Efficiency of Information Transmission by Biochemical Co-factors 207 



The informational performances at the decision point are related to the 

 reduction of uncertainty, AH, at these points, i.e. the difference in uncertainty 

 before and after: 



A//i = H{C) - H{C.A) 

 AHii = H{C.A) - H{C.A.S) 

 AHiji = H{C) - HiC.A.S) 



The comparable functions for artificial situations are given by: 



AHi* = H{B) - H{B.A) 

 AHii* = H{B.A) - H{B.A.S) 

 AH*iji = H(B) - H{B.A.S) 



There is a fundamental difference between natural and artificial functions. 

 The quantities H{C) as well as H{C.A) and H(C.A.S) do not depend on the 

 experimenter; furthermore, because of the constancy of the internal environ- 

 ment, they can be considered to be numbers approximating natural constants, 

 subject to relatively small fluctuations. The function AHjji represents the 

 normal informational performance achieved in the particular metabolic process 

 considered, whose average value has been placed at 9 bits (1). The quantity 

 H{B), on the other hand, is completely or partially controlled by the experi- 

 menter, who regulates the availability of substances in B; H(B.A) and H{B.A.S) 

 depend on apo-enzyme, substrate and on the experimenter. Accordingly, the 

 AH* functions have, in general, very little interest since it is easy to make AH* 

 vanish by offering only a single co-factor which can be used, or to give it a 

 very high value by introducing numerous compounds which are known not to 

 react with the apo-enzyme or substrate. 



A great body of data is available, however, which lends itself to an examina- 

 tion of the AH* functions as well as H{B.A) and H{B.A.S) from the standpoint 

 of the systems' responses to a series of compounds closely resembling the natural 

 co-factors. The values obtained may be regarded as a sort of minimum residual 

 uncertainty associated with the various systems, and they form the subject of 

 this report. 



We shall define the uncertainty functions H{B.A) and H(B.A.S) as: 



H(B.A) = -i:pJog,p, 



H(B.A.S)=-i:p,,log,p„, 



where p^ and p^^ are the normalized biological activities of the compounds 

 tested in a particular system. Thus if four compounds were tested for their 

 ability to combine with the apo-enzyme and all were found to be equally active, 

 their /7^ would each be 0.25 and H{B.A) would be 2. This method of calculation 

 takes into account the fact that with equal concentrations, equal activity may 

 not be observed and that the information is of necessity related to the concentra- 

 tion required to produce a complex. 



A word is in order as to the mechanics of calculation. The basic data were 

 derived in large part from Williams and co-workers' treatise on the B vitamins 

 (2) ; data on thyroxine are due mainly to the work of Bruice, Kharasch and 



