Development and analysis of mathematical models for the quantification of the number of antibodies needed for virus neutralization, and for estimating the rates at which viral escape variants arise under selection pressure induced by the antibody response

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In the early 1980s, a new virus began to spread that caused severe damages of the immune system; the human immunodeficiency virus (HIV). Despite intensive studies of this virus, no successful vaccine against HIV has been found yet. All the existing vaccines, e.g. against measles, rubella or influenza stimulate the immune system to produce antibodies. These antibodies neutralize invading viruses when entering the host. Beside the difficulties to determine broadly neutralizing antibodies directed against HIV, quantitative aspects might add to the riddle, why no vaccine candidate could successfully prevent HIV infection. The vaccine candidates might not be able to stimulate the production of enough antibodies to neutralize all invading virions. To test this, I will study the number of antibodies needed to neutralize one virion in a first project. I will combine the concept of stoichiometries that was recently introduced into virology, with the chemical concept of binding kinetics. With this link it will be possible to determine the number of antibodies needed for neutralization out of titration curves. These titration curves are widely used in virology to characterize the neutralization potential of antibodies. If a vaccine cannot stimulate the immune system to produce enough antibodies sufficient to clear all the invading virions, the evolution of viral variants resistant to antibody neutralization is possible. In the second project, I will estimate the rates at which variants arise that are resistant against antibody binding. To this end, I will use a mathematical model describing the viral dynamics of two different viral strains. With this model, it is possible to determine the escape rates to various antibody responses. Combining the two projects, vaccine candidates can be tested whether they stimulate sufficiently high antibody titers. If this is not the case, it can be tested how fast resistant viral variants arise against the stimulated antibody response.