Neutralization titers reveal the structure of polyclonal antibody responses

The composition of a polyclonal antibody response is hard to measure experimentally but contains vital information about the robustness of immunity. Here, we argue that the statistics of neutralization titers alone can be used to make quantitative predictions about the composition of the response, circumventing challenges arising through sequencing and monoclonal antibody expression. We show that the response against influenza within a cohort can be either driven by a collective phenomenon where many antibodies contribute to neutralization, or dominated by just a few strong binders, leading to a broad distribution of titers across individuals described by a Gumbel distribution from extreme value theory. Comparing titers across cohorts, we find that Gumbel statistics accurately describe individuals prior to an immune challenge. We propose an equilibrium binding model that quantitatively captures titer data and illustrates the structure of the polyclonal response. Our approach extends generically to immune responses to other pathogens.