Biomolecular Agent Differential Games for Modeling Protein Dynamics

Protein dynamics characterize structural fluctuations and transitions among conformational states relevant to biomolecular function, complementing static structural descriptions. Such dynamics involve heterogeneous residue motions and inter-residue couplings within the evolving protein structure. However, many learning-based approaches model a protein as a single dynamical object, leaving these residue-wise dynamics implicit. We propose Biomolecular Agent Differential Games, a centralized differential game that coordinates biomolecular agents through local feedback policies. We characterize the protein residue coalition by a cooperative Nash equilibrium and recast the resulting game as a centralized stochastic control problem. Its optimality is characterized by the Hamilton-Jacobi-Bellman (HJB) equation and an equivalent forward-backward stochastic differential equation (FBSDE). We optimize the policy profile through fictitious play, where each agent assimilates the central planner proposal according to its algorithmic Nash gap. We extend the framework to protein-ligand dynamics by formulating the joint dynamics of the residue coalition and a distinct ligand agent as a non-cooperative game. Across diverse biomolecular systems, our framework achieves improvements over baselines in protein dynamics modeling and ligand-pocket interaction fidelity. These results indicate that biomolecular agent coordination provides a principled framework for accurate and faithful biomolecular dynamics modeling.