198 Herman Branson 



Responsive : A membrane is responsive to a substance if tlie concentrations 

 of that substance differ on each side at the same time. But 

 neither concentration is zero. Thus, Q ^ Cq for some t. 

 Exclusive: A membrane is exclusive with respect to a given substance 

 if, for all time, the concentration on one side is finite but the 

 concentration on the other is zero. Thus, Q = and Q 7^ 0, 

 or Q ^ and Q = 0, for all t. 

 The analysis of this paper will be limited to substances to which a given 

 membrane is responsive. It must not be concluded, however, that indifferent 

 and exclusive substances are of no biological significance. There are examples 

 where seemingly the most important role of a membrane is its action to exclude 

 a given substance from the internal medium or keep a component from diffusing 

 out. 



The preliminary work (2) on a responsive membrane attempted to derive 

 by the methods of irreversible thermodynamics an expression for the negen- 

 tropy production of a membrane maintaining a concentration difference. 

 The approach rested upon the concept that the entropy is an absolute maximum 

 at equilibrium. Hence any deviation from equilibrium would mean a decrease 

 in the entropy. Expanding the change in entropy, A^, in a Taylor's series about 

 the equilibrium point yields as the first approximation, since the first derivative 

 terms vanish at equilibrium, 



A5=-l/2 2gj.m«i«m • 0) 



Equation (1) was combined with some descriptive equations for the membrane 

 and the final result 



^ = fta (2) 



was deduced. In equation (2), H is the negentropy or the information (3), a is 

 the rate constant governing the rapidity with which the membrane would 

 approach uniform concentration on each side if it were not actively maintaining 

 the concentration difference and k is Boltzmann's constant (1.380 X 10"^^ ergs 

 per degree). 



Equation (2) had to be examined to determine if it is apphcable to a mem- 

 brane maintaining a considerable concentration difference. Its significance 

 with respect to the relation 



A5ir,. = A: In Q/Q (3) 



had to be clarified (4). Equation (3) gives the irreversible production of entropy 

 for the passage of a single particle from concentration Q to the concentration 

 Co. If Co is greater than Q-, we have the situation postulated for the membrane, 

 thereupon A^'u-r. is negative and may be equated to information, H. 



Derivation of the Rate of Production of Information 



The methods of irreversible thermodynamics as presented by DeGroot (5) 

 are applicable to effect the derivation. Following DeGroot's nomenclature, 

 we have 



^S = J^X, + J^nXm + h^, (4) 



