KINETICS or COMPLEX ENZYME REACTION TYPES 



37 



strate molecule (e.g. if « > 1, the affinity for the second substrate mole- 

 cule is less than for the first). If a is very high, the equation becomes the 

 classic Michaelis Eq. 2-7, because the second substrate will be bound to a 

 very small extent: 



K, + ^(S)/a «>1 ^^ (S) 



F„ 



(S)/c/ -f A', + A%V(S) 



(S) + K, 



(2-39) 



If a = 1 (no effect on affinity) and /5 = (reaction 2-32 does not occur) 



the equation becomes: 



(S) 



(2-40) 



= F„ 



(S) + A, -^ (S)VA, 



_whichj-epresents one tj^e^^f^substxate ji^ihibition^, si nce at high (S) most 

 of the enzyme will be in the form SES and this is inactive. If « = /? = 1, 

 no effect of the first substrate molecule on the binding or reaction of the 

 second occurring, it may be noticed that the kinetics deviate from the sim- 

 ple Michaelis equation when (S) is near K^ but follow the Michaelis equation 

 when (S) is greater than approximately 5^,. The explanation of this devia- 

 tion can be made as follows: (ES)-r(SES) will not be equal to the value of 

 (ES) when a single substrate only is involved and hence the rate of for- 

 mation of P will differ from the simple case. When (S) = K^, then (ES)/(E^) 

 = 1/2 for the simple one substrate reaction, but [(ES) ^ (SES)]/(E^) = 2/3, 

 for the reaction with two substrate molecules, the rate for the latter being 

 greater than if only one substrate molecule reacts. Equation 2-39 is plotted 

 in Fig. 2-6 to illustrate the effects of variations in u and /?. 



lOOmM 



Fig. 2-6. Plots of Eq. 2-39 for different values of or and /5. A'^ = 0.3 mil/ and F„ = 



100. Curve 1: « = 1, ^ = 1; curve 2: « = CC, ^3 = 1; curve 3: a = 10, /3 = 1; curve 4: 



a. = 0.5, /3 = 1; curve 5: « = 1, /3 = 0.2; curve 6: « = 1, /3 =: 2; curve 7: a = 0.5, 



^ =: 2, curve 8: « = 10, /3 = 0.2. 



