The importance of designing proteins, such as high affinity antibodies, has become ever more apparent. Computational Protein Design can cast such design problems as optimization tasks with the objective of maximizing K*, an approximation of binding affinity. Here we lay out a graphical model framework for K* optimization that enables use of compact AND/OR search spaces. We introduce two distinct graphical model formulations, a new K* heuristic, AOBB-K* - an efficient depth-first branch-and-bound algorithm, and modifications that improve performance with theoretical guarantees. As AOBB-K* is inspired by algorithms from the well studied task of Marginal MAP, this work provides a foundation for adaptation of state-of-the-art mixed inference schemes to protein design.