Stackelberg Games for Robust Vaccine Design

Drug and vaccination therapies are important tools in the battle against infectious diseases such as HIV and influenza. However, many viruses, including HIV, can rapidly escape the therapeutic effect through a sequence of mutations. We propose to design vaccines, or, equivalently, antibody sequences that make such evasion difficult. We frame this as a bilevel combinatorial optimization problem of maximizing the escape cost, defined as the minimum number of virus mutations to evade binding an antibody. Binding strength can be evaluated by a protein modeling software, Rosetta, that serves as an oracle and computes a binding score for an input virus-antibody pair. However, score calculation for each possible such pair is intractable. We propose a three-pronged approach to address this: first, application of local search, using a native antibody sequence as leverage, second, machine learning to predict binding for antibody-virus pairs, and third, a poisson regression to predict escape costs as a function of antibody sequence assignment. We demonstrate the effectiveness of the proposed methods, and exhibit an antibody with a far higher escape cost (7) than the native (1).