to inhibitor is (E^)/iif ,, and with 

 respect to any component X is (E,)/iir_j.. We shall designate these different 

 specific concentrations as (E/), (E/), and (E^'). Since specific concentrations 

 are more significant than ordinary concentrations in mutual depletion sys- 

 tems, it will be convenient to formulate the inhibition equations accordingly. 



Noncompetitive Inhibition in Mutual Depletion Systems 



No general formulation including the different kinds of inhibition has 

 been made for systems of this type and, indeed, it would l^e mathematically 

 complex. The basic concepts involved are most clearly illustrated in non- 

 competitive inhibition where only the inhibitor concentration is of impor- 



