218 



THE ANTIGEN-ANTIBODY REACTIONS 



When we come to the results obtained in partial neutralization, or partial 

 adsorption experiments, we find that they are not compatible with the concept of 

 firm union in constant proportions ; but that they afford no secure basis for dis- 

 tinguishing between an adsorption reaction and a combination due to intramolecular 

 forces that is subject to the law of mass action. 



The law which describes the relation between the amount of a given substance adsorbed 

 from a solution, and the concentration of that substance remaining in solution when 

 equilibrium has been reached, has been formulated by Freundlich (see Freundhch 1906, 

 1922, Freundhch and Neumann 1909), and expressed in the form of the following equation : 



TO 



where x is the amount of the substance adsorbed by the surface m, C is the final concentra- 

 tion of the substance in the fluid, a is a constant depending on the units of measurement, 

 and ra is a constant less than unity. 



If we let X represent the adsorption on unit surface, the equation will become: 



x = aC^ 



or log .r = log a-\- n log C. 



The curves of the two equations are shown in Figs. 35 and 36. 



LogX^Loga+nLogC 



C= Concentration-^ 

 Fig. 35. 



LogC- 



FiG. 36. 



It is clear that this formula expresses the fact that the amount of substance adsorbed 

 by unit surface increases with increasing concentration, not in direct proportion to this 

 increase, but to some root value of it. If, for instance, the value of n were 0-5, the amount 

 adsorbed by unit surface would increase as the square-root of the concentration. It 

 follows that proportionately more of a dissolved substance will be adsorbed from a weak 

 solution than from a strong one. 



The figures recorded in many antigen-antibody re9,ctions, and particularly in 

 the neutraUzation of toxin by antitoxin, fit a curve of this type very closely over 

 a considerable part of their range, but the calculated and observed values usually 

 differ significantly with a very great excess of either reagent (see, for instance, 

 von Krogh 1911). This discrepancy is not surprising (see Marrack 1938). The 

 Freundlich isotherm, in its classical form, does not approach to a maximum at 

 high concentration of one reagent, but rises continuously, though at a decreasing 

 rate. This seems very unlikely to describe the course of any antigen-antibody 

 reaction. The adsorbing reagent would be expected to become fully saturated 



