SOME MEMBRANE PHENOMENA FROM THE 

 POINT OF VIEW OF INFORMATION 



THEORY* 



Herman Branson 



Howard University, Washington 1, D.C., U.S.A. 



Abstract — The methods of information theory and of irreversible thermodynamics are applied 

 to membranes. Equations are derived for the negentropy production of a membrane maintain- 

 ing a concentration difference. The results are converted to bits. When applied to typical 

 data for a nerve transporting Na+ against a concentration gradient, the equation gives for the 

 negentropy or information production, 



H=7.3 X 10^^ bits/cm'' second. 



Enumeration based on Na+ : Cl~ : K+ = 1 : 1 : 10 gives a value of 



4.3 X 10'^ bits/cm* second. 



In a classification of the significant problems of biophysics Danielli (1) listed 

 four. Two of these relate intimately to membranes and their role in biological 

 systems: cell permeability and cell electrophysiology. It is almost mandatory, 

 then, to inquire into the behavior of membranes from the point of view of 

 information theory. For if information theory is to have relevance to important 

 biological problems, a coherent relation should be exhibited for membrane 

 phenomena. This attitude was exhibited in the initial attempts to discuss 

 biological problems within this discipline in Quastler's pioneering book (2). 

 The formidable complexity of biological membranes is a recurring theme 

 in the immense amount of experimental data which are being accumulated. 

 Phenomena encountered in biological membranes may range from those 

 explainable by the assumption of simple pores of various sizes, to those requiring 

 charged pores, and on to those necessitating a picture of the surface as possessing 

 pores, binding sites, permeability barriers, enzymes, and transport mechanisms. 

 It is possible, however, to ignore the details of structure and specific mechanism 

 — as is usually the case in thermodynamics — and formulate a limited model 

 of membrane activity satisfactory to our analysis. Thus membranes may be 

 classified by the manner in which they react to or treat a given substance. 

 If we schematize the membrane as separating two media in each of which the 

 reference substance is soluble, calling one region the 'inside' and the other 

 the 'outside', we may introduce the following notation : 



Indifferent: A membrane is indifferent to a substance if the concentration 

 of that substance is the same on both sides of the membrane 

 at all times. Thus Q = Q, for all /. 



* This work has been supported in part by the U.S. Atomic Energy Commission, 

 AT(30-l)-892. 



197 

 14 



