1250 THE TEMPERATURE FACTOR CHAP. 31 



selection of the "minimum temperature/' 8, the rate can be made to dis- 

 appear at the lower limit of the "biokinetic" range. 



Equation (31.11) is an empirical interpolation formula, and no theo- 

 retical interpretation has been suggested for it. Whether an empirical 

 formula of an apparently wider, but still limited, range (it does not include, 

 for example, the reversal of the trend above the optimum) is to be preferred 

 to a theoretical equation, which is valid over a narrower range, depends on 

 the use one wants to make of it— whether one is primarily interested in 

 extrapolation, or in theoretical interpretation. Those who frown on the 

 application of physicochemical theories to living systems will deprecate 

 attempts to "impose" the Arrhenius law (or any other theoretical equa- 

 tion) on the complex processes in the living cell ; others will see more sig- 

 nificance in the existence of a temperature range, albeit a narrow one, in 

 which a biochemical process follows the exponential formula, and will try 

 to find a physicochemical explanation for deviations from it. 



When the temperature course of a reaction is found to depart from the 

 simple exponential law, it is often attempted to represent it by the com- 

 bination of several temperature-dependent processes, each with its own 

 activation energy. The reaction steps may be either competitive or con- 

 secutive. As an example of two parallel competing processes, we may 

 consider a reaction that proceeds partly directly, and partly by means of a 

 catalyst. The catalytic reaction normally has a smaller "temperature- 

 independent" factor A in (31.4) (because of the low concentration of the 

 catalyst, or a low affinity of the catalyst for the substrate) but a much lower 

 activation energy. Consequently, at low temperatures, the catalytic 

 reaction will predominate; while at higher temperatures, it may be replaced, 

 more or less completely, by the direct uncatalyzed transformation. If we 

 assume that the direct and catalyzed reactions are of the same order, e. g., 

 of the first order (with respect to the substrate S) we obtain the scheme : 



V = [S]Ae-Ea/RT 



I direct I 



(31 • 12) S <^ ^.^^^ catalyst j 



Ea > e, 



p 



A »a 



= [8]ae-ea/RT 



where S stands for substrate, and P for product. 



The two reactions velocities, V and v, are equal when : 



(31.13) In {A/a) = (Ea - ea)/RTa 



The transition temperature is thus: 



(31.14) Tc = .-5° ~/;, , 



^ ^ 4.57 log {A /a) 



Above Te, the temperature dependence of the over-all rate of conversion 



