17 : 1/ Enzyme Kinetics of Hydrolytic Reactions 317 



concentrations, and the new carbonic acid formed per unit of time. 

 Analytically, this may be expressed by the differential equation 



d[H ^° 3] = -^[H 2 C0 3 ] + * 2 [H 2 0].[C0 2 ] 



where the square brackets represent concentrations. One may also 

 write a similar equation for the carbon dioxide 



S3= +il[ H 2 C03]-yH 2 0].[C0 2 ] 



Notice that k 1 and k 2 have different units; those of k-^ are sec -1 , whereas 

 the units of k 2 are concentration -1 sec -1 . 



In the foregoing paragraph, it was stated that k ± and k 2 are rate 

 constants. They certainly are rates but it is by no means obvious that 

 they are constants, even if temperature andpH are maintained constant. 

 The quantities k x and k 2 will be constants for many reactions, provided 

 a number of conditions are met. The first is that the reaction scheme 

 is complete and does not involve other steps. The addition of an 

 enzyme which alters the reaction means that new rate constants must be 

 defined in the presence of the enzyme. The second is that the reactants 

 are sufficiently free to move about so that the probability of their 

 colliding is proportional to their concentrations. (This is sometimes 

 referred to as the law of mass action.) The final condition is that one 

 really considers only the average behavior of large numbers of molecules, 

 so that one may identify the rate of reaction with the concentration times 

 the probability of a molecular reaction. 



The foregoing examples illustrate the types of reactions analyzed in 

 studies of enzyme kinetics ; this type of reasoning has proved attractive 

 to biophysicists and physical chemists. Enzyme studies have become 

 part of biophysics for several additional reasons. For instance, many 

 reactions are observed by the use of complex physical instruments such 

 as recording spectrophotometers and paramagnetic resonance equip- 

 ment. These have demanded a certain degree of training in physics (as 

 well as skill in electronics) for their construction, maintenance, and the 

 interpretation of their data. A quite different reason for including 

 enzyme studies in biophysics is that enzyme kinetics are necessary for a 

 study of enzyme thermodynamics. Physics, to the extent it has any 

 unifying factor, has emphasized the point of view that energy is the 

 most fundamental, most significant quantity. This approach, expressed 

 through thermodynamics as applied to enzyme systems, is presented in 

 Chapter 22. 



