DC-Flow: Target-Conditioned Cyclic Peptide Design via Delayed-Coupling Flow Matching

Yitian Wang; Minjie Cheng; Yaning Cui; Maohua Yang; Dongdong Wang; Hongteng Xu

cs.LGOct 11, 2026

DC-Flow: Target-Conditioned Cyclic Peptide Design via Delayed-Coupling Flow Matching

Authors: Yitian Wang, Minjie Cheng, Yaning Cui, Maohua Yang, Dongdong Wang, Hongteng Xu

Organizations: Gaoling School of Artificial Intelligence, Renmin University of China · DP Technology · Cyclon Therapeutics · Beijing Key Laboratory of Research on Large Models and Intelligent Governance · Engineering Research Center of Next-Generation Intelligent Search and Recommendation, MOE

Abstract

Target-conditioned cyclic peptide design requires coordinating interfacial side chains with macrocyclic closure. Existing end-to-end generators concurrently update geometric and chemical variables from noise, assigning residues to disordered coordinates. Meanwhile, predictor-assisted workflows often get stuck in local traps because they lack feedback in the propose-and-filter stage and ignore 3D structural proposals during sequence search. To overcome the drawbacks of these two paradigms, we propose DC-FLOW, a staged generative framework built around Delayed-Coupling Flow Matching. In principle, DC-FLOW postpones sequence and side-chain activation until a target-conditioned backbone takes shape, resolving structural ambiguity before chemical assignment. Then, it feeds delayed activations back into the backbone, achieving co-evolution of backbone geometry and emerging residue identities by coupling their flows. This mechanism enables more reliable macrocyclic closure and favorable interface packing. For predictor-assisted workflows, DC-FLOW supplies 3D proposals with in-trajectory guidance, enabling cascaded test-time scaling to prune redundant backbones and terminate unpromising refinement early. Extensive experiments show that DC-FLOW improves cyclization fidelity, diversity, and interface energetics, substantially increasing the yield of confident cyclic peptide binders under a fixed final-candidate budget. Our code is available at https://github.com/mianqiu00/DCFlow.

Figures & tables

Figure 1: DC-Flow and Two Design Paradigms. (a) End-to-end generators simultaneously update sequence and structure from noise, resulting in early disorder and limited explore space. (b) Predictor-assisted workflows rely on iterative oracle evaluations without dynamic structure-sequence feedback, resulting in redundant exploration. (c) DC-Flow resolves early structural ambiguity by delaying chemical assignment, then couples their flows to achieve continuous co-adaptation for both end-to-end design and predictor-assisted refinement.

Figure 2: The overview of DC-Flow . (a) Delayed coupling: Modality clocks activate backbone, sequence (augmented by ProteinMPNN prior), and side chains sequentially, enabling continuous co-adaptation in a shared network. (b) Cascaded search: At $\tau_{\mathrm{s}}$ , backbones are pruned to diverse roots, each branching into $M$ oracle-guided continuations ( $N=K_{0}M$ ). After a few-step warm-up, candidates are screened by score $Q$ to restrict expensive refinement.

Method	Cyc. $\uparrow$		Stability $\downarrow$		$D_{\mathrm{seq}}\uparrow$		$D_{\mathrm{struct}}\uparrow$		Rosetta $dG\downarrow$
Method	ood	id	ood	id	ood	id	ood	id	ood	id
PepFlow	92.9	94.6	-961.10	-590.27	0.686	0.619	0.948	0.670	-24.78	-17.24
PepGLAD	97.5	87.4	-720.20	-579.45	0.895	0.872	0.932	0.817	-15.59	-13.50
DiffPepBuilder †	92.2	94.6	-939.25	-574.79	0.446	0.286	0.979	0.732	-20.66	-18.05
APM	97.3	100.0	-869.51	-497.36	0.173	0.120	0.938	0.754	-25.06	-16.50
Genie 3 †	83.6	81.6	-726.29	-399.28	0.253	0.242	0.823	0.796	-14.07	-10.16

Table 1: Direct full-atom cyclic peptide generation on LNR. Evaluated across in-distribution (ID) and out-of-distribution (OOD) targets. Both DC-Flow variants attain 100% cyclization success on ID targets. DC-Flow (SS) achieves the highest closure fidelity and structural diversity (

D_{\text{struct}}

) across splits, whereas DC-Flow (HT) provides superior binding energetics (Rosetta dG) and sequence exploration (

D_{\text{seq}}

), highlighting their complementary topological profiles.

Method	Summary	ipTM $\uparrow$	Peptide pLDDT $\uparrow$	Interface iPAE $\downarrow$	Hotspot iPAE $\downarrow$	Composite $S\uparrow$	Strict hits (%) $\uparrow$
RFPeptides	Mean	0.666	61.21	0.334	0.234	1.944	29.2
RFPeptides	Best	0.877	84.90	0.170	0.115	2.556	29.2
HFGuidedDesign	Mean	0.674	61.60	0.334	0.234	1.957	33.3
HFGuidedDesign	Best	0.889	86.57	0.161	0.104	2.593	33.3
DC-Flow	Mean	0.683	62.50	0.326	0.228	1.982	36.7
DC-Flow	Best	0.903	87.26	0.146	0.091	2.629	36.7

Table 2: Cofolding performance across 12 targets. All methods use AFCyc optimization; HFGuidedDesign and DC-Flow also use generation-time guidance. Mean summarizes all 384 candidates; Best averages the target-wise Top-1 candidates selected by composite score.

Figure 3: Target-wise Rosetta interface quality across 12 targets. Mean averages four sampled candidates per target; AF Top-1 uses the AF-selected candidate. Each candidate’s scores are averaged over five models. Rounded bands show interquartile ranges, with median lines and 1.5-IQR whiskers; dots denote targets and larger circles denote across-target means. Energy density is

100\Delta G_{\mathrm{sep}}/\Delta\mathrm{SASA}

. Complete metrics are reported in Table 11 .

Inference setting	Cyc. $\uparrow$		Stability $\downarrow$		$D_{\mathrm{seq}}\uparrow$		$D_{\mathrm{struct}}\uparrow$		Rosetta $dG\downarrow$
Inference setting	ood	id	ood	id	ood	id	ood	id	ood	id
w/o coupling (HT)	97.1	99.5	112.60	-255.79	0.937	0.824	0.933	0.439	-4.54	-12.92
w/o coupling (SS)	97.1	99.6	-167.87	-249.78	0.639	0.213	0.989	0.936	-7.97	-12.95
w/o MPNN prior (HT)	97.3	99.8	-914.12	-583.86	0.933	0.836	0.948	0.427	-27.56	-17.36
w/o MPNN prior (SS)	97.1	99.7	-808.71	-503.13	0.639	0.271	0.948	0.936	-18.88	-16.37
w/o delay, $\tau_{\mathrm{s}}=0$ (HT)	97.1	99.3	-905.72	-591.57	0.934	0.829	0.940	0.453	-20.40	-17.17

Table 3: Ablations on LNR. The default

\tau_{\mathrm{s}}=0.5

achieves the highest overall cyclization success within each topology and the best HT Stability and Rosetta dG scores. Freezing backbone motion substantially worsens Stability for both topologies, while removing the MPNN prior weakens interface scores and removing the delay produces topology-dependent effects. Earlier activation at

\tau_{\mathrm{s}}=0.2

improves overall sequence and structure diversity, indicating a trade-off between diversity and interface scores. OOD/ID correspond to 37/56 receptors.

Figure 4: Effect of inference-time search on cofolding. Both DC-Flow configurations use guidance and AfCycDesign optimization. Search improves Mean and Best on all four confidence metrics and increases the strict-hit rate from 32.6% to 75.5%. Best averages target-wise Top-1 candidates selected by

S_{\mathrm{hotspot}}

; strict hits are measured over all 384 candidates. Detailed results appear in Table 13 .

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
$R$	Receptor structure and its representation
$L,\Gamma,\xi$	Peptide length, cyclization specification, and joint conditions $\xi=(L,\Gamma)$
$\mathcal{A}$	Amino-acid alphabet
$t\in[0,1]$	Global generation time, distinct from the local modality clocks
$B_{t}$	Peptide backbone frames and carbonyl-orientation state at time $t$
$S_{t},S_{1}$	Continuous sequence carrier during generation and decoded endpoint sequence $S_{1}\in\mathcal{A}^{L}$

Appendix

Table 4: Principal notation for generation, prior integration, and cascaded search.

Figure 5: Detailed architecture and inference interfaces of DC-Flow . (a) Receptor features and cyclic graph features form topology-conditioned residue and pair representations. (b) Modality clocks control both state progression and input visibility. (c) A shared geometric trunk predicts backbone, angular, and sequence endpoints; sampled sequences re-enter subsequent predictions while the backbone remains active. (d) Frozen ProteinMPNN predictions from the current intermediate backbone enter sequence logits through a trainable residual gate. Optional oracle feedback supplies persistent sequence biases. (e) The cofolding cascade selects backbone roots, branches guided continuations, and allocates further refinement after a short screen.

Component	Configuration
Residue / pair channels	128 / 64
Geometric blocks	6
IPA heads	8
IPA query/key / value points	8 / 12 per head
Transformer layers / heads	2 per block / 4
Transformer feed-forward width	128; dropout 0

Appendix

Table 5: Architecture settings of the shared generator. The frozen ProteinMPNN branch is external to the six geometric blocks.

	Strict Quality Pipeline			Relaxed Quality Pipeline
Sub-Dataset	Head-to-Tail	Disulfide	Total	Head-to-Tail	Disulfide	Total
CPTrans	26,189	4,191	30,380	34,391	14,150	48,541
CPBind	29,149	10,390	39,539	38,897	35,315	74,212
CPCore	1,997	640	2,637	2,583	2,141	4,724
CPSea_PDB	772	191	963	1,058	663	1,721
Total	58,107	15,412	73,519	76,929	52,269	129,198

Appendix

Table 6: Dataset statistics under the Strict and Relaxed quality filtering regimes.

Figure 6: Geometric QC by training corpus. Models trained on Strict CPSea show lower FAIL and combined WARN+FAIL rates across all seven generators under the operational geometric audit described in the appendix. Right-hand values report WARN+FAIL reductions relative to CPCore in percentage points; WARN alone increases for PepGLAD.

Component	Setting
Energy function	ref2015
FastRelax repeats	5
Minimizer iteration cap	1,000 per minimization stage
Outputs	One relaxed structure per input
Receptor mobility	Backbone and side chains permitted to relax
Closure-restraint weight	1.0; constraint ramping disabled

Appendix

Table 7: Settings of the common Rosetta relaxation and interface analysis protocol. Closure restraints act during relaxation and are excluded from the reported energy scores.

Setting	Value
Base guidance scale	50.0
Maximum probed positions	3
Alternatives per position	3
Number of events	4
Event steps	125, 150, 175, 199 of the 200-point schedule
Maximum evaluations per event	9 single-residue alternatives plus 1 unchanged sequence

Appendix

Table 8: Generation-time AfCycDesign guidance settings for DC-Flow . Position and alternative limits apply per candidate and per event.

Method	Cyc. (%) $\uparrow$			Stability $\downarrow$			Rosetta $dG\downarrow$
Method	All	ood	id	All	ood	id	All	ood	id
PepFlow	94.0	92.9	94.6	-737.76	-961.10	-590.27	-20.23	-24.78	-17.24
PepGLAD	91.4	97.5	87.4	-635.44	-720.20	-579.45	-14.33	-15.59	-13.50
DiffPepBuilder †	93.7	92.2	94.6	-719.75	-939.25	-574.79	-19.09	-20.66	-18.05
APM	98.9	97.3	100.0	-645.42	-869.51	-497.36	-19.90	-25.06	-16.50
Genie 3 †	82.4	83.6	81.6	-530.93	-726.29	-399.28	-11.73	-14.07	-10.16

Appendix

Table 9: Direct full-atom cyclic peptide generation on LNR. DC-Flow (SS) achieves the highest cyclization success across All/OOD/ID, reaching 99.1% overall, while both DC-Flow variants reach 100% on ID receptors. DC-Flow (HT) achieves the best overall Stability and Rosetta

dG

scores, together with the highest sequence diversity on All and OOD. DC-Flow (SS) leads structural diversity across all three splits. Bold and underlined values indicate the best and second-best results, respectively, within each split.

Method	Guide	AFCyc optim.	ipTM $\uparrow$		Peptide pLDDT $\uparrow$		Interface iPAE $\downarrow$
Method	Guide	AFCyc optim.	Mean	Best	Mean	Best	Mean	Best
RFPeptides	–	No	0.516	0.763	47.97	71.42	0.434	0.262
RFPeptides	–	Yes	0.666	0.877	61.21	84.90	0.334	0.170
HFGuidedDesign	No	No	0.470	0.627	41.65	57.39	0.477	0.365
	No	Yes	0.662	0.886	60.27	85.57	0.341	0.167
	Yes	No	0.519	0.720	46.38	67.36	0.442	0.295

Appendix

Table 10: Detailed cofolding performance across 12 targets. Each configuration contains 384 candidates (32 per target), independently evaluated with five AlphaFold-Multimer-v3 models and three recycles. Mean aggregates all candidates; Best averages the target-wise Top-1 candidates selected by composite score.

Method	Guide	AFCyc optim.	$\Delta G_{\mathrm{sep}}\downarrow$		$100\Delta G_{\mathrm{sep}}/\Delta\mathrm{SASA}\downarrow$		$\Delta\mathrm{SASA}\uparrow$
			(REU)		(REU/ $100\,\text{\AA}^{2}$ )		( $\text{\AA}^{2}$ )
			Mean	Best	Mean	Best	Mean	Best
RFPeptides	–	No	-30.289	-32.745	-2.824	-3.079	1062.6	1071.8
RFPeptides	–	Yes	-35.891	-40.984	-3.170	-3.494	1123.4	1174.1
HFGuidedDesign	No	No	-31.437	-34.868	-2.758	-2.942	1128.1	1166.5
	No	Yes	-34.938	-40.634	-3.037	-3.412	1138.1	1186.4

Appendix

Table 11: Detailed Rosetta interface metrics for cofolding across 12 targets. Mean and Best are shown separately for each of the ten generation and optimization configurations.

Inference setting	Topo.	Cyc. (%) $\uparrow$			Stability $\downarrow$			Rosetta $dG\downarrow$
Inference setting	Topo.	All	ood	id	All	ood	id	All	ood	id
w/o coupling	HT	98.5	97.1	99.5	-109.23	112.60	-255.79	-9.59	-4.54	-12.92
w/o coupling	SS	98.6	97.1	99.6	-217.19	-167.87	-249.78	-10.97	-7.97	-12.95
w/o MPNN prior	HT	98.8	97.3	99.8	-715.25	-914.12	-583.86	-21.42	-27.56	-17.36
w/o MPNN prior	SS	98.7	97.1	99.7	-624.71	-808.71	-503.13	-17.37	-18.88	-16.37
w/o delay, $\tau_{\mathrm{s}}=0$	HT	98.4	97.1	99.3	-716.55	-905.72	-591.57	-18.46	-20.40	-17.17

Appendix

Table 12: Ablations on LNR. The default

\tau_{\mathrm{s}}=0.5

achieves the highest overall cyclization success within each topology and the best HT Stability and Rosetta

dG

scores. Freezing backbone motion substantially worsens Stability for both topologies, while removing the MPNN prior weakens interface scores and removing the delay produces topology-dependent effects. Earlier activation at

\tau_{\mathrm{s}}=0.2

improves overall sequence and structure diversity, indicating a trade-off between diversity and interface scores. All/OOD/ID correspond to 93/37/56 receptors.

Method	Guide	AFCyc optim.	Search	ipTM $\uparrow$		Peptide pLDDT $\uparrow$
Method	Guide	AFCyc optim.	Search	Mean	Best	Mean	Best
DC-Flow	Yes	Yes	No	0.651	0.904	57.90	87.92
DC-Flow	Yes	Yes	Yes	0.849	0.937	79.91	94.69

Appendix

Table 13: Detailed performance of DC-Flow with and without search across 12 targets. Both configurations use generation-time guidance and AFCyc optimization. This experiment reports the hotspot-based composite score

S_{\mathrm{hotspot}}

Method	Guide	AFCyc optim.	Search	$\Delta G_{\mathrm{sep}}\downarrow$		$100\Delta G_{\mathrm{sep}}/\Delta\mathrm{SASA}\downarrow$		$\Delta\mathrm{SASA}\uparrow$
				(REU)		(REU/ $100\,\text{\AA}^{2}$ )		( $\text{\AA}^{2}$ )
				Mean	Best	Mean	Best	Mean	Best
DC-Flow	Yes	Yes	No	-38.386	-42.298	-3.396	-3.524	1091.5	1154.6
	Yes	Yes	Yes	-38.841	-43.514	-3.567	-3.724	1107.4	1180.5

Appendix

Table 14: Detailed Rosetta interface metrics for DC-Flow with and without Search across 12 targets. Both configurations use generation-time guidance and AFCyc optimization.

Method	ipTM $\uparrow$	Peptide pLDDT $\uparrow$	Interface iPAE $\downarrow$	Hotspot iPAE $\downarrow$	Hotspot $S_{\mathrm{hotspot}}\uparrow$
RFPeptides	0.868 / 0.873	26.82 / 30.38	0.808 / 0.725	0.751 / 0.623	1.385 / 1.555
HFGuidedDesign	0.867 / 0.868	25.52 / 27.44	0.818 / 0.790	0.749 / 0.705	1.374 / 1.438
DC-Flow	0.868 / 0.873	26.96 / 33.42	0.810 / 0.689	0.753 / 0.583	1.384 / 1.624
DC-Flow (Search)	0.864 / 0.877	38.41 / 49.79	0.677 / 0.632	0.576 / 0.524	1.673 / 1.851

Appendix

Table 15: Cofolding results on the challenging TL1A-trimer case. Each cell reports Mean / AF Top-1. Search improves peptide confidence, interface iPAE, and hotspot-specific metrics, while mean ipTM remains similar across methods.

Figure 7: Cyclic peptide designs generated directly by DC-Flow across 6 targets and 2 cyclization modes in LNR. Local interface views show the target in light blue and the designed peptide in orange. Dashed lines indicate hydrogen-bond/polar contacts (green), salt bridges (magenta), and hydrophobic contacts (gray), inferred from relaxed model geometry.

Figure 8: Cyclic peptide designs generated by DC-Flow (Search) across 12 targets in HFGuidedDesign test set. Local interface views show the target in light blue and the designed peptide in orange. Dashed lines indicate hydrogen-bond/polar contacts (green), salt bridges (magenta), and hydrophobic contacts (gray), inferred from relaxed model geometry.

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FAR-DPO: Feasibility-Aware and Robust Direct Preference Optimization for Cyclic Peptide Design

Guofeng Zhang, Rong Han, Xiaoyu Wang, Zhiyun Li+3

Beijing University of Posts and Telecommunications, Beijing, China · Shenzhen University, Shenzhen, China · Tsinghua University, Beijing, China

Molecular Generation Constrained Generative Modeling Direct Preference Optimization Protein Design Protein Binder Design

Open paper AskPDF arXiv

Cyclic peptides are emerging as promising molecular scaffolds in drug discovery due to their high binding affinity and structural stability. However, extending generative models from linear to cyclic peptide design remains challenging, as cyclization sharply restricts the feasible design space through coupled geometric and biophysical constraints. Moreover, limited training data has led existing approaches to rely largely on zero-shot generation or post hoc filtering, resulting in low yields of feasible designs and limited control over multi-objective trade-offs. To address these limitations, we propose FAR-DPO (Feasibility-Aware and Robust Direct Preference Optimization), an architecture-agnostic framework that steers generative models toward structurally and biophysically feasible cyclic peptide designs, particularly for challenging targets. FAR-DPO integrates feasibility-aware preference construction with difficulty-aware group-robust optimization. Specifically, it constructs within-target preference pairs through feasibility-gated multi-objective dominance and adaptively reweights predefined difficulty groups according to their current preference losses. On the CPSea LNR benchmark, under a fixed generation budget, FAR-DPO increases overall success rate from 46.89% to 57.79% on PepGLAD and from 47.96% to 49.57% on PepFlow. These gains also extend to the hardest target quartile and are accompanied by more favorable best-per-target binding scores. Together, these results demonstrate FAR-DPO's effectiveness in improving feasibility and target-wise robustness.

Abstract

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