CKAN-ATHP: a predictor for antihypertensive peptides based on sample augmentation and loss improvement strategies using the convolutional Kolmogorov–Arnold network

Abstract

Abstract

Antihypertensive peptides (AHTPs) are short-chain peptides derived from food or bioproteins through enzymatic hydrolysis, fermentation, or chemical synthesis, and they have demonstrated promising blood pressure–lowering effects. These peptides primarily function by inhibiting angiotensin-converting enzyme (ACE), regulating the renin–angiotensin system (RAS), and enhancing nitric oxide (NO) production in endothelial cells. Owing to their high bioactivity and safety, AHTPs have attracted considerable attention in both functional food and pharmaceutical research. In this study, we propose CKAN-ATHP, a predictive framework that integrates three pre-trained encoders—DistilProtBert, PubChem10M, and Prot-T5—to effectively represent peptide sequences. To mitigate data imbalance and enhance model generalization, a sample augmentation strategy is introduced in the feature space. Subsequently, a Convolutional Kolmogorov–Arnold Network (CKAN) is constructed and optimized using a hybrid loss function combining label smoothing with Kullback–Leibler divergence and cross-entropy loss. Benchmark experiments demonstrate that CKAN-ATHP consistently outperforms seven state-of-the-art methods under class-imbalanced conditions, achieving improvements of 12–24% in MCC and 5–15% in BACC, while maintaining competitive ACC and AUC. Case studies and kernel density estimation analyses further validate the robustness and discriminative capability of the proposed framework. All data and code are available at https://github.com/Njq0104/CKAN-ATHP.

Scientific contribution

CKAN-ATHP integrates protein language model embeddings with chemical molecular descriptors and employs a CKAN to capture nonlinear sequence features under class imbalance, enabling effi cient and robust antihypertensive peptide prediction while showing residues 4-7 as critical for peptide recognition.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13321-026-01173-x.

Introduction

Hypertension [1], commonly referred to as high blood pressure, is a condition characterized by a persistent elevation of the pressure exerted by blood on the walls of the arteries, making it a prevalent chronic disease [2]. Due to the high incidence and severe consequences of hypertension, it is regarded as one of the leading causes of death in many countries where it remains inadequately controlled. Therefore, it is crucial to actively develop novel pharmacological agents to prevent and treat hypertension to reduce its associated complications [3, 4].

The renin-angiotensin system [5] plays a key role in blood pressure regulation and fluid balance. The mechanism involves the secretion of renin [6] from juxtaglomerular cells, which converts angiotensinogen into angiotensin I [7]. Angiotensin I is then converted into angiotensin II [8] by the angiotensin-converting enzyme. Angiotensin II increases blood pressure and volume by inducing vasoconstriction, stimulating the secretion of aldosterone and antidiuretic hormone, and activating the sympathetic nervous system, thus achieving dynamic regulation of blood pressure and fluid levels. In recent years, bioactive peptides with antihypertensive effects have provided new ideas for developing antihypertensive drugs with fewer side effects [9]. These peptides inhibit ACE activity [10], interfere with the generation of angiotensin II, and thereby block its effects of vasoconstriction and sodium-water reabsorption, effectively lowering blood pressure. Due to their natural origin and specific actions, ATHPs offer advantages over traditional drugs in terms of fewer side effects and resistance, becoming an emerging research hotspot in hypertension treatment [11–13].

The growing capabilities of artificial intelligence have enabled the widespread use of machine learning in computational drug screening [14, 15]. Initially, Wang et al. constructed a quantitative structure–activity relationship (QSAR) model using the partial least squares regression method incorporating G-scale descriptors [16]. In 2018, Win et al. proposed a PAAP method based on random forest (RF) for predicting AHTPs, utilizing amino acid composition (AAC), dipeptide composition (DPC), and pseudo-amino acid composition (PseAAC) [17]. Later, Manavalan et al. developed the mAHTPred model, which used six machine-learning algorithms and 51 feature sets generated from eight different encoding methods. The ERT model was used as a baseline predictor, and its output probabilities were used as input features for meta-predictors constructed from four machine learning algorithms (ERT, GB, RF, SVM) through a two-step feature selection protocol [18]. These ATHPs prediction methods are all based on traditional machine learning algorithms, combined with manually designed feature representations, such as amino acid composition, dipeptide composition, and pseudo-amino acid composition. While these methods have achieved remarkable performance, their predictive power largely depends on the quality and completeness of the manually designed features. Such manually designed feature representations may be insufficient to capture complex sequence patterns, especially for long peptide sequences. Furthermore, using multi-stage feature selection processes increases model complexity and computational cost, which may limit the model's scalability and robustness. Deep learning has become increasingly important in antihypertensive peptide (ATHP) prediction, largely driven by ongoing developments in computational biology and bioinformatics [19, 20]. These models, by constructing complex neural network architectures, can automatically extract features from large biological datasets for pattern recognition and classification. In 2022, Zhuang et al. constructed a deep ensemble model by averaging the predictions of nine independently trained sub-models, combining pre-trained protein embedding algorithms and convolutional neural networks to capture the rich semantic features in antihypertensive peptide sequences [21]. More recently, Du et al. developed the pLM4ACE predictor, which is based on protein language models (pLM) and evolutionary scale models (ESM-2) [22] to screen peptides with strong ACE inhibitory activity. This model utilized ESM-2 embeddings and five machine learning methods, with the logistic regression classifier combined with ESM-2 embeddings achieving the best performance, with a balanced accuracy (BACC) of 88%. Additionally, this study compared 12 traditional peptide embedding methods and five machine learning models [23].

In the task of predicting ATHPs, traditional deep learning models (such as standard CNNs) often have limitations due to their fixed activation functions and rigid architectures, making it challenging to flexibly capture the complex nonlinear relationships and local details inherent in protein sequence feature spaces. The Kolmogorov–Arnold Network (KAN), an innovative neural network architecture inspired by the Kolmogorov–Arnold representation theorem, offers the unique advantage of learnable activation functions at the edges of the network, enabling more nuanced modeling of intricate nonlinear patterns within the input features. This flexibility is particularly well-suited to protein sequence prediction tasks, as critical functional patterns within protein sequences often manifest as highly complex nonlinear features.

KAN is particularly suitable for ATHP prediction because it can adaptively learn nonlinear interactions among heterogeneous features using spline-based representations. This capability enables the model to capture subtle differences between sequence-derived and chemical features, which is essential for identifying biologically active peptides. The antihypertensive activity of peptides is known to depend on both local sequence motifs—such as C-terminal residues including Proline, Tyrosine, or Phenylalanine—and long-range contextual patterns, such as the distribution of hydrophobic, charged, or bulky residues along the sequence. These characteristics are highly nonlinear and differ substantially between active and inactive peptides. Moreover, when integrating high-dimensional and sparse representations from multiple pre-trained models and chemical descriptors, KAN achieves effective parameter efficiency, improving generalization and interpretability without compromising predictive performance.

In this paper, a model named CKAN-ATHP is proposed. The core motivation for designing CKAN-ATHP is precisely grounded in these advantages of the KAN architecture. By extending KAN into a convolutional structure (CKAN), the model further strengthens its ability to capture local spatial features within sequences. Convolutional operations are particularly effective for detecting biologically meaningful motifs or conserved subsequences, which may correspond to binding sites or functional domains associated with ACE inhibition [24]. Meanwhile, the KAN component continues to model complex feature interactions in a flexible, data-driven manner.

By integrating convolution operations with KAN's nonlinear activation mechanism, CKAN effectively learns both local features and global contextual relationships within sequences. This structural innovation allows the model not only to accurately distinguish positive from negative samples but also to exhibit superior generalization performance and robustness in antihypertensive peptide prediction tasks. Together, these properties make CKAN a biologically informed and computationally efficient model, well-suited to capture the multiscale dependencies inherent in peptide-based therapeutic prediction. The following points highlight the original contributions of this study:

1. We integrated datasets from previous studies and identified that an excessive number of short peptide sequences (fewer than five amino acid residues), compared with long peptides, can produce apparently favorable experimental results without reflecting a genuine improvement in antihypertensive peptide prediction. We therefore curated the dataset by removing very short peptides and redundant sequences using CD-HIT to improve evaluation reliability.

2. We comprehensively reviewed existing feature encoding methods, including 35 approaches encompassing handcrafted features, pre-trained model representations, and chemical molecular descriptors. A comparative evaluation was then conducted to select the most effective encoding methods.

3. To address persistent data imbalance in antihypertensive peptide research, we adopted a sample augmentation strategy and optimized the loss function calculation method, thereby improving model robustness.

4. To the best of our knowledge, this is the first attempt to apply the Convolutional Kolmogorov-Arnold Network (CKAN) to the task of antihypertensive peptide identification. Comprehensive empirical evaluations and theoretical insights consistently show that the proposed model surpasses seven competitive methods.

Data and methods

Data collection and preprocessing

Datasets summarized in previous studies and peptide sequences obtained from existing databases were collected and curated. Peptide sequences shorter than five amino acids were excluded, and sequences exhibiting more than 90% similarity were filtered using CD-HIT to eliminate redundancy. The processed dataset was subsequently partitioned into training and testing subsets, constituting 80% and 20% of the data, respectively, using a fixed random seed of 34 to ensure reproducibility. An ensemble learning approach was employed to systematically evaluate 35 distinct feature encoding methods, including traditionally handcrafted encodings [25], pre-trained model encodings [26], and chemical molecular descriptors of peptides [27]. Based on Matthews correlation coefficient (MCC) scores, the top-performing encodings identified were Prot-T5_xl_uniref50, DistilProtBert, and PubChem10M. Various combinations of these selected features were further examined, ultimately resulting in an optimal feature embedding with a dimensionality of 2816. These feature embeddings were then utilized as inputs to a CKAN classifier to predict peptide sequence classification labels. The overall workflow of CKAN-ATHP is illustrated in Fig. 1.

Fig. 1.

The overall architecture of CKAN-ATHP: A data collection and preprocessing. B feature selection. C feature combination and analysis. D model architecture. E schematic diagram of KAN. F Model evaluation

Dataset collection and curation

In the experiment, the primary data source was the Food-derived Bioactive Peptide Database (DFBP) [28], which focuses on bioactive peptides extracted from food sources, including those with antihypertensive properties. Additionally, the dataset compiled by Du et al. in pLM4ACE was also utilized.

To reduce the risk of overfitting caused by high sequence homology and to enhance the generalizability of the model, CD-HIT clustering was applied during dataset preprocessing [29]. Multiple sequence identity thresholds (80%, 85%, 90%, and 95%) were examined to evaluate the impact of redundancy reduction on dataset composition and downstream model performance. Lower identity thresholds impose stricter redundancy removal and substantially reduce the number of retained sequences, whereas higher thresholds preserve more homologous peptides. Based on this analysis, a 90% sequence identity threshold was selected as a balanced setting that effectively removes highly similar peptides while retaining sufficient sequence diversity for model training. Redundancy reduction was performed prior to dataset partitioning. Specifically, each CD-HIT threshold produced an independent non-redundant dataset, and dataset splitting was conducted separately within each threshold-specific dataset. For a given threshold, CD-HIT was first applied to the original dataset to construct a corresponding non-redundant dataset. The resulting dataset was then divided into training and test sets using an 80:20 split with a fixed random seed (seed = 34), ensuring full reproducibility of the data partitioning process. The resulting dataset statistics and performance comparisons under different CD-HIT thresholds are summarized in Supplementary Tables S8 and S9.

Following homology filtering using CD-HIT at a 90% sequence identity threshold, peptide sequences shorter than five amino acids were excluded during dataset construction [18]. Previous studies have shown that most experimentally identified ATHPs, particularly angiotensin-converting enzyme (ACE) inhibitory peptides, predominantly consist of very short sequences such as dipeptides and tripeptides [30], which have been extensively investigated [31]. In this study, peptide sequences containing fewer than five amino acid residues are defined as short peptides. However, the primary objective of this work is to identify ATHPs with longer sequence lengths that are more relevant to practical screening scenarios rather than to re-investigate well-characterized short peptides. Accordingly, short peptide sequences were excluded during dataset construction to maintain a consistent training distribution focused on longer peptides. Although many peptides in the dataset are shorter than 10 residues, peptides with lengths of 5–9 residues retain substantially more positional and contextual information than peptides shorter than five residues, which is critical for reliable feature extraction and residue-level learning. In addition, inspired by occlusion sensitivity analysis [32], we performed residue-level occlusion by systematically masking individual residue positions and quantifying the resulting changes in prediction probability, showing that position-specific contributions require sufficient sequence context; detailed procedures and results are provided in Supplementary File S4.

After length filtering and redundancy reduction using CD-HIT with a 90% sequence identity threshold, the final dataset consisted of 732 positive AHTPs and 1601 negative samples. Redundancy filtering was performed prior to dataset partitioning, ensuring that no peptide sequences sharing 90% or higher sequence identity were present across the training and testing subsets. The dataset was subsequently divided into training and test sets at a ratio of 80% and 20%, respectively, using stratified random sampling based on class labels with a fixed random seed of 34. This strategy preserves the original class imbalance ratio in both subsets and allows model performance to be evaluated under a realistic imbalanced data distribution. In the final dataset, peptide sequence lengths range from 5 to 60 amino acid residues, with an average length of approximately 13.1 residues.

Feature representation and selection

Pre-trained Bert embedding feature

DistilProtBert [33] encodes the input amino acid sequence into a fixed-length feature vector. Typically, for each amino acid, DistilProtBert outputs a 1024-dimensional vector. Furthermore, to further reduce the dimensionality of the features and aggregate the information across the entire sequence, a pooling operation can be applied to the feature matrix, transforming it into a 1024-dimensional global feature vector that effectively captures the characteristics of the entire protein sequence.

Chemical transformer feature

Using PubChem10M_SMILES_BPE_450k [34] for protein sequence feature extraction results in a typical feature dimension of 768. Specifically, each amino acid is encoded as a 768-dimensional vector. By applying pooling operations, the feature matrix is transformed into a 768-dimensional global feature vector that captures the characteristics of the entire protein sequence.

Prot-T5_xl_uniref50 feature

Prot-T5_xl_uniref50 [35, 36] is an advanced protein sequence encoding model based on the T5 (Text-to-Text Transfer Transformer) architecture developed by Google, specifically optimized for bioinformatics applications. The model is trained on the UniRef50 dataset, which comprises deduplicated protein sequences representing millions of distinct proteins, thereby providing a comprehensive background for protein sequence analysis. The primary advantage of this model lies in its Transformer-based architecture, which can capture complex contextual relationships within input sequences and effectively modeling long-range dependencies. Each protein sequence with length $L$ is transformed into a 1024-dimensional numerical representation.

Comparative evaluation of feature representations

To systematically compare different feature representations for AHTP prediction, a total of 35 feature representations belonging to three categories were evaluated: (1) handcrafted sequence-based features, (2) embeddings derived from pre-trained protein language models, and (3) chemical molecular representations. All feature representations were extracted independently and evaluated under an identical experimental protocol. For each feature type, an ensemble classifier composed of LR, SVM, and MLP was trained. This ensemble architecture was adopted solely for feature comparison purposes to minimize model-dependent bias and ensure a fair assessment of representation quality.

The dataset used for feature representation comparison was the final dataset described in Sect. “Dataset collection and curation”. The dataset was split into training and test sets using the same fixed partition described in the Dataset section, and the identical test set was used for all feature representations. Given the inherent class imbalance of the dataset, MCC was used as the primary metric for ranking feature representations. BACC was additionally reported to provide an unbiased assessment of classification performance on imbalanced data, while ACC, SE, SP, F1-score, and AUC were included as supplementary metrics for completeness. All results are presented with two decimal places, consistent with the statistical precision of the evaluation.

In addition to evaluating individual feature representations, different feature fusion strategies were investigated to assess the effectiveness of integrating multiple representations. As a baseline approach, the three selected feature representations—DistilProtBert, ProtT5-XL-UniRef50, and PubChem10M—were directly concatenated into a single feature vector. Furthermore, three alternative fusion strategies were evaluated for comparison: attention-weighted concatenation, learned gating mechanisms, and tensor fusion. Attention-weighted concatenation applies learnable weights to each feature representation prior to concatenation. The learned gating mechanism introduces trainable gates to modulate the contribution of each representation, while tensor fusion explicitly models higher-order interactions among feature representations. All fusion strategies were evaluated using the same dataset and experimental protocol described above. The corresponding performance results are reported in Table 1.

Table 1.

Performance comparison of different feature fusion strategies

Fusion strategy	MCC	BACC	ACC	F1	SE	SP	AUC	AP
PCA	0.54	0.77	0.81	0.69	0.67	0.87	0.85	0.67
Tensor fusion	0.62	0.82	0.83	0.75	0.78	0.86	0.90	0.75
Attention-weighted concatenation	0.63	0.81	0.84	0.74	0.71	0.90	0.89	0.79
Learned gating mechanism	0.67	0.84	0.86	0.77	0.76	0.91	0.89	0.81
Simple concatenation	0.72	0.86	0.88	0.81	0.81	0.91	0.93	0.87

Sample augmentation

We employed a sample augmentation [37] method that generates synthetic samples by applying a noise-based oversampling technique, which perturbs the original samples in the feature space. This method supports the generation of additional data instances. To enhance the predictive capability of the ATHP model, peptide-level data augmentation was performed to increase the quantity of both positive and negative training examples. Specifically, for each sample in the training set, a random perturbation vector with the same dimensionality as the original feature vector is generated, where each element is drawn from a uniform distribution over the interval [0, 1]. This perturbation vector is then element-wise multiplied with the original feature vector and scaled by a fixed perturbation factor. The resulting values are added to the original feature to produce an augmented synthetic sample. The mathematical description for generating new samples $F(new)$ used for model training is as follows

$$F\left(\mathit{new}\right)=F\left(i\right)\ast V\ast a+F\left(i\right)$$ 1

where $F(i)$ denotes the original feature vector of the $i-th$ training sample. $V$ represents a perturbation vector with the same dimensionality as $F(i)$, where each element is sampled uniformly from the interval [0, 1]. $a$ is the perturbation coefficient used to control the strength of the augmentation, after training and testing with different settings, we set the perturbation factor to 0.05. We evaluated multiple perturbation factors in the range of 0.01–0.1 and found that 0.05 consistently yielded stable improvements in ACC and MCC across validation folds. Perturbation factors larger than 0.05 introduced excessive noise and degraded model performance, whereas smaller values resulted in limited augmentation effects. Accordingly, 0.05 was adopted in the final experiments. $F\left(\mathit{new}\right)$ is the resulting augmented feature vector. To improve the model's learning, peptide data augmentation is performed by adding noise drawn from a Gaussian distribution to the training samples, while no data augmentation is applied to the test set.

Loss function optimization

Label smoothing

Antihypertensive peptide prediction faces several significant challenges. Firstly, positive samples are relatively scarce compared to negative samples. Secondly, standard loss functions, such as Cross-Entropy loss, may lead to the model becoming overly confident in certain predictions, resulting in overfitting and poor generalization. Furthermore, the input features, which include embeddings from pre-trained models and chemical descriptors, are complex and high-dimensional, thus complicating the training process.

To address these challenges, the CKAN-ATHP model employs label smoothing and a combined loss function strategy. Label smoothing [38] is a regularization technique aimed at preventing the model from becoming overly confident during training, thereby enhancing its generalization ability. The technique introduces a degree of uncertainty into the true label distribution by redistributing a portion of the probability mass to non-true classes. This approach mitigates the risk of the model assigning excessive probability to the correct class, which could lead to overfitting.

Assume there is a class $K$, and the original one-hot label $y$ is as follows

$$y_i=\left\{\begin{array}{c}1,ifi=target\\ 0,ifi\ne target\\ \end{array}\right)$$ 2

After label smoothing, the label $\tilde{y}$ is transformed into

$${\tilde{y}}_i=\left\{\begin{array}{c}1-\epsilon ,ifi=target\\ \frac{\epsilon }{K-1},ifi\ne target\\ \end{array}\right)$$ 3

Where $\epsilon$ is the smoothing factor set to 0.1. Following common practice in classification tasks, several small smoothing values were evaluated, and $\epsilon$ = 0.1 was adopted in the final experiments.

Loss function

The Kullback–Leibler (KL) [39] divergence loss is combined with the Cross-Entropy (CE) loss shown in Fig. 2. The KL divergence loss quantifies the difference between two probability distributions under label smoothing, measuring the distance between the model's predicted distribution and the smoothed label distribution. The CE loss is used to compare the distribution of the true labels with the predicted probability distribution from the model [40].

Fig. 2.

The structure of the loss method

For a binary classification problem, the Cross-Entropy loss $L_{\text{CE}}$ can be expressed as

$$L_{\text{CE}}=-\frac{1}{N}\sum _1^N\left(y_{i}log\left(p_i\right)+\left(1-y_i\right)log\left(1-p_i\right)\right)$$ 4

Where $N$ is the number of samples, $y_i$ is the true label of a sample $i$ (0 or 1), and $p_i$ is the predicted probability of the positive class for the sample $i$.

The Kullback–Leibler divergence loss is defined as

$$L_{\mathit{KL}}=\frac{1}{N}\sum _{i=1}^N\sum _{j=1}^C{q}_i\left(j\right)log\left(\frac{q_i\left(j\right)}{p_i\left(i\right)}\right)$$ 5

Where $N$ is the number of samples, $C$ is the number of classes, $p_i(j)$ is the predicted probability of sample $i$, $q_i(j)$ is the smoothed label distribution for sample.

Specifically, loss calculation can be divided into the following four steps:

1. Generation of smoothed label distributions:

   The original hard labels are first transformed into soft target distributions using label smoothing. In this process, a fixed confidence value is assigned to the true class, and the remaining probability mass is uniformly distributed across the other classes. This transformation improves generalization by discouraging overconfident predictions.

2. Computation of cross-entropy loss:

   Standard categorical cross-entropy loss is computed between the model’s raw outputs and the original class labels. This component encourages the model to align its predictions with the known targets.

3. Computation of KL divergence loss:

   The model outputs are first converted into log-probability distributions via a log-softmax operation. The KL divergence is then calculated between these predicted log-probabilities and the smoothed target distributions. This term serves as a regularization mechanism that penalizes deviations from the softened label distribution. The loss is averaged over all samples in a mini-batch.

4. Combination of loss components:

   The total loss is obtained by summing the cross-entropy loss and the KL divergence loss, weighted by a hyperparameter ${\lambda }_{\text{KL}}$, which controls the relative contribution of the KL term. In our experiments, this weight was set to 1.0. The final objective can be formulated as

   $$L_{\text{Total}}=L_{\text{CE}}+{\lambda }_{\text{KL}}{L}_{\text{KL}}$$ 6
   In addition to the loss function adopted in our final model, several commonly used loss functions for handling class imbalance were also evaluated for comparison. In particular, a weighted binary cross-entropy loss was considered [41], in which different weights were assigned to positive and negative samples to alleviate the effect of class imbalance during training. For a binary classification task, the loss function was defined as:

   $$L=-\frac{1}{N}\sum _{i=1}^N\left[w_1{y}_{i}log\left({\widehat{y}}_i\right)+w_0\left(1-y_i\right)log\left(1-{\widehat{y}}_i\right)\right]$$ 7
   Where $y_i\in \left\{0,1\right\}$ denotes the ground-truth label of the $i$-th sample, ${\widehat{y}}_i\in \left[0,1\right]$ is the predicted probability for the positive class, and $N$ is the total number of training samples. The class weights $w_1$ and $w_0$ were set inversely proportional to the sample frequencies of the corresponding classes in the training set, as follows:

   $$w_1=\frac{n_0+n_1}{2n_1},w_0=\frac{n_0+n_1}{2n_0}$$ 8

   Where $n_1$ and $n_0$ represent the numbers of positive and negative samples, respectively. This weighting scheme balances the contributions of different classes to the overall loss, alleviates the bias toward the majority class, and improves the learning of minority-class samples.

   Furthermore, Focal Loss [42] was included as an additional comparative baseline, which emphasizes hard-to-classify samples by down-weighting well-classified ones. All loss functions were evaluated under the same training protocol to ensure a fair comparison. For binary classification, Focal Loss is defined as follows. First, an intermediate term is introduced:

   $$p_i=\left\{\begin{array}{c}{\widehat{y}}_i,\text{if}{y}_i=1,\\ 1-{\widehat{y}}_i,\text{if}{y}_i=0,\\ \end{array}\right)a_i=\left\{\begin{array}{c}a,\text{if}{y}_i=1,\\ 1-a,\text{if}{y}_i=0,\\ \end{array}\right)$$ 9

   Where ${\widehat{y}}_i$ denotes the predicted probability for the positive class.

   The Focal Loss is then formulated as:

   $$L_{\mathit{FL}}=-\frac{1}{N}\sum _{i=1}^N{a_i\left(1-p_i\right)}^{\gamma }log\left(p_i\right)$$ 10

   Here, $y_i\in \left\{0,1\right\}$ denotes the ground-truth label of the $i$-th sample, ${\widehat{y}}_i\in \left[0,1\right]$ represents the predicted probability of the positive class, and $p_i$ is the predicted probability of the true class for the $i$-th sample. The parameter $a\in \left[0,1\right]$ is a class-balancing factor, while $\gamma >0$ is the focusing parameter that reduces the loss contribution of well-classified samples and emphasizes hard examples. $N$ denotes the total number of training samples. When $\gamma =0$, the Focal Loss reduces to the standard cross-entropy loss.

Model parameters

The proposed model consists of a KAN-based convolutional layer followed by a max-pooling layer and two fully connected layers. The hidden fully connected layer contains 256 neurons, and the output layer includes two neurons corresponding to the binary classification task. The model was optimized using the Adam optimizer with a learning rate of 0.005 and a batch size of 64, and trained for up to 80 epochs. Specific implementation details are provided in Supplementary File S2.

An early stopping strategy was applied during training to mitigate overfitting. Specifically, 10% of the training data was further split as an independent validation set using stratified sampling based on class labels. This validation set was excluded from parameter updates and used exclusively for monitoring validation performance. The same validation split was consistently applied across all embeddings to ensure fair comparison. Training was terminated if the BACC on the validation set did not improve for 10 consecutive epochs. The validation set consisted of 187 peptide samples, including 128 negative and 59 positive instances.

Given the relatively limited number of samples, additional regularization strategies were employed, including label smoothing to reduce overconfident predictions and maintaining a moderate model complexity to balance representational capacity and generalization.

Model workflow of CKAN-ATHP

CKAN-ATHP primarily consists of three parts: 1) Feature encoding; 2) Convolutional kolmogorov-arnold network module; 3) Fully connected layer. The workflow of the model proposed in this study is shown in Fig. 3. A detailed description of the model workflow, including the implementation of feature extraction, the CKAN module, and the fully connected classification layers, is provided in Supplementary File S2.

Fig. 3.

Model workflow of CKAN-ATHP

Visualization of feature representations

After model training, three dimensionality reduction techniques—PCA, t-SNE, and UMAP—were applied to visualize the high-dimensional feature representations extracted from both the training and test sets, as shown in Fig. 4. PCA was employed as a linear projection method to capture the principal directions of variance in the feature space. t-SNE was used to preserve local neighborhood structures and facilitate visualization of potential clustering patterns, while UMAP was applied to provide a complementary view that balances local and global data topology. These dimensionality reduction methods were used solely for qualitative visualization purposes, aiming to provide an intuitive illustration of the distribution of AHTPs and non-AHTPs in the reduced feature space, rather than serving as quantitative performance evaluations.

Fig. 4.

Dimensionality reduction visualization on training set and test set

Ablation experiment design

Ablation experiments were conducted to evaluate the contribution of individual components in the proposed model. Specifically, ablation was performed by systematically removing or modifying one component at a time while keeping all other experimental settings unchanged under the selected 90% sequence identity dataset, including feature representations, training protocol, and evaluation metrics. The ablation settings include loss function ablation, where different loss configurations were compared, and sample augmentation ablation, where the model was trained with and without the proposed augmentation strategy. The corresponding analyses are reported in Sect. "Analysis of the ablation experiment".

Comparative deep learning frameworks for CKAN evaluation

To position the proposed CKAN within the context of modern deep learning architectures for biological sequence analysis, representative models from different architectural paradigms were selected for comparison. CNN and DO-Conv [43] were employed as convolution-based baselines, which learn hierarchical local patterns through sliding kernels and serve as widely used reference architectures in sequence modeling tasks. Attention-based Transformer models were incorporated to explicitly model long-range contextual dependencies across peptide sequences, enabling global information integration beyond local receptive fields. GNN models were further introduced to represent peptides as residue-level graphs, allowing the modeling of relational and interaction-aware features among residues [44]. In addition, EfficientNet-based architectures were included as representative parameter-efficient convolutional designs to evaluate scalable and lightweight network variants [45]. All comparison models were trained and evaluated under the same dataset split, training protocol, and evaluation metrics to ensure a fair assessment of architectural contributions. The corresponding performance results and comparative conclusions are presented and analyzed in Sect. "Comparison with representative deep learning architectures".

Representative methods from different research directions

To ensure a fair and comprehensive evaluation, a total of nine representative deep learning–based models from different research directions were selected for comparison. These models were originally developed for various peptide-related or sequence-based prediction tasks, including antimicrobial peptide identification, bitter peptide prediction, RNA modification site prediction, anticancer peptide recognition, antiviral peptide prediction, and cell-penetrating peptide classification. Owing to their diverse feature modeling strategies and learning paradigms, these methods provide complementary perspectives for assessing the generalization capability of the proposed model.

AMP-RNNpro [46] adopts a two-stage learning framework in which multiple base classifiers are first trained using diverse sequence-derived features, and their output probabilities are subsequently fed into a recurrent neural network for secondary modeling, emphasizing probabilistic feature fusion and temporal dependency modeling. BitterEN [47] is an ensemble-based predictor for bitter peptide identification that integrates multiple physicochemical and sequence features by combining conventional machine learning methods with neural networks, enabling effective discrimination of short peptide sequences. DHUpredET [48], designed for RNA dihydrouridine modification site prediction, employs Extra Trees classifiers built upon multiple position-related features, highlighting the role of feature selection and ensemble learning in biological sequence analysis. MLAFP-XN [49] is a neural network–based model for antifungal peptide prediction that combines various sequence and physicochemical features, further enhanced by feature selection strategies.

In addition, several recent deep learning approaches were included to enrich the comparison. SiameseCPP [50] utilizes a Siamese network architecture with contrastive learning to capture discriminative representations of peptide sequences. ACP-CapsPred [51] applies capsule networks to anticancer peptide prediction, aiming to preserve hierarchical feature relationships in sequence representations. ACP-ONE [52] adopts a multi-view ensemble learning strategy that integrates heterogeneous features for anticancer peptide identification. DeepAIP [53] leverages attention mechanisms together with pretrained language model embeddings to enhance feature representation for peptide activity prediction. AVP-IFT [54] introduces an iterative feature transformation framework for antiviral peptide prediction, progressively refining feature representations to improve classification performance.

Evaluation strategy and metrics

This study adopts two evaluation strategies for different experimental purposes. For the main experiments and ablation studies, a hold-out evaluation strategy with a fixed train-test split is employed. The dataset is divided into training and testing subsets at a ratio of 80% and 20% using a fixed random seed of 34. A validation subset is obtained from the training data by further separating 10% of the samples through stratified sampling based on class labels. Consequently, the validation set retains the same positive-to-negative sample ratio as the full dataset and contains 187 peptide samples, including 128 negative and 59 positive instances. The validation set is excluded from model training and is used exclusively for early stopping, while the test set remains completely unseen until final evaluation. Model training is halted when the BACC on the validation set shows no improvement over 10 consecutive epochs (patience = 10). This evaluation protocol enables controlled comparisons in the main experiments and ablation analyses, with the corresponding results reported from the fixed hold-out split.

For the comparison with state-of-the-art predictors, five-fold cross-validation is additionally conducted as an independent and supplementary evaluation strategy. Under this protocol, the entire dataset is randomly shuffled and partitioned into five mutually exclusive subsets using stratified sampling based on class labels, ensuring that the class distribution in each fold is consistent with that of the full dataset. In each fold, four subsets are used for training and the remaining subset is used for testing. This procedure is repeated five times so that each subset serves once as the test set, and the final performance is reported as the mean and standard deviation across the five folds. Early stopping is not applied during the cross-validation experiments, and cross-validation is not used for hyperparameter optimization. All comparative methods evaluated under the five-fold cross-validation setting are tested using the same data partitions and evaluation metrics to promote fair comparison.

For fair comparison and reproducibility, the same training configuration and evaluation metrics are applied to CKAN-ATHP and all comparative baseline models under both evaluation strategies.

This study uses nine commonly used evaluation metrics to assess the performance of CKAN-ATHP, including accuracy (ACC), sensitivity (SE), specificity (SP), balanced accuracy (BACC), precision, F1-score (F1), Matthews correlation coefficient (MCC), area under the ROC curve (AUC), and average precision (AP). The calculation formulas for these metrics are as follows:

$$\text{Precision =}\frac{\mathit{TP}}{TP+FP}$$ 11

$$SE=\frac{\mathit{TP}}{TP+FN}$$ 12

$$SP=\frac{\mathit{TN}}{FP+TN}$$ 13

$$\text{MCC}=\frac{(TP\times TN)-(FP\times FN)}{\sqrt{(TP+FN)(TN+FP)(TP+FP)(TN+FN)}}$$ 14

$$F1=\frac{2\times TP}{2\times TP+FP+FN}$$ 15

$$\text{ACC}=\frac{TP+TN}{TP+FP+FN+TN}$$ 16

$$\text{AP}={\int }_0^{1}p(r)dr$$ 17

$$\text{BACC}=\frac{SE+SP}{2}$$ 18

where TP and TN represent correctly predicted positive and negative ATHPs, respectively, while FP and FN denote incorrectly predicted positive and negative samples. BACC is adopted to provide a balanced evaluation under class-imbalanced conditions by equally weighting SE and SP.

The ROC curve is an important evaluation metric for assessing model performance, as it does not rely on a specific decision threshold. Therefore, AUC is used to estimate the overall discriminative ability of the model. In addition, ROC and PR curves are plotted to provide more detailed performance comparisons between different models.

Case study design

To further examine model behavior on independent data, a case study was conducted using 17 experimentally verified antihypertensive peptide sequences collected from the DFBP database that were strictly excluded from the training, validation, and testing datasets used for model development.

For each peptide in the case study dataset, prediction probabilities were generated using CKAN-ATHP as well as the compared predictors included in this study. The predicted probabilities were recorded for comparative analysis across models.

To facilitate an intuitive comparison of prediction score distributions across different models, the prediction results were visualized using a heatmap representation for qualitative analysis, where each row corresponds to a peptide sample and each column corresponds to a prediction model.

Kernel density estimation for probability visualization

Kernel density estimation (KDE) was employed to visualize the distribution of predicted probabilities produced by CKAN-ATHP on the independent test set. KDE is a non-parametric density estimation technique that provides a smooth approximation of the underlying probability distribution without relying on discrete binning.

In this analysis, the predicted probabilities range from 0 to 1, representing the model’s confidence in classifying a peptide as antihypertensive. The horizontal axis denotes the predicted probability values, while the vertical axis represents the estimated probability density obtained by KDE. Separate density curves were generated for positive and negative samples to facilitate comparison of their distribution patterns.

Due to the smoothing nature of KDE, the estimated density curves may extend slightly beyond the [0, 1] interval; however, the actual predicted probabilities remain strictly within valid bounds.

Experimental results

Feature representation comparison

Handcrafted features

Traditional handcrafted features are derived from biological priors such as amino acid composition and physicochemical properties. While these features offer interpretability, their predictive performance was generally inferior to that of learned representations. The performance of 22 handcrafted feature types is summarized in Supplementary Table S1, revealing moderate MCC values across most descriptors.

Protein language model-based features

Several representative protein language models, including DistilProtBert, Prot-Bert, Prot-T5, and ESM-2, were evaluated within the same experimental framework. Among them, ProtT5-XL-UniRef50 achieved the highest MCC and demonstrated consistently strong performance across multiple evaluation metrics. DistilProtBert, a distilled and computationally efficient variant of BERT, also showed competitive predictive performance. Notably, DistilProtBert and ESM-2 exhibited comparable performance in terms of MCC and BACC under the same evaluation protocol. Despite this similarity in predictive performance, ESM-2 requires substantially higher computational and memory resources for embedding extraction, which may reduce its practicality in large-scale and iterative experimental settings. By contrast, DistilProtBert provides a favorable balance between predictive effectiveness and computational efficiency, making it suitable for the intended application of this study.

In contrast, ESMFold-based representations yielded the lowest MCC among protein-based features (0.55), suggesting that explicit 3D structural representations may not be optimal for AHTP prediction under the current setting. Detailed results are provided in Supplementary Table S2.

Chemical molecular features

Chemical molecular representations included PubChem10M, ChemBERTa-77 M-MLM, RDKit descriptors, Mordred descriptors, circular fingerprints, and SMILES2img. Performance comparisons were primarily analyzed using MCC and BACC as the main selection criteria, as these metrics are more robust to class imbalance and better reflect the discriminative capability of the models. Under this criterion, PubChem10M achieved the best overall performance, yielding the highest MCC (0.59) and BACC (0.80), indicating a strong balance between sensitivity and specificity. ChemBERTa-77 M-MLM also demonstrated competitive performance, with relatively high MCC and BACC values, particularly showing stable discrimination ability. In contrast, RDKit and Mordred descriptors exhibited moderate performance, while circular fingerprints and SMILES2img showed consistently lower MCC and BACC values, suggesting limited effectiveness under the current experimental setting. Detailed results are summarized in Supplementary Table S3.

Comparison of feature fusion and dimensionality reduction strategies

Based on MCC ranking across all evaluated feature types, the top three feature representations were identified as ProtT5-XL-UniRef50, DistilProtBert, and PubChem10M. BACC was used as a complementary criterion to confirm the stability of this ranking under class-imbalanced conditions, and these representations achieved higher MCC values than other evaluated features on the same test set. The MCC values obtained from all 35 feature representations are summarized and visualized in Supplementary Fig. S2. The detailed performance metrics for each feature type are reported in Supplementary Tables S1-S3. These three selected representations were subsequently used for feature fusion and dimensionality reduction experiments.

In addition to the feature fusion strategies listed above and the feature comparison protocol described in Sect. "Comparative evaluation of feature representations", principal component analysis (PCA) was also evaluated as an alternative feature combination and dimensionality reduction approach. PCA was applied independently to each selected feature representation, including DistilProtBert, PubChem10M, and Prot-T5, retaining principal components that together explain 95% of the cumulative variance (ratio = 0.95). The resulting low-dimensional feature representations were then used as input for model training. The performance comparison of different feature fusion and dimensionality reduction strategies is summarized in Table 1.

Using simple concatenation of the three selected feature representations as a baseline, the integration of multiple features resulted in improved predictive performance compared with individual representations. Among all evaluated fusion strategies, simple concatenation achieved the highest MCC and BACC on the independent test set, suggesting that direct feature aggregation can effectively capture complementary information across heterogeneous representations under the current experimental setting.

More sophisticated fusion strategies, including attention-weighted concatenation, learned gating mechanisms, and tensor fusion, produced comparable but not consistently superior results across evaluation metrics. In particular, attention-weighted concatenation demonstrated competitive performance in terms of F1-score, but did not consistently outperform simple concatenation in MCC or BACC. Similarly, gating-based fusion and tensor fusion showed stable performance but failed to achieve systematic improvements over the baseline across all evaluation criteria.

Overall, the results indicate that while more sophisticated fusion strategies can provide modest performance gains, the improvements over simple concatenation are limited, suggesting that straightforward feature concatenation remains an effective and competitive integration approach under the current experimental setting.

It is noteworthy that high-dimensional features may provide richer discriminative information while also increasing the risk of overfitting. In this study, the model was trained for a fixed number of epochs with multiple regularization strategies to control model complexity. The visualizations shown in Fig. 4 are based on the concatenated feature representation composed of DistilProtBert, ProtT5-XL-UniRef50, and PubChem10M. These dimensionality reduction results provide an intuitive, qualitative illustration of the distribution patterns of AHTPs and non-AHTPs in the reduced feature space for both the training and test sets. The observed separation trends indicate that the fused feature representation captures discriminative characteristics relevant to the classification task.

Analysis of the ablation experiment

Loss function optimization

In this study, different loss calculation strategies were evaluated to assess their overall impact on model performance, as summarized in Table 2. Using MCC as the primary evaluation metric, the results indicate that the combined KL + CE loss provides consistent and notable improvements over the conventional CE loss. In contrast, focal loss achieves performance comparable to standard CE loss, without yielding a clear advantage in terms of MCC. These observations suggest that incorporating KL divergence–based regularization can enhance the model’s discriminative capability under class-imbalanced conditions.

Table 2.

Performance comparison of different loss functions

Method	MCC	BACC	ACC	F1	SE	SP	AUC	AP
CE loss (weighted)	0.65	0.83	0.85	0.77	0.80	0.87	0.91	0.82
CE loss	0.67	0.86	0.86	0.77	0.78	0.89	0.92	0.84
Focal Loss	0.67	0.86	0.86	0.78	0.78	0.89	0.91	0.84
KL loss + CE loss	0.72	0.86	0.88	0.81	0.81	0.91	0.93	0.87

From a BACC perspective, the optimized loss functions achieve comparable or improved performance relative to standard CE loss, indicating a more balanced treatment of positive and negative samples. In particular, KL + CE exhibits the most favorable overall behavior, achieving the highest MCC while maintaining a high BACC, which reflects a balanced trade-off between sensitivity (SE) and specificity (SP).

Overall, these findings indicate that loss function optimization contributes to more robust and balanced predictive performance. While the observed improvements are moderate, the consistent gains in MCC and BACC support the effectiveness of the proposed loss design and highlight loss optimization as a promising direction for further enhancing model robustness and generalization.

Contribution of sample augmentation strategies

As reported in Table 3, the sample augmentation strategy led to improvements across multiple evaluation metrics. SE increased from 0.76 to 0.81, corresponding to an absolute increase of 0.05 in the identification of positive samples. At the same time, MCC increased from 0.67 to 0.72, indicating an overall improvement in predictive performance under class-imbalanced conditions.

Table 3.

Performance of CKAN with sample augmentation

Method	MCC	BACC	ACC	F1	SE	SP	AUC	AP
CKAN	0.67	0.83	0.86	0.78	0.76	0.91	0.90	0.85
CKAN with sample augmentation	0.72	0.86	0.88	0.81	0.81	0.91	0.93	0.87

In addition, BACC increased from 0.83 to 0.86, reflecting concurrent changes in SE and SP. Notably, the increase in SE was not accompanied by a decrease in SP, which remained stable at 0.91. The AUC increased from 0.90 to 0.93, and AP increased from 0.85 to 0.87, showing consistent improvements in discrimination and ranking performance.

Comparison with representative deep learning architectures

The performance comparison of CKAN with representative deep learning architectures is summarized in Table 4.

Table 4.

Performance of different deep learning architectures

Method	MCC	BACC	ACC	F1	SE	SP	AUC	AP
CNN	0.58	0.77	0.82	0.69	0.63	0.91	0.88	0.79
DO-Conv	0.61	0.77	0.84	0.70	0.61	0.94	0.89	0.79
GNN	0.61	0.81	0.83	0.73	0.73	0.88	0.90	0.81
Transformer	0.64	0.82	0.84	0.75	0.75	0.89	0.90	0.80
EfficientNet	0.66	0.83	0.85	0.77	0.78	0.88	0.92	0.83
CKAN	0.72	0.86	0.88	0.81	0.81	0.91	0.93	0.86

Among convolution-based deep learning architectures, the standard CNN framework shows relatively limited discriminative capability under class imbalance, achieving an MCC of 0.58 and a BACC of 0.77. DO-Conv introduces increased kernel flexibility and yields a moderate improvement in MCC (0.61); however, its BACC remains comparable to that of CNN, indicating limited performance gains under the current experimental setting.

More advanced deep learning frameworks demonstrate clearer performance gains. Transformer-based models achieve an MCC of 0.64 and a BACC of 0.82, demonstrating competitive performance among the evaluated architectures. GNNs obtain comparable MCC values (0.61) with a higher BACC (0.81), reflecting a balanced trade-off between SE and SP. EfficientNet-based architectures further improve overall performance, reaching an MCC of 0.66 and a BACC of 0.83, which highlights the effectiveness of parameter-efficient architectural scaling in enhancing robustness under class-imbalanced conditions.

The proposed CKAN model achieves the highest MCC (0.72) and BACC (0.86) among the evaluated deep learning architectures. AUC values are reported for completeness, although ROC-based metrics may be influenced by class imbalance. CKAN achieves consistently higher MCC and BACC values while maintaining a balanced SE–SP trade-off under the current experimental setting.

Comparative evaluation with representative methods from different research directions

These representative models were selected to cover a broad range of modeling paradigms commonly used in peptide-related studies. Brief descriptions of these methods and their original application scopes are provided in Sect. "Comparative deep learning frameworks for CKAN evaluation" to clarify the comparative setup. All methods were evaluated under the same experimental setting as the proposed CKAN-ATHP model, using identical data partitions and evaluation metrics without additional model-specific tuning. The quantitative comparison results are summarized in Table 5.

Table 5.

Performance comparison with representative deep learning models

Method	MCC	BACC	ACC	F1	SE	SP	AUC	AP
BitterEN	0.53	0.70	0.80	0.57	0.42	0.98	0.87	0.79
ACP-CapsPred	0.59	0.80	0.82	0.72	0.73	0.86	0.87	0.73
AMP-RNNpro	0.66	0.84	0.85	0.77	0.79	0.88	0.92	0.84
DHUpredET	0.66	0.83	0.85	0.77	0.79	0.88	0.92	0.84
SiameseCPP	0.68	0.85	0.86	0.79	0.80	0.90	0.92	0.85
MLAFP-XN	0.69	0.85	0.86	0.79	0.81	0.89	0.92	0.85
ACP-ONE	0.70	0.86	0.87	0.80	0.82	0.90	0.93	0.86
DeepAIP	0.71	0.86	0.87	0.80	0.82	0.91	0.93	0.86
CKAN-ATHP	0.72	0.86	0.88	0.81	0.81	0.91	0.93	0.87

Performance comparison with state-of-the-art predictors

We summarized the key characteristics of the compared predictors, including their publication year, feature extraction strategies, model architectures, and validation schemes. Detailed information is provided in Supplementary Table S4.

As shown in Table 6, CKAN-ATHP achieves the best overall performance among all compared methods across most evaluation metrics. In particular, CKAN-ATHP attains the highest MCC (0.72), indicating superior balanced classification performance. Consistently high values are also observed for BACC, ACC (0.88), F1-score (0.81), AUC (0.93), and AP (0.87), demonstrating strong discriminative capability and reliable ranking performance under class-imbalanced conditions.

Table 6.

The comparison results with state-of-the-art methods

Method	MCC	BACC	ACC	F1	SE	SP	AUC	AP
mAHTPred	0.48	0.71	0.79	0.60	0.51	0.92	0.88	0.53
AHPred-DE	0.54	0.74	0.81	0.65	0.54	0.93	0.88	0.77
AHPCG	0.55	0.79	0.79	0.70	0.77	0.81	0.83	0.63
PAAP	0.55	0.81	0.82	0.65	0.82	0.80	0.86	0.72
pLM4ACE	0.56	0.77	0.82	0.68	0.66	0.88	0.88	0.57
AHTpin	0.56	0.79	0.82	0.69	0.85	0.74	0.88	0.78
LSTM-AHP	0.60	0.81	0.82	0.73	0.78	0.84	0.85	0.66
CKAN-ATHP	0.72	0.86	0.88	0.81	0.81	0.91	0.93	0.87

Several baseline methods exhibit relatively high specificity (SP); however, their MCC and BACC values remain comparatively lower. In contrast, CKAN-ATHP maintains balanced performance between sensitivity and specificity, as reflected by its MCC and BACC values.

To further assess robustness, five-fold cross-validation experiments were conducted, and the corresponding results are reported in Table 7. CKAN-ATHP achieves the highest mean values in MCC (0.66 ± 0.01) and BACC (0.83 ± 0.03), with consistent performance across ACC, F1-score, AUC, and AP. The small standard deviations across folds indicate stable performance under different data partitions.

Table 7.

The comparison with the state-of-the-art methods using fivefold cross validation

Method	MCC	BACC	ACC	F1	SE	SP	AUC	AP
AHPG	0.44 ± 0.22	0.73 ± 0.19	0.77 ± 0.05	0.56 ± 0.28	0.60 ± 0.30	0.85 ± 0.08	0.77 ± 0.14	0.57 ± 0.13
PAAP	0.49 ± 0.03	0.73 ± 0.03	0.79 ± 0.01	0.63 ± 0.03	0.57 ± 0.04	0.89 ± 0.02	0.83 ± 0.02	0.66 ± 0.04
mAHTPred	0.50 ± 0.03	0.73 ± 0.03	0.80 ± 0.01	0.62 ± 0.03	0.54 ± 0.04	0.91 ± 0.01	0.88 ± 0.02	0.79 ± 0.03
AHTpin	0.52 ± 0.04	0.74 ± 0.01	0.80 ± 0.02	0.65 ± 0.02	0.59 ± 0.02	0.90 ± 0.02	0.86 ± 0.02	0.76 ± 0.03
LSTM-AHP	0.53 ± 0.03	0.77 ± 0.03	0.79 ± 0.02	0.69 ± 0.02	0.74 ± 0.03	0.81 ± 0.03	0.84 ± 0.01	0.69 ± 0.03
AHPred-DE	0.55 ± 0.04	0.78 ± 0.09	0.80 ± 0.01	0.69 ± 0.05	0.73 ± 0.12	0.83 ± 0.05	0.87 ± 0.01	0.74 ± 0.02
pLM4ACE	0.55 ± 0.03	0.76 ± 0.09	0.81 ± 0.01	0.67 ± 0.05	0.64 ± 0.12	0.89 ± 0.05	0.88 ± 0.01	0.77 ± 0.02
CKAN-ATHP	0.66 ± 0.01	0.83 ± 0.03	0.85 ± 0.01	0.77 ± 0.01	0.78 ± 0.04	0.89 ± 0.02	0.91 ± 0.01	0.89 ± 0.02

Although CKAN-ATHP does not achieve the highest SP among all compared methods, its specificity remains at a comparable level while maintaining higher MCC and BACC values.

The ROC and PR curve comparisons shown in Fig. 5 further support these findings. CKAN-ATHP consistently exhibits superior curve coverage across a wide range of decision thresholds. In addition, the radar chart presented in Supplementary Fig. S3 illustrates the overall performance distribution, where CKAN-ATHP demonstrates clear advantages in MCC, BACC, AUC, and F1-score.

Fig. 5.

The ROC and PR curve of seven comparing methods on test datasets

Overall, these results show that CKAN-ATHP achieves competitive and stable performance compared with the evaluated state-of-the-art predictors under the current experimental setting.

Evaluation of sampling strategies based on AUC performance indicators

The experimental results of the sampling-based evaluation are presented in Fig. 6. Each point corresponds to a pair of AUC values obtained by CKAN-ATHP and a corresponding compared predictor on the same sampled subset, where the x-axis denotes the AUC of the compared model and the y-axis denotes the AUC of CKAN-ATHP. The diagonal line represents equal performance between the two models.

Fig. 6.

Sampling performance comparison based on AUC

As shown in Fig. 6, the majority of data points are distributed above the diagonal line across all compared predictors, indicating that CKAN-ATHP yields higher AUC values on most sampled subsets. Only a limited number of points appear near or below the diagonal line.

In addition, the distribution of points exhibits relatively low dispersion, suggesting consistent AUC performance of CKAN-ATHP under repeated sampling of the evaluation dataset. These results indicate that the relative performance advantage of CKAN-ATHP is maintained across different sampled subsets.

Occlusion-based identification of a key sequence region

Occlusion analysis shows that the model assigns noticeably higher importance to residues located at positions 4–7, as masking this region leads to the largest decrease in prediction probability. The mean residue importance scores across sequence positions are presented in Fig. S5, indicating that the model relies more heavily on this short segment than on other parts of the sequence when making predictions.

To further understand why this region is important, residue frequency analysis was performed. At the level of the entire dataset, ATHP sequences are mainly composed of residues P, Y, V, M, A, H, E, and T, as summarized in Supplementary Table S6. When focusing specifically on positions 4–7, residues P, Y, V, A, and M remain highly frequent, showing strong agreement with the global residue distribution, as reported in Supplementary Table S7. This overlap suggests that the model does not base its prediction on unusual or rarely occurring residues, but instead focuses on a region whose residue composition reflects the general characteristics of ATHP sequences.

In addition, residues G and T appear more frequently within positions 4–7 compared with their overall distribution. This indicates that, beyond capturing global sequence characteristics, the model is also sensitive to local residue preferences within this key region. Taken together, these findings support the relevance of positions 4–7 in model prediction and provide interpretative insight into residue-level contributions. Detailed methods and extended analyses are provided in Supplementary File S4.

Case study

A case study was conducted to validate the enhanced prediction and generalization capabilities of the proposed model. Seventeen experimentally verified antihypertensive peptide sequences, sourced from DFBP and excluded from the training and subsequent phases, were tested. The predicted scores across multiple models were compared. Here, the predicted score represents the probability output by each model for classifying a peptide as an antihypertensive peptide. The detailed prediction results and performance comparisons for these peptides are provided in Supplementary Table S5. Among the evaluated models, CKAN-ATHP, AHP_CNN-GRU, and pLM4ACE successfully identified these new ATHPs. However, compared to AHP_CNN-GRU and pLM4ACE, CKAN-ATHP's predicted probabilities were generally closer to the true label values. Higher prediction scores indicate that CKAN-ATHP's refined feature extraction and processing capabilities enable it to better recognize and differentiate subtle variations in peptide sequences. This suggests that features extracted by the pre-trained language model are more effective than traditional features. CKAN-ATHP correctly identified all new samples, with prediction results closely aligning with the true values. This demonstrates that the model maintains relatively high prediction probabilities across most data points, reflecting strong robustness. In comparison to other models, the prediction distribution of CKAN-ATHP is more uniform and tends to be higher, with no extremely low prediction probabilities, especially when handling complex and hard-to-distinguish data, where it performed particularly well. In addition, in order to more intuitively understand the prediction performance of different models for the case study dataset, we use a heat map to visualize the prediction results, as shown in Fig. 7.

Fig. 7.

Heatmap of prediction results for different models on the case study dataset

Kernel density estimation of predicted probabilities for CKAN-ATHP

The kernel density estimation of predicted probabilities for CKAN-ATHP is presented in Fig. 8, illustrating the distribution patterns of prediction scores for positive and negative samples on the independent test set.

Fig. 8.

The distribution of prediction probabilities on test dataset

The predicted probabilities of negative samples are predominantly concentrated at lower values, whereas positive samples exhibit distributions skewed toward higher probability ranges. A limited overlap between the two density curves is observed, corresponding to samples with intermediate prediction confidence.

Overall, the separation between the probability density distributions of the two classes indicates that CKAN-ATHP assigns distinct probability scores to positive and negative samples across the test set.

Confusion matrix heatmap for CKAN-ATHP

A detailed examination of misclassified samples reveals that errors are not randomly distributed, but are instead associated with specific sequence-level characteristics, including short sequence length, reduced hydrophobicity, and the absence of canonical C-terminal motifs (e.g., P, F, W, Y).

Among the false positives (FPs), the average peptide length was 7 residues, which is markedly shorter than the test set average of 14 residues. Sequences such as “IYVPPL” (length = 6, Prob₁ = 0.86) and “AYPWF” (length = 5, Prob₁ = 0.83) exemplify this pattern. Although both sequences are labeled as inactive, they contain prominent terminal or internal hydrophobic and aromatic residues, which likely contributed to high predicted activity. Notably, 31% of FP sequences end with Proline or an aromatic residue (F/W/Y), compared to 27% in the full dataset, suggesting increased reliance on C-terminal residue cues during positive prediction.

Conversely, false negatives (FNs), which are true AHTPs incorrectly predicted as inactive, tended to be slightly longer on average (10 residues) but exhibited weaker physicochemical signals. For instance, “VSLPEW” (length = 6, Prob₁ = 0.48) ends with W but lacks sufficient hydrophobic content elsewhere, while “RLSGQTIEVTSEYLFRH” (length = 17, Prob₁ = 0.06) is comparatively long and consists predominantly of polar residues without a clear C-terminal motif. Across all FNs, only 11% end in canonical terminal motifs, indicating that the absence of such motifs is associated with a higher likelihood of false-negative predictions.

Hydrophobicity further contributes to this trend. Using the standard set of hydrophobic residues (A, I, L, V, F, W, Y, M, C), the average hydrophobic content in the full test set is 41%, compared to 37% for FPs and 40% for FNs. In total, 62% of all misclassified peptides have fewer than 10 residues and hydrophobicity below 40%, highlighting a persistent difficulty in classifying short sequences with weak hydrophobic signals. These peptides lack sufficient structural or residue-level cues for confident categorization, resulting in predictions close to the decision boundary. Specifically, 48% of FPs and 54% of FNs have predicted probabilities within the range of 0.40 to 0.60.

This pattern is further supported by the confusion matrix heatmap (see Supplementary Fig. S4), which shows that accuracy and recall for both positive and negative classes are generally balanced. Nevertheless, the presence of false positive and false negative predictions indicates that a substantial number of sequences remain misclassified. From a practical perspective, false negatives are of particular concern, as they may result in the exclusion of peptides with genuine antihypertensive potential. Consequently, reducing the false-negative rate without substantially increasing false-positive errors is important for maximizing biological discovery. Approaches such as threshold calibration, cost-sensitive learning, or uncertainty-based post-filtering may be used to adjust decision boundaries in order to recover more true positives.

In addition, several FP examples, such as “GLVYP” (Prob₁ = 0.77) and “IPQPL” (Prob₁ = 0.72), illustrate a recurring pattern in which short sequences contain partial motif-like features but lack sufficient global characteristics. This suggests that local residue patterns alone may be insufficient for reliable classification. In contrast, FN examples such as “EHFFLGLA” (Prob₁ = 0.38) indicate that hydrophobic content by itself does not guarantee correct prediction when motif clarity is limited or sequence context is ambiguous.

Taken together, these observations indicate that the model’s misclassifications exhibit identifiable sequence-dependent tendencies rather than occurring randomly. Errors are primarily concentrated among short peptides with relatively low hydrophobicity and without distinct C-terminal motif features. This suggests that such peptides occupy a borderline region in the feature space, where the model has difficulty producing confident predictions. These findings provide insight into the current limitations of the model and reflect the inherent complexity of antihypertensive peptide classification.

Heatmap of predicted score distribution for CKAN-ATHP

The prediction score distribution of different models on the test dataset is illustrated in Fig. 9 using a heatmap. The predictions are generated by models trained on a dataset that excludes short peptide sequences. This visualization enables direct comparison of how multiple models assign prediction scores to the same samples. By encoding probabilities as color intensity, the heatmap visually reflects differences in prediction confidence across models.

Fig. 9.

Prediction score distribution of each comparing method on the test dataset

In this figure, the horizontal axis corresponds to different models, while the vertical axis represents the test samples arranged sequentially without specific numerical meaning. The vertical ordering is used to align samples across models for comparison. The color scale on the right indicates the prediction probability, where darker shades represent values closer to 1.0, corresponding to a higher likelihood of being an antihypertensive peptide, and lighter shades represent values closer to 0.0, corresponding to a higher likelihood of being a non-antihypertensive peptide.

The heatmap indicates that CKAN-ATHP exhibits a more concentrated score distribution compared with the other methods. AHTP sequences in the test set are predominantly mapped to darker regions, while non-AHTP sequences are generally concentrated in lighter regions. In contrast, the predictions of other models appear more dispersed, with a higher proportion of intermediate shades, suggesting less distinct separation between classes.

Taken together, these observations suggest that CKAN-ATHP provides clearer separation between positive and negative samples under the current experimental setting. The concentrated dark and light regions indicate that the model tends to produce more confident predictions compared with alternative approaches.

Discussion

The present study proposes CKAN-ATHP, a deep learning framework for antihypertensive peptide prediction that integrates heterogeneous feature representations derived from protein language models and chemical molecular descriptors. By combining DistilProtBert, ProtT5-XL-UniRef50, and PubChem10M embeddings, the proposed model captures complementary biological information spanning local sequence semantics, global contextual dependencies, and physicochemical properties, thereby enabling a more comprehensive characterization of peptide bioactivity.

Each feature representation contributes distinct information to the prediction task. DistilProtBert primarily models short-range contextual relationships among neighboring residues, which are particularly relevant for identifying discriminative local motifs. ProtT5-XL-UniRef50 captures long-range dependencies across entire sequences, providing holistic contextual representations even for moderately long peptides. In contrast, PubChem10M introduces a chemistry-oriented perspective by encoding physicochemical attributes such as hydrophobicity, charge distribution, and structural tendencies through SMILES-based representations. The fusion of these embeddings allows CKAN-ATHP to move beyond single-representation sequence modeling and incorporate complementary chemical information that is closely related to ACE inhibitory activity.

Although the resulting fused embeddings exhibit limited direct mechanistic interpretability at the residue or structural level, their biological relevance is supported by prior evidence that protein language models implicitly encode functional and physicochemical properties from large-scale training corpora. In this study, dimensionality reduction analyses using PCA, t-SNE, and UMAP further indicate that the fused feature space yields improved separability between antihypertensive and non-ATHPs. These observations suggest that the integrated feature space captures biologically meaningful signals rather than dataset-specific noise, supporting its utility for peptide activity prediction.

A key consideration in this work is whether the increased representational and architectural complexity provides meaningful advantages over simpler modeling strategies. It is therefore important to clarify that, at the feature representation and selection stage, performance evaluation was conducted using an ensemble classifier composed of LR, SVM, and MLP. This ensemble-based evaluation was intentionally adopted to assess the intrinsic discriminative capability of different feature representations while minimizing bias introduced by complex downstream models. The results reported in the corresponding section show that the selected feature representations achieve competitive performance under relatively simple classifiers, suggesting that the effectiveness of the proposed framework does not depend entirely on the complexity of the CKAN architecture.

Building upon these validated feature representations, CKAN-ATHP further enhances predictive performance by modeling nonlinear interactions among heterogeneous features. Rather than relying on excessive parameterization, the framework adopts a parameter-efficient design that leverages pre-trained representations, avoiding the need to train large models from scratch. In this context, the observed performance gains are associated with the integration of multiple information sources and the nonlinear modeling capacity of the Convolutional Kolmogorov-Arnold Network.

From a biological perspective, antihypertensive activity is known to depend on both local residue patterns and global sequence characteristics. The occlusion analysis performed in this study indicates that residues located at positions 4–7 are associated with noticeable changes in prediction outcomes, suggesting the relevance of this sequence region. Notably, the residue composition within this region shows substantial overlap with the global residue frequency distribution of ATHPs, suggesting that the model focuses on biologically reasonable sequence features rather than rare or anomalous patterns.

Analysis of misclassified samples further provides insight into the intrinsic difficulty of antihypertensive peptide prediction. False positive and false negative cases are predominantly associated with short peptides, weak hydrophobic signals, or incomplete terminal motif features, indicating that these sequences occupy a transitional region between active and inactive classes. This observation suggests that certain peptides exhibit ambiguous characteristics that may complicate clear classification between active and inactive categories.

Taken together, these findings suggest that CKAN-ATHP achieves stable predictive performance and maintains consistency across evaluation settings, supporting its applicability to antihypertensive peptide prediction.

Limitations and future work

Despite the encouraging performance of CKAN-ATHP, several limitations should be acknowledged, which also point to directions for future research.

First, the size of the available dataset is constrained by the limited number of experimentally validated ATHPs, resulting in approximately 2300 samples for training, validation, and testing. Although the use of pre-trained representations and regularization strategies helps mitigate overfitting, the current dataset may not fully capture rare or atypical peptide patterns. Future studies would benefit from larger, more diverse, and experimentally validated datasets to further improve model generalization.

Second, this study primarily focuses on mainstream feature representations derived from protein language models and chemical molecular descriptors. While these features demonstrate strong performance, other potentially informative modalities—such as structural predictions, evolutionary profiles, or peptide–target interaction features—were not extensively explored. Incorporating such information may further enhance predictive accuracy and biological interpretability.

Third, although multiple feature fusion strategies were evaluated, a comprehensive exploration of all possible feature combinations was not conducted due to computational constraints. The integration of large-scale pre-trained embeddings remains resource-intensive, and future work may investigate more efficient fusion mechanisms or lightweight representations to improve scalability.

Fourth, while loss function optimization and sample augmentation improve robustness under class imbalance, the observed performance gains remain moderate. Further research into imbalance-aware learning strategies, such as cost-sensitive learning, uncertainty-aware prediction, or adaptive threshold calibration, may help reduce false negatives without substantially increasing false positives.

Finally, although CKAN was compared with several representative deep learning architectures, the rapidly evolving landscape of sequence modeling suggests that additional architectures may yield further improvements. Future work will explore emerging models and hybrid architectures, as well as enhance interpretability through tighter integration of residue-level analysis and physicochemical reasoning.

Conclusion

In the past decade, ATHPs have gained increasing attention as potential therapeutic agents for managing hypertension. Despite their potential, conventional experimental approaches for identifying novel ATHPs remain labor-intensive, costly, and time-consuming. Recent progress in machine learning and computational biology has significantly streamlined the peptide discovery process, offering more efficient alternatives to traditional wet-lab screening.

In this work, we introduce CKAN-ATHP, a deep learning-based framework designed to predict ATHPs. A total of thirty-five features are utilized, including traditional handcrafted feature encodings, pre-trained model embeddings, and chemical molecular features of peptides. An ensemble learning model is employed to rank feature representations and select the top three for subsequent integration. Additionally, an effective analysis of the feature combinations is conducted. The results indicate that pre-trained models significantly contribute to the recognition of ATHPs.

Furthermore, an improved loss formulation is introduced to mitigate prediction overconfidence and support stable generalization. The process involves utilizing the optimal feature combination obtained from the feature selection phase, applying sample augmentation to balance positive and negative samples, and employing the CKAN as a classifier. The final classification is generated through a fully connected output layer. On the testing dataset, CKAN-ATHP demonstrates consistent improvements over existing approaches in MCC and BACC, with respective increases of approximately 12%–24% and 5%–15%.

This study introduces an improved approach for predicting ATHPs and contributes meaningful conceptual guidance for future studies on peptides with antihypertensive potential. Furthermore, it provides practical suggestions for researchers exploring the integration of pre-trained models and chemical structure information in feature extraction.

Abbreviations

AAC

Amino acid composition

ACC

Accuracy

ACE

Angiotensin-converting enzyme

AMP

Antimicrobial peptide

AP

Average precision

ATHP

Antihypertensive peptide

AUC

Area under the receiver operating characteristic curve

BACC

Balanced accuracy

CD-HIT

Clustering and database of high identity with tolerance

CKAN

Convolutional Kolmogorov–Arnold network

CNN

Convolutional neural network

DFBP

Food-derived bioactive peptide database

DL

Deep learning

DO-Conv

Depthwise over-parameterized convolution

F1

F1-score

FN

False negative

FP

False positive

GNN

Graph neural network

KAN

Kolmogorov–Arnold network

KDE

Kernel density estimation

KL

Kullback–Leibler divergence

MCC

Matthews correlation coefficient

MLP

Multilayer perceptron

PCA

Principal component analysis

PR

Precision–recall

RAS

Renin–angiotensin system

RF

Random forest

ROC

Receiver operating characteristic

SE

Sensitivity

SP

Specificity

t-SNE

T-distributed stochastic neighbor embedding

UMAP

Uniform manifold approximation and projection

Author contributions

Sen Yang: Conceptualization, Methodology, and Supervision. Jiaqi Ni: Data curation, Writing-Original draft preparation. Xinye Ni: Methodology,Visualization. Yan Wang: Methodology,Software. All authors reviewed the manuscript.

Funding

This research was funded by Natural Science Foundation of Jiangsu Province of China (Grant No. BK20230626), the National Natural Science Foundation of China (Grant No. 62502053), supported by the Open project of State Key Laboratory of Animal Biotech Breeding (Grant No. 2024SKLAB6-1), the Fourth Batch of Leading Innovative Talents Introduction and Training Projects under the Longcheng Talent Plan in Changzhou City (Basic Research and Innovation) (Grant No. CQ20230086) and also supported by Changzhou Sci&Tech Program (Grant No. CJ20241083). and Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. SJCX24_1670).

Availability of data and materials

The code and data are available at https://github.com/Njq0104/CKAN-ATHP. The data used in this manuscript were obtained from the following sources: DFBP (http://www.cqudfbp.net/); BIOPEP-UWM (https://biochemia.uwm.edu.pl/biopep/peptide_data.php); and AHTPDB (https://webs.iiitd.edu.in/raghava/ahtpdb/).

Declarations

Ethics approval and consent to participate

This article does not contain any studies with animals performed by any of the authors.

Competing interests

The authors declare no competing interests.