348 C. E. SCHWERDT 



Another approach to testing the hypothesis that one virus particle may 

 initiate infection is through a statistical analysis of the dose-response curve 

 in which the percentage incidence of positive test animals (i.e., animals show- 

 ing an all-or-none reaction, such as death or survival) is plotted against log 

 virus dilution. Parker (1938) made such an analysis using vaccinia infection 

 in rabbits as his model system. According to the Poisson law of small numbers, 

 successive sampling of a suspension of particles independently distributed in 

 a liquid medium will yield aliquots containing 0, or 1, or 2, etc., particles 

 in proportions related in a definite way to the mean number of particles per 

 aliquot. From this, in turn, the proportion of aliquots containing at least 1, or 

 2, or 3, etc., particles can be calculated. A plot of the per cent, of positive 

 aliquots (i.e., aliquots containing at least some arbitrarily selected minimum 

 number of particles such as 1, or 2, or 3, etc.) against the log of the mean 

 number of particles per ahquot yields a family of S-shaped curves, the slopes 

 of which increase in steepness with increasing values of the minimum number 

 of particles required for a positive result. When Parker (1938) constructed 

 such a set of theoretical curves and superimposed upon them experhnental 

 dose-response curves, he found the latter to fit best the curve calculated on 

 the hypothesis that one particle per aliquot is sufficient to yield a positive 

 response. This correspondence between experimental curves for vaccinia 

 titration in rabbits and the so-called hypothetical "one-particle" curve was 

 confirmed by Sprunt et at. (1940) and also found with Shope papilloma 

 (Bryan and Beard, 1940b) and myxoma viruses (Parker, 1940). 



Agreement on the above statistical inference that infection can be initiated 

 by a single particle is by no means unanimous. Bryan and Beard (1940b) 

 contend that the usual apparent correspondence between experimental and 

 theoretical "one-particle" dose-response curves is not necessarily proof of the 

 hyjjothesis that infection is due wholly to the chance presence or absence of an 

 infective virus particle in the inoculum. They interpret the dose-response 

 curves observed with Shope papilloma virus, as well as those observed by 

 Parker (1938) with vaccinia virus in rabbits, as expressions only of the 

 variable susceptibiHties of the test animals employed. According to their 

 postulate, the hosts exhibit a distribution of sensitivity to infection by virus 

 at any one dilution similar to that found for response to drugs. Thus they 

 have derived an expression which fits virus titrations as weU as or better than 

 the model proposed by Parker, particularly in those instances where the 

 dose-response curve is somewhat flatter than tha,t predicted by the "one- 

 particle" hypothesis. 



The decision as to which of these two hypotheses is better able to explain 

 the dose-response curve is difficult to make with certainty at this time. It 

 may be that both mechanisms play more or less of a role in determining the 

 shape of the curve, depending upon the virus-host system under study. In 



