Dynamics of Antibody Binding and Neutralization during Viral Infection.

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 (K/K) 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 = K/(K + d + r), where d is the virus decay rate and r is the infection growth rate. Because in vivo d can be large, the amount of binding as well as the effect of K on binding are substantially reduced. When neutralization is added, the effect of K is similarly small which may help explain the relatively high K 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 K in vivo may point to mechanisms of neutralization beyond stoichiometry. Our results suggest reporting K and K separately, rather than focusing on affinity, until the situation is better resolved both experimentally and theoretically.