170 UNITY AND DIVERSITY IN BIOCHEMISTRY 



of the substrate and [X] the concentration of the enzyme-substrate com- 

 plex. When the enzyme-substrate reaction is at equilibrium : 



\X} 



= K (equilibrium constant for the enzyme-substrate reaction) (1) 



[E] [S] 



Each molecule of the enzyme-substrate complex contains a molecule 

 of enzyme and a molecule of substrate so 



[E], = [E] + [X] (2) 



Equation (1) can therefore be written : 



[X] 



{[E]o - [X])[S] 



= K (3) 



Now, it is the concentration of the complex [X] which governs the 

 velocity of the reaction 



V = k,[X] (5) 



The dissociation of the complex X is veiy far from the position of equili- 

 brium and we may neglect the velocity of the reaction 



S +E-^X 

 From (4) and (5), 



KKjEUS] 



'' = TTk[S] ^^^ 



K (the equilibrium constant of the enzyme-substrate reaction) is often 

 replaced by its reciprocal 1 jK = Km, or the Michaelis constant. 

 If we replace i^ by 1 /Km, equation (6) becomes 



^ k,IK„>[EUS] 



l+{llKm)[S] ^^ 



It can be shown that Km, the Michaelis constant, which has the dimen- 

 sions of concentration (moles/1.), is in fact the substrate concentration 

 corresponding to a value of half the maximum velocity (Fig. 35). Know- 

 ledge of the Michaelis constant for a given enzymatic reaction, allows v to 

 be calculated for any value of [S], provided that Ag is known. 



