Physics-Based Machine Learning Trains Hamiltonians and Decodes the Sequence–Conformation Relation in the Disordered Proteome

Intrinsically disordered proteins and regions (IDPs) are involved in vital biological processes. To understand the IDP function, often controlled by conformation, we need to find the link between sequence and conformation. We decode this link by integrating theory, simulation, and machine learning (ML) where sequence-dependent electrostatics is modeled analytically while nonelectrostatic interaction is extracted from simulations for many sequences and subsequently trained using ML. The resulting Hamiltonian, combining physics-based electrostatics and machine-learned nonelectrostatics, accurately predicts sequence-specific global and local measures of conformations beyond the original observable used from the simulation. This is in contrast to traditional ML approaches that train and predict a specific observable, not a Hamiltonian. Our formalism reproduces experimental measurements, predicts multiple conformational features directly from sequence with high throughput that will give insights into IDP design and evolution, and illustrates the broad utility of using physics-based ML to train unknown parts of a Hamiltonian, rather than a specific observable, in combination with known physics.