56 Hubert P. Yockey 



may be thrown into an excited tautomeric form from which it recovers by 

 relaxation. Possibly one can account for biological recovery by such a 

 mechanism. The consideration of recovery is omitted from this paper for 

 simplicity and we shall need only the notion expressed in the first sentence of 

 this paragraph. 



In view of the above remarks we may write the following equation for the 

 rate of change of /?,()) with A: 



idldX) p,ij) = -y,,(A) p,{j) + c,,(A) (4) 



The first terni represents the loss in nucleotides responsible for the {i,j) 

 transition. The second term is due to the gain in nucleotides engaging in the 

 (i,j) transition coming from other nucleotides altered by the deleterious agent. 

 This can be brought into sharper focus by thinking of the binary case. Suppose 

 q is the correct and p is the incorrect read-off probability. We are calculating the 

 equivocation, or damage to the message, resulting from point errors. This means 

 that, accordingly, a letter is not deleted but is read off either correctly or 

 incorrectly. This letter switching process may continue until half the letters are 

 correct and half are incorrect; at that point p = Ijl and q = 1/2. The infor- 

 mation content vanishes. In the case of a four letter alphabet a letter which is 

 acted upon and which may therefore change or may retain its original read-off 

 character has an a priori probabiUty of 1/4 to remain or to become a correct 

 letter. Thus the second term is required by the normalization condition. 



Equation (4) describes the effect of the interaction of the deleterious agent, 

 say the x-ray dose, with the information bearing molecules in the cell. It 

 corresponds to current views of reaction kinetics. Should it be discovered that 

 some effect, for example, inter-symbol influence, should be taken into account 

 then equation (4) may be altered suitably. The following argument would then 

 still be cogent except that the new form of equation (4) would be used. Present 

 experimental evidence substantiates equation (4) and we have no present 

 justification for greater complication. In fact the /./A) and c-j{X) represent more 

 detail than is available. Sum equation (4) over ally: 



2 (d/dX) pij) = - 2 JM plj) + 1 cM (5) 



Since J J 



IPi(j)=l; I(dldX)p,(j) = (6) 



j j 



o = -2^a)AO')+2c.>a) (7) 



3 3 



If the /,/A) and the c^/A) may be replaced by an average value J(X) and c(l), 

 equation (7) becomes, for a four-letter alphabet: 



= -J{X) + 4 cU) (8) 



c(X) = +yiX) (9) 



Equation (4) may be written as follows: 



(dldX) p,(j) - -7(A) p,{j) + i/(A) ( 1 0) 



