FlowBack-Adjoint: Physics-Aware and Energy-Guided Conditional Flow-Matching for All-Atom Protein Backmapping

TL;DR

FlowBack-Adjoint enhances a deep generative model for protein all-atom backmapping by incorporating physical energy considerations, significantly reducing structural errors and clashes, and enabling stable molecular dynamics initializations.

Contribution

It introduces a physics-aware post-training enhancement to the FlowBack model, improving accuracy and physical plausibility in protein all-atom structure generation.

Findings

Median energy reduction of ~78 kcal/mol per residue.

Over 92% error reduction in bond lengths.

Over 98% elimination of molecular clashes.

Abstract

Coarse-grained (CG) molecular models of proteins can substantially increase the time and length scales accessible to molecular dynamics simulations of proteins, but recovery of accurate all-atom (AA) ensembles from CG simulation trajectories can be essential for exposing molecular mechanisms of folding and docking and for calculation of physical properties requiring atomistic detail. The recently reported deep generative model FlowBack restores AA detail to protein C-alpha traces using a flow-matching architecture and demonstrates state-of-the-art performance in generation of AA structural ensembles. Training, however, is performed exclusively on structural data and the absence of any awareness of interatomic energies or forces within training results in small fractions of incorrect bond lengths, atomic clashes, and otherwise high-energy structures. In this work, we introduce FlowBack-Adjoint as a lightweight enhancement that upgrades the pre-trained FlowBack model through a one-time, physics-aware post-training pass. Auxiliary contributions to the flow introduce physical awareness of bond lengths and Lennard-Jones interactions and gradients of a molecular mechanics force field energy are incorporated via adjoint matching to steer the FlowBack-Adjoint vector field to produce lower-energy configurations. In benchmark tests against FlowBack, FlowBack-Adjoint lowers single-point energies by a median of ~78 kcal/mol.residue, reduces errors in bond lengths by >92%, eliminates >98% of molecular clashes, maintains excellent diversity of the AA configurational ensemble, and produces configurations capable of initializing stable all-atom molecular dynamics simulations without requiring energy relaxation. We propose FlowBack-Adjoint as an accurate and efficient physics-aware deep generative model for AA backmapping from C-alpha traces.