206 SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



binding and hence the specificity of a particular catalyst for a particular 

 reaction. 



Not all of the assumptions made nor the conditions assumed in the fore- 

 going analysis are always met. Because equilibrium does not always exist 

 in reaction 1, K m can better be expressed as (£_, + k 2 )/k ] , which of course 

 reduces to l/K = k_ ] /k ] if k_ x >> k 2 , the case we have studied already. 

 There are further complications, such as competition by two or more reac- 

 tants for the one active site, which introduce more terms in the expression 

 for v. Although these are of pragmatic interest in biological chemistry, 

 further discussion here is beyond our scope — our purpose is simply to illus- 

 trate complex formation and saturation of a catalyst. 



It should be remembered that the rate constant, k 2 , can be factored into 



k T 



h 



Because the change in entropy AS 1 accompanying activation gives an indi- 

 cation of the change in the freedom of motion within the complex ES 1 , deter- 

 minations of AS 1 and A// 1 have become very powerful tools for understand- 

 ing the mechanism on a molecular scale. Some values are given in Table 

 8-5. A very interesting success story of this kind centers on myosin, the con- 

 tractile substance in muscle and the catalyst for ATP hydrolysis. The "state 

 of the art 1 ' is reviewed briefly in Chapter 10. 



TABLE 8-5. Kinetic Parameters for Some Enzyme-Catalyzed Reactions.* 



Enzyme Substrate (deg C) pH (moles ') (sec ] ) E 2 * ±S 2 * 



Pepsin carbobenzoxy-1-glu- 



tamyl-1-tyrosine 32 4.0 560 0.0014 20.2 4.6 



a-Chymo- benzoyl-1-tyrosine 



trypsin ethyl ester 25 7.8 250 78 9.2 -21.4 



Urease urea [CO(NH 2 ) 2 ] 21 7.1 250 20,000 9.7 - 7.2 



Myosin adenosine triphos- 



phate (ATP) 25 7.0 79,000 104 13.0 - 8.0 



\/K m . equilibrium constant for formation of ES complex (see Figure 8-5). 

 k 2 : specific rate constant for unimolecular breakdown of the ES complex. 

 £,* : energy of activation of ES complex. 

 AS 2 *: entropy of activation of ES complex. Negative values are usually interpreted 

 as evidence for the freeing of charged groups resulting in orientation of water 

 molecules during activation. 



Values in the last three columns were taken at high substrate concentration 

 and therefore refer to the activation of ES complex into product. 



*See the book bv Laidler 15 for collections of data. 



