  Protein interactions and assembly formation are fundamental to most
biological processes. Predicting the assembly structure from constituent
proteins -- referred to as the protein docking task -- is thus a crucial step
in protein design applications. Most traditional and deep learning methods for
docking have focused mainly on binary docking, following either a search-based,
regression-based, or generative modeling paradigm. In this paper, we focus on
the less-studied multimeric (i.e., two or more proteins) docking problem. We
introduce DockGame, a novel game-theoretic framework for docking -- we view
protein docking as a cooperative game between proteins, where the final
assembly structure(s) constitute stable equilibria w.r.t. the underlying game
potential. Since we do not have access to the true potential, we consider two
approaches - i) learning a surrogate game potential guided by physics-based
energy functions and computing equilibria by simultaneous gradient updates, and
ii) sampling from the Gibbs distribution of the true potential by learning a
diffusion generative model over the action spaces (rotations and translations)
of all proteins. Empirically, on the Docking Benchmark 5.5 (DB5.5) dataset,
DockGame has much faster runtimes than traditional docking methods, can
generate multiple plausible assembly structures, and achieves comparable
performance to existing binary docking baselines, despite solving the harder
task of coordinating multiple protein chains.
