Integration of pre-trained protein language models with equivariant graph neural networks for peptide toxicity prediction

Abstract

Background

Peptide-based therapeutics have great potential due to their versatility, high specificity, and suitability for a variety of therapeutic applications. Despite these advantages, the inherent toxicities of some peptides pose challenges in drug development. Several computational methods have been developed to allow rapid and efficient large-scale screening of peptide toxicity. However, these methods mainly rely on the primary sequence and often ignore critical structural information, which limits their predictive accuracy.

Results

In this study, we introduce a novel framework named StrucToxNet that integrates a pre-trained protein language model with an equivariant graph neural network to improve peptide toxicity prediction. By combining sequence embeddings from the ProtT5 language model and 3D structural data predicted by ESMFold, StrucToxNet can capture both sequential and spatial characteristics of peptides. Testing on the independent dataset indicates that StrucToxNet outperforms existing sequence-based models in various metrics, achieving higher balanced accuracy and overall performance.

Conclusions

The results demonstrate the robustness and generalizability of StrucToxNet, marking it a reliable tool in the computational screening of toxic peptides and facilitating safer peptide-based drug development.

Supplementary information

The online version contains supplementary material available at 10.1186/s12915-025-02329-1.

Background

Peptides are short chains of amino acids linked by peptide bonds, and they are ubiquitous in a wide variety of organisms, from simple microorganisms to complex multicellular life forms [1]. Peptides can be derived from a range of natural sources, such as venoms, food products, and marine organisms [2–5]. They may also be synthesized chemically or produced by recombinant techniques [6]. These molecules often fold into secondary structures, such as α-helices and β-sheets, and can also assemble into even more complex structures [7–10]. Compared with traditional small molecule drugs, peptide drugs have unique advantages, such as higher selectivity and affinity, fewer side effects, and better biocompatibility [6, 11]. A well-known example is insulin, a peptide hormone used in the treatment of diabetes. These inherent advantages make them an ideal choice for various therapeutic applications, including anti-bacterial, anti-cancer, anti-angiogenic, and immunomodulatory effects [12–15].

However, despite their therapeutic promise, some peptides exhibit inherent toxicities, with documented cytotoxic, tissue-damaging, and neurotoxic properties [16, 17]. Therefore, identifying and mitigating such toxic effects is crucial for advancing peptide-based therapeutics [18, 19]. The evaluation of peptide toxicity in biomedical experimental settings demands complex experimental design, rigorous conditions, and lengthy screening cycles, which limits large-scale screening. Computational approaches are an effective solution because they have the potential to perform large-scale preliminary screening before clinical trials [20–26]. In recent years, several deep learning prediction tools have been developed to identify protein and peptide toxicity. Typical examples include ToxinPred series [17, 27], CSM-Toxin [28] and ATSE [29]. While these methods have successfully used 1D residue sequences for toxicity prediction, they often overlook the explicit modeling of structural information. Yet, it is well established that the 3D conformation of proteins and peptides is key to determining their diverse biological functions and physicochemical properties [30]. Recent advances in structural biology, particularly in computational methods like RoseTTAFold, ESMFold, and AlphaFold2, have made it faster and easier to obtain reliable structural data [31–34]. Studies have shown that predicted protein structures are highly valuable for related tasks, including protein–nucleic acid binding site prediction, identification of antimicrobial peptides, and B-cell epitopes prediction [35–37]. This provides an opportunity to enhance the performance of toxicity prediction by leveraging predicted structural information.

In this study, we integrate a protein large language model (PLM) with an equivariant graph neural network (EGNN) and propose a novel predictor named StrucToxNet. As shown in Fig. 1, StrucToxNet leverages structural and sequence representations for accurate peptide toxicity prediction. Due to the lack of experimentally determined 3D structures, we use ESMFold to predict the structures of all peptides due to its rapid processing speed and high accuracy [33]. StrucToxNet is built on an E(3) EGNN architecture that incorporates symmetry-aware graph convolutions, allowing it to handle transformations involving translation, rotation, and reflection in 3D space [38]. Inspired by the notable successes of PLMs, we integrate embeddings from the widely used ProtT5-XL-U50 (ProtT5) to refine the sequence-based node features in the EGNN framework [39]. We demonstrate that StrucToxNet outperforms state-of-the-art (SOTA) sequence-based methods in predicting peptide toxicity. By leveraging both sequence and structure, our approach can capture a more comprehensive representation, thereby improving the performance of the model).

Fig. 1.

Framework of StrucToxNet for peptide toxicity prediction

Results

Comparative performance with existing methods

In this section, we evaluate StrucToxNet on the test dataset and compare its performance with five SOTA methods, including three general methods for proteins and peptides (CSM-Toxin, ToxinPred2 and ToxinPred3) and two methods specifically designed for peptides (ToxIBTL and CAPTP). All of these compared methods are sequence-based, and the results are summarized in Table 1. StrucToxNet shows significant improvements in key metrics, with a BACC increase of 1.6% and an SP increase of 2.2% compared to the second-ranked model CAPTP. In addition, the AUC score of StrucToxNet improved by 0.9%, and its average precision (AP) increased by 1.1% (Fig. 2A, B). This demonstrates that incorporating structural information has a clear advantage in improving performance compared to sequence-only models. 

Table 1.

Comparison of StrucToxNet and existing methods using the independent test dataset

Model	Type	BACC (%)	AUC	SN (%)	SP (%)	MCC
CSM-Toxin	protein	47.81	0.400	4.06	91.56	−0.076
ToxinPred2	protein	64.22	0.874	95.94	32.51	0.299
ToxinPred3	protein	85.57	0.926	82.19	88.96	0.692
ToxIBTL	peptide	91.56	0.916	91.56	91.56	0.803
CAPTP	peptide	91.59	0.959	90.63	92.56	0.811
StrucToxNet	peptide	93.18	0.968	91.56	94.79	0.852

Fig. 2.

ROC curves (A) and precision–recall curves (B) for the compared methods. t-SNE visualizations of the feature spaces learned by StrucToxNet (C), ProtT5 encoding (D), the CNN model (E), and the LSTM model (F)

Comparison with other sequence-based methods

To comprehensively evaluate the performance of StrucToxNet, we compare it with other sequence-based approaches, including traditional classifiers and neural network-based models. In this analysis, the protein language model ProtT5 is used as a feature extractor to generate sequence embeddings. These embeddings are subsequently processed by either traditional classifiers or neural network architectures. Traditional classifiers directly use the pooled sequence embeddings for training, while neural networks including convolutional neural networks (CNN) and long short-term memory networks (LSTM) further extract meaningful patterns and capture sequence features relevant to toxicity prediction. This is also a standard approach in protein-related tasks and has achieved good results. The results are summarized in Table 2.

Table 2.

Comparison of StrucToxNet and other sequence-based methods on the independent test dataset

Model	BACC (%)	AUC	SN (%)	SP (%)	MCC
RF	85.70	0.954	73.75	97.64	0.769
XGBoost	89.29	0.970	80.94	97.64	0.822
LightGBM	87.92	0.971	79.06	96.77	0.792
SVM	87.26	0.958	78.12	96.40	0.779
CNN	91.52	0.961	89.38	93.67	0.818
LSTM	91.03	0.968	88.75	93.30	0.807
StrucToxNet	93.18	0.968	91.56	94.79	0.852

The results in Table 2 show that StrucToxNet outperforms both traditional classifiers and neural network models across multiple evaluation metrics. While some traditional classifier-based models, such as LightGBM and XGBoost, achieve high AUC scores comparable to StrucToxNet and show strong SP, they do not reach the same levels of BACC or MCC. All neural network models achieve more balanced performance with high SN, BACC, and MCC, demonstrating their ability to further learn and extract useful information from the original ProtT5 embeddings. Overall, StrucToxNet maintains more consistent performance on all metrics, demonstrating the advantage of incorporating structural information for toxicity prediction tasks.

To further analyze the feature representations learned by StrucToxNet, we apply t-SNE to visualize the feature space learned by these models. Figure 2C–F shows the resulting plots, where each point represents a peptide. In the original ProtT5 embedding space, there is moderate separation between two classes with some overlap, suggesting that there is room for improvement. StrucToxNet achieves the clearest separation between classes, indicating that it can effectively extract discriminative information from the original ProtT5 embeddings. In comparison, embeddings learned by other neural networks show further separation of samples relative to ProtT5 but do not achieve the same clarity as StrucToxNet. These results demonstrate the effectiveness and robustness of StrucToxNet.

Peptide length range analysis

To investigate the impact of peptide length on predictor performance, we compare the misclassification rates of various predictors on toxic and non-toxic peptides across a range of lengths using the independent test set. The results are shown in Fig. 3A, B. For toxic peptides, deep learning models generally perform better across all peptide length ranges, with StrucToxNet achieving the best performance in each range. In contrast, machine learning models perform poorly for most peptide lengths, with particularly high misclassification rates for shorter sequences. For non-toxic peptides, machine learning models perform well across all length ranges. Interestingly, deep learning models tend to have higher misclassification rates for mid-length sequences. StrucToxNet shows comparable performance to the best-performing models across a wide range of peptide lengths. Considering results from both positive and negative samples, our model consistently shows stable and competitive performance, making it a reliable choice for a wide range of peptide lengths.

Fig. 3.

Heat maps showing misclassification rates across different peptide length ranges for positive (A) and negative (B) samples. Density of positive (C) and negative (D) samples at varying prediction confidence levels. Distribution of pLDDT scores in the training and test sets, before and after removal of low-quality samples (E). Comparison of model performance trained on samples with different structure prediction qualities (F)

Confidence distribution analysis

We further compare these models using confidence distribution analysis, which evaluates the certainty of predictions. Figure 3C, F shows the prediction confidence distribution of different models for correctly predicted positive and negative samples. StrucToxNet shows high confidence in its predictions for both positive and negative samples, with a peak near high confidence scores. In contrast, other models exhibit more uncertainty in one or both classes, as seen in their broader distribution across lower confidence levels. StrucToxNet also shows a lower density in the mid-confidence range, indicating greater certainty in its predictions. These results indicate that StrucToxNet consistently produces more confident predictions, demonstrating its reliability and robustness in predicting peptide toxicity.

Ablation study

To evaluate the relative contribution of each core component of StrucToxNet, we perform an ablation study by excluding each part from the full architecture on the test data. To evaluate the impact of using PLM embeddings as node features, we replace them with one-hot encoding to obtain amino acid-level sequence-based features (w/o PLM). We also study the contributions of structural features (w/o Structure) and contrastive learning (w/o CL). Table 3 shows the performance of these variants of StrucToxNet on the test metrics.

Table 3.

The performance of StrucToxNet when removing each core module

Model	BACC (%)	AUC	SN (%)	SP (%)	MCC
w/o PLM	88.88	0.940	87.19	90.57	0.755
w/o Structure	92.80	0.966	90.94	94.67	0.845
w/o CL	91.49	0.965	87.81	95.16	0.830
StrucToxNet	93.18	0.968	91.56	94.79	0.852

As shown in Table 3, removing the PLM embeddings led to a decrease of 4.3% in BACC and 9.7% in MCC. This change indicates that the ProtT5 embeddings can capture important sequence information for our prediction. Excluding structural features slightly lowered BACC and MCC, indicating that structural information also contributes positively to model performance. Finally, the contrastive learning helps balance the model and thus improves the overall performance. In summary, the full model achieves the highest scores across all metrics, confirming that each component contributes to the overall predictive performance.

Effect of the quality of predicted structure

Given that our model relies heavily on peptide structures predicted by ESMFold, it is important to evaluate how the quality of these predictions affects peptide toxicity prediction outcomes. Structural predictions could introduce errors, and low-confidence predictions may negatively impact model performance. ESMFold provides a confidence metric called predicted local distance difference test (pLDDT) for each predicted structure (Fig. 3E). The pLDDT score ranges from 0 to 100, where higher scores indicate greater confidence in the accuracy of the predicted structure. To investigate the impact of structure prediction confidence on model performance, we filtered out samples with pLDDT scores below 60 and retrained the model on this refined dataset. As shown in Fig. 3F, key metrics such as BACC, AUC, and MCC have all improved, with BACC reaching 94.98% and AUC improving to 0.977. This improvement demonstrates the importance of reliable structural data for improving prediction accuracy. The performance of the model could improve even more if high-confidence structures from experiments are available.

Discussion

Identifying toxic peptides is an essential step for guiding safe drug development and therapeutic applications. Previous computational tools for peptide toxicity prediction are mainly sequence-based models that rely on contextual features from sequential neighbors, although some have attempted to capture long-range interactions using various techniques. The proposed StrucToxNet framework demonstrates superior performance over traditional sequence-based approaches across various metrics. Despite these promising results, there are several limitations worth considering. First, StrucToxNet relies on structures predicted by ESMFold, which may introduce inaccuracies, especially for short and flexible peptides. The improved performance after filtering low-confidence structures demonstrates that the model depends on the accuracy of predicted conformations. Incorporating multiple predicted conformations or leveraging experimentally determined structures where available could potentially improve robustness and reduce structural bias. Second, the current framework is designed for linear peptides. Many therapeutic peptides are cyclic or undergo post-translational modifications, which are not captured by the current model. Extending StrucToxNet to include cyclic peptides or modified residues would improve its applicability in drug discovery scenarios. Third, the model currently provides general toxicity classification without considering specific toxic mechanisms such as hemolytic, immunotoxic, or neurotoxic effects. Future work could integrate toxicity subtype annotations and develop multi-task learning architectures that simultaneously predict toxicity type and severity. Lastly, the current model still functions as a black-box model. Enhancing the transparency of the model through attention-based visualization or explainable AI techniques could help uncover the biochemical and structural features associated with peptide toxicity.

Conclusions

In this work, we propose a novel structure-based framework for peptide toxicity prediction by explicitly incorporating structural data and modeling spatial relationships. By combining 3D structural information predicted by ESMFold alongside sequence embeddings from ProtT5, our model outperforms existing sequence-based methods. Performance analysis demonstrates the robustness and generality of StrucToxNet, especially in handling unbalanced datasets and providing reliable predictions across different peptide lengths. Furthermore, we demonstrate the potential of further improving the accuracy of toxicity predictions when more accurate experimental structural data become available by analyzing the impact of structure prediction quality. Overall, these results demonstrate the potential of incorporating structural context into peptide-level tasks and provide a promising direction for developing safer peptide-based therapeutics through computational screening.

Methods

Datasets and performance evaluation

The main peptide dataset utilized for training and the independent test dataset employed are sourced from the previous CAPTP work [40]. In brief, peptides with toxicity are considered as ToxPs, whereas those without known toxic activity are non-ToxPs. The training dataset contains 1818 ToxPs and 4569 non-ToxPs, with an independent test set of 320 ToxPs and 806 non-ToxPs.

The datasets used here have an unbalanced distribution of positive and negative samples. To conduct a comprehensive evaluation of the proposed model, we employed a set of evaluation metrics, including balanced accuracy (BACC), sensitivity (SN), specificity (SP), Matthews correlation coefficient (MCC), area under the precision-recall curve (AUPRC) and area under the receiver operating characteristic curve (AUC). These metrics are all widely used in biological sequence analysis tasks [41, 42]. The definitions and formulas of these metrics are as follows: 

$$SN=\frac{\mathit{TP}}{TP+FN}$$ 1

$$SP=\frac{\mathit{TN}}{TN+FP}$$ 2

$$BACC=\frac{1}{2}\left(S,N,+,S,P\right)$$ 3

$$MCC=\frac{TP\times TN-FP\times FN}{\sqrt{\left(T,P,+,F,P\right)\left(T,P,+,F,N\right)\left(T,N,+,F,P\right)\left(T,N,+,F,N\right)}}$$ 4

where true positives (TP) represent samples correctly predicted as positive, while true negatives (TN) indicate samples correctly predicted as negative. False positives (FP) are samples incorrectly predicted as positive, and false negatives (FN) are samples incorrectly labeled as negative. Here, SN measures the model’s ability to identify positive samples, while SP measures its ability to identify negative samples. The remaining metrics provide an assessment of the model’s overall performance.

Overview framework of StrucToxNet

As shown in Fig. 1, StrucToxNet combines the predicted structure with the information from the pre-trained language model. The peptide sequence is input into ESMFold and ProtT5 simultaneously: ESMFold generates the peptide structure from which the corresponding structural features are extracted, while ProtT5 generates the node embeddings. These structure-based features and node embeddings are then combined to form the final node features. The resulting structures are represented as 3D graphs, where nodes represent residue information and edges define the spatial relationships between them. EGNN is subsequently employed to update the node representations and coordinates. Finally, a prediction module is used to determine whether the input sequence is toxic. To address class imbalance, a contrastive learning strategy is also incorporated following the CAPTP framework. The StrucToxNet model was implemented using PyTorch (v2.4.1) and the PyTorch Geometric (PyG) library (v2.6.1). The training was conducted on an NVIDIA A100 GPU for up to 200 epochs. Hyperparameter optimization was performed using fivefold cross-validation on the training set, and the search space along with the selected optimal configuration is summarized in Additional file 1: Table S1. For a fair comparison, all baseline models were trained using the same set of hyperparameters.

Peptide structure prediction

To capture the geometric properties of each amino acid, we utilized esmfold_v1 (ESMFold) to predict the structure for each peptide [33]. Unlike traditional methods, ESMFold does not rely on multiple sequence alignment (MSA) or complex evolutionary data. Instead, it uses a large protein language model, trained on millions of protein sequences, combined with an end-to-end neural network to directly infer protein structure. This enables ESMFold to provide atomic-level structure predictions at high speed. It is 60% faster than AlphaFold2 while maintaining similar accuracy. This speed advantage makes ESMFold particularly useful for predicting the structures of our entire peptide dataset mentioned above.

Graph construction

The specific arrangement of residues determines the 3D positions of all the atoms within the peptide, forming what is known as the structure. A residue includes elements like an amino group, a carboxylic acid group, and a side chain group that defines its type. These components connect to a central carbon atom known as the Cα. Following previous studies and for simplicity, we use only the Cα to represent the main backbone structure of each peptide [43]. For sequence $P$ with the 3D coordinates of all Cα $x\in {\mathcal{R}}^{n\times 3}$, two residues $i$ and $j$ are considered to be in contact if the Euclidean distance $d_{\mathit{ij}}$ between their corresponding Cα atoms falls within 8 Å. In this case, the structure of a peptide is defined as a residue-level graph $\mathcal{G}=\left(\mathcal{V},,,\mathcal{E}\right)$, where $\mathcal{V}$ represents the residues in the sequence $P$, and $\mathcal{E}$ represents the edges between residues, with each edge connecting two residues that are in contact.

Node feature generation

For each residue in the predicted structures, we extracted two types of features: sequence-based and structure-based node features. The sequence-based features are embeddings from a protein large language model, while the structure-based features capture key physicochemical and geometric properties of each residue. By combining these two types of features, we create the final node feature set of the model.

Language model representation

We choose ProtT5 as the feature extractor to generate residue embeddings as one type of node feature [39, 44]. ProtT5 is a powerful tool for extracting meaningful sequence features from peptides, capturing the complex biophysical and biochemical properties of residues. It was pretrained on a large corpus of protein sequences in a self-supervised fashion and has been shown to capture some of the “grammar” behind the language of life encoded in protein sequences. For given input peptide sequence $P=\left(p_1,,,p_2,,,\cdots ,,,p_n\right)$ of length $n$, ProtT5 use its encoder to generate a context-aware embedding matrix of shape $n\times 1024$, as shown in formula (5). To avoid massive activations, the embedding values are then normalized to a range between 0 and 1 using formula (6).

$$h=\text{ProtT5Encoder}(P)$$ 5

$$x^{\prime }=\frac{x-x_{\mathit{min}}}{x_{\mathit{max}}-x_{\mathit{min}}}$$ 6

where ProtT5Encoder refers to the encoder of ProtT5 that processes the input sequence without additional fine-tuning, with $h$ representing the embedding matrix it generates. $x$ represents the original value in generated embeddings, $x_{\mathit{min}}$ and $x_{\mathit{max}}$ are the minimum and maximum values of that feature type in the training set, respectively. This normalization ensures consistent scaling of embedding values across the dataset.

Structure-based node feature generation

We use a variety of structure-based node features to capture the geometric and spatial properties from the predicted structures. These features include: (1) secondary structures; (2) relative solvent accessibility; (3) local geometric features; (4) residue orientation; (5) relative sequence position; (6) relative spatial position; (7) virtual surface area; and (8) residue contact count. A detailed description of these features is provided in Table 4. Together, these structural feature vectors form a 45-dimensional feature set.

Table 4.

Summary of structure-based node features

Feature	Description	Dimension
Secondary structure	Encodes both 3-state and 8-state secondary structures using one-hot encoding	11
Relative solvent accessibility	One-hot encoding is applied to both 2-state and 8-state relative solvent accessibility (RSA) features. For the 2-state RSA, a threshold of 50 is used to distinguish between states. For a more detailed representation, the 8-state RSA features are encoded with RSA values divided into eight discrete bins: 0–30, 30–60, 60–90, 90–120, 120–150, 150–180, 180–210, and > 210	10
Local geometric	Sine and cosine values of backbone torsion angles (α, Φ, Ψ), normalized virtual bond and torsion angles, and the normalized tetrahedral geometry derived from the N, Cα, and C atoms of the residues	14
Residue orientation	Unit vectors pointing towards the directions of $C{a}_{\left(i,-,1\right)}-C{a}_i$ and $C{a}_{\left(i,-,1\right)}-C{a}_i$ for residue $i$.	6
Relative sequence position	Inverse of the sequence position of the residues	1
Relative spatial position	Inverse of the Euclidean distance between the Cα atom of the residue and the centroid of the entire structure	1
Virtual surface area	Inverse of the virtual convex hull surface area of each amino acid residue, where the hull is formed by its constituent atoms	1
Contact count	Normalized number of spatial neighbors of each residue, where two residues are considered in contact if the Euclidean distance between their Cβ atoms is < 8 Å	1

Edge and coordinate feature generation

For edge features in the graph $\mathcal{G}=\left(\mathcal{V},,,\mathcal{E}\right)$, we compute the Euclidean distance in 3D space between residue pairs $i$ and $j$, defined as $d_{\mathit{ij}}={\Vert x_i-x_j\Vert }_2$. These scalar distances are then transformed into informative edge representation vectors using a Gaussian radial basis function (RBF), resulting in edge features $e_{\mathit{ij}}$. This mapping captures the spatial relationship within the graph structure in a form that can be more effectively utilized during message passing. In addition, the Cartesian coordinates ($x,y,z$) of $\mathit{Ca}$ atoms, which represent the spatial positions of nodes in 3D space, are also included as coordinate features and are updated within StrucToxNet.

Equivariant graph neural network module

We apply the E(3) EGNN framework to effectively capture spatial information within a graph structure by integrating both node and edge features during message passing. EGNN is a translation, rotation, reflection, and permutation equivariant graph neural network that does not rely on expensive spherical harmonics [38]. EGNN has been shown to be able to effectively capture and model complex spatial relationships and has already been successfully applied to similar tasks. The EGNN framework consists of a stack of equivariant graph convolutional layers (EGCL), with each layer updating the coordinates and node features by integrating edge information along with the coordinates and node features from the previous layer. The initial node features are first linearly transformed to produce a set of node embeddings. These transformed embeddings, along with edge information and the coordinates, are then fed into the subsequent EGCL layers for updating. The StrucToxNet architecture consists of three stacked EGCL layers, each with a hidden dimension of 256. In particular, each EGCL layer updates both the node embeddings and coordinates as defined below:

$$m_{\mathit{ij}}={\varphi }_e\left(h_i^l,,,h_j^l,,,e_{\mathit{ij}}\right)$$ 7

$$x_i^{l+1}=x_i^l+C\sum _{j\ne i}\left(x_i^l,-,x_j^l\right){\varphi }_x\left(m_{\mathit{ij}}\right)$$ 8

$$m_i=\sum _{j\ne i}{m}_{\mathit{ij}}$$ 9

$$h_i^{l+1}={\varphi }_h\left(h_i^l,,,m_i\right)$$ 10

For each layer $l$, $m_{\mathit{ij}}$ represents the message from node $j$ to node $i$. Here, $h_i^l$ and $h_j^l$ are node embeddings, while $x_i^l$ and $x_j^l$ are their corresponding coordinates. The edge feature $e_{\mathit{ij}}$ represents the edge attribute between node $i$ and $j$. In all equations, $\varphi$ represents a non-linear operation implemented through a multi-layer perceptron (MLP). The EGCL maintains equivariance by integrating coordinate updates directly into the message-passing mechanism. Specifically, the update of the coordinates $x_i^{\left(l,+,1\right)}$ for node $i$ at layer ($l+1)$ depends on its relative positions of node $i$ with respect to all other nodes. This is achieved by summing the coordinate differences $\left(x_i^l,-,x_j^l\right)$ for all $j\ne i$, effectively capturing the spatial context of each node within the entire structure. To normalize the impact of neighboring nodes, a scaling factor $C=\frac{1}{N-1}$ is applied, where $N$ is the total number of nodes. In addition to updating coordinates, the EGCL layer also aggregates messages from neighboring nodes to update the embeddings. The aggregated message $m_i$ for node $i$ is obtained by summing the pairwise messages $m_{\mathit{ij}}$ from all neighboring nodes. The update of node embedding $h_i^{\left(l,+,1\right)}$ is based on the current embedding $h_i^l$ and the aggregated message $m_i$. By recursively updating both node embeddings and coordinates layer by layer, EGNN builds a comprehensive representation of spatial relationships.

Prediction module

The final component of StrucToxNet is an MLP referred to as the prediction module, which receives the output node embeddings from the last EGNN layer. These node embeddings are aggregated using max pooling to generate a sequence-level representation. The prediction module then maps the high-dimensional learned sequence-level features into discrete class predictions, effectively serving as the decision-making component to estimate the probability of peptide toxicity via:

$$y^{\prime }=\text{Sigmoid}\left(H,W,+,b\right)$$ 11

where $\text{H}\in {\mathbb{R}}^{\text{n}\times d}$ represents the output of last EGNN layer; $\text{W}\in {\mathbb{R}}^{\text{d}\times 2}$ is a learnable weight matrix that projects the embeddings into a two-dimensional output space; and $\text{b}\in {\mathbb{R}}^{1\times 2}$ is the bias term. The sigmoid function then converts the raw scores into probabilities within a range of 0 to 1, yielding a two-dimensional matrix $y\prime$ that provides probabilistic estimates for toxicity.

Abbreviations

PLM

Protein language model

EGNN

Equivariant graph neural network

SOTA

State-of-the-art

ToxPs

Toxic peptides

non-ToxPs

Non-toxic peptides

BACC

Balanced accuracy

SN

Sensitivity

SP

Specificity

MCC

Matthews correlation coefficient

AUPRC

Area under the precision-recall curve

AUC

Area under the receiver operating characteristic curve

MSA

Multiple sequence alignment

RBF

Radial basis function

EGCL

Equivariant graph convolutional layer

MLP

Multi-layer perceptron

AP

Average precision

RF

Random forest

SVM

Support vector machine

XGBoost

Extreme gradient boosting

LightGBM

Light gradient boosting machine

CNN

Convolutional neural network

LSTM

Long short-term memory network

pLDDT

Predicted local distance difference test

AI

Artificial intelligence

Authors’ contributions

S.J. and Q.Z. conceived and designed the experiment. S.J. and X.Y. performed the experiment. S.J. analyzed the results. S.J. and X.Y. wrote the manuscript. Q.Z., W.H. and T.S. reviewed and revised the manuscript. All authors read and approved the final manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (No. 62450002 and 62301368), JSPS KAKENHI (No. JP23H03411 and JP22K12144), and JST (No. JPMJPF2017).

Data availability

All data generated or analysed during this study are included in this published article, its supplementary information files and publicly available repositories, which are available in the Zenodo repository (https://zenodo.org/records/15599677) and the GitHub repository (https://github.com/jiaoshihu/StrucToxNet).

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.