Prediction of protein–protein interaction based on interaction-specific learning and hierarchical information

Abstract

Background

Prediction of protein–protein interactions (PPIs) is fundamental for identifying drug targets and understanding cellular processes. The rapid growth of PPI studies necessitates the development of efficient and accurate tools for automated prediction of PPIs. In recent years, several robust deep learning models have been developed for PPI prediction and have found widespread application in proteomics research. Despite these advancements, current computational tools still face limitations in modeling both the pairwise interactions and the hierarchical relationships between proteins.

Results

We present HI-PPI, a novel deep learning method that integrates hierarchical representation of PPI network and interaction-specific learning for protein–protein interaction prediction. HI-PPI extracts the hierarchical information by embedding structural and relational information into hyperbolic space. A gated interaction network is then employed to extract pairwise features for interaction prediction. Experiments on multiple benchmark datasets demonstrate that HI-PPI outperforms the state-of-the-art methods; HI-PPI improves Micro-F1 scores by 2.62%–7.09% over the second-best method. Moreover, HI-PPI offers explicit interpretability of the hierarchical organization within the PPI network. The distance between the origin and the hyperbolic embedding computed by HI-PPI naturally reflects the hierarchical level of proteins.

Conclusions

Overall, the proposed HI-PPI effectively addresses the limitations of existing PPI prediction methods. By leveraging the hierarchical structure of PPI network, HI-PPI significantly enhances the accuracy and robustness of PPI predictions.

Supplementary information

The online version contains supplementary material available at 10.1186/s12915-025-02359-9.

Background

Protein–protein interactions (PPIs) play a pivotal role in regulating cellular processes and biological functions [1–3]. Predicting PPIs serves as a critical resource for identifying potential therapeutic targets and developing interventions for various diseases [4, 5], thereby facilitating the development of innovative therapies and the design of targeted drugs. While in vitro experiments, such as yeast two-hybrid [6] and tandem affinity purification [7], are reliable for identifying PPIs, they are time-consuming and labor-intensive [8, 9]. To address the constraints of in vitro experiments, deep learning methods have received increasing research interest [10–12].

In recent years, methods based on graph neural network (GNN) have demonstrated remarkable capabilities in capturing the topological information within PPI network [13], achieving superior performance in PPI prediction. GNN-PPI [14] was the first method to apply GNN to PPI prediction, leveraging a Graph Isomorphism Network [15] to encode PPI graphs. AFTGAN [16] integrates the attention-free transformer (AFT) with the graph attention network (GAN) to capture global information between proteins. HIGH-PPI [17] proposed a dual-view graph learning model that incorporates both protein structure and PPI network structure. MAPE-PPI [18] extends heterogeneous GNNs to handle the multi-modal nature of protein data.

Still, the previous GNN-based PPI prediction methods primarily focus on the node-specific properties (e.g., degree distribution and neighborhood information) among proteins, while the valuable natural hierarchical structure is often overlooked. In biological systems, protein–protein interaction (PPI) networks exhibit a strong hierarchical organization, ranging from molecular complexes to functional modules and cellular pathways. The hierarchical information encompasses the organization of proteins into functional groups or layers of biological processes [19, 20], providing a comprehensive perspective of the entire graph and enhancing the biological interpretability of protein functions [21, 22]. Specifically, hierarchical information includes the central-peripheral structure, which distinguishes core and peripheral proteins within the PPI network [23], as well as protein clusters associated with specific biological functions [24] and the layered properties of the network. Among the existing PPI prediction methods, HIGH-PPI [17] constructs a hierarchical graph by integrating both the global PPI network and the local graph structure of individual proteins, effectively capturing the hierarchy between the molecular and residue levels. However, the hierarchical relationships between proteins themselves remain largely unexplored.

Furthermore, although the GNN-based modules in existing methods effectively aggregate neighborhood information for each protein, they fail to adequately capture the unique interaction patterns of specific protein pairs. This insufficient modeling of the to-be-predicted protein pairs constrains both the predictive performance and the generalization ability of PPI prediction models.

To address the aforementioned issues, we propose a novel interaction-specific framework, HI-PPI (Hyperbolic graph convolutional network and Interaction-specific learning for PPI prediction), which bridges hierarchical information and interaction patterns in a unified framework. First, the structure and sequence of each protein are used as the primary source for feature extraction. Subsequently, HI-PPI incooperates hyperbolic geometry and graph convolutional network (GCN) to learn the embedding of proteins in the PPI network. Finally, a gated interaction network is employed to extract the unique patterns between each pair of proteins. In HI-PPI, the hierarchical structure of the PPI network is captured by the hyperbolic GCN, while interaction-specific information between protein pairs is learned through the interaction-specific network. Extensive experimental results demonstrate that HI-PPI outperforms the state-of-the-art methods in classical benchmark datasets.

The main contributions of our work can be summarized as follows:

• We address the critical issue of the missing consideration of interaction patterns and hierarchical information, which has been largely overlooked in previous studies. To the best of our knowledge, this work represents the first attempt to utilize interaction-specific learning for PPI prediction.

• We propose HI-PPI, a unified framework that integrates hyperbolic space with interaction networks. This approach resolves the inconsistency in identifying the hierarchical structure within PPI network.

• We empirically demonstrate the benefit of incorporating hierarchical information and interaction patterns into PPI prediction. Experiments on classical benchmark datasets show that HI-PPI significantly outperforms state-of-the-art PPI prediction methods.

• The use of hyperbolic geometry facilitates/enables a better representation of the hierarchy in PPI networks, contributing to the identification of hub proteins and other hierarchical relationships within the network.

Results

Overview of HI-PPI

Although GNN and its variants have been extensively explored for PPI prediction, they often lack mechanisms to effectively simulate the natural hierarchical information and interaction properties inherent to biological systems. To address these limitations, we propose HI-PPI, an interaction-specific and hierarchy-specific framework. HI-PPI is designed to integrate two critical aspects: (i) modeling the hierarchical relationships between proteins in hyperbolic space and (ii) capturing pairwise information between to-be-predicted PPIs by incorporating interaction networks. This dual-specific framework enables HI-PPI to achieve efficient and accurate representations of PPIs.

In the feature extraction stage, the structure and sequence data are processed independently. For protein structure, a contact map is constructed based on the physical coordinates of the residues. Encoded structural features are derived using a pre-trained heterogeneous graph encoder and a masked codebook [18]. For protein sequence data, representations are obtained based on physicochemical properties. The feature vectors from protein structure and sequence are concatenated to form the initial representation of proteins. As shown in Fig. 1, hyperbolic GCN layer is employed to iteratively update the embedding of each protein (node) by aggregating the neighborhood information in PPI network. To effectively capture the hierarchical information, we apply the classical GCN layer within hyperbolic space, in which the level of hierarchy is represented by the distance from the origin. Furthermore, a task-specific block is employed for interaction prediction. The hyperbolic representations of protein are propagated along pairwise interaction; the Hadamard product of protein embeddings is filtered through a gating mechanism, which dynamically controls the flow of cross-interaction information.

Fig. 1.

A schematic diagram of HI-PPI. a The preprocess of protein data. The heterogeneous GNN encoder is adopted to extract the latent representation in contact map of protein structure. b A PPI graph is constructed based on PPI network and extracted feature. The node representation of each protein is updated iteratively by hyperbolic graph convolutional layer. Subsequently, the importance of pairwise information is controlled by a gating mechanism in interaction-specific network. The resulting embedding of PPI is processed to a classifier for prediction

Benchmark evaluation of HI-PPI

We train and evaluate HI-PPI on SHS27K and SHS148K [25, 26], which are classical benchmark datasets that derived from STRING database [27]. Both datasets are Homo sapiens subset of STRING, SHS27K contains 1690 proteins and 12,517 PPIs, and SHS148K contains 5189 proteins and 44,488 PPIs. The training and test sets are constructed using the Breadth-First Search (BFS) and Depth-First Search (DFS) strategies proposed by Lv et al. [14]. For each dataset, 20% of the PPIs are selected as the test set based on the above strategies, while the remaining PPIs are used as the training set.

To validate the performance of our method, we compare HI-PPI with six state-of-the-art PPI prediction methods from four perspectives, including (1) the overall performance with multiple evaluation metrics, (2) the generalization ability on different PPI types, (3) the robustness of HI-PPI against edge perturbation, and (4) ablation study with commonly used deep learning models.

The benchmark methods include PIPR [25], LDMGNN [28], AFTGAN [16], BaPPI [29], HIGH-PPI [17], and MAPE-PPI [18]. The performance results of all methods were obtained by running on the same dataset split. We conducted each experiment five times, and the final results are reported in two decimal places.

HI-PPI shows the best performance, generalization and robustness

As shown in Table 1, HI-PPI achieves superior performance across all evaluation metrics. Specifically, in terms of Micro-F1, HI-PPI outperforms BaPPI by an average of 2.10% on the SHS27K dataset and exceeds MAPE-PPI by an average of 3.06% on the SHS148K dataset. The improvements on SHS148K are higher than SHS27K, which could result from the percentage of unseen proteins in dataset. These results demonstrate the effectiveness of the hyperbolic operation and interaction-specific learning framework of HI-PPI. Overall, HI-PPI achieves the best performance in 15 out of the 16 evaluation schemes, highlighting its consistent superiority. More precisely, in the DFS scheme of SHS27K, our method achieves 0.7746 in Micro-F1, 0.8235 in AUPR, 0.8952 in AUC, and 0.8328 in accuracy. BaPPI ranks second on SHS27K, while MAPE-PPI achieves the second-best results on SHS148K. To evaluate the significance of the performance improvements achieved by HI-PPI, we have conducted a two-sample t-test comparing HI-PPI to the second-best method, MAPE-PPI. The P values obtained for the SHS27K(BFS), SHS27K(DFS), SHS148K(BFS), and SHS148K(DFS) datasets were 0.0023, 0.0001, 0.0003, and 0.0006, respectively. All of P values are below the 0.05 threshold, indicating a statistically significant difference in performance between HI-PPI and MAPE-PPI, confirming that the improvements achieved by HI-PPI are statistically significant.

Table 1.

Performance comparison on SHS27K and SHS148K with different partition schemes, data are presented as mean ± std

Dataset	Method	F1-score ($\%$)	AUPR ($\%$)	AUC ($\%$)	ACC ($\%$)
SHS27K (BFS)	PIPR	$48.18\pm 5.54$	$53.61\pm 1.76$	$72.47\pm 2.07$	$69.35\pm 1.23$
	LDMGNN	$67.21\pm 2.57$	$72.88\pm 5.88$	$85.17\pm 7.87$	$79.62\pm 4.91$
	AFTGAN	$68.83\pm 0.01$	$72.88\pm 0.02$	$85.17\pm 0.01$	$79.62\pm 0.01$
	HIGH-PPI	$70.54\pm 1.15$	$80.15\pm 1.82$	$88.98\pm 0.86$	$81.11\pm 0.66$
	BaPPI	$75.57\pm 1.00$	$81.53\pm 2.14$	$89.08\pm 0.73$	$80.74\pm 1.49$
	MAPE-PPI	$72.82\pm 1.52$	$80.43\pm 1.48$	$\mathbf{89.76}\pm \mathbf{0.74}$	$81.65\pm 1.38$
	HI-PPI	$\mathbf{77.46}\pm \mathbf{0.26}$	$\mathbf{82.35}\pm \mathbf{0.25}$	$89.52\pm 0.18$	$\mathbf{83.28}\pm \mathbf{0.21}$
SHS27K (DFS)	PIPR	$54.57\pm 1.77$	$55.29\pm 0.75$	$74.64\pm 0.67$	$70.63\pm 0.82$
	LDMGNN	$68.12\pm 0.76$	$70.33\pm 0.84$	$85.26\pm 0.77$	$79.15\pm 0.31$
	AFTGAN	$70.44\pm 0.94$	$71.63\pm 0.78$	$87.43\pm 0.68$	$80.62\pm 0.45$
	HIGH-PPI	$72.62\pm 0.64$	$80.27\pm 0.94$	$89.93\pm 0.49$	$82.51\pm 0.67$
	BaPPI	$76.69\pm 0.79$	$83.99\pm 0.64$	$89.16\pm 0.17$	$83.04\pm 1.15$
	MAPE-PPI	$74.29\pm 0.79$	$75.91\pm 1.11$	$85.02\pm 1.17$	$79.35\pm 1.33$
	HI-PPI	$\mathbf{79.57}\pm \mathbf{0.53}$	$\mathbf{86.27}\pm \mathbf{1.57}$	$\mathbf{90.64}\pm \mathbf{0.47}$	$\mathbf{85.82}\pm \mathbf{0.64}$
SHS148K (BFS)	PIPR	$56.80\pm 1.62$	$63.50\pm 1.99$	$75.37\pm 1.62$	$75.45\pm 0.66$
	LDMGNN	$71.86\pm 0.01$	$78.24\pm 0.02$	$86.91\pm 0.02$	$82.03\pm 0.01$
	AFTGAN	$71.19\pm 0.01$	$75.67\pm 0.02$	$85.25\pm 0.02$	$79.03\pm 0.01$
	HIGH-PPI	$73.16\pm 0.94$	$81.48\pm 1.91$	$89.09\pm 1.03$	$80.80\pm 0.95$
	BaPPI	$76.26\pm 0.52$	$80.17\pm 0.26$	$89.70\pm 0.24$	$82.49\pm 0.27$
	MAPE-PPI	$76.52\pm 0.67$	$80.43\pm 1.21$	$89.26\pm 0.67$	$83.65\pm 0.63$
	HI-PPI	$\mathbf{79.15}\pm \mathbf{0.60}$	$\mathbf{82.05}\pm \mathbf{1.18}$	$\mathbf{91.00}\pm \mathbf{0.06}$	$\mathbf{84.05}\pm \mathbf{0.25}$
SHS148K (DFS)	PIPR	$58.95\pm 1.46$	$63.23\pm 2.06$	$78.72\pm 1.01$	$80.57\pm 0.72$
	LDMGNN	$78.47\pm 0.00$	$85.86\pm 0.01$	$91.80\pm 0.00$	$84.86\pm 0.00$
	AFTGAN	$80.87\pm 0.00$	$84.70\pm 0.01$	$92.40\pm 0.00$	$85.33\pm 0.00$
	HIGH-PPI	$77.16\pm 0.39$	$84.35\pm 1.43$	$91.51\pm 0.32$	$84.31\pm 0.24$
	BaPPI	$81.15\pm 0.24$	$82.66\pm 0.41$	$89.39\pm 0.35$	$84.75\pm 0.18$
	MAPE-PPI	$81.97\pm 0.65$	$85.61\pm 1.67$	$91.02\pm 1.26$	$85.75\pm 0.63$
	HI-PPI	$\mathbf{84.12}\pm \mathbf{0.24}$	$\mathbf{91.87}\pm \mathbf{0.17}$	$\mathbf{93.04}\pm \mathbf{0.05}$	$\mathbf{89.32}\pm \mathbf{0.20}$

Bold text indicates the best result

We also observe that the structure-based methods (HI-PPI, MAPE-PPI, and HIGH-PPI) achieve better performance than the other methods that rely solely on sequence data. This can be attributed to the fact that a protein’s structure directly determines its function, and the spatial biological information provided by protein contributes to PPI prediction. PIPR gets relatively poor performance, due to its inability to effectively model global information within the PPI network.

We conduct an in-depth analysis of the BFS and DFS schemes of SHS27K. Compared to SHS148K, SHS27K exhibits a lower percentage of known proteins (proteins present in both the training and test sets), establishing it as a practical benchmark dataset for evaluating the trade-off between precision and recall. The precision-recall (PR) curves for each method are presented in Fig. 2. HI-PPI achieves the highest area under the PR curve and demonstrates superior performance at most 50% thresholds. Additionally, as indicated by the shaded regions, HI-PPI exhibits significantly greater stability compared to other methods. Under the BFS scheme, HI-PPI achieves the best performance when precision ranges from 0.4 to 1, whereas under the DFS scheme, it achieves the best performance when precision ranges from 0.57 to 1. In terms of secondary performance, HIGH-PPI ranks second under the BFS scheme, while BaPPI achieves the second-best results under the DFS scheme. It is worth noting that although all methods perform better under the DFS scheme, the variance across thresholds and fluctuations between thresholds increase significantly. This can be attributed to the sparsely distributed proteins selected by the DFS strategy, which introduces bias into both the training and test datasets.

Fig. 2.

Precision-recall curves of PPI prediction of SHS27K, showing the performance of HI-PPI compared to MAPE-PPI, HIGH-PPI, BaPPI, AFTGAN, LDMGNN, and PIPR across five independent replicates. a Under the BFS partitioning. b Under the DFS partitioning. The shade indicates the range between the highest and lowest results

Robustness is another important evaluation metric for deep learning models. Here, we analyze the model tolerance against data perturbation. In order to simulate unknown or undiscovered interactions, we randomly remove existing interactions in SHS27K with different percentages and apply 5-fold cross validation. The Micro-F1 of each ratio is displayed in the boxplot of Fig. 3. HI-PPI maintains an average of 0.82 Micro-F1 score with 20% perturbation ratio. When the ratio increases from 0.2 to 0.8, HI-PPI keeps relatively stable performance. The difference between original dataset and 0.8 perturbation is around 0.25, indicating the great robustness of HI-PPI. The variance of Micro-F1 also increases with perturbation ratio.

Fig. 3.

Robustness evaluation of HI-PPI against random perturbations with different ratios, performed across 12 independent replicates

HI-PPI address the imbalanced distribution of PPI types

In STRING database, interactions between proteins can involve one or more of the following types: reaction, binding, post-translational modification (ptmod), activation, inhibition, catalysis, and expression. The distribution of PPI types varies across the dataset. For instance, these interaction types account for 34.97%, 33.73%, 1.85%, 4.86%, 3.09%, 20.91%, and 0.60% of the total interactions in SHS27K, respectively. The bias introduced by the imbalance in PPI type affects the predictive performance of deep learning-based methods, making the accurate prediction of the minority types a critical metric for assessing generalization ability.

We evaluated the Micro-F1 for each interaction type in the SHS27K dataset, comparing the performance of HI-PPI with advanced methods from previous studies. As shown in Fig. 4, our proposed method demonstrates superior performance in predicting reaction, binding, activation, inhibition, and expression interaction types. Notably, the improvements achieved by HI-PPI are more significant for minority interaction types. The gated interaction-specific mechanism enabled the identification of diverse interactions between different regions of the same protein pair, resulting in stable predictions for minority PPI types. For the rarest interaction type, HI-PPI outperformed competing methods with improvements ranging from 20% to 100%, highlighting its strong generalization capability in addressing the imbalance of interaction types in PPI datasets. MAPE-PPI achieved the best overall performance and demonstrated stability across most interaction types. In contrast, HIGH-PPI excelled in predicting majority types but was less effective for minority types.

Fig. 4.

The performance of four advanced PPI prediction methods on PPI types of SHS27K

We also conducted a case study on post-translational modification (PTM) in the test set of SHS27K. HI-PPI successfully predict PTMs between 9 pairs of proteins that other methods failed to identify. In the prediction result, proteins ENSP00000215832 and ENSP00000250971 occur frequently, revealing their central role in the regulation of cellular process. Furthermore, as PTM-mediated interactions are often dysregulated in diseases, the related proteins can contribute to the identification of novel drug targets or mechanisms of action. The details of protein pairs are available in Table S1 in supplementary file.

Interaction-specific learning and hyperbolic operation improves the performance

We investigate the effectiveness of interaction-specific learning and hyperbolic operations by conducting an ablation study. The omission of the hyperbolic operation, referred to as w/o hyperbolic, involves replacing the hyperbolic GCN with a standard Graph Isomorphism Network (GIN). Similarly, the exclusion of element-wise product operations and the self-attention mechanism is denoted as w/o inter A and w/o inter B, respectively.

The results of the ablation study are presented in Table 2, showing a substantial performance decline without the hyperbolic GCN and interaction-specific learning components. These results demonstrate the notable performance improvements achieved by our proposed method, validating its effectiveness in addressing the limitations of modeling PPI network and pairwise interactions. The removal of hyperbolic GCN lead to a more significant decline in performance than removing interaction-specific operation. This result highlights the critical importance of hierarchical structure learning within the PPI graph for accurately predicting unknown protein–protein interactions. Among the four evaluation metrics, the decline is most pronounced in the area under the precision-recall curve (AUPR), demonstrating that HI-PPI consistently achieves improvements across varying thresholds. Additionally, the performance of HI-PPI is significantly more stable than other conditions, indicating that the integration of hyperbolic operations and interaction-specific learning contributes to both improved and more stable performance.

Table 2.

Ablation study on components of HI-PPI

Dataset	Method	F1-score ($\%$)	AUPR ($\%$)	AUC ($\%$)	ACC ($\%$)
SHS27K (BFS)	HI-PPI	$\mathbf{77.46}\pm \mathbf{0.26}$	$\mathbf{82.35}\pm \mathbf{0.25}$	$\mathbf{89.52}\pm \mathbf{0.18}$	$\mathbf{83.28}\pm \mathbf{0.21}$
	w/o hyperbolic	$73.72\pm 0.77$	$73.63\pm 1.76$	$87.81\pm 0.85$	$81.73\pm 0.72$
	w/o inter A	$74.07\pm 1.10$	$78.02\pm 2.08$	$89.44\pm 0.82$	$81.69\pm 0.81$
	w/o inter B	$76.11\pm 1.29$	$82.43\pm 1.86$	$89.87\pm 0.93$	$82.80\pm 0.85$
SHS27K (DFS)	HI-PPI	$\mathbf{79.57}\pm \mathbf{0.53}$	$\mathbf{86.27}\pm \mathbf{1.57}$	$\mathbf{90.64}\pm \mathbf{0.47}$	$\mathbf{85.82}\pm \mathbf{0.64}$
	w/o hyperbolic	$74.54\pm 0.26$	$80.98\pm 0.59$	$89.22\pm 1.17$	$83.09\pm 0.24$
	w/o inter A	$75.49\pm 0.20$	$81.92\pm 1.41$	$89.85\pm 0.45$	$83.69\pm 0.22$
	w/o inter B	$78.00\pm 0.84$	$84.55\pm 1.79$	$90.16\pm 0.95$	$84.97\pm 1.21$
SHS148K (BFS)	HI-PPI	$\mathbf{79.15}\pm \mathbf{0.60}$	$\mathbf{82.45}\pm \mathbf{1.18}$	$\mathbf{91.00}\pm \mathbf{0.06}$	$\mathbf{84.05}\pm \mathbf{0.25}$
	w/o hyperbolic	$76.00\pm 0.49$	$80.34\pm 1.36$	$82.92\pm 0.67$	$81.31\pm 0.54$
	w/o inter A	$76.66\pm 0.78$	$82.17\pm 1.09$	$89.78\pm 0.60$	$81.78\pm 0.71$
	w/o inter B	$76.48\pm 0.95$	$82.46\pm 1.46$	$89.56\pm 0.58$	$82.29\pm 1.02$
SHS148K (DFS)	HI-PPI	$\mathbf{84.12}\pm \mathbf{0.24}$	$\mathbf{91.87}\pm \mathbf{0.17}$	$\mathbf{93.04}\pm \mathbf{0.05}$	$\mathbf{89.32}\pm \mathbf{0.20}$
	w/o hyperbolic	$78.23\pm 0.42$	$86.38\pm 0.31$	$91.86\pm 0.19$	$85.20\pm 0.93$
	w/o inter A	$79.58\pm 0.24$	$87.73\pm 0.55$	$91.45\pm 0.18$	$85.17\pm 0.21$
	w/o inter B	$82.86\pm 0.65$	$88.34\pm 0.92$	$92.87\pm 0.73$	$88.74\pm 0.76$

Bold text indicates the best results. The term w/o hyperbolic refers to the exclusion of the hyperbolic GCN. Similarly, w/o inter A denotes the use of element-wise product instead of gated interaction network, while w/o inter B denotes the use of a self-attention mechanism

HI-PPI efficiently identifies the hierarchical level of proteins in PPI network

Hierarchical levels are crucial for understanding the functional organization of PPI networks. In hyperbolic space, the distance between a vector and the origin inherently represents its position in the hierarchy. Consequently, the node embeddings computed by HI-PPI naturally capture the hierarchical relationships present in the PPI network. Compared to commonly used identifiers for hub proteins [30], such as node degree, hyperbolic distance provides a direct representation of hierarchical levels. Consequently, utilizing hyperbolic distance helps to distinguish hub proteins from “bridge” proteins—those that primarily function to connect different clusters within the PPI network without exerting control over multiple cellular processes.

Here, we select proteins with node degrees ranging from 30 to 40 in the SHS27K dataset. For each protein, we compute its hyperbolic distance, which is the distance between the origin and the corresponding node embedding computed by HI-PPI. The hierarchical level of each protein is assessed using closeness centrality, defined as the sum of the shortest paths from a node to all other nodes—a commonly used indicator of hierarchical level. Proteins with higher closeness centrality are typically more central within the hierarchical structure, whereas a shorter hyperbolic distance to the origin corresponds to a higher hierarchical level. As shown in Table 3, closeness centrality decreases with increasing hyperbolic distance. The correlation coefficient between hyperbolic distance and closeness centrality is −0.6504, which is substantially stronger than the correlation coefficient of 0.3005 between node degree and closeness centrality. These experimental results confirm a significant relationship between hierarchical level and hyperbolic distance to origin, demonstrating the effectiveness of hyperbolic embedding in capturing hierarchical information within protein–protein interaction networks.

Table 3.

The node degree, hyperbolic distance, and closeness centrality of proteins with node degrees ranging from 30 to 40

Protein ID	Hyperbolic distance	Node degree	Closeness centrality	Protein ID	Hierarchical distance	Node degree	Closeness centrality
251630	5.53	30	0.32	255465	16.8	34	0.31
200135	28.1	30	0.29	229179	28	34	0.28
070846	42	30	0.28	256442	15.54	34	0.31
202773	36.3	30	0.26	228872	14.35	34	0.33
222254	24.44	31	0.30	200181	21.18	34	0.30
207437	38.64	31	0.29	217188	20.17	35	0.33
223095	14.46	31	0.32	006101	28.38	35	0.30
204961	29.14	32	0.30	080059	19.02	35	0.30
241453	5.97	32	0.32	206249	17.24	35	0.34
253055	6.43	32	0.32	254101	15.7	36	0.30
013807	24.16	32	0.29	262187	1.5	36	0.32
262039	1.74	32	0.31	217185	20.1	36	0.33
209884	27	32	0.27	240055	1.08	36	0.28
209728	23.65	32	0.31	256196	6.35	37	0.32
158166	18.35	32	0.29	259089	3.07	37	0.33
210313	16.35	32	0.33	251337	8.27	37	0.31
257430	8.01	33	0.30	262300	3.17	37	0.31
261890	3.02	33	0.33	014930	34.44	37	0.26
155926	23.87	33	0.32	171111	29.7	37	0.29
241463	8.55	33	0.32	248996	8.27	37	0.32
245304	8.55	33	0.32	225831	15.23	37	0.33
248706	8.55	33	0.32	229328	24.87	38	0.30
256953	3.69	33	0.32	222390	12.62	38	0.34
217233	15.61	33	0.32	246792	10.62	39	0.32
262160	1.56	33	0.33	245451	15.44	39	0.31
173229	33.99	33	0.30	248975	19.58	40	0.33
172229	14.19	33	0.31	250559	8.4	40	0.32
257430	8.01	33	0.30

Only the last six digits of the identifier are included in this table. The full STRING identifier is prefixed with 9606.ENSP00000

Furthermore, to explore the hierarchical structure captured in hyperbolic space, we provide a visualization of a subgraph from the SHS27K dataset, comprising 195 proteins associated with PTMs interactions. In hyperbolic space, the origin can serve as a root node, and the distance to the origin provides a natural way to encode hierarchical relationships without requiring additional constraints. As illustrated in Fig. 5, the 195 nodes are divided into 12 groups, each located at varying distances from the origin. Notably, the proteins in group 5 (ENSP00000005340, ENSP00000078429, ENSP00000228307, ENSP00000206249, ENSP00000261991, ENSP00000251630, ENSP00000259089, ENSP00000256078, ENSP00000220507, ENSP00000256953, ENSP00000244741, ENSP00000254654, ENSP00000179259) are positioned closer to the origin, indicating their higher-level status and suggesting their role as core proteins for PTMs interactions. Detailed information about each group is provided in Additional file 1: Table 2.

Fig. 5.

The visualization of 195 proteins related in 2D hyperbolic space

HI-PPI maintains relatively stable performance on proteins with a large number of residues

The protein structure data used in our experiments are provided by AlphaFold2 [31], one of the most advanced deep learning models for protein structure prediction. While AlphaFold2 achieves remarkable accuracy, its performance is limited for long protein sequences, particularly those exceeding 1000 residues. As a result, variations in the quality of predicted structures may occur. To assess the impact of these variations on HI-PPI, we conducted a case study using the SHS27K test set. The test set comprises 1524 protein pairs, of which 221 involve at least one protein with more than 1000 residues (referred to as group A), while the remaining 1303 pairs involve only proteins with 1000 or fewer residues (group B). As shown in Table 4, the Micro-F1 and accuracy of HI-PPI on group A are 0.0213 and 0.0142 lower than those of group B, respectively. This marginal decline suggests that the presence of proteins with more than 1000 residues does not significantly impact HI-PPI’s performance. Therefore, HI-PPI maintains stable predictive performance despite variations in the quality of input structural data.

Table 4.

Performance of HI-PPI on protein pairs that relate to different size of proteins

	Micro-F1	Accuracy	Precision	Recall
Group A	0.7632	0.8352	0.7654	0.7611
Group B	0.7845	0.8494	0.7488	0.8238

Discussion

Our study introduces HI-PPI, an end-to-end framework for protein–protein interaction (PPI) prediction that leverages a graph convolutional network (GCN) embedded in hyperbolic space, combined with a gating mechanism for interaction-specific representation learning. Experimental results on classical benchmark datasets demonstrate that HI-PPI outperforms state-of-the-art methods, achieving a Micro-F1 score of 0.7746 on the SHS27K dataset—surpassing the second-best method by 0.037. This performance gain is primarily attributed to the effective modeling of hierarchical relationships between proteins in hyperbolic space, where the hierarchical level of each node is naturally represented by its distance to the origin.

Ablation studies highlight the importance of each component in HI-PPI. Removing either the hyperbolic embedding or the gating mechanism leads to a notable drop in performance. Among them, the hyperbolic GCN contributes the most, demonstrating its strength in capturing hierarchical relationship in graph structure. Further visualization of the learned hyperbolic embeddings shows that HI-PPI can successfully identify experimentally validated hub proteins. It also verifies the relationships between a protein’s position in the PPI hierarchy and its hyperbolic distance from the origin.

Conclusions

In this paper, we propose HI-PPI, a novel data-driven model for protein–protein interaction (PPI) prediction. To capture the hierarchical relationships between proteins, the PPI graph is modeled in hyperbolic space. Additionally, a gated interaction-specific network is designed to preserve pairwise information between proteins effectively.

The extensive experiments on commonly used PPI datasets demonstrate the empirical superiority of HI-PPI over leading PPI prediction methods. The interaction-specific learning component exhibits strong generalization capabilities for unseen proteins and robustness against random perturbations in the PPI network. Furthermore, HI-PPI serves as a valuable tool for understanding the hierarchical organization of proteins by analyzing their node embeddings in hyperbolic space.

Despite the improvements achieved by our proposed method, we describe two main limitations of HI-PPI. First, HI-PPI shares a common constraint inherent to GNN-based methods; it relies on message passing and neighborhood aggregation to learn node representations. This limits its ability to predict interactions for protein pairs that are completely isolated from the current PPI graph. A potential solution is to integrate HI-PPI with non-graph-based approaches within a unified framework to enhance predictive performance for isolated pairs. Additionally, the current model does not explore the directionality of protein–protein interactions. Investigating asymmetric relationships between proteins could provide deeper biological insights and improve the accuracy of PPI prediction.

Methods

Problem formulation

Here, we formulate PPI prediction as a multi-label prediction task. The protein set is denoted as $\mathcal{P}=\{p_1,p_2,\dots ,p_n\}$. The interaction set is denoted as $\mathcal{Y}=\{y_{\mathit{ij}}\}$, $y_{\mathit{ij}}$ is a binary vector, and each element of $y_{\mathit{ij}}$ represents one interaction type between $p_i$ and $p_j$. The proteins and interactions are served as nodes and edges for constructing a PPI graph $\mathcal{G}=(\mathcal{P},\mathcal{Y})$. The objective is to learn a model $\mathcal{F}:(p_i,p_j)\to \widehat{y}$; $\widehat{y}$ is the prediction of interaction between $p_i$ and $p_j$.

Feature extraction

Physicochemical features. We utilize three classical methods to measure the physicochemical characteristics of protein sequence, including Pseudo Amino Acid Composition (PAAC) [32], Composition/Transition/Distribution Transition (CTDT) [33], and global position information [34]. PAAC is the combination of conventional fraction of each amino acid and discrete sequence correlation factors, which relates the hydrophobicity, hydrophilicity, and side-chain mass of amino acids. CTDT refers to the transition descriptor in composition, transition, and distribution of protein sequence. The amino acids are divided into three functional groups by the 13 physicochemical properties; the grouped amino acid transition descriptor is calculated. Global position information is the sum of relative position information of amino acids in sequence.

Structural features. To extract the spatial structural information of proteins, we utilize the pre-trained heterogeneous graph encoding model proposed by Wu et al. [18], trained on 14,952 protein structures predicted by AlphaFold2 [31]. This heterogeneous graph represents atomic-level connections within PPI network and incorporates three types of edges, including (i) connections between atoms belonging to the same residue; (ii) connections between atoms that are within a specified cutoff distance in the contact map; and (iii) connections between atoms identified as K-nearest neighbors.

The physicochemical and structural features are concatenated as the initial representation of each protein.

Graph learning in hyperbolic space

We construct a PPI graph in hyperbolic space based on the PPI network, where proteins and interactions are considered as nodes and edges, respectively. The hyperboloid model [35, 36] is employed to map the input sequence to hyperbolic space. For a space with m dimension, the hyperboloid model ${\mathbb{H}}^n$ is a manifold embedded in a $n+1$ dimensional Minkowski space with curvature $-1/K,K>0$. The inner product of two points in this space is defined as follows:

$$\begin{array}{c}\hfill {⟨x,y⟩}_{\mathbb{H}}=-x_0{y}_0+\sum _{i=1}^n{x}_i{y}_i,\end{array}$$ 1

and the distance between two vectors is:

$$\begin{array}{c}\hfill d(x,y)=\text{arcosh}(-{⟨x,y⟩}_{\mathbb{H}}).\end{array}$$ 2

Let $\text{o}=\{\sqrt{K},0,\dots ,0\}$ denote the origin in $\mathbb{H}$, an Euclidean vector $x^E$ is mapped into hyperbolic manifold by its exponential of hyperboloid model:

$$\begin{array}{c}\hfill x^H={\text{exp}}_o^K(x^E)=\left(\sqrt{K},\text{cosh},\left(\frac{||x^E{||}_2}{\sqrt{K}}\right),,,\sqrt{K},\text{sinh},\left(\frac{||x^E{||}_2}{\sqrt{K}}\right),\frac{x^E}{||x^E{||}_2}\right).\end{array}$$ 3

Compared to the other isometric models in hyperbolic space, the hyperboloid model avoids the numerical instability and provide efficient space for Riemannnian optimization [37]. In HI-PPI, we set curvature as learnable parameter that initialized to 1.0, rather than hyperparameter. To capture and propagate the information of PPI graph, the hyperbolic representation of proteins are iteratively updated based on their neighborhoods. A weighted aggregation operation [38] is used to aggregate neighborhood information in hyperboloid manifold. For the ith protein $p_i$, and its neighborhood set $\mathcal{N}(i)$, the weighted aggregation based on the input $x_i^H$ is:

$$\begin{array}{c}\hfill {\text{AGG}}^K{(x^H)}_i={\text{exp}}_{x_i^H}^K\left(\sum _{j\in \mathcal{N}(i)},w_{\mathit{ij}},{\text{log}}_{x_i^H}^K,(x_j^H)\right),\end{array}$$ 4

where $w_{\mathit{ij}}$ is the trainable weight computed by MLP and activation function:

$$\begin{array}{c}\hfill w_{\mathit{ij}}=\text{softmax}\left(\text{MLP},(,{log}_o^K,(x_i^H),|,|,{log}_o^K,(x_j^H)\right),j\in \mathcal{N}(\mathcal{i})\end{array}$$ 5

This aggregation operation preserves node hierarchies through relative distances in the hyperboloid manifold with minimal distortion. The hyperbolic representation of each individual protein is then processed to the next stage for the learning of the pair-wise information.

Interaction-specific learning

The relational information between node-level embedding of proteins is handled by a gated interaction network. Let $x_i,x_j$ denote the feature vectors of a pair of proteins. First, the interaction is represented by the Hadamard product $x_i\circ x_j$. A gate vector g is used to determine the contribution of interaction to final output:

$$\begin{array}{c}\hfill g=\text{sigmoid}\left(W,·,\text{concatenate},(x_i,x_j),+,b^{(1)}\right),\end{array}$$ 6

where W and $b^{(1)}$ denote the weight matrix and bias, respectively. It is clear that g is a vector of numeric values that ranges from 0 to 1. The gated interaction h is computed by:

$$\begin{array}{c}\hfill h=g\circ (x_i\circ x_j).\end{array}$$ 7

The gate vector facilitates a focus on essential interaction features, thereby enhancing the model’s generalization ability. Compared to the commonly used self-attention mechanism, gating mechanism is inherently more scalable as it requires only a limited number of matrix multiplications and element-wise operations. This makes it particularly well-suited for large-scale PPI datasets.

Classifier and loss function

The interaction-specific vector h is then processed to a fully connected (FC) layer with an output dimension equal the number of interaction types; ${\widehat{y}}_{\mathit{ij}}=\text{sigmoid(FC(}h$)) is the final prediction result. Binary cross entropy is used as the loss function:

$$\begin{array}{c}\hfill L=\frac{1}{\mathit{IC}}\sum _{i=1}^I\sum _{j=1}^C-y_{\mathit{ij}}log{\widehat{y}}_{\mathit{ij}}-(1-y_{\mathit{ij}})log(1-{\widehat{y}}_{\mathit{ij}}),\end{array}$$ 8

where I is the size of sample set and C denotes number of PPI types.

Abbreviations

PPI

Protein–protein interaction

GNN

Graph neural network

HGCN

Hyperbolic graph convolutional network

STRING

Search Tool for the Retrieval of Interacting Genes/Proteins

AFT

Attention-free transformer

GAN

Graph attention network

BFS

Breadth-First Search

DFS

Depth-First Search

AUPR

Area under precision/recall curve

AUC

Area under the curve

FC

Fully connected layer

MLP

Multi-layer perceptron

Authors' contributions

Y.L., P.W., and S.Y. supervised the study. T.T. and Y.L. conceived and designed the experiment. T.T. and T.S. performed the experiment. T.T. and W.L. analyzed the result. Y.L., J.J., and X.C. revised the manuscript. All authors read and approved the final manuscript.

Funding

This work was partly supported by the National Nature Science Foundation of China (62202236, 62372159, 62202153, 62172002, 62206108, 62476109) and the Science and Technology Innovation Program of Hunan Province (2022RC1100, 2022RC1101).

Data availability

All data generated or analyzed during this study are included in this published article, its supplementary information files, and publicly available repositories. The dataset and source code used in this project are freely available at GitHub repository (https://github.com/ttan6729/HI-PPI), Zenodo (https://doi.org/10.5281/zenodo.15702410), and Figshare (https://doi.org/10.6084/m9.figshare.29364119).

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.