Escaping the Phylogenetic Trap: Persistent Homology Enables Cross-Species Ion Channel Classification via Multimodal Graph Neural Networks

Arezoo Bybordi; Favour Achimba; Mariam Gelashvili; Jessy Ramirez; Weigang Qiu; Mandë Holford; Anita Raja

cs.LGOct 21, 2026

Escaping the Phylogenetic Trap: Persistent Homology Enables Cross-Species Ion Channel Classification via Multimodal Graph Neural Networks

Authors: Arezoo Bybordi, Favour Achimba, Mariam Gelashvili, Jessy Ramirez, Weigang Qiu, Mandë Holford, Anita Raja

Organizations: The Graduate Center, City University of New York · Hunter College, City University of New York · Tandon School of Engineering, New York University · Weill Cornell Medicine ·

Abstract

Protein classifiers are highly sensitive to evaluation protocol: random train/test splits induce phylogenetic leakage, allowing models to exploit taxon-specific correlations and substantially overestimate out-of-distribution performance. This issue is particularly acute for venom compound classification by ion-channel target (Ca2+, K+, Na+), where reported accuracies of 80-90% do not reflect generalization to unseen taxa. We formulate cross-species prediction as a structured distribution shift in which taxonomic identity acts as a confounder, requiring representations that capture structural features invariant across phylogeny. Using a shared multimodal backbone that fuses ESM-2 sequence embeddings with a disulfide-aware graph attention network, we systematically compare five structural inductive biases (spectral, Riemannian, SE(3)-invariant, statistical-manifold, and persistent-homology representations) under a leave-one-taxon-out evaluation protocol on a benchmark of 1,373 ColabFold-predicted venom compounds spanning five taxa. The persistent-homology representation summarizes backbone geometry through topological descriptors that are robust to local structural perturbations, providing an inductive bias toward phylogenetically invariant learning. Under conventional i.i.d. splits, all models achieve similar accuracy (81-86%), masking differences in inductive bias. Under taxonomic shift, this parity collapses: a sequence-only baseline drops to approximately 30%, the remaining geometric priors cluster at 54-55%, while our persistent-homology model (PH-GNN) achieves 63.4%, outperforming the next-best method by over 8 percentage points. These results demonstrate that random-split evaluation obscures meaningful differences in representation quality and identify topological representations as an effective inductive bias for learning under structured biological distribution shift.

Figures & tables

Figure 1: PH-GNN Multimodal Architecture (M2). Our framework extracts three parallel representations from the ColabFold-predicted input data: (1) sequence embeddings via a pre-trained ESM-2 language model. The three modalities are concatenated into a joint representation and passed through a fusion Multi Layer Perceptron (MLP) to predict the target ion channel class ( $Ca^{2+}$ , $K^{+}$ , $Na^{+}$ ), (2) structural embeddings via a disulfide-aware Graph Attention Network (GAT) operating on all-atom proximity graphs, and (3) topological features via Alpha complex filtration of $C\alpha$ coordinates.

Rank	Model	Test Acc	Ca F1	K F1	Na F1	Macro F1	Best Epoch
1	(M1) Stat. Manifold	86.2%	0.73	0.93	0.86	0.84	9/50
2	(M2) PH-GNN	85.8%	0.69	0.90	0.88	0.82	15/50
3	(M3) Spectral	84.0%	0.68	0.90	0.85	0.81	11/50
4	Baseline (ESM+GAT)	82.9%	0.68	0.92	0.83	0.81	11/50
5	(M4) Riemannian	82.9%	0.57	0.90	0.84	0.77	4/50
6	(M5) Invariant SE(3)	81.1%	0.65	0.91	0.81	0.79	9/50

Table 1: In-Distribution Performance: Random split (80/20, stratified, seed=42). Results report overall accuracy, per-class F1 scores, and macro F1 based on the optimal checkpoint selected within a maximum 50-epoch budget using early stopping. Best results per column are bolded.

Rank	Model	Snake	Cone Snail	Spider	Scorpion	Sea Anemone	Mean	Std	$p_{\text{holm}}$
1	(M2) PH-GNN	75.3%	51.2%	46.7%	74.1%	69.6%	63.4%	12.0%	—
2	(M5) Invariant SE(3)	49.4%	52.0%	41.4%	61.1%	73.3%	55.4%	10.9%	$6.3\times 10^{-14}$
3	(M1) Stat. Manifold	46.8%	46.5%	43.1%	70.0%	69.6%	55.2%	12.0%	$2.7\times 10^{-5}$
4	Baseline (ESM+GAT)	45.5%	52.0%	43.1%	66.7%	68.9%	55.2%	10.7%	$4.8\times 10^{-17}$
5	(M3) Spectral	48.1%	48.8%	41.2%	62.8%	70.8%	54.3%	10.8%	$2.6\times 10^{-9}$
6	(M4) Riemannian	45.5%	52.8%	41.4%	61.9%	68.9%	54.1%	10.2%	$7.9\times 10^{-11}$

Table 2: Out-of-Distribution Performance: Taxa leave-one-out cross-validation accuracy (%) per taxa, mean among all taxa and the standard deviation for all the models. Last fold for baseline 7 was out of memory. McNemar exact test vs. PH-GNN on paired per-protein predictions pooled across folds (

N=1{,}373

), Holm-corrected.

Figure 2: Visualization of the phylogenetic trap. UMAP projection of the learned 512-dimensional concatenated structure and sequence embeddings (prior to fusion) from the baseline multimodal GNN. Left: Colored by ion channel target. Right: Colored by organism taxon. The strong clustering by taxon rather than target class visually demonstrates the model’s reliance on evolutionary lineage, explaining the catastrophic collapse during out-of-distribution evaluation.

Figure 3: Residue-Level Explainable AI (XAI). Our interactive visualization framework maps attention weights directly onto the ColabFold-predicted 3D structure. The residue attention bar chart (top right) and structural heatmap (bottom right) reveal exactly which topological loops and explicit disulfide bonds drive the prediction, bridging the gap between abstract mathematical embeddings and actionable biophysics.

OOD Generalization

Out-of-distribution generalization studies how machine-learning models perform when test data, domains, tasks, or environments differ from training.

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Masked Autoencoders Self-Supervised Pre-Training Invariant Representation Learning Protein Representation Learning Molecular Representation Learning

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Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale, non-redundant benchmark for protein fold classification constructed from the Encyclopedia of Domains (TED) and Foldseek-clustered AlphaFold structures. We show that on TEDBench, current protein representation learning methods either require very large models or fail to deliver strong performance. To address this challenge, we propose Masked Invariant Autoencoders (MiAE), a self-supervised framework for protein structure representation learning. MiAE uses an extremely high masking ratio of up to 90% with an

\mathrm{SE(3)}

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Abstract

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