Model Agnostic Conditioning of Boltzmann Generators for Peptide Cyclization

Abstract

Macrocyclic peptides offer strong therapeutic potential due to their enhanced binding affinity and protease resistance, but their design remains a challenge due to limited structural data and tools that address only a narrow set of cyclization chemistries. Moreover, existing models are built to only consider ground state or mean conformations, rather than conformational ensembles that more accurately describes peptides. We introduce CO_SCPLOWYCC_SCPLOWLOPS (a Cyclic Loss for the Optimization of Peptide Structures), a model-agnostic framework that conditions Boltzmann generators to sample valid cyclic conformations--without retraining. To overcome the scarcity of cyclic peptide data, we reformulate the design problem in terms of conditional sampling over linear peptide structures via chemically informed loss functions. CO_SCPLOWYCC_SCPLOWLOPS encompasses 18 possible inter-amino acid crosslinks enabled by 6 diverse chemical reactions, and is readily extensible to many more. It leverages tetrahedral geometry constraints, using six interatomic distances to define a kernel density-estimated joint distribution from MD simulations. We demonstrate CO_SCPLOWYCC_SCPLOWLOPSs versatility via two distinct generative models: a modified Sequential Boltzmann Generator (SBG) (Tan et al., 2025) and the Equivariant Normalizing flow (ECNF) of Klein & Noe (2024). In both settings, CO_SCPLOWYCC_SCPLOWLOPS successfully biases the Boltzmann distribution toward chemically plausible macrocycles.