542 F. M. BURNET 



antibody molecules and antigenic sites on virus particles, effective collisions 

 requiring to be sterically correct. If A and F are the concentrations of anti- 

 body and virus at the beguuiing of reaction, s the number of reactive sites 

 for virus particle and y the number of antigen-antibody complexes, the 

 equilibrium condition will be: 



at s 



(combined antibody) 



or — ; — q— = constant 



(free sites) (free antibody) 



(b) The nature of neutralization of infectivity is obscure and a number of 

 possible models can be selected for mathematical treatment. Matters needing 

 consideration are the proportion of nonviable particles and the various 

 possibilities of there being critical and noEcritical sites on the virus particle 

 or sites which differ in the probability that union with an antibody molecule 

 will destroy infectivity. 



(c) If an equilibrium system is involved, it becomes very difficult to allow 

 quantitatively for the dissociation unavoidably associated with various 

 phases of the Dulbecco technique. In particular, washing the plates to which 

 experimental mixtures have been added introduces what might be called an 

 asymmetric dilution of an equilibrium system. 



(d) In a comparison between the implications of Dulbecco's formulation 

 (D) and an appropriately elaborated formulation (F) of the reversible inter- 

 action hypothesis, Fazekas de St. Groth and Reid (1957) find that both will 

 account for the kinetic and multiplicity curves given by Dulbecco et al. The 

 changes associated with dilution are in accord with F, not with D. The per- 

 sistent fraction is not independent of the type of antibody used, as would 

 be expected on D. The use of Smoluchowski's equation in accounting for re- 

 activation of neutralized virus by collision is inappropriate to a system re- 

 quiring orientated collision. If the necessary modifications are made, the 

 discrepancy with the observed result involves a factor of about 10^. On F, 

 the results follow naturally, since the system by hopothesis is a reversible 

 one. 



It may be that a majority of experimental virologists will be skeptical of 

 aU attempts to provide too precise a quantitative formulation of the situation. 

 It is interesting to note how, m Dulbecco's experiments, there are systematic 

 differences in the behavior of poliovirus as compared to WEE vims, and of 

 immune horse serum as compared with immune rabbit serum. In Burnet et 

 al.'s (1937) work, every new species of virus examined show some individual 

 deviation from what was expected to be "normal" behavior. Anyone with 

 experience in this field also knows that there are virus strains that "behave" 



