Cross-Chirality Generalization by Axial Vectors for Hetero-Chiral Protein-Peptide Interaction Design

Conference: ICML2026
arXiv: 2602.20176
Code: https://github.com/YZY010418/PepMirror
Area: Scientific Computing / Protein-Peptide Design / Equivariant Neural Networks
Keywords: D-peptide design, axial vectors, \(SE(3)\) equivariance, mirror enantiomers, latent space diffusion

TL;DR

This paper proposes AFI (Axial Feature Injection), which injects axial vector features into the polar vector channels of \(E(3)\)-equivariant scalarized models via linear mixing to reduce them to \(SE(3)\)-equivariance and enable chirality sensitivity. By applying this to UniMoMo, the authors developed PepMirror, which generates hetero-chiral (D-L) peptide binders in a zero-shot manner using only homo-chiral (L-L) training data. Wet-lab experiments on the CD38 target validated it as the first experimentally confirmed AI de novo D-peptide design framework.

Background & Motivation

Background: Natural proteins consist almost entirely of L-amino acids (homo-chirality). D-peptides are promising therapeutic molecules due to protease resistance, long half-lives, and low immunogenicity. However, traditional D-peptide binder screening relies on mirror-image display—requiring the synthesis of D-protein targets, which is extremely difficult. While ML-based peptide design has flourished, most models focus on L-L interfaces.

Limitations of Prior Work: Existing equivariant protein generation models cannot directly design D-peptide binders. The first category (RFDiffusion, PepFlow, D-Flow, etc.) uses rigid-body local coordinate systems that hardcode right-handed chirality as a prior, making structural mirror images indistinguishable after rotation. The second category (PepGLAD, UniMoMo, PocketXMol) depends on \(E(3)\)-equivariant backbones, which are strictly equivariant under spatial inversion \(P=-I_3\). This leads to models outputting mixed chirality when given D-target inputs—failing to generate stable single-chirality binders. The only specialized attempt, D-Flow, remains limited to dry-lab validation.

Key Challenge: To design hetero-chiral interfaces, a model must achieve both chirality perception (separable latent codes for \(X\) and \(-X\)) and latent stability (\(-X\) must still be recognized as the same amino acid type, just with flipped chirality, rather than shifting to a different class). \(E(3)\)-equivariance ensures stability but destroys perception; breaking equivariance completely may lead to unstable representations. Existing chirality-aware methods (SphereNet's torsion, ChIRo, or high-order spherical harmonics in Tensor Field Networks) are either only validated for classification/property prediction or are computationally expensive and prone to overfitting.

Goal: (i) To provide a lightweight chirality-aware plugin for scalarized equivariant models; (ii) To theoretically guarantee that the generated latent codes satisfy "\(dist(X, -X) < dist(X, X')\)"; (iii) To implement a latent diffusion-based D-peptide binder designer for wet-lab confirmation.

Key Insight: Classical physics distinguishes between polar vectors (e.g., position, velocity, which change sign under \(P\)) and axial vectors (e.g., angular momentum, magnetic field, which are invariant under \(P\)). Scalarized \(E(3)\)-equivariant models typically use only polar vectors; adding axial vectors maintains \(SE(3)\)-equivariance (rotation, translation) while breaking \(P\)-equivariance, enabling chirality differentiation.

Core Idea: Axial vectors (constructed via cross product, triple product, or commutator) are injected into the polar vector channels before each EPT layer's FFN via channel-wise linear mixing \(\tilde v_{i,k}=A_k^\top v_{i,:}+B_k^\top a_{i,:}\). This reduces the model from \(E(3)\) to \(SE(3)\) equivariance. Integrated into UniMoMo's VAE+latent diffusion framework, this results in PepMirror.

Method

Overall Architecture

To generate D-peptide binders zero-shot using an L-L homo-chiral trained model, the core issue is that \(E(3)\)-backbones are strictly invariant under spatial inversion \(P=-I_3\), causing mirror targets to map to identical latent codes. PepMirror adds an axial vector injection plugin to reduce \(E(3)\) to \(SE(3)\)-equivariance—preserving roto-translation invariance while gaining sensitivity to spatial inversion. The system adopts UniMoMo's two-stage latent diffusion: the encoder EPT (Equivariant Pretrained Transformer) maps the point cloud \(\mathcal{G}\) to invariant scalars \(H\in\mathbb{R}^{N\times K}\) and equivariant vectors \(V\in\mathbb{R}^{N\times 3\times K}\). The diffusion stage denoises the binder latent code conditioned on the pocket latent code \(c\), and the decoder reconstructs the 3D structure. The primary modification is replacing \(V\) with the injected \(\widetilde V\) before each GVP-FFN, creating AFI-EPT. During inference, mirror-image display logic is used: the L-target \(\mathcal{G}_t\) is inverted to a D-target, the model generates an L-binder, and the output is inverted back: \(\mathcal{G}_b=P(f_\theta(P(\mathcal{G}_t)))\).

graph TD
    A["L-Target Point Cloud (L-L Training Only)"] -->|"Spatial Inversion P"| B["D-Target P(G_t)"]
    B --> C
    subgraph UM["AFI-EPT Embedded in UniMoMo (Latent Diffusion)"]
        direction TB
        C["AFI-EPT Encoder<br/>AFI: Mixing Polar/Axial Vectors before FFN"] --> D["Invariant Scalars H + Equivariant Vectors V"]
        D --> E["Latent Diffusion Denoising<br/>Condition = Pocket Latent"]
        E --> F["Decoder → L-Peptide Binder"]
    end
    F -->|"Inversion P"| G["D-Peptide Binder (for Original L-Target)"]

Key Designs

1. Axial Feature Injection (AFI): Separating Polar and Axial Vectors for Chirality Sensing

Classical physics categorizes 3D vectors into polar vectors (e.g., position, changing sign under \(P\): \(v(-X)=-v(X)\)) and axial vectors (e.g., angular momentum, transforming as \(a(Rx)=\det(R)\,Ra(x)\), thus invariant under \(P\)). Since standard scalarized models only use polar vectors, mirror images remain indistinguishable. AFI performs channel-wise linear mixing \(\tilde v_{i,k}(X)=A_k^\top v_{i,:}(X)+B_k^\top a_{i,:}(X)\) (\(A_k,B_k\in\mathbb{R}^K\) are learnable). Because \(a\) is invariant while \(v\) flips sign, \(\widetilde V\) differs for \(X\) and \(-X\), reducing the symmetry group to \(SE(3)\) and enabling chirality perception. Axial vectors are constructed from adjacent channels \(u,v,w\in\mathbb{R}^3\) of \(V'\): cross product \(u\times v\) (cross), scalar triple product projection \((w\cdot(u\times v))\,w\) (triple), and commutator \((u\cdot v)(u\times v)\) (commu.). Compared to high-order spherical harmonics, AFI uses only low-order tensors, making the computational overhead negligible.

2. Theoretical Closed-loop of Zero-shot Generalization: Difference + Stability + Diffusion Continuity

For hetero-chiral generalization to work, latent codes must be separable for mirrors (chirality perception) but stable enough such that \(-X\) is not misidentified as a different residue (latent stability). Difference is established by Theorem 3.1: with randomly sampled mixing coefficients, \(\|c(X)-c(-X)\|\ge c_W\varepsilon\) holds with high probability. Stability is measured by \(d(X_1,X_2)=\|H(X_1)-H(X_2)\|+\|\widetilde V(X_1)-\widetilde V(X_2)\|\). Since \(H(-X)=H(X)\) and \(a(-X)=a(X)\), the mirror distance \(d(X,-X)=\|2Av(X)\|\) is explicitly controlled by coefficient \(A\), supporting the property \(d(X,X')>d(X,-X)\)—i.e., mirror images are closer than distinct amino acids. Diffusion Continuity (Theorem 3.4) implies that similar latent codes yield similar binder distributions, allowing generalization to D-targets despite zero D-L training data.

3. AFI-EPT in UniMoMo: End-to-end de novo D-peptide Design Pipeline

The AFI-EPT backbone replaces the standard EPT in UniMoMo's VAE and diffusion network. Three variants are derived: PepMirror(cross/triple/commu.). UniMoMo is selected as the base because it does not hardcode rigid-body frames, allowing AFI to function directly, and latent diffusion provides better computational efficiency and stability compared to atom-level diffusion.

Loss & Training

The model is trained solely on L-L homo-chiral protein-peptide complexes. The objective includes standard VAE reconstruction loss and latent diffusion denoising loss. No D-peptide data or explicit chirality supervision is used; hetero-chiral capability emerges zero-shot via AFI and the inversion inference framework.

Key Experimental Results

Main Results

Evaluated on the LNR (Large Non-Redundant) test set for both L and D tasks using chirality correctness and AutoDock Vina scores:

Model	Task	Chirality Rate (min)	Suc.%	Avg. Vina	Top Vina	IMP%
RFDiffusion	L	99.57	99.52	-3.30	-5.14	44.09
RFDiffusion	D	99.15	98.58	-1.77	-3.78	16.13
D-Flow	D	98.54	97.52	-3.11	-4.54	22.58
PepGLAD(ideal)	D	99.04	95.08	-3.26	-5.11	43.01
UniMoMo(all)	D	15.70	—	—	—	—
PepMirror(cross)	L	99.83	99.67	-4.27	-5.81	69.89
PepMirror(cross)	D	99.81	99.76	-4.15	-5.69	63.44

PepMirror improves IMP (Improvement Percentage) by ~20 percentage points over the next best model, PepGLAD(ideal), and exhibits the smallest "L-D gap."

Ablation Study

Configuration	D-Task Chirality Rate	Note
UniMoMo(pep.)	23.90	\(E(3)\)-equivariant baseline; outputs mostly L residues
UniMoMo(all)	15.70	Multi-modal training version; still limited by equivariance
AFI w/ cross	99.81	Cross product axial injection
AFI w/ triple	99.75	Triple product axial injection
AFI w/ commu.	99.88	Commutator axial injection (best)

Latent space analysis shows that \(\|c(X)-c(-X)\|\) jumps from \(\sim 10^{-6}\) to \(10^{-2}\) with AFI, while remaining significantly smaller than the distance between different amino acids (\(\sim 1\)), confirming the "Difference + Stability" mechanism.

Key Findings

• AFI is a necessary and sufficient chirality switch: Without it, PepMirror collapses to mixed-chirality outputs (correctness < 25%).
• Wet-lab confirmation: Designed 5,000 D-peptides for CD38. 12 were synthesized, resulting in one 10-mer binder D-1412 ("trikhytyce") with \(K_D\approx 10\,\mu\)M, the first AI de novo D-peptide binder validated experimentally.
• Minimal L→D performance drop: Unlike RFDiffusion, which sees significant drops in Vina scores for D-tasks, PepMirror's performance remains consistent across chiralities.

Highlights & Insights

• Leveraging classical physics: The polar/axial decomposition provides the lowest-cost symmetry-breaking design, acting as a plug-and-play module for any scalarized backbone.
• Theoretical assurance: The three-step proof (Difference, Stability, Continuity) elevates zero-shot generalization from an empirical observation to a guaranteed mechanism.
• Challenge to stereoselectivity: The discovery that D-1412's L-enantiomer also binds CD38 suggests that target-binder interactions may be less stereoselective than traditionally assumed, potentially due to conformational flexibility.

Limitations & Future Work

• AFI's theoretical guarantees depend on "genericity" of mixing coefficients; specific initializations could lead to degeneracy.
• Only validated within the UniMoMo framework; the applicability to frame-based models (like RFDiffusion) requires further testing.
• Wet-lab validation was limited to one target (CD38); broader statistical validation across more targets is needed.
• Future work could involve explicitly maximizing \(d(X, -X)\) via regularization or incorporating stereoselectivity as an optimization target.

Related Work & Insights

• vs D-Flow: D-Flow also uses inversion-based inference but relies on frame-based models and only dry-lab validation. PepMirror utilizes \(E(3)\) backbones with AFI to break symmetry and achieved wet-lab success.
• vs PepGLAD / UniMoMo: These strictly \(E(3)\)-equivariant models generate mixed chirality. AFI addresses this at the architectural level rather than as a post-processing step.
• vs High-order TFNs: While spherical harmonics can encode chirality, they are computationally intensive. AFI serves as a lightweight alternative using only low-order tensors.

Rating

• Novelty: ⭐⭐⭐⭐⭐ Elegant use of polar/axial vectors for symmetry breaking.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ Comprehensive in-silico metrics and rare wet-lab validation.
• Writing Quality: ⭐⭐⭐⭐⭐ Clear structure with strong theoretical and empirical alignment.
• Value: ⭐⭐⭐⭐⭐ Significant impact on de novo D-peptide drug discovery.

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