  In vivo in infection, virions are constantly produced and die rapidly. In
contrast, most antibody binding assays do not include such features. Motivated
by this, we considered virions with n=100 binding sites in simple mathematical
models with and without the production of virions. In the absence of viral
production, at steady state, the distribution of virions by the number of sites
bound is given by a binomial distribution, with the proportion being a simple
function of antibody affinity (Kon/Koff) and concentration; this generalizes to
a multinomial distribution in the case of two or more kinds of antibodies. In
the presence of viral production, the role of affinity is replaced by an
infection analog of affinity (IAA), with IAA=Kon/(Koff+dv+r), where dv is the
virus decaying rate and r is the infection growth rate. Because in vivo dv can
be large, the amount of binding as well as the effect of Koff on binding are
substantially reduced. When neutralization is added, the effect of Koff is
similarly small which may help explain the relatively high Koff reported for
many antibodies. We next show that the n+2-dimensional model used for
neutralization can be simplified to a 2-dimensional model. This provides some
justification for the simple models that have been used in practice. A
corollary of our results is that an unexpectedly large effect of Koff in vivo
may point to mechanisms of neutralization beyond stoichiometry. Our results
suggest reporting Kon and Koff separately, rather than focusing on affinity,
until the situation is better resolved both experimentally and theoretically.
