THE TOXIN-ANTITOXIN REACTION 239 



filtrate that is neutralized, or nearly neutralized, by one unit of the standard anti- 

 toxin, and then determining the amount of the antitoxic serum under test that 

 will neutralize, or nearly neutralize, this amount of toxic filtrate. This amount 

 of the antitoxic serum will contain 1 A.U. Since the two tests are performed within 

 a few days of one another there will be no significant change of toxin to toxoid 

 during the interval, and the proportions of the two reagents in the toxic filtrates 

 will remain constant. 



This method of titration led to the definition of two other doses of toxin — 

 " toxin " here, as in the case of the M.L.D., referring in practice to a toxic filtrate, 

 containing both toxin and toxoid. 



The Limes Nul {Lq) dose of di-phtheria- toxin is the largest amount of toxin that, when 

 mixed with one unit of antitoxin and injected subcutaneously into a guinea-pig of 

 250 gm. weight, will, on the average, give rise to no observed reaction. 



Actually, the Lq dose is usually recorded as the dose that, when tested in this 

 way, gives rise to a minimal local oedema. 



The Limes Tod {L^) dose of diphtheria toxin is the smallest amount of toxin that, 

 when mixed with one unit of antitoxin and injected subcutaneously into a guinea- 

 pig of 250 gm. weight, will, on the average, kill that guinea-pig within ninety-six 

 hours. 



Other doses of toxin, determined by other methods of testing, have been defined 

 in terms of their combining power for antitoxin, and are now commonly employed 

 for standardization purposes (see Chapter 61), but the relation between the 

 Lq and L^ doses is the matter that concerns us here. 



If toxin combined with antitoxin in constant proportions giving firm chemical 

 union it would be expected that 



L^toxin — Lotoxin = 1 M.L.D. 

 In fact it does not. The difference between the L^ and the Lo dose has been 

 found, with difi'erent toxic filtrates, to vary from 10 M.L.D. to 100 M.L.D. or more. 



EhrUch attempted to account for this phenomenon, to which his name has often 

 been attached, by postulating the existence, in toxic filtrates, of a special modification 

 of toxoid, epitoxoid, having less afiinity than toxin, or unmodified toxoid, for antitoxin. 

 Over the range between Lg and L+ doses he assumed that the additional toxin added merely 

 displaced epitoxoid, and that only when aU epitoxoid had been displaced from its union 

 with antitoxin did the added toxin remain free to exert its lethal effect. Whether toxoid 

 differs from toxin in its affinity for antitoxin, or whether varieties of toxoid exist that 

 differ from one another in this respect, we do not know with any certainty. Since we 

 have many reasons other than the observed difference between the Lg and the L+ doses 

 of toxic filtrates for discarding the hypothesis of chemical union in constant proportions 

 between antigen and antibody, we are not faced with Ehrhch's dilemma, and have no 

 need to postulate the existence of epitoxoid, or of any of the other special varieties of toxin 

 and toxoid that he evolved to explain the results observed in his later studies on partial 

 neutralization. 



These studies, and those of many subsequent observers, made it clear that, 

 when varying amounts of antitoxin are added to a constant amount of toxin, the 

 curve of neutralization is not linear, as it would be if we were studying the neutrahza- 

 tion of a strong acid by a strong base. (See Arrhenius and Madsen 1902, 1904, 

 Arrhenius 1915, von Krogh 1911, Glenny et al. 1925.) The observed departure from 

 linearity is not peculiar to diphtheria toxin and antitoxin, but is characteristic of 

 toxin- antitoxin reactions in general (see, for instance, Burnet 1931) ; and, as we 



