EFFECTS OF TEMPERATURE: ENZYMES 767 



mole, which with the rather small change in free energy would imply a 

 large entropy factor. Although this situation is different from that usually 



investigated, the principles used in the calculations would be the same 

 for any temperature range. 



Effects of Inhibition on the Optimal Temperature 



The temperature at which the rate of an enzyme reaction is maximal is 

 determined usually by a balance between the two major effects of temper- 

 ature, the elevation of the rate with rise in the temperature, due mainly 

 to the increase in ^2 for the breakdown of the ES complex, and the progres- 

 sive thermal inactivation of the enzyme. A system such as 15-16 is generally 

 assumed and the variation in the rate, given by Eq. 15-17, with temperature 

 is related to the changes in the constants, k2, K„j, and K. Since the temper- 

 ature dependence of these constants is determined by the respective en- 

 thalpies, these constants may be expressed in terms of the thermodynamic 

 quantities as follows: 



k, = Ae-^-'H*iRT) e i^'S'/R) (15-33) 



K, = e^-^HsiRT) e-^-^SsiR) (15-34) 



K = e^'niRT) g-(JS/R) (15-35) 



and substituted in Eq. 15-17. If the Michaelis constant is not an equi- 

 librium constant, K„ each of the rate constants — k^, k_-^, and k^ — must 

 be expressed as in Eq. 15-33. If it is further assumed that the substrate 

 concentration is low so that it may be neglected in the denominator, the 

 rate is given by: 



_ ^(E,)(S)e''^*/^' ( e-^-'H'iRT) j 



In order to determine the temperature at which the rate is maximal, 

 dvjdT may be set equal to zero. Since the term outside the brackets is 



