QUANTITATIVE EXPRESSION OF ENZYME INHIBITION 475 



enzyme. The problems posed by the possibility that this enzyme is a com- 

 ponent of a multienzyme system within the cell and that the intracellular 

 environment may be quite different from an artificial medium have been 

 treated already. The kinetics of enzymes enclosed within membranes that 

 limit the diffusion of substrates have been developed by Best (1955 b) 

 and Blum (1956; Blum and Jenden, 1957) and have been applied to hexo- 

 kinase and /5-fructofuranosidase in yeast cells (Best, 1955c). It may 

 be stated generally that when an enzyme is within a cell, the Michaelis- 

 Menten kinetics no longer hold in their simple form and that the usual 

 reciprocal plots are often no longer linear or easily interpreted. The bearing 

 of these factors on intracellular inhibition will now be outlined for certain 

 situations. 



The Factor of Diffusion into Cells of Different Shapes 



The kinetics of an enzyme enclosed within a membrane through which 

 its substrate must diffuse were presented in the simplest possible form in 

 Chapter 2 and it will be necessary to extend this treatment somewhat to 

 provide a basis for the discussion of inhibition. The reciprocal equation for 

 the situation when diffusion of substrate is a factor in determining the rate 

 of the reaction can be obtained from the expressions for the rate of entry 

 and the enzyme rate (Best, 1955b): 



--4- + ^ ^ '9-21) 



VJ8) 



A-o(S) 



where kg is the permeability constant, (S) is the external concentration of 

 substrate, and K, is the substrate constant for the enzyme (as in Chapters 2 

 and 5, K^. will be used to express the Michaelis-Menten constant but need 

 not imply that it is a dissociation constant). When (S) is large, the slope 

 of the 1/y — 1/(S) plot will be KJV,,^ as it would be without the membrane, 

 but when (S) is small, the slope w^ill be greater and equal to KJVyn + 

 I/Aq, as shown in Fig. 9-9. It may be easily shown that both competitive 

 and noncompetitive inhibition will increase the slopes and intercepts to 

 the same degree as in homogeneous systems. The determination of K^ 

 thus presents no special problems, but if the change of slope is so close to 

 the Ifv axis that a constant slope is assumed, it is possible to obtain an 

 erroneous value for K^. A method for calculating the various constants of 

 the uninhibited system, including k^, based on the original treatment of 

 Lineweaver and Burk (1934), has been outlined by Best (1955b). 



Extensions of this treatment can be made to cells of different shapes. 

 A long cylindrical cell, e.g. nerve or muscle, in which the enzyme is homo- 

 geneously distributed, has been considered by Blum (1956) and two re- 



