CycloFlow: Internal Coordinate Flow Matching and Geometric Ring Closure for Cyclic Peptide Conformer Generation

A cyclic peptide is a short peptide whose backbone is closed into a ring. Cyclic peptides can engage broad protein interfaces while remaining cell membrane permeable. Both properties depend on a conformational ensemble rather than on a single structure, so the conformational ensemble is what has to be predicted. A generative model of that ensemble has to choose the coordinates it works in. Internal coordinates suit a cyclic peptide. Ring closure ties the torsion angles to one another, and the representation encodes that dependency for free where a Cartesian one has to learn it. We present CycloFlow, which transports a bond length, a bond angle and a torsion angle at every heavy atom by flow matching, each from a prior chosen for that internal coordinate, and closes the ring by solving six of these internal coordinates. On CREMP tetra-, penta- and hexapeptides, CycloFlow leads the strongest baseline by 4.8 and 10.4 points of ring and all-atom coverage, reduces the Wasserstein distance to the reference ensembles, and clashes in only 1.4% of its conformers. It follows the reference distribution of each internal coordinate closely, and places pairs of ring torsion angles, holding more of their coupling. The code is available at https://anonymous.4open.science/r/cycloflow.