408 



Thermodynamics of Enzyme Reactions /22 : 3 



3. Absolute Rate Theory 



The proportionality constant a in Equation 2 of the collision theory is 

 a sort of " correction factor" to make theory and experiment agree. In 

 the case of gaseous reactions, a is often very small, having values in some 

 reactions as low as 10" 10 . A somewhat different thermodynamic 

 analysis called absolute rate theory has been outstandingly successful in 



predicting these small values of 

 a for gaseous reactions. Its 

 application to reactions in liquids 

 is considerably more tenuous, 

 although the theory is widely 

 accepted. 



In order to describe absolute 

 rate theory, it is convenient to 

 again use the potential energy 

 diagram of the form found in 

 Figures 1 and 2. Now, three 

 separate regions must be distin- 

 guished as shown in Figure 4. 

 The abscissa does not have to 

 be regarded as simply a distance 

 apart. It is called the reaction 

 coordinate and will, in general, 

 have the dimension of length. 

 When the reactants are far out 

 on the reaction coordinate, they 

 are considered as separate mole- 

 cules A and B. Above the 

 highest part of the potential 

 barrier, they are considered as an activated complex^! • B. % Finally, in the 

 region of the potential well there is a single molecular species C. This 

 method of analysis is an approximation method because the region in 

 which the activated complex exists is arbitrary. 



The reasoning employed is very similar to that used to develop 

 Michaelis-Menten kinetics in Chapter 17. The complexes introduced 

 in that chapter and here both control reaction rates. However, the 

 intermediate complex of enzyme kinetics stays in existence for a much 

 longer time, and its rate of breakdown cannot be determined on a priori 

 grounds. The rate of breakdown of the activated complex A ■ B*, on 

 the contrary, is always 



1 d[A-B*] RT 



Figure 4. The absolute rate theory. The 

 absolute rate theory postulates an activated 

 complex A-B*, which must be in equilib- 

 rium with A + B in order to apply this 

 theory to k. The rate of crossing the 

 barrier from A-B % to C is an absolute 

 quantity if certain general assumptions are 

 valid. 



\A'&\ 



dt 



Nh 



e + AS t IR 



