150 5. DETERMINATION OF MECHANISMS AND CONSTANTS 



terns or utilized for the accurate topological characterization of an active 

 center — it is absolutely essential that the nature of the constants be un- 

 derstood. The pitfalls of interpretation increase with the complexity of 

 the enzyme system and most of the important enzymes of cell metabolism 

 are now realized to be quite complex. 



The primary purpose of this chapter is to present several methods for 

 the plotting of enzyme kinetic data and to indicate how misinterpretation 

 of mechanisms and constants may be avoided. To facilitate explanation 

 of the graphical techniques we shall illustrate each by simple competitive 

 inhibition, then proceed to a generalized presentation, and finally give the 

 plotted curves expected for the more important types of inhibition discuss- 

 ed in the previous two chapters. The different characteristics of these plots 

 are more readily understood by directly examining the graphs rather than 

 by inspection of the kinetic equations and hence emphasis has been placed 

 on illustration; it is a simple matter to transform any of the previous rate 

 or inhibition equations into the equation to be plotted but it is not always 

 easy to visualize the results of the plotting. 



THE METHODS OF GRAPHICAL ANALYSIS 



The rate equation for completely competitive inhibition (Eq. 3-12): 



""'■ ''" {S)+K,[l +a)IK,] 

 may be rearranged into four forms conducive to useful plotting. 



The Plot of ^|VJ against 1/(S) (Type A) 



This method of plotting was outlined by Lineweaver and Burk (1934) 

 and the results are frequently referred to as Lineweaver-Burk plots or 

 as double-reciprocal plots. The transformed equation is: 



1 1 K„ 



Vi F,„ F,„(S) 



-t 



(5-1) 



Plotting 1/y, against 1/(S) one obtains a straight line with a slope equal to 

 {K„JV,J [1 -|- {l)IK^] and intercepting the l/v^ axis at 1/F,„. The compara- 

 ble equation for the uninhibited system is: 



— = — + — ^- (5-2) 



which gives a line of less slope but of the same intercept. This and the 

 other methods of plotting are illustrated for competitive inhibition in 

 Fig. 5-1. 



