Stackelberg games for vaccine design

Stackelberg game models have recently seen considerable practical and academic success in security applications, with defender as the leader, and attacker the follower. The key conceptual insight of Stackelberg security games is that defense needs to be proactive, optimally accounting for attacker's response to a defensive posture. We propose that this insight has relevance in another important application domain: vaccination. 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. Formally, we model the interaction between a vaccine and a virus as a Stackelberg game in which the vaccine designer chooses an antibody, and the virus chooses a minimal sequence of mutations to escape it. Our crucial observation is that we can leverage protein modeling software, Rosetta, as an oracle to compute binding score for an input virus-antibody pair. This observation enables us to develop a fully automated bi-level stochastic optimization algorithm for optimal antibody "commitment" strategy. A key technical challenge is that score calculation for each possible antibody-virus pair is intractable. We therefore propose a novel simulation-based bi-level optimization algorithm to address this, which consists of three elements: 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).