DeepStackVEGF a stacking ensemble deep learning framework for vascular endothelial growth factor prediction

Abstract

Vascular Endothelial Growth Factor (VEGF) plays a central role in angiogenesis, regulating both physiological processes such as wound healing, tissue repair, and bone formation, and pathological events including tumor progression, metastasis, and diabetic retinopathy. Due to its crucial role in vascular biology, VEGF serves as an important therapeutic target in anti-angiogenic drug development and precision medicine. However, conventional experimental methods for VEGF identification are costly and time-consuming, emphasizing the need for efficient computational approaches. To address this challenge, we introduce DeepStack-VEGF, an advanced deep learning framework designed for accurate and robust VEGF prediction. The model integrates diverse sequence-derived features, including physicochemical descriptors, sequential patterns, evolutionary information, and secondary structure motifs, further enhanced by pretrained embeddings from UniProt and ProtBert. Feature optimization was achieved using Support Vector Machine–Recursive Feature Elimination. DeepStack-VEGF employs a stacking ensemble of three architectures including Feedback Generative Adversarial Network Gated Recurrent Unit and Capsule Convolutional Neural Network each contributing distinct representational capabilities. Comprehensive evaluations demonstrate that the fused feature set and stacking ensemble substantially outperform individual models, achieving superior accuracy, robustness, and generalization. By combining deep learning with biological insight, DeepStack-VEGF provides a reliable and scalable computational framework for VEGF identification, supporting rational drug discovery, anti-angiogenic therapy design, and precision medicine applications.

Introduction

VEGF plays a vital role in various physiological activities, including tumor growth, embryonic development, and wound healing. It is produced by several cell types, such as tumor cells, macrophages, and endothelial cells¹. VEGF is a pivotal signaling protein that drives angiogenesis, the formation of new blood vessels. When tissues require increased blood flow, such as during embryonic development or wound healing, VEGF production is upregulated locally. By promoting the growth, migration, and survival of endothelial cells, VEGF enables the formation of a robust vascular network².

VEGF is also critical for bone formation, as it coordinates blood vessel growth with bone tissue development. It stimulates the proliferation and differentiation of osteoblasts, the cells responsible for synthesizing the bone matrix. Adequate blood vessel formation ensures the efficient delivery of nutrients and oxygen to bone cells, maintaining optimal bone health. Conversely, dysregulated VEGF signaling can contribute to bone-related diseases, including impaired fracture healing and osteoporosis³.

In addition, VEGF is a key driver of tumor angiogenesis, allowing cancer cells to access the nutrients and oxygen required for growth and metastasis. Targeting VEGF through anti-angiogenic therapies has become a promising strategy for cancer treatment. Drugs such as bevacizumab, sorafenib, and sunitinib inhibit VEGF signaling, effectively disrupting the tumor’s blood supply and hindering its growth⁴. Anti-VEGF therapies, often administered via intravitreal injections, are also used to manage various ocular diseases by targeting abnormal angiogenesis. These treatments are frequently combined with chemotherapy or radiation therapy, representing a significant advancement in both cancer and eye care⁵.

One major challenge in developing treatments with VEGF lies in determining its precise structure. Scientists typically use methods such as Crystallography⁶, Nuclear Magnetic Resonance (NMR) Spectroscopy⁷, and Immunohistochemistry (IHC)⁸ to study VEGF. While effective, these techniques are expensive, time-consuming, and labor-intensive.

Deep learning (DL) has emerged as a powerful paradigm with the potential to transform computational protein analysis by offering improved speed, accuracy, and deeper biological insight. DL-based tools facilitate the identification of novel therapeutic targets and enhance understanding of VEGF behavior under both physiological and pathological conditions. Existing approaches, such as Deep-VEGF⁹ and VEGF-ERCNN¹⁰, have demonstrated the feasibility of integrating DL architectures with evolutionary features derived from position-specific scoring matrices (PSSMs)¹¹. Although these methods report encouraging predictive performance, several key limitations remain. First, their strong dependence on handcrafted evolutionary descriptors restricts their ability to capture higher-order semantic, structural, and long-range contextual information inherent in protein sequences. Second, most existing models do not leverage modern protein language models (PLMs)¹², which have proven effective in learning rich representations that encode protein structure, function, and evolutionary relationships directly from raw sequences. Third, the absence of systematic interpretability analyses constrains the biological interpretability and experimental applicability of current predictors, limiting their utility for downstream biological validation and translational research.

To overcome the limitations of existing VEGF prediction methods, we propose DeepStack-VEGF, a stacking ensemble deep learning framework designed to more comprehensively model the complex sequence–function relationships of VEGF proteins. Unlike prior approaches that rely primarily on handcrafted evolutionary descriptors, DeepStack-VEGF integrates multi-source information derived from protein sequences, capturing complementary physicochemical, evolutionary, sequential, structural, and contextual characteristics that are essential for accurate VEGF identification.

The predictor incorporates representations learned from modern protein language models, which are capable of encoding long-range dependencies and higher-order semantic information that traditional feature descriptors often fail to capture. These learned embeddings are combined with carefully designed sequence- and structure-based descriptors to form a rich and diverse feature space. To mitigate redundancy and noise inherent in such high-dimensional representations, a discriminative feature selection strategy namely Support Vector Machine-Recursive Feature Elimination (SVM-RFE)¹³ is employed to retain only the most informative features for classification.

The selected features are then analyzed using a stacking ensemble of DL models including Feedback Generative Adversarial Network (FBGAN)¹⁴, Capsule Convolutional Neural Network (CapCNN)¹⁵, and Gated Recurrent Unit (GRU)¹⁶, where each base learner is tailored to capture distinct biological patterns, such as sequential dependencies, hierarchical motif relationships, and robust feature transformations. By integrating the outputs of multiple complementary models through a meta-classifier, DeepStack-VEGF effectively leverages their individual strengths and improves prediction stability and generalization.

The proposed method is systematically evaluated using fivefold cross-validation and independent testing, demonstrating superior performance compared with existing VEGF predictors. The results highlight the effectiveness of integrating protein language model embeddings with ensemble deep learning strategies, leading to a more accurate solution for VEGF prediction. An overview of the proposed framework is illustrated in Fig. 1.

Fig. 1.

Graphical view of the proposed model. Initially, we collected VEGF and non-VEGF sequences from PDB, UniProt, and Pfam and constructed training and testing datasets. Features are explored by NMBAC, S-PSSM-ACT, GDPC, KSCTD, TAC, UniRep, ProtBert, and combined Fused-set. Model training is performed via CapCNN, GRU, and FBGAN. These algorithms are ensembled by stacking and perform prediction of VEGF and non-VEGF.

Material and methods

Dataset selection criteria

The datasets used in this study were constructed following a systematic and reproducible protocol, consistent with established practices in computational protein classification and our prior related studies⁹,¹⁰. Protein sequences were collected exclusively from publicly available databases to ensure data reliability, annotation accuracy, and reproducibility. VEGF and non-VEGF protein sequences were retrieved from UniProt¹⁷, Protein Data Bank (PDB)¹⁸, and Pfam¹⁹, based on explicit functional annotations and family/domain assignments. UniProt was used as the primary source due to its high-quality manually reviewed annotations, while PDB sequences were included to introduce experimentally resolved structural diversity. Pfam was incorporated to capture domain- and family-level variation across VEGF-related and non-VEGF proteins.

In total, 1,191 VEGF and 1,158 non-VEGF sequences were obtained from UniProt, 456 VEGF and 502 non-VEGF sequences from PDB, and 747 VEGF and 729 non-VEGF sequences from Pfam. All sequences were collected in FASTA format and cross-checked to remove duplicates across databases.

Preprocessing steps

To ensure dataset quality and minimize noise, several preprocessing steps were applied. First, protein sequences shorter than 50 amino acids were excluded, as very short sequences often lack sufficient contextual information for reliable feature extraction and classification. This length threshold has been widely adopted in protein prediction studies to improve model robustness.

Second, sequence redundancy was reduced using the CD-HIT clustering algorithm^20,21 with a 40% sequence identity cutoff. This threshold was selected to balance sequence diversity and dataset size, ensuring that closely related homologous sequences did not bias the learning process. From each cluster, only one representative sequence was retained, thereby improving the generalizability of the trained models and preventing overfitting to highly similar samples.

Final dataset composition and partitioning

After preprocessing and redundancy reduction, the final dataset was divided into training and independent testing subsets using a 90:10 split ratio²², a commonly adopted strategy in machine learning-based bioinformatics studies. Specifically, 2,058 VEGF and 2,045 non-VEGF sequences were assigned to the training set, while 229 VEGF and 228 non-VEGF sequences were reserved for independent testing.

Feature encoding methods

Physicochemical properties

Physicochemical properties are fundamental to understanding and predicting protein functionality, forming the basis for numerous computational approaches in bioinformatics²³. In this study, we considered six key physicochemical descriptors: hydrophobicity (H), side-chain volume, polarizability, polarity, net charge index of side chains, and solvent-accessible surface area. To generate feature representations from these descriptors, we applied the Normalized Moreau–Broto Autocorrelation (NMBAC)²⁴. NMBAC quantifies the degree of correlation between amino acid residues based on their physicochemical characteristics. The correlation values are computed according to the spatial distribution of amino acids along the sequence, where each protein is encoded as a vector of normalized physicochemical property scores. This representation captures intrinsic structural patterns that are critical for accurate protein function prediction.

1

2

where denotes the specific physicochemical descriptor, indicates the positional index of a residue within the sequence , corresponds to the total number of residues in the sequence, and defines the sequential spacing between two residues under comparison.

We calculated the optimal lag values ranging from 1 to 30, as suggested by Guo et al. (2008). This resulted in 30 × 6 = 180 features for each protein sequence derived from the six physicochemical properties. Additionally, we computed the frequency of the 20 amino acids, yielding another 20 features. Thus, the final feature dimension for each protein sequence totaled 30 × 6 + 20 = 200.

Slice-position specific scoring matrix-autocorrelation transformation

Correlation information between amino acids can provide valuable insights into protein function^25,26. To capture this information, we employed a method called S-PSSM-ACT. In this approach, the PSSM is initially split into three slices to capture local amino acid patterns. Subsequently, an autocorrelation transformation (ACT) is applied to each slice to determine the correlation information between amino acids. The ACT for each slice is determined using , , and expressions, which are listed below.

3

4

5

where, are the correlation factors and is the difference between residues.

The S-PSSM-ACT method captures the evolutionary information encoded in PSSMs, which highlights residue-level conservation across homologous sequences. Dividing PSSMs into slice enables the analysis of local patterns, offering a structured representation of sequence segments. Additionally, the autocorrelation process identifies correlations between amino acids, revealing critical evolutionary and structural dependencies essential for protein function²⁷. This method has several advantages. It focuses on evolutionary information to identify biologically significant patterns. The data is compressed into a compact, 60-dimensional vector, reducing computational overhead while retaining essential features.

Grouped dipeptide composition

Simple dipeptide composition (DPC)¹⁹ deliberates the frequency of all possible pairs of consecutive residues in a protein sequence. GDPC is an enhanced version of DPC that classifies the 20 residues into five groups on the basis of their physical properties. These five groups, labeled G1, G2, G3, G4, and G5, are:

• G1: Hydrophobic amino acids (Val, Leu, Ile, Pro, Phe, Trp, Met)

• G2: Small hydrophilic amino acids (Gly, Ala, Ser, Thr)

• G3: Acidic amino acids (Asp, Glu)

• G4: Basic amino acids (Lys, Arg, His)

• G5: Aromatic amino acids (Tyr, Phe, Trp)

Grouping amino acids, GDPC can capture more subtle patterns in protein sequences. GDPC groups amino acids together based on their chemical properties, which allows us to extract more informative features from protein sequences. The dimension of GDPC is expressed as:

6

where, is the number of groups, represents the frequency of dipeptide of residues, and is the peptide sequence length.

GDPC enhances traditional dipeptide composition by grouping amino acids based on their physicochemical properties, such as hydrophobicity, acidity, and size. This grouping allows it to capture subtle patterns in protein sequences while leveraging the biological relevance inherent in amino acid groupings²⁸.

GDPC reduces noise caused by individual amino acid variability and highlights biologically meaningful patterns. Its low-dimensional, 25-vector representation ensures computational efficiency. Additionally, it encodes chemical behavior, making the extracted features more interpretable and aligned with the protein’s functional characteristics²⁹.

K-spaced conjoint triad descriptor

KSCTD²⁰ is implemented and described in this section following the text and procedure originally reported in our prior works³⁰, and was adapted from the iFeature framework³¹. It is a sequence-based feature extraction method designed to quantify structural and functional characteristics of protein sequences through the analysis of residue group patterns.

The KSCTD algorithm is based on the concept of triad groups of three amino acids, which capture local sequence motifs critical for protein structure and function³². Unlike conventional triad-based descriptors, KSCTD incorporates a k-spacing parameter that allows residues within a triad to be separated by k positions along the sequence. This design enables the extraction of both local and long-range sequence dependencies, effectively capturing non-local residue interactions that are important for modeling protein functionality and structural organization³³.

For each protein sequence, KSCTD generates a fixed-length 343-dimensional feature vector that encodes the frequency distribution of spaced conjoint triads. This representation provides a compact yet informative description of sequence patterns and is particularly suitable for downstream deep learning models used in this study.

Secondary structure-based profile

Secondary structure (SS)³⁴ of proteins refers to the local spatial arrangement of the polypeptide backbone, stabilized by hydrogen bonds. These structures are categorized into regular patterns, primarily alpha-helices (α-helices), beta-sheets (β-sheets), and random coils. These arrangements are crucial for the overall protein function. The most crucial types of SS are listed below.

Secondary structure composition SSC³⁵ plays a critical role in understanding protein structure and function. It provides insights into the proportion of alpha-helices, beta-sheets, and random coils in a protein, which are directly associated with its functional properties³⁶. For instance, proteins rich in alpha-helices are often involved in flexible binding interactions or serve as structural elements in membranes, whereas those with high beta-sheet content typically have roles in structural stability or enzymatic activity. SSC is a key determinant in understanding the biochemical roles of protein.

This approach parallels amino acid composition analysis, but instead of quantifying the frequency of individual amino acid residues, it focuses on the occurrence of specific sequence patterns. SSC can be computed as:

7

where, is protein length and

8

Here, the secondary structure at position , denoted as , represents the structural motif (e.g., α-helix, β-sheet, or random coil) at that specific position in the protein sequence, while corresponds to one of the three distinct structural motif symbols.

Torsional Angles Auto-Covariance Torsional angles³⁷, specifically phi (ϕ) and psi (ψ) angles, are critical dihedral angles in a protein’s backbone that define its local conformation and secondary structure. These angles describe the rotation around bonds between atoms in the polypeptide chain and play a key role in determining the folding and spatial arrangement of the protein. TAC³⁸ is a mathematical representation that captures the correlation between torsional angles at different positions along the protein sequence. It provides insights into the spatial dependencies and structural patterns within the protein, making it an essential secondary feature in computational models for tasks like protein fold recognition, stability prediction, and function annotation.

TAC captures correlations between torsional angles at different sequence positions, reflecting the interdependence of residues in forming the overall secondary structure. This is particularly useful for identifying structural motifs like helices or beta-sheets. Since torsional angles define secondary structure elements, the TAC feature provides a quantitative way to encode secondary structure properties. This allows computational models to leverage spatial patterns in the protein for improved accuracy.

To compute the TAC, the process begins with extracting the torsional angles from the protein structure. Specifically, the phi (φ) and psi (ψ) angles are obtained for each residue in the protein sequence. These angles describe the rotation around the bonds in the polypeptide backbone, providing key structural information³⁹. Once the torsional angles are extracted, they are standardized to account for periodicity. This normalization can be achieved by converting the angles into a range using sine and cosine transformations. Standardizing the angles ensures that the computations are robust and not affected by the cyclical nature of the dihedral angles⁴⁰.

The next step is to compute the auto-covariance for a given lag value (). This involves calculating the covariance between the torsional angle at position and the angle at position . The formula for this is given by:

9

where represents the total number of residues in the sequence, is the mean of the torsional angles, and is the lag value. This step captures the correlation between angles at specific distances within the sequence, providing insights into structural dependencies. To fully capture these dependencies, the TAC is computed for a range of lag values, typically from to a predefined . This ensures that correlations over varying sequence distances are taken into account, representing both short-range and long-range interactions within the protein. Finally, the TAC values for φ and ψ angles across all lags are combined to create a feature vector. In this study, we found that the best results were achieved when k = 26, resulting in 80-dimentional vector.

Protein Language Models PLMs⁴¹ are advanced computational frameworks inspired by natural language processing techniques that are applied to protein sequences. These models treat protein sequences as “biological languages”, where the amino acid sequences (composed of 20 standard amino acids) are analogous to sentences made up of words. Using deep learning architectures, PLMs learn patterns, relationships, and functional motifs from massive datasets of protein sequences⁴². In this work, we implemented UniRep and ProtBert, which are detailed below.

UniRep UniRep²⁰ protein language model employs Long Short-Term Memory (LSTM)⁴³ neural networks as its core architecture. The model undergoes an intensive training process, where it predicts the next amino acid in a sequence and compares its predictions to the actual sequence data. This iterative process gradually optimizes the parameters of the LSTM network, enhancing its predictive accuracy.

UniRep generates a unique feature representation for each protein sequence by averaging the activations of the hidden units across multiple LSTM layers. Trained on a large-scale dataset comprising approximately 24 million protein sequences from the UniRef50 database, UniRep’s training was conducted over three days using multiple GPUs to ensure convergence and model robustness. A key strength of UniRep lies in its ability to encode protein sequences of varying lengths into a fixed 1900-dimensional feature vector. This standardized representation enables seamless integration into downstream analyses and facilitates comparisons across proteins. Additionally, UniRep exhibits a remarkable capacity to cluster protein sequences with low sequence identity into groups that share significant structural similarities, highlighting its ability to capture higher-order sequence-structure relationships⁴⁴.

In this study, UniRep was utilized to extract feature representations for VEGF. By encoding these peptides into 1900-dimensional feature vectors, UniRep effectively captured their global features, providing a rich and comprehensive representation for subsequent computational analyses. This enables a deeper understanding of VEGF and enhances predictive modeling in related tasks.

ProtBert ProtBert⁴⁵ protein language model is built upon the Transformer architecture and is pretrained on an extensive dataset containing over two billion protein sequences derived from UniRef protein databases. This large-scale training allows ProtBert to capture the complex statistical and biological patterns embedded in protein sequences. By leveraging the power of its architecture, ProtBert encodes protein sequences of varying lengths into consistent 1024-dimensional feature vectors, enabling a unified representation suitable for downstream tasks.

A distinctive strength of ProtBert lies in its use of the multi-head attention mechanism, a core component of the Transformer architecture⁴⁶. This mechanism enables the model to effectively capture both local and global features of protein sequences. While the local features reflect the sequence-level motifs and short-range dependencies, the global features encapsulate long-range interactions and overall sequence characteristics, providing a comprehensive understanding of the protein.

ProtBert has the ability to generate high-quality feature representations, which contributes significantly to its strong performance in these tasks⁴⁷. In this study, ProtBert was employed to extract feature representations from VEGF. By encoding the VEGF into 1024-dimensional feature vectors, the model captured both global and local features of the sequences, enabling an informative representation for subsequent analyses.

Concatenation of multi-source protein feature fusion The concatenation of diverse features, such as physicochemical properties, S-PSSM-ACT, GDPC, KSCTD, secondary structure features, and PLMs, creates a comprehensive representation of proteins. Each of these features contributes unique insights into various aspects of protein structure and function, enhancing the ability to capture both specific and global characteristics. This integrated approach provides a more accurate and complete understanding of proteins, ultimately improving predictive models.

Physicochemical properties, such as hydrophobicity and charge, are fundamental to understanding protein behavior. These properties influence critical aspects of protein structure, including folding, stability, and interactions⁴⁸. They provide valuable insights into how proteins function and serve as the basis for structural predictions. By incorporating these properties, the model captures intrinsic characteristics that are essential for understanding protein dynamics.

S-PSSM-ACT captures evolutionary information embedded within protein sequences⁴⁹. This feature highlights conserved residues and their interactions, offering an evolutionary perspective on protein function. By analyzing how specific residues are conserved across homologous sequences, S-PSSM-ACT helps uncover important functional and structural dependencies that may not be apparent from sequence alone.

GDPC enhances the traditional dipeptide composition method by classifying amino acids into five groups based on their chemical properties. This grouping helps capture subtle patterns in protein sequences, reducing the noise that may arise from individual amino acid variability⁵⁰. The result is a more interpretable and biologically relevant representation of protein sequences, which improves the model’s ability to identify functional motifs and relationships.

KSCTD focuses on long-range residue interactions, which are often crucial for protein function. This feature extracts informative patterns by considering the spatial arrangement of triads of consecutive amino acids. KSCTD allows the model to capture both local motifs and distant interactions between residues, providing a more comprehensive view of sequence properties and enhancing the understanding of protein function.

Secondary structure features, such as SSC and TAC, are directly related to the protein’s architecture. SSC provides insights into the distribution of α-helices, β-sheets, and random coils, which are essential for understanding protein function⁵¹. Meanwhile, TAC captures the spatial dependencies between torsional angles, offering a quantitative representation of the secondary structure elements and their interactions. These features are crucial for predicting protein stability and function.

PLMs, like UniRep and ProtBert, offer advanced tools for extracting rich feature representations from protein sequences. These models leverage DL techniques to capture complex patterns and relationships within sequences. PLMs are particularly powerful because they encode both local motifs and global sequence context, allowing them to reveal intricate structural and functional relationships that are often difficult to detect with traditional methods.

The combination of these diverse feature sets provides a multidimensional view of protein sequences. By integrating features that reflect different biological, structural, and functional aspects of proteins, this approach enhances the robustness and accuracy of predictive models. The various features complement one another, offering a richer biological context that leads to a more reliable and comprehensive understanding of proteins.

Furthermore, the integration of these features helps reduce noise while maintaining biologically meaningful patterns. Methods like GDPC and secondary structure features simplify the data by focusing on relevant structural elements, improving the interpretability of the model. By bridging both local residue-level details and global sequence-level context, the concatenation of these features enables the model to make more informed and accurate predictions. The concatenation of all feature sets is referred to as fused set in this manuscript. The dimensional vector of each method is listed in Table 1.

Table 1.

Dimensional vector of each method.

S.#	Method	Dimension
1	NMBAC	200
2	S-PSSM-ACT	60
3	GDPC	25
4	KSCTD	343
5	SSC	3
6	TAC	80
7	UniRep	1900
8	ProtBert	1024
	Total	3635

SVM-RFE (Support Vector Machine-Recursive Feature Elimination) is a powerful feature selection technique that uses SVM classifier to iteratively eliminate less important features. This process results in a ranked list of features based on their importance. It is particularly effective for high-dimensional datasets.

Working mechanism: The working of SVM-RFE begins with all features included in the dataset. An SVM model with a linear kernel is trained to classify the data by determining a hyperplane that separates the classes. The importance of each feature is then calculated based on the magnitude of its weight in the decision boundary equation⁵². Features with smaller weights have less impact on the classification and are considered less significant. Using the squared weight values, all features are ranked, and the least important feature is eliminated. The SVM is retrained on the reduced feature set, and this process continues recursively until a predefined number of features remain or all features are ranked. The final order of elimination provides the ranking of feature importance, with the last feature removed being the most significant⁵³.

One of the key merits of SVM-RFE is its ability to handle high-dimensional data, especially in cases where the number of features exceeds the number of samples. It produces interpretable results by ranking features based on their importance and often leads to higher classification accuracy by focusing only on the most relevant features⁵⁴. After the selection process, the best feature subset is presented in Table 2.

Table 2.

List of the best feature subset.

S.#	Method	Dimension
1	NMBAC	123
2	S-PSSM-ACT	47
3	GDPC	14
4	KSCTD	203
5	SSC	3
6	TAC	67
7	UniRep	1134
8	ProtBert	754
	Total	2345

It is also robust in handling noisy data, as irrelevant features are ranked lower and eventually removed. SVM-RFE was used to perform feature ranking and selection on the feature sets derived from NMBAC, S-PSSM-ACT, GDPC, KSCTD, TAC, UniRep, and ProtBert. Significant features were determined based on their ranks, and only those features that contributed to enhancing model performance were selected. The rankings of all features are provided in the supplementary file.

Model training

This study employs a stacking-based DL that integrates FBGAN, CapCNN, and GRU. Each component is designed to capture complementary characteristics of protein sequence representations derived from NMBAC, S-PSSM-ACT, GDPC, KSCTD, TAC, UniRep, ProtBert, and the combined Fused-set. The architectural design, training strategy, and optimization objectives of each model are described in detail to ensure reproducibility and clarity. Each framework details are described in the subsequent sections.

Feedback generative adversarial network

A FBGAN is a type of GAN that incorporates a feedback strategy to enhance the superiority of outputs. It consists of two neural networks: a generator and a discriminator. These networks compete in a zero-sum game⁵⁵. The generator’s goal is to produce synthetic data that is indistinguishable from real data. Conversely, the discriminator’s objective is to accurately classify input data as either real or generated. A FBGAN modifies this framework by adding a feedback loop from the discriminator to the generator, enhancing the generator’s learning by providing more refined information on how to improve its outputs⁵⁶.

The FBGAN is incorporated as a feature enhancement and regularization module to improve the robustness of learned protein representations. The generator network receives a 100-dimensional latent noise vector as input and consists of two fully connected layers with 256 and 512 neurons, respectively. ReLU activation functions are used in the hidden layers, while a Tanh activation is applied at the output layer to generate synthetic feature representations⁵⁷. The discriminator network is designed to distinguish real protein embeddings from generated ones and consists of two dense layers with 512 and 256 neurons, respectively, followed by LeakyReLU activation with a slope coefficient of 0.2 and a dropout rate of 0.3 to prevent overfitting. A sigmoid activation function is used in the output layer to produce a probability score indicating whether an input feature vector is real or synthetic.

A feedback mechanism is implemented by propagating discriminator gradients and confidence information back to the generator, enabling iterative refinement of synthetic features. Both generator and discriminator are optimized using binary cross-entropy loss and trained using the Adam optimizer with a learning rate of 0.0002, β₁ set to 0.5, and β₂ set to 0.999. The FBGAN is trained for 200 epochs with two feedback iterations per epoch. In the context of globular protein classification, this module enhances feature diversity and stability, reducing distributional sparsity and improving downstream classification robustness.

Capsule convolutional neural network

CapCNN is an advanced neural network framework constructed to address the shortcomings of conventional CNNs⁵⁸, mostly in understanding spatial hierarchies and handling variations in object orientation, scale, and position. Capsule networks were introduced by Geoffrey Hinton to improve feature representation and create more robust models for tasks like object recognition⁵⁹.

The CapCNN is employed as a primary feature extractor and classifier to preserve hierarchical relationships among amino acid motifs encoded in protein embeddings. The network begins with a convolutional layer consisting of 256 filters and a kernel size of 3, using ReLU activation to capture local motif-level patterns. The output of this layer is passed to a primary capsule layer composed of 32 capsules, each with an eight-dimensional output vector. These capsules encode the presence and properties of local features. A digit capsule layer with a 16-dimensional output vector is then used to represent class-level information, with dynamic routing applied over three iterations to replace traditional max-pooling operations. This routing mechanism allows the network to preserve spatial and hierarchical dependencies among features⁶⁰. A dropout rate of 0.3 is applied during training to improve generalization.

The CapCNN is trained using a margin loss function, which encourages the correct class capsules to have larger vector magnitudes while suppressing incorrect ones. The model is optimized using the Adam optimizer with a learning rate of 0.0005 and trained for 100 epochs. This architecture is particularly effective for globular protein identification, as it retains relative positional and hierarchical relationships among sequence motifs that are essential for distinguishing protein structures⁶¹.

Gated recurrent unit

A GRU is designed to handle sequential data by capturing dependencies over time without suffering from vanishing gradients. GRUs were developed as a simpler and more efficient alternative to Long Short-Term Memory (LSTM), using fewer parameters while still effectively learning long-term relationships in data sequences⁶².

The GRU model is employed to capture sequential dependencies within protein feature representations, particularly long-range contextual information present in transformer-based embeddings²⁴. The network consists of two bidirectional GRU layers with 128 hidden units per layer, enabling the model to process sequence information in both forward and backward directions. A dropout rate of 0.4 and a recurrent dropout rate of 0.2 are applied to reduce overfitting and stabilize training. The output of the GRU layers is passed through a fully connected layer with 64 neurons, followed by a sigmoid activation function to produce the final prediction.

The GRU model is trained using binary cross-entropy loss and optimized with the Adam optimizer at a learning rate of 0.001. Training is conducted for 80 epochs with a batch size of 64, and early stopping with a patience of 10 epochs is employed to prevent overfitting. The GRU component enables the model to effectively learn long-range dependencies that are not explicitly captured by convolutional or capsule-based architectures⁶³.

Stacking-based DL learning

Stacking-based deep ensemble learning is an advanced technique that concatenates multiple models to boost a model’s performance⁴³. In this approach, CapCNN, FBGAN, and GRU are stacked in a layered fashion. Each model specializes in different aspects of data representation, and their outputs are combined to create a stronger predictive system, often achieving better results than any individual model.

Working mechanism

In a stacking-based deep ensemble learning approach (referred as DeepStack), CapCNN, FBGAN, and GRU models are each selected for their unique strengths in data representation. CapCNNs capture spatial hierarchies and complex features within the data, especially useful for recognizing patterns that vary in orientation and scale⁶⁴. FBGANs contribute by generating synthetic data that reflects the underlying data distribution, enhancing model robustness through iterative feedback and reducing overfitting. Meanwhile, GRUs handle sequential data effectively, capturing temporal dependencies and managing information flow through gating mechanisms, which helps the model retain or forget information as needed. Together, these models are trained independently and then combined in a meta-learning layer to advance predictive performance.

In the stacking process of this ensemble learning approach, each model is trained independently on the same dataset or on different segments, capturing unique aspects of the data. CapCNN focuses on spatial relationships, FBGAN generates synthetic data to capture distributional nuances, and GRU addresses temporal dependencies. Once these models have been trained, their predictions are fed into a meta-learner, commonly a simple model like logistic regression, that learns to combine the strengths of each base model. This meta-learning step averages insights from each model, optimizing for both accuracy and robustness by leveraging the individual strengths of each component.

In the prediction phase, new input data is passed through each of the stacked models, with each model independently processing the data to capture its spatial, sequential, and distributional characteristics. The outputs from these models are then combined by the meta-learner, which aggregates their results to produce a final prediction. This ensemble approach allows the model to deliver a comprehensive prediction that benefits from the diversity of insights captured by CapCNN, FBGAN, and GRU, enhancing the overall performance and generalization of the model.

Hyperparameter tuning of DL algorithms during model training

To ensure reproducibility and fair comparison across models, all experiments were conducted using fixed random seeds and consistent training protocols. Model hyperparameters were selected using grid search approach. The hyperparameters and their values are listed in Table 3.

Table 3.

Hyperparameter settings and training configuration.

Model	Parameter	Value	Notes
General	Random seed	42	Used across NumPy, DL framework, CUDA
GRU	Layers/hidden units	2 layers/128 units	Bidirectional GRU
	Dropout/recurrent dropout	0.4/0.2	Regularization
	Optimizer/LR	Adam/0.001	Binary Cross-Entropy loss
	Batch Size/epochs	64/80	Early stopping = 10
CapCNN	Conv Filters/kernel	256/3	He normal init
	Capsule Dimensions	Primary = 8, Digit = 16	Routing iterations = 3
	Optimizer/LR	Adam/0.0005	Margin loss
	Batch Size/epochs	64/100	Dropout = 0.3
FBGAN	Latent dimension	100	Generator input
	Generator layers	256, 512	ReLU/Tanh
	discriminator layers	512, 256	LeakyReLU (0.2)
	Optimizer/LR	Adam/0.0002	β1 = 0.5, β2 = 0.999
	Batch Size/epochs	128/200	Feedback iterations = 2

Model assessment methods

To ensure the robustness of the proposed model, it was validated using established methodologies. A popular approach in bioinformatics is fivefold cross-validation (CV)^65,66. Model performance was evaluated using metrics, like Matthews Correlation Coefficient (MCC), specificity (Sp), accuracy (Acc), sensitivity (Sn), Precision (Pre), F1-score (F1), and area under curve (AUC). These metrics are computed using equations below.

10

11

12

13

14

15

represents correctly identified VEGF, while denotes non-VEGF that are correctly predicted. Similarly, represents non-VEGF that are predicted as VEGF, and refer to VEGF mistakenly identified as non-VEGF.

Results and discussion

Results analysis of DL models

Table 4 provides a comprehensive comparison of the performance achieved by various deep learning models, including GRU, FBGAN, CapCNN, and DeepStack, across multiple feature representation techniques, such as NMBAC, S-PSSM-ACT, GDPC, KSCTD, TAC, UniRep, ProtBert, and the combined Fused-set. Performance is evaluated using accuracy, sensitivity, specificity, and MCC, offering detailed insights into how each model and feature representation strategy contributes to predictive accuracy and robustness. NMBAC provides a baseline with relatively low discriminative power. Among the classifiers, DeepStack yields the highest performance for this feature set, with an accuracy of 79.76% and MCC of 0.687, indicating its ability to optimize even simple feature representations. S-PSSM-ACT shows improved results compared to NMBAC due to its ability to capture evolutionary information.

Table 4.

Comparison of DL models performance before feature selection.

Model	Feature	Acc (%)	Sn (%)	Sp (%)	Pre (%)	F1 (%)	AUC (%)	MCC
GRU	NMBAC	76.65	75.56	77.98	77.92	76.72	81.77	0.643
	S-PSSM-ACT	78.98	77.09	78.99	79.47	78.26	83.04	0.664
	GDPC	75.43	76.42	75.28	74.41	75.41	80.35	0.632
	KSCTD	76.87	76.46	76.95	77.35	76.91	81.7	0.646
	SSC	78.81	79.22	77.12	78.44	78.83	83.17	0.664
	TAC	77.16	78.34	79.31	78.79	78.56	82.82	0.653
	UniRep	81.73	83.22	82.46	80.36	81.76	86.84	0.697
	ProtBert	83.41	83.68	83.97	83.96	83.82	88.83	0.713
	Fused set	85.76	85.58	85.32	85.07	85.32	90.55	0.737
FBGAN	NMBAC	75.21	76.56	74.96	73.89	75.21	80.11	0.634
	S-PSSM-ACT	77.55	77.74	78.02	78.3	78.02	82.88	0.652
	GDPC	75.14	76.43	75.98	75.56	76.0	80.56	0.639
	KSCTD	76.83	77.33	76.09	76.42	76.87	81.71	0.647
	SSC	78.17	79.69	78.16	77.22	78.44	83.92	0.663
	TAC	79.01	80.13	79.48	78.88	79.5	84.75	0.676
	UniRep	82.54	83.47	81.88	81.95	82.66	87.68	0.680
	ProtBert	84.87	84.10	84.18	84.43	84.26	89.14	0.705
	Fused set	86.99	86.58	86.39	86.16	86.36	91.69	0.723
CapCNN	NMBAC	77.18	77.32	78.57	77.86	77.59	82.95	0.664
	S-PSSM-ACT	78.53	79.26	78.15	77.87	78.56	83.71	0.672
	GDPC	77.23	78.37	77.48	76.11	77.22	82.43	0.667
	KSCTD	78.66	79.85	79.05	78.97	79.41	83.45	0.678
	SSC	79.83	80.39	80.56	79.54	79.96	84.2	0.684
	TAC	80.99	81.67	80.79	80.56	81.11	85.23	0.693
	UniRep	83.88	84.34	83.97	83.61	83.97	88.16	0.724
	ProtBert	85.98	85.69	85.43	85.18	85.43	91.7	0.741
	Fused set	87.86	87.60	87.85	87.47	87.53	93.86	0.765
DeepStack	NMBAC	79.76	80.65	79.73	78.86	79.75	84.19	0.687
	S-PSSM-ACT	80.44	80.23	81.05	80.57	80.4	85.74	0.690
	GDPC	79.09	79.37	80.11	78.78	79.08	84.6	0.682
	KSCTD	81.85	80.59	81.90	81.59	81.47	86.74	0.705
	SSC	82.39	82.75	82.64	82.29	82.51	87.51	0.715
	TAC	84.84	83.21	84.32	84.04	84.17	89.08	0.734
	UniRep	86.95	86.52	87.31	86.39	86.77	91.13	0.758
	ProtBert	88.98	87.74	88.42	88.12	88.45	93.58	0.773
	Fused set	90.59	90.75	90.80	90.25	90.5	95.71	0.794

GRU and CapCNN achieve moderate improvements, however DeepStack outperforms, achieving an accuracy of 80.44% and an MCC of 0.690. GDPC, which captures dipeptide-level patterns, provides slightly better results than NMBAC but remains limited compared to higher-dimensional methods. CapCNN and FBGAN show incremental improvements, while DeepStack achieves the best performance with an accuracy of 79.09% and MCC of 0.682, reflecting its strength in leveraging subtle patterns. KSCTD shows a noticeable performance boost over GDPC, highlighting its ability to capture long-range interactions. CapCNN delivers improved results with MCC of 0.678, while DeepStack achieves superior performance with an accuracy of 81.85% and MCC of 0.705, showcasing the utility of KSCTD in enhancing predictions.

TAC outperforms KSCTD across most classifiers, emphasizing the importance of secondary structure information. FBGAN and CapCNN achieve notable improvements, with MCCs of 0.676 and 0.693, respectively. DeepStack outperforms all other models, achieving an accuracy of 84.84% and MCC of 0.734, further demonstrating the value of torsional angle covariance. UniRep, as a Protein Language Model, captures complex sequence patterns and provides significant improvements across all classifiers. GRU obtains an MCC of 0.697, while CapCNN delivers slightly better results with MCC of 0.724. DeepStack secures the highest performance with an accuracy of 86.95% and MCC of 0.758, highlighting UniRep’s strength in high-dimensional sequence representation. ProtBert demonstrates the highest performance among individual feature extraction methods. GRU achieves an MCC of 0.713, and CapCNN improves further to 0.741.

DeepStack attains the best performance with an accuracy of 88.98% and MCC of 0.773, showcasing ProtBert’s ability to capture both local and global sequence patterns effectively. Finally, the Fused set, which integrates all feature representations, consistently yields the best results. GRU and FBGAN show strong improvements, but CapCNN and DeepStack dominate.

Results analysis of DL models after feature selection

We applied SVM-RFE to eliminate irrelevant and less informative features, focusing only on the feature sets that significantly contribute to model performance. The results of the selected features are presented in Table 5. NMBAC, as a feature set, continues to provide a baseline with moderate improvements post-feature selection. DeepStack achieves the highest performance for this feature, with an accuracy of 80.57% and MCC of 0.694, illustrating its capacity to extract meaningful insights from reduced feature dimensions. S-PSSM-ACT shows a significant improvement in performance compared to NMBAC due to its focus on evolutionary information. CapCNN generates an MCC of 0.683, while DeepStack outperforms with an accuracy of 81.65% and MCC of 0.709.

Table 5.

Comparison of DL models performance after feature selection.

Model	Feature	Acc (%)	Sn (%)	Sp (%)	Pre (%)	F1 (%)	AUC (%)	MCC
GRU	NMBAC	77.87	76.64	78.54	77.68	77.16	81.47	0.653
	S-PSSM-ACT	79.43	78.14	79.65	79.07	78.60	82.84	0.671
	GDPC	76.67	77.21	76.09	76.66	76.93	80.48	0.665
	KSCTD	77.56	77.36	77.89	77.60	77.48	81.51	0.654
	SSC	79.49	80.51	78.98	79.66	80.08	83.73	0.675
	TAC	78.87	79.99	80.66	79.84	79.91	84.34	0.688
	UniRep	82.65	84.83	83.65	83.71	84.27	88.45	0.703
	ProtBert	84.49	84.86	84.32	84.56	84.71	88.82	0.728
	Fused set	86.32	87.43	86.58	86.78	87.10	91.36	0.745
FBGAN	NMBAC	76.33	77.47	75.81	76.54	77.00	80.47	0.642
	S-PSSM-ACT	78.76	78.31	79.13	78.73	78.52	82.66	0.665
	GDPC	76.43	77.42	76.97	76.94	77.18	81.05	0.643
	KSCTD	77.65	78.37	77.43	77.82	78.09	81.80	0.656
	SSC	79.21	80.98	79.55	79.91	80.44	84.28	0.676
	TAC	80.67	81.88	80.97	81.17	81.53	85.50	0.685
	UniRep	83.80	84.23	82.48	83.50	83.87	87.52	0.699
	ProtBert	85.79	85.43	85.78	85.67	85.55	89.89	0.713
	Fused set	87.98	87.77	87.65	87.80	87.78	92.10	0.736
CapCNN	NMBAC	78.34	78.69	79.54	78.86	78.77	83.07	0.662
	S-PSSM-ACT	79.43	80.87	79.28	79.86	80.36	84.08	0.683
	GDPC	78.59	79.38	78.98	78.98	79.18	83.14	0.676
	KSCTD	79.53	80.38	80.47	80.13	80.25	84.45	0.683
	SSC	80.87	81.73	81.62	81.41	81.57	85.76	0.690
	TAC	81.96	82.65	81.55	82.05	82.35	86.20	0.706
	UniRep	84.86	85.22	84.44	84.84	85.03	89.07	0.769
	ProtBert	86.57	86.43	86.79	86.60	86.51	90.94	0.757
	Fused set	88.28	88.80	89.35	88.81	88.80	93.53	0.798
DeepStack	NMBAC	80.57	81.11	80.76	80.81	80.96	84.98	0.694
	S-PSSM-ACT	81.65	81.65	82.89	82.06	81.86	86.38	0.709
	GDPC	81.72	80.24	81.26	81.07	80.65	84.79	0.695
	KSCTD	82.47	81.80	83.76	82.68	82.24	86.92	0.713
	SSC	83.65	82.78	84.84	83.76	83.27	88.00	0.725
	TAC	85.97	85.14	85.68	85.60	85.37	89.68	0.753
	UniRep	87.76	87.34	88.56	87.89	87.61	92.35	0.779
	ProtBert	89.57	88.48	89.52	89.19	88.83	93.45	0.797
	Fused set	94.69	93.38	94.27	94.11	93.75	98.52	0.848

GDPC demonstrates better performance than NMBAC but remains less effective compared to higher-dimensional methods. CapCNN and FBGAN show steady improvements, while DeepStack achieves an accuracy of 81.72% and MCC of 0.695, indicating its ability to optimize dipeptide-level features. KSCTD provides a clear performance boost over GDPC due to its ability to capture long-range interactions. CapCNN obtains an MCC of 0.683, while DeepStack outperforms, reaching an accuracy of 82.47% and MCC of 0.713, indicating its strength in modeling complex sequence motifs. TAC surpasses KSCTD in performance, emphasizing the relevance of secondary structure features in protein prediction tasks. CapCNN delivers notable improvements, yielding MCC of 0.706, while DeepStack secures the highest performance with an accuracy of 85.97% and MCC of 0.753. UniRep provides significant performance enhancements across all classifiers. CapCNN accomplishes MCC of 0.769, and DeepStack secures the best results with an accuracy of 87.76% and MCC of 0.779, demonstrating UniRep’s ability to capture meaningful sequence features.

ProtBert outperforms UniRep and demonstrates the best performance among individual feature extraction methods. CapCNN produces MCC of 0.757, while DeepStack delivers superior results, attaining an accuracy of 89.57% and MCC of 0.797, highlighting ProtBert’s capacity to capture both local and global sequence-level patterns. Finally, the Fused-set, combining all feature representations, consistently achieves the best overall results.

CapCNN generates MCC of 0.798, while DeepStack improves performance with an accuracy of 94.69% and MCC of 0.848. The results underscore the efficacy of the SVM-RFE feature selection approach in enhancing model performance by utilizing discriminative features and reducing redundancy for more accurate and robust predictions. The DeepStack performance is onward, validated by ROC curve which drawn in Fig. 2. The ROC curve reflects that DeepStack performance superlative than other applied DL models.

Fig. 2.

Comparative ROC curves of all applied DL models.

SHAP-based interpretation of the deepStack

To better understand the interpretability of the DeepStack model, we applied SHAP (SHapley Additive exPlanations) analysis on the best fused feature set. The SHAP plot highlights the top 20 discriminative features, showing both their direction (positive or negative contribution) and strength of influence on classification as shown in Fig. 3. Among the selected features, several important indices can be attributed to ProtBert embeddings (e.g., 151, 121, 111, 191), which show broad SHAP distributions (≈ –1.0 to + 1.5). Their consistently high positive contributions (red clusters on the right side) indicate that ProtBert effectively captures deep contextual and evolutionary patterns from protein sequences, thereby driving strong discriminative decisions.

Fig. 3.

Interpretation of significant features using SHAP.

Similarly, UniRep features (e.g., 71, 101, 211, 279) exhibit stable contributions with moderate SHAP ranges, reflecting their ability to encode long-range dependencies and global sequence-level information. These features complement ProtBert by providing a different representation space derived from unsupervised protein sequence modeling. The secondary structure-derived features (e.g., 14, 33, 51, 234) demonstrate localized yet impactful contributions. Their narrower SHAP spreads suggest that while fewer in number, they provide critical structural signals that help refine the decision boundary between antigenic and non-antigenic proteins.

Finally, other descriptors such as handcrafted PSSM-based or physiochemical indices (e.g., 321, 351, 391, 375) show varied SHAP contributions, some with highly positive influence and others negatively weighted. This highlights that even classical descriptors, though less dominant compared to deep embeddings, supply complementary information such as motif-level conservation and compositional biases that deep embeddings alone may overlook.

Overall, this SHAP-guided feature fusion demonstrates that ProtBert and UniRep embeddings dominate the decision space, while secondary structure and handcrafted descriptors refine and stabilize predictions. This integration enabled DeepStack to achieve its best performance (Acc: 94.69%, AUC: 98.52%, MCC: 0.848), confirming that combining heterogeneous yet complementary features yields both interpretability and predictive robustness.

Comparative analysis of the model’s performance on the testing set

The comparative analysis of Table 6 evaluates the performance of GRU, FBGAN, CapCNN, and DeepStack-VEGF on the testing dataset, providing insights into their predictive capabilities. The GRU model achieves an accuracy of 82.14%, sensitivity of 79.64%, specificity of 84.89%, and an MCC of 0.664. These results demonstrate that GRU serves as a reliable baseline, effectively capturing temporal dependencies for sequence-based prediction.

Table 6.

Evaluation of model performance on the testing set.

Model	Acc (%)	Sn (%)	Sp (%)	Pre (%)	F1 (%)	AUC (%)	MCC
GRU	82.14	79.64	84.89	82.22	80.91	86.38	0.664
FBGAN	83.65	80.79	85.26	83.23	81.99	87.18	0.673
CapCNN	83.78	80.98	85.47	83.41	82.18	87.39	0.677
DeepStack-VEGF	84.45	81.16	87.59	84.40	82.75	88.59	0.689

In comparison, FBGAN improves upon GRU, achieving an accuracy of 83.65%, sensitivity of 80.79%, specificity of 85.26%, and MCC of 0.673. The enhanced performance suggests that adversarial learning contributes to more robust feature extraction, especially in distinguishing subtle variations in the input patterns. CapCNN slightly surpasses Feedback GAN, with an accuracy of 83.78%, sensitivity of 80.98%, specificity of 85.47%, and MCC of 0.677. The higher MCC and specificity indicate its strength in maintaining spatial hierarchies and achieving balanced classification, particularly for challenging or borderline cases.

The best performance is observed with DeepStack-VEGF, which attains an accuracy of 84.45%, sensitivity of 81.16%, specificity of 87.59%, and an MCC of 0.689. These results highlight the advantage of model ensembling, where DeepStack-VEGF integrates multiple feature perspectives to improve generalization and predictive stability across diverse test samples.

Ablation experiments result of stacking ensemble learning model on testing dataset

Table 7 presents the results of ablation experiments conducted using the fused feature set, evaluating the performance of various model combinations: GRU + FBGAN, FBGAN + CapCNN, CapCNN + GRU, and the full ensemble model DeepStack-VEGF. The analysis provides insights into how different architectural pairings contribute to classification performance in terms of accuracy, sensitivity, specificity, and MCC, highlighting the complementary nature of the models.

Table 7.

Ablation experiments results using fused set.

Model	Acc (%)	Sn (%)	Sp (%)	MCC
GRU + FBGAN	82.14	79.64	84.89	0.664
FBGAN + CapCNN	83.65	80.79	85.26	0.673
CapCNN + GRU	83.78	80.98	85.47	0.677
DeepStack-VEGF	84.45	81.16	87.59	0.689

The GRU + FBGAN combination yields an accuracy of 82.14%, sensitivity of 79.64%, specificity of 84.89%, and MCC of 0.664. While this model pairing enhances sequential modeling through GRU and adversarial feature learning via Feedback GAN, the performance gains are modest. The limited synergy between the two suggests that combining only temporal and adversarial signals may not be sufficient to capture the full complexity of the fused features.

In contrast, the Feedback GAN + CapCNN pairing achieves 83.65% accuracy, 80.79% sensitivity, 85.26% specificity, and an MCC of 0.673, demonstrating a more effective collaboration. This improvement is attributed to the GAN’s generative-discriminative strengths combined with CapCNN’s ability to preserve hierarchical spatial relationships. The resulting model better differentiates between classes in the fused space, indicating higher discriminative power.

The CapCNN + GRU combination further enhances performance with an accuracy of 83.78%, sensitivity of 80.98%, specificity of 85.47%, and MCC of 0.677. This architecture successfully integrates the spatial awareness of CapCNN with GRU’s temporal dynamics, yielding a more balanced and generalizable representation. The improvement in MCC and sensitivity suggests this pairing effectively captures both global and sequential patterns, leading to stronger classification reliability.

Finally, the DeepStack-VEGF model, which fuses all three models such as GRU, FBGAN, and CapCNN achieves the highest performance across all metrics, with accuracy of 84.45%, sensitivity of 81.16%, specificity of 87.59%, and an MCC of 0.689. This result underscores the power of full ensemble integration, leveraging the unique strengths of each model to construct a robust, diverse decision-making system. The improved specificity and MCC indicate reduced false positives and better overall prediction quality.

Comparative performance with existing methods

We compared the performance of our DeepStack-VEGF model with two recently published state-of-the-art VEGF prediction methods: Deep-VEGF⁸ and VEGF-ERCNN⁹. As shown in Table 8, our proposed DeepStack-VEGF model consistently outperforms these existing methods across all key performance metrics. Specifically, DeepStack-VEGF achieves an accuracy of 94.69%, a sensitivity of 93.38%, a specificity of 94.27%, and an MCC of 0.848. Our model’s accuracy of 94.69% is notably higher, being 3.60% greater than Deep-VEGF (91.09%) and 2.57% greater than VEGF-ERCNN (92.12%). While Deep-VEGF demonstrates a lower sensitivity (93.06% vs. 94.38%), our model maintains a higher sensitivity, indicating strong detection of true positives. Furthermore, the specificity of our model at 94.27% is significantly improved, being 5.02% greater than Deep-VEGF (89.25%) and 3.83% greater than VEGF-ERCNN (90.44%), which points to a substantially reduced rate of false positives. The MCC of 0.848 for DeepStack-VEGF also indicates superior overall performance, showing an improvement of 0.025 over Deep-VEGF (0.823) and 0.011 over VEGF-ERCNN (0.837). These comprehensive results collectively demonstrate the superior predictive capability and robustness of our framework, underscoring its advantages over current approaches in the field of VEGF prediction.

Table 8.

Comparison with existing methods.

Model	Acc (%)	Sn (%)	Sp (%)	MCC
Deep-VEGF9	91.09	93.06	89.25	0.823
VEGF-ERCNN10	92.12	93.56	90.44	0.837
DeepStack-VEGF (Proposed model)	94.69	94.38	94.27	0.848

Conclusion and future direction

This study presents a novel predictor for the VEGF prediction using a DL stacking and ensemble framework. Given VEGF critical role in physiological processes like wound healing and bone formation, as well as in pathological contexts like tumor growth and metastasis, efficient identification methods are essential. Current experimental approaches, while valuable, are often resource-intensive and time-consuming. Our proposed model addresses these challenges by leveraging sequence-based data and an advanced ensemble strategy that combines the strengths of multiple DL models, including FBGAN, CapCNN, GRU, and stacking ensemble model with feature extraction approach encompassing NMBAC, S-PSSM-ACT, GDPC, KSCTD, TAC, UniRep, ProtBert, and the combined Fused-set. The fused feature set and stacking ensemble model deliver superior predictive accuracy, outperforming individual models and highlighting the efficacy of this integrated approach.

Future research could focus on integrating advanced deep learning strategies, such as transfer learning, to further enhance model performance. Additionally, the development of an online web server would provide valuable resources for researchers and academicians, facilitating broader accessibility and practical use. Expanding this framework to encompass other protein families could also transform it into a versatile tool for bioinformatics research, with significant implications for drug discovery applications.

Author contributions

**Farman Ali:** Drafted and composed the manuscript, contributed to the interpretation of results. **Majdi Khalid:** Performed the experiments, assisted in data acquisition. **Abdulmohsen Algarni:** Conducted validation analyses, contributed to data verification. **Naif Waheb Rajkhan:** Substantively revised the manuscript, contributed to critical editing. **Othman Asiry:** Reviewed the manuscript, contributed to critical feedback, and interpretation. **Meng-Ze Du:** Supervision.

Data availability

We have made all datasets, feature extraction sets, and classifier codes freely available on GitHub at the following link: https://github.com/Farman335/DeepStack-VEGF

Declarations

Competing interests

The authors declare no competing interests.

Ethics approval

No human or animal subjects are involved in this work.

Consent for publication

All authors agree on the publication of the paper.