406 Thermodynamics of Enzyme Reactions /22 : 2 



2. Collision Theory Applied to Enzyme Reactions 



Qualitatively, one may picture an enzyme as acting by lowering the 

 potential energy barrier AG*. However, the detailed application of 

 collision theory to enzyme reactions is difficult for two reasons. The 

 first is that it is possible to make measurements only over a narrow 

 temperature range. A more fundamental limitation is our inability to 

 compute either the probability factor a or the collision rate Z for 

 reactions in the liquid phase. To understand this phase, let us con- 

 sider briefly some ideas contained in the kinetic theory of liquids. 



In a liquid, as in a solid, there are equilibrium distances from one 

 molecule to the next molecule. In a solid, these are maintained in a 

 regular pattern for astronomically large numbers of molecules. In a 

 liquid, by contrast, the order is only local, falling off rapidly a few 

 molecular diameters away. Diffusion in a liquid occurs as a result of 

 the diffusing molecule jumping from one quasi-equilibrium lattice 

 position to the next. As the molecule is in the quasi-stable position, 

 it vibrates and rotates, colliding many times with its neighbors before 

 moving on to its next position. The period of time during which two 

 reacting molecules are in neighboring sites is called an encounter. The 

 rate of encounter Z e can be readily computed. In contrast, the kinetic 

 theory of liquids is far too poorly developed to compute the collision 

 rate Z. 



Two extreme types of reactions can be distinguished. In the first, 

 called diffusion limited, each encounter leads to a reaction. Anything 

 lowering the diffusion rate will decrease the encounter rate and hence, 

 decrease the reaction rate. For a diffusion-limited reaction, the reaction 

 rate and encounter rate are the same, that is 



k = Z e (4) 



The encounter rate will be proportional to the diffusion constant. In 

 this case, the slope of the Arrhenius plot represents the temperature 

 dependence of the diffusion constant and yields no information relative 

 to the reacting molecules. For water the slope of the log of the diffusion 

 rate plotted against l/RTis around 3 kcal/mole for many solutes. This 

 suggests that reactions with a /x of 6 kcal/mole or more are not diffusion 

 controlled, whereas those with a /x of around 3 kcal/mole may be. 

 (However, this is not a good criterion for diffusion control. For if the 

 molecular shape is temperature dependent, it is possible to imagine 

 diffusion-controlled reactions with much larger values of fx than 3 kcal/ 

 mole. In this case, it would indicate the temperature dependence of 

 the change of shape of the reacting molecules. Likewise, even though 

 fx = 3 kcal/mole, the reaction need not be diffusion controlled.) 



