46 INFLUENCE OF TEMPERATURE ON BIOLOGICAL SYSTEMS 



differences in the temperature response of enzymes of the same tyjie from 

 different animals, but so far this question has been very imperfectly sur- 

 veyed. 



Moreover, most published records do not include a measure of the ex- 

 perimental variability, so that one is denied the opportunity of using 

 statistical methods for narrowing the choice among the various types of 

 relationship that could be fitted by eye to the results, and one is often left 

 to wonder also whether apparent differences between enzymes from dif- 

 ferent sources, or in the same enzyme in the hands of different workers, are 

 real or fortuitous. 



A more fundamental difficulty is posed first by the nature of the reaction, 

 which is thought to have the form 



E + S ^'— ES — ^ ES* -. E + products (/) 



in which ES* is the 'activated complex' of the theory of absolute reaction 

 rates (20) ; and secondly by the limitations of present techniques for de- 

 termining reaction velocity, which measure only the rate of disappearance 

 of substrate or the rate of accumulation of products. Thus the data obtained 

 refer only to the speed of the overall reaction, a limitation by no means 

 peculiar to the hydrolysis of ACh by ChE. The formal equivalent of the 

 equilibrium constant, K, is, therefore, provided one may assume a steady 

 state, 



K = ki/(k2 + ka) . {2) 



Evidently, plotting log K in the usual manner against 1/Tai,s gives a curve 

 whose slope is a composite function that includes, in undetermined pro- 

 portions, both heat of reaction to form ES and heat of activation to con- 

 vert ES to ES*. For this reason, measurements of the temperature depend- 

 ence of K cannot be used to derive meaningful values for the standard 

 thermodynamic constants, except under the limiting conditions, ko > > k;^ , 

 ka < < ks (cf. ref. 25; pp. 176-177). Some authors have adopted such prem- 

 ises in order to calculate the constants in question, though without direct 

 justification, which would require a means of measuring the relative mag- 

 nitude of ko and k^ . 



However, the reaction velocity is 



V = k3-Eo-K-S/(l + K-S) {3) 



where Eo is the total concentration of enzyme and S the concentration of 

 substrate. Thus, at high substrate concentrations, 



Vmax = ka-Eo. (4) 



