The Quantitative Determination of the Fixation of Complement by Immune Serum and Antigen
Authors: Wadsworth Augustus , Maltaner Elizabeth , Maltaner Frank 
Published: January 2023

Summary and Conclusions
The relations which exist between complement and the various reagents used in complement-fixation tests have been investigated in order to develop more consistent and quantitative methods of determining the fixation of complement by immune serum and antigen.
By titration of the hemolytic activity of complement, alone and in the presence of the reagents of the test, the course of the reaction was determined. It was not altered by differences in the degree of the sensitization of the cells; but it was altered by preliminary incubation of the complement. The course of the reaction was constant after preliminary incubation, either of complement alone or in the presence of the reagents of the test when the concentration of the serum constituents was not too greatly decreased or the amounts of complement too greatly increased or diminished; under these conditions, the course of the reaction was not influenced by the degree of sensitization of the cells.
With suitable constants, the experimental data obtained in all the different conditions of these comparative titrations, within the slight variation of technical error, proved identical with the theoretical data derived by the alternation formula which von Krogh developed from experiments on hemolysis with vibriolysin, sodium hydroxide, and amboceptor and complement.
An accurate method of determining the change in the activity of any given complement resulting from the presence of any or all of the reagents of the test, was demonstrated. The amount of complement (B) giving some degree of partial hemolysis under any given condition was compared with the amount of the original complement (A) giving the same degree of reaction. The difference in these amounts indicated the change in activity at that particular degree of hemolysis and the formula represented a unit value which proved practically constant at different points of partial hemolysis, not too near the point of complete hemolysis nor of complete inhibition of hemolysis. An accurate determination was obtained only under conditions in which the course of the hemolytic reaction was constant.
The titration of complement to the point of complete hemolysis for the unit value, as compared with titration to the point of 50 per cent hemolysis, proved so inaccurate as to obscure completely the true quantitative relations that exist in the course of the reaction.
The determination of changes due to a given reagent varied when different complements were used and it was not possible to eliminate these variations by taking into consideration the non-specific reactions of the individual reagents. The specific activity of sera, therefore, could not be measured directly in hemolytic units regardless of the accuracy of the determinations, and present methods of interpreting the results of the test by evaluating one activity of complement, fixation, in terms of another activity, hemolysis, which are not invariably proportional, can not be considered accurate quantitative determinations.
Although the values obtained with different complements varied, the relationship between the values derived from titration of different complements with different dilutions of the immune serum were constant under those conditions in which the course of the reactions was constant. The change in activity of the individual complements in the presence of the different dilutions of immune serum was directly proportional to the increase in the concentration of the serum. These constant relations made it possible to establish a unit value of complement activity based upon the specific fixability of the complement and thus to determine the activity of any dilution of an immune serum consistently, with different complements.