METHODS OF GRAPHICAL ANALYSIS 



153 



The Plot of 1//, against (I) (Type D) 



One of the most useful methods, developed particularly by Dixon (1953 b), 

 allows direct determination of K^ and is based on the equation: 



1 



Km 



A^„(I) 



(5-5) 



If plots are made for two different substrate concentrations, the intersec- 

 tion of these straight lines will occur at an ordinate of — K^. When the 

 constants for the uninhibited reaction are known, a plot for only one sub- 

 strate concentration will provide means of calculating K^, using either the 

 slope or the (I) intercept. When the intersection method is used, it is evi- 

 dent that the two substrate concentrations should be as far apart as possible 

 so that the intersection point can be accurately located. 



The Plot of 1// against 1/(1) (Type E) 

 The inhibition equation for competitive inhibition (Eq. 3-13): 



. _ (I) 



' (I) + K^ [1 + (S)/AJ 



can be transformed into the reciprocal equation: 



1 



1 + 



K^ 



(I) 



1 + 



K,„ 



(5-6) 



and when l/i is plotted against 1/(1), straight lines intersecting on the 

 Iji axis are obtained. This method will not provide K^ unless ^,„ is 

 known but if the slopes at two different substrate concentrations are 

 plotted against (S), the intercept will give K, since the slope approaches 

 Ki as the substrate concentration decreases. 



The Single-Curve Plot (Type F) 



This method was introduced by Hunter and Downs (1945) in connection 

 with their studies on the inhibition of arginase by amino acids and is a very 

 efficient and accurate procedure in certain instances. For competitive inhi- 

 bition the equation used is of the form: 



(I)(l 



K,+ 



Kii^) 

 K„, 



(5-7) 



and when (I)(l — ^)/^ is plotted against (S) a straight line is obtained which 

 gives — K,,i on the (S) intercept and K^ on the (I)(l — i)li intercept, the 

 slope being the ratio KJK^^. 



