22 : 2/ Thermodynamics of Enzyme Reactions 407 



The other extreme type of reaction is one in which most encounters 

 end by the molecules jumping apart. Then, decreasing the diffusion 

 rate decreases the number of encounters per unit time but increases the 

 length of each encounter. Accordingly, the collision rate Z will not 

 be greatly altered, and the reaction rate should be independent of the 

 coefficient of diffusion. Such a reaction is called a diffusion-independent 

 reaction. The slope of xx of the Arrhenius plot for such a reaction is an 

 intrinsic property of the reacting molecules. Its interpretation, however, 

 is exceedingly difficult unless one uses absolute rate theory, presented 

 in the next section. (By making the incorrect assumption that the collision 

 rate is the same in gases and liquids, one can arrive at values of a. 

 Although, by definition, a is less than one, this misleading calculation 

 produces values of a much larger than one for some enzyme reactions!) 



In spite of its limitations, xx is a characteristic of a given enzyme 

 reaction and can be used to compare different enzyme preparations and 

 different types of enzymes, as well as to express in one number the 

 temperature dependence of the reaction. Actually, an equivalent 

 quantity called Q 10 is used more frequently. By definition, it is the 

 ratio of the reaction rates measured at two temperatures 10°C apart. 

 That is, symbolically defined 



«i. = ^ (5) 



where the subscripts on the k's indicate the temperatures. By manipu- 

 lating Equations 5 and 2, one can show that 



10u 



Qio — e RT * 



or 



RT 2 



P = 



10 



In Q 10 (6) 



For biological reactions, Q 10 is generally in the range of 1.2 to 4, with 

 the majority of reactions having Q 10 's very close to 2.0. Expressed in 

 terms of xx, these values are 3.4 kcal/mole to 25 kcal/mole with a maxi- 

 mum number of reactions having fi = 12.5 kcal/mole. The quantity 

 Q w is easier to compute and is used more widely than xx. Since most 

 biological reactions can be observed only over a narrow range of tem- 

 peratures, the representation of the data in terms of Q 10 is completely 

 equivalent to describing them in terms of the slope /x of the Arrhenius 

 plot. 



