152 5. DETERMINATION OF MECHANISMS AND CONSTANTS 



The symbol K^ is used in the graphs but it must be remembered that 

 it is the Michaelis constant which is often determined by the graphical 

 procedures. The difference between KJ,^ and Kg has been discussed in Chap- 

 ter 2. In the interest of the correct historical attribution of these graphical 

 procedures, it is necessary to point out that the plot of \jv against 1/(S) 

 was initially described in 1932 by Haldane and Stern in their book, " Allge- 

 meine Chemie der Enzyme " (1932, p. 119) as the result of a suggestion by 

 B. Woolf. The plots of i;/(S) against v and (S)/v against (S) were also discuss- 

 ed. These methods were originally applied only to uninhibited enzyme 

 reactions; however, Haldane and Stern distinguished between competitive 

 and noncompetitive inhibition. 



Thus a characteristic of these plots for competititive inhibition is that 

 the slopes vary with inhibitor concentration but the 1/v, intercept remains 

 constant. The intercept gives the value of 7,„ and from the slope of the 

 uninhibited reaction the value of ^„, may be determined; the slope from 

 the inhibited reaction may then be used to calculate K^. The value of K^ 

 should be independent of the inhibitor concentration used and it is advisable 

 to plot at different inhibitor concentrations to confirm this and increase 

 the accuracy in the determination of K^. 



The Plot of (S)/i',- against (S) (Type B) 



This procedure, also suggested by Lineweaver and Burk, provides par- 

 allel straight lines of constant slope 1/F,,,, the constants K^^ and K^ now 

 being calculated from the {^)^v^ intercepts or the (S) intercepts as indicated 

 by the following equation: 



(S) ^ (S) /i, 



V; F,„ V,, 



-1 



(5-3) 



There are certain instances, as in substrate inhibition, where this method 

 has advantages over the previous one. 



The Plot of Vj against Vjj{S) (Type C) 



This method was originally used by Augustinsson (1948) in his studies 

 on cholinesterase and elaborated by Hofstee (1956) who claimed certain 

 advantages which will be considered later. The equation: 



v. = V - ''^ 



(S) 



1 + ^ 



K> 



(5-4) 



shows that straight lines of negative slope will be obtained, from which 

 the constants may be calculated directly. 



