Some Membrane Phenomena from the Point of View of Information Theory 203 



information units, the bits, appearing in equations (15) and (16) are identical with 

 those used in discussing the information content of the printed page, the 

 interpretation is that a cm^ of nerve has an enomious rate of production. The 

 analogy of course is to a person who is called upon to separate red balls (Na+) 

 from white (K+) and blue (CI ) balls in a box where he would reach in, pick 

 up a ball, look at it, and if it is red it is taken out, and if not it is replaced. 

 The nerve has some equivalent separating mechanism with the infomiation 

 rate of equation (15). In terms of a familiar example, taking the information 

 content of a single printed page as 10* bits (9), equation (15) requires that the 

 cm^ of nerve surface produce information equivalent to that contained in a 

 library of 7.3 million volumes of a thousand pages each second — this is over 

 half the number of books in the Library of Congress! The value given by 

 equation (15) is not inordinate, however, in comparison with the estimates of the 

 information content of biological objects (9), where for man the value is of the 

 order of 10^5 bits. 



The result in equation (16) may be viewed as the minimum information 

 production necessary to effect the separation of sodium. The numerical value 

 may be in error, for the choice could be from among more ions than the three 

 employed. It is of interest to note that the nerve does not possess perfect 

 coding inasmuch as it uses 1 .7 times as much information to effect the separation 

 as is required. Alternatively the information efficiency may be expressed as 

 59 per cent. These comparisons may be without substance because of the 

 inadequacy of the data. The only relevant comparison may be that the physio- 

 chemical determination of information production as summarized in equation 

 (15) is of the same order of magnitude as the value determined by enumeration 

 in equation (16). 



REFERENCES 



1. J. F. Danielli: Cytological research and biophysics. Nature, Loud. 162, 753 (1948). 



2. H. R. Branson: A definition of information from the thermodynamics of irreversible 

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 Illinois Press, Urbana (1953). 



3. L. Brillouin: Science and Information Theory, Academic Press, New York (1956). 



4. R. C. Tolman and P. C. Fine: On the irreversible production of entropy. Rev. Mod. 

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5. S. R. DeGroot: Thermodynamics of Irreversible Processes, Interscience, New York (1952). 



6. R. W. Stacy, D. T. Williams, R. E. Worden, and R. O. McMorris: Essentials of Bio- 

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7. H. LrNSCHiTz: Information and physical entropy. In: Information Theory in Biology. qA. 

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8. S. M. Dancoff and H. Quastler: The information content and error rate of living things. 

 In: Information Theory in Biology, ed. by H. Quastler, 263-273, University of Illinois Press, 

 Urbana (1953). 



9. A. L. Hodgkin and R. D. Keynes: Active transport. Symp. Soc. Exp. Biol. 8, 423-437 

 (1954). 



