SOME INTRODUCTORY IDEAS CONCERNING THE 

 APPLICATION OF INFORMATION THEORY 



IN BIOLOGY 



Hubert P. Yockey 



Oak Ridge National Laboratory, Oak Ridge, Tennessee 



Abstract — The model of protein synthesis in the cell which has been built up as the result of 

 the work of many researchers has been used as a basis for applying the principles of infor- 

 mation theory in biology. The main Une of the argument has been the role of noise in the 

 genome. The discussion has been kept as independent as possible of special models. 



It was shown that in a real organism noise must exist in the genome and that an ensemble 

 of organisms may be represented by a probability distribution in H, p{H, A). Individuality is 

 thus incorporated in a very natural way. Dancoff 's principle requires that there be a lower 

 limit for viability for this distribution. Ha. 



The action of a deleterious agent which induces errors in the genome by acting on nucleo- 

 tide pairs is assumed to be represented by an equation of the first order: 



^ = -j(X)p,(j) + ija) 



where /(A) measures the effectiveness of the deleterious agent, of which A is a measure, 

 in producing defects. A differential equation for H(X) is derived and it is shown that 

 {dHldX)E^ as a function of A behaves like J{,X). 



I. INTRODUCTION 



Information theory finds its place in biological thought through its ability 

 to deal quantitatively with organization and specificity. The importance of 

 these concepts has long been recognized in biology, but this realization is 

 rather sterile unless a quantitative form of expression can be found. One is 

 reminded of a quotation from Lord Kelvin, 'When you can measure what 

 you are speaking about and express it in numbers, you know something about 

 it, but when you cannot measure it, when you cannot express it in numbers, 

 your knowledge is of a meagre and unsatisfactory kind.' 



The need for expressing biological quantities in numbers is clear but solving 

 the problem of how to do it is very much like belling the cat. Biology doesn't 

 seem to have any problems both really simple and terribly important such as 

 some which occur in the physical sciences. The application of first principles 

 has come much more slowly in biology for perhaps this reason. That ideas 

 of great general application do exist in biology is exemplified by Mendel's 

 laws and by the theory of evolution. 



One of the purposes of this article, and indeed one of the purposes of this 

 book, is to explore the practical and theoretical consequences that may be 

 found in the discovery that biochemical specificity of proteins is carried, largely 

 at least, by the exact order of twenty amino-acid residues. The suggestion of 



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