Expected Hamiltonians for General Biopolymer Design and Beyond

The design of intrinsically disordered proteins (IDPs) remains challenging due to their conformational flexibility and lack of stable structures. In this work, we introduce a computational framework that defines protein sequences probabilistically and simulates their behavior using molecular simulations. By combining this probabilistic representation with gradient-based optimization techniques, we efficiently design IDPs with specific properties, such as target ensemble dimensions, sensors sensitive to environmental stimuli, and binders with tailored conformational preferences. This framework provides a versatile approach for the de novo design of biopolymers with target sequence-ensemble-function relationships. Furthermore, by relaxing the assignment of particle identities to continuous space, we enable new inference problems in physics-based simulations. As an example of this broader applicability, we present preliminary results on particle tracking.