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 therapeautic 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).
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