Designing Cyclic Peptides via Harmonic SDE with Atom-Bond Modeling

TL;DR

Cyclic peptides offer therapeutic advantages but are difficult to design due to cyclization constraints and sparse 3D data. The authors propose CpSDE, a diffusion-based framework that couples AtomSDE (a harmonic SDE-based all-atom structure generator with bond modeling) and ResRouter (a residue-type predictor) through routed sampling to generate cyclic peptides conditioned on a protein target and a cyclization graph, enabling all cyclization types. AtomSDE leverages a harmonic prior with explicit bond information and a 3D-aware SE(3)-equivariant score network, while ResRouter predicts amino-acid types from denoised structures via a joint objective, allowing iterative refinement of sequence and structure. Empirical results across multiple protein pockets show CpSDE achieves strong stability and binding affinity with high diversity, validated by molecular dynamics and MM-PBSA analyses in case studies of SMYD2 and SET8 inhibitors. Overall, this work advances structure-guided cyclic peptide design by integrating full-atom modeling with sequence co-design, offering a path toward diverse, high-affinity cyclic therapeutics.

Abstract

Cyclic peptides offer inherent advantages in pharmaceuticals. For example, cyclic peptides are more resistant to enzymatic hydrolysis compared to linear peptides and usually exhibit excellent stability and affinity. Although deep generative models have achieved great success in linear peptide design, several challenges prevent the development of computational methods for designing diverse types of cyclic peptides. These challenges include the scarcity of 3D structural data on target proteins and associated cyclic peptide ligands, the geometric constraints that cyclization imposes, and the involvement of non-canonical amino acids in cyclization. To address the above challenges, we introduce CpSDE, which consists of two key components: AtomSDE, a generative structure prediction model based on harmonic SDE, and ResRouter, a residue type predictor. Utilizing a routed sampling algorithm that alternates between these two models to iteratively update sequences and structures, CpSDE facilitates the generation of cyclic peptides. By employing explicit all-atom and bond modeling, CpSDE overcomes existing data limitations and is proficient in designing a wide variety of cyclic peptides. Our experimental results demonstrate that the cyclic peptides designed by our method exhibit reliable stability and affinity.

Figures (15)

• Figure 1: Comparative advantages of cyclic peptides over linear peptides. Linear peptides are easily degraded, whereas cyclic peptides are protected against enzyme hydrolysis, allowing them to function more effectively within the human body. Cyclic peptides generally exhibit better stability and affinity.
• Figure 2: Overview of CpSDE. The generative process is structured as follows: (1) A cyclization type is initially selected, which subsequently determines the associated 2D chemical graph; (2) At time $t$, given the entire chemical graph defined by both cyclization (highlighted with a yellow shadow) and the predicted residue types, the all-atom structure is initially denoised using AtomSDE and then re-noised in accordance with the integration step of the reverse-time SDE. The updated structures are then preserved in the Atom73 representation; (3) ResRouter predicts the residue types not constrained by cyclization, based on the denoised structure. Consequently, the chemical graph and the all-atom structures are updated using the Atom73 representation Steps (2) and (3) are iteratively executed. The incorporation of the cyclization chemical graph, with chemical bonds as edges, ensures that the generated peptide forms a cyclic structure.
• Figure 3: Discovery of new SMYD2 cyclic peptide inhibitors via applications of CpSDE. Upper: Visualization of conformational ensembles for the designed peptides sampled by MD. Bottom: RMSD analysis of all heavy atoms within the designed peptides.
• Figure 4: Discovery of new SET8 cyclic peptide inhibitors via applications of CpSDE. Upper: Visualization of conformational ensembles for the designed peptides sampled by MD. Bottom: RMSD analysis of all heavy atoms within the designed peptides.
• Figure 5: Two examples of cyclic peptide drugs. Voclosporin van2022voclosporin, an analog of ciclosporin, is an immunosuppressant used to treat lupus nephritis. Lanreotide caplin2014lanreotide, an analog of somatostatin, is an oncology drug that inhibits growth hormone release and is used to manage carcinoid syndrome.