Results
A cellular senescence-related classifier was constructed for TNBC. The prognoses of patients with TNBC were verified using bulk RNA-seq and scRNA-seq data. The flow chart of the study design is presented in Fig. S1 .

First, 38,582 cells were obtained by screening the data from nine samples ( Table S1 , Figure 1A ); these were clustered and 11 subpopulations were obtained ( Figure 1B ). Subsequently, these cells were subjected to TSNE dimensionality reduction analysis, and the 11 subpopulations were annotated based on some classical markers of immune cells ( Figure 1C and Table S2 ). Among them, subpopulation C1 comprised CD8 T cells expressing CD8A, CD3D, GZMA, and CD8B; C6 comprised CD4 T cells expressing CD4 and CD3D; C2 and C9 comprised macrophages expressing CD163 and CD68; C3 and C10 comprised monocytes expressing S100A8; C5 comprised B cells expressing CD19, CD79A, and MS4A1; C4 comprised plasma cells expressing CD79A and JSRP1; C0 comprised epithelial cells expressing EPCAM; C3 and C8 contained fibroblasts expressing ACTA2, FAP, PDGFRB, and NOTCH3, and C7 contained endothelial cells expressing PECAM1. We also screened marker genes among these subpopulations and analyzed their corresponding expression ( Figure 1D ). For instance, CD24 and KRT19 were highly expressed in epithelial cells in C0 and were the marker genes of C0.

The proportion of these nine subpopulations in each sample was further analyzed ( Figure 1E ). Subsequently, changes in CNVs in single cells were predicted to distinguish normal from tumor cells in each sample ( Figure 1F ). In total, 7,709 cancer cells and 30,298 normal cells were identified. Subsequently, the proportion of malignant and non-malignant cells in each sample was calculated ( Figure 1G ). The cells in samples CID3946 , CID44041 , and CID4465 were all non-malignant, while the other samples comprised both malignant and non-malignant cells.

The senescence characteristics of single cells were further assessed. Cellular senescence-related pathway scores were higher in malignant relative to the non-malignant cells ( Figure 2 ).

Cellular senescence-related pathways were highly expressed in malignant cells at the single cell level relative to the non-malignant cells, with aberrant expression. Therefore, their expression in tumor and normal tissue samples was further analyzed using a bulk RNA-seq dataset. GSEA results suggested that REACTOME_CELLULAR_SENESCENCE, and P53_SIGNALING_PATHWAY were significantly enriched in tumor tissues in TCGA dataset ( Figure 3A ). ssGSEA of the bulk RNA-seq dataset ( Figure 3B ) revealed that the enrichment scores of REACTOME_DNA_DAMAGE_TELOMERE_STRESS_INDUCED_SENESCENCE, P53_SIGNALING_PATHWAY, REACTOME_CELLULAR_SENESCENCE, REACTOME_DNA_DAMAGE_TELOMERE_STRESS_INDUCED_SENESCENCE were higher in some cancer tissues relative to the para-cancerous tissues. Therefore, these three cellular senescence-related pathways may exhibit regulatory complexity in cancerous tissues.

Three cellular senescence-related pathways, including REACTOME_CELLULAR_ SENESCENCE, and P53_SIGNALING_PATHWAY, REACTOME_DNA_DAMAGE_ TELOMERE_STRESS_INDUCED_SENESCENCE, were significantly enriched in TNBC tissues. Therefore, we further analyzed the genes enriched in these three pathways.

The above pathways comprised 253 genes, of which 186 were present in TCGA dataset. Subsequently, a univariate analysis of these 186 genes yielded seven prognosis-related genes, including ETS2, SERPINE1, FOS, SHISA5, IL1A, TP53AIP1, and IGFBP7 ( Figure 4A ). Mutations in these seven genes in TNBC were further examined. Among SNVs, ETS2 showed the highest mutation frequency (primarily mutation type: missense) ( Figure 4B ). Among CNVs, IGFBP7 had the highest frequency of acquired CNVs (CNV_gain), whereas SHISA5 had the highest frequency of deletion mutations (CNV_loss) ( Figure 4C ). The levels of these seven genes in normal versus tumor tissues were analyzed by the “wilcox.test” ( Figure 4D ). The expressions of SHISA5, SERPINE1 , and IL1A were markedly high in tumor tissues, whereas those of TP53AIP1, ETS2 , and FOS were high in the normal tissues.

Consensus clustering of 113 TNBC samples in TCGA dataset was performed based on these seven key prognosis-related genes. Stable clustering results were achieved at k = 3 ( Figs. 4E – 4F ). Therefore, three subtypes (clusters) were obtained ( Figure 4G ). Significant differences in the prognostic characteristics among the subtypes were found ( Figure 4H ). Overall, cluster 1 showed the best prognosis, followed by clusters 2 and 3. These seven genes showed the highest expression in cluster 3 ( Figure 4I ).

The expression of genes in these three senescence-related pathways among the three clusters was compared by “kruskal.test” ( Fig. S2 ). Among the three pathways, genes in cluster 2 showed the lowest expression, while those in cluster 3 showed the highest expression.

The distribution of clinical characteristics across molecular subtypes was compared by chi-square test to assess the differences among the three subtypes in TCGA. The survival statuses of these patients differed significantly among the three subtypes. In particular, the proportion of dead patients was high in cluster 3.

Differences in mutations among cellular senescence-related subtypes were analyzed. TCGA data suggested some differences in CNVs among the three subtypes ( Figs. 5A and 5C ). For instance, cluster 1 had the lowest degree of gene gain and lose. While cluster 3 exhibited the highest degree of CNV gain. Additionally, clusters 2 and 3 had similar CNV loss on chromosomes 2, 3, 4 and 5. Furthermore, TP53, TTN, MUC16, SYNE1 , and FAT3 had the highest SNV frequency ( Figure 5B ).

Cancer cells can induce cellular senescence through the inhibition of the cell cycle, and cell cycle protein-dependent kinases (CDK inhibitory proteins), such as InK4a and p21, are upregulated in senescent cells, which causes cell cycle arrest ( Wang, Lankhorst & Bernards, 2022 ). A previous study Cuzick et al. (2011) identified 31 genes associated with cell cycle progression (CCP). We computed the CCP scores of each sample in TCGA dataset by ssGSEA. clusters 1 and 2 had slightly higher CCP scores relative to cluster 3 (wilcox.test) ( Figure 6A ). No significant differences were observed among the three subtypes in the G1/S phase (wilcox.test) ( Figure 6B ), whereas the scores for G2 checkpoints were slightly lower in cluster 3 relative to clusters 1 and 2 (wilcox.test) ( Figure 6C ). Prognostic analysis suggested that patients in cluster 3 showed a worse prognosis. Therefore, the cell cycle may be one of the factors influencing cellular senescence. Other mechanisms may also regulate cellular senescence along with the cell cycle.

Similarly, inhibition of telomerase induces cellular senescence ( Wang, Lankhorst & Bernards, 2022 ). Cancer cells usually circumvent telomere attrition by activating telomerase activity. Telomere elongation scores for telomerase in cluster 3 were lower than those in clusters 1 and 2, with the latter showing the highest score. Therefore, other mechanisms may co-regulate cellular senescence with telomerase activity (wilcox.test) ( Figure 6D ).

However, in addition to conveying the message “please kill me”, the factors secreted by senescent cells also affect surrounding cells ( Yu et al., 2021 ). This effect can promote tumor migration and metastasis by promoting EMT. Senescent tumor cells can promote the production of blood and lymphatic vessels by recruiting specialized macrophages that provide oxygen and nutrients necessary for growth to other tumor cells, thus promoting tumor growth and metastasis. We calculated the EMT scores. Cluster 2 had a lower EMT score than clusters 1 and 3, indicating that patients in cluster 3 were more likely to experience metastasis (wilcox.test) ( Figure 6E ).

Based on genes in the HALLMARK_HYPOXIA pathway, the hypoxia scores of the samples were computed by ssGSEA. Angiogenesis scores of samples were also analyzed based on 24 genes from the literature ( Masiero et al., 2013 ) (wilcox.test) ( Figs. 6F – 6G ). Enrichment scores for 10 pathways associated with tumors in each sample in TCGA dataset were computed by the ssGSEA method described previously ( Sanchez-Vega et al., 2018 ). Only two of the ten pathways (NOTCH and TGF-beta signaling) exhibited significant differences (wilcox.test).

Finally, genes in the HALLMARK_INFLAMMATORY_RESPONSE pathway from GSEA-based MSigDB were analyzed for inflammation-related scores by ssGSEA. Cluster 2 had a significantly lower inflammation-related score relative to clusters 1 and 3 (wilcox.test) ( Figure 6H ).

The relationship between cellular senescence-related subtypes and immunity was analyzed to investigate the immune characteristics of these subtypes. The immune scores of patients in TCGA dataset were calculated by “ESTIMATE”. Significant differences were observed among the three subtypes, with a high degree of immune infiltration in clusters 1 and 3 (kruskal.test) ( Figure 7A ).Subsequently, the scores for the relevant cells were calculated. Significant differences were noted for all cells except CD8 T cells and cytotoxic lymphocytes (kruskal.test) ( Figure 7B ). Similarly, T cells CD4, also displayed distinct difference among three groups in TIMER and EPIC analysis ( Figs. 7C – 7D ). Although the results were obtained from different algorithms, these results all together suggested higher immune infiltration status in clusters 3. The expression of immune checkpoint genes, including NRP1, CD200, BTLA, LAIR1, and TNFRSF14 differed significantly among the three subtypes (kruskal.test) ( Figure 7E ).

Finally, the putative clinical efficacy of immunotherapy was assessed among these molecular subtypes. High TIDE scores in cluster 3 in TCGA cohort suggested that patients of this subtype were less likely to benefit from immunotherapy owing to a higher likelihood of immune escape (wilcox.test) ( Figure 7F ).

Differential analysis was separately performed between cluster 1 and non-cluster 1; cluster 2 and non-cluster 2, and cluster 3 and non-cluster 3. Finally, 2 down-regulated and 34 up-regulated DEGs were screened between cluster 1 and non-cluster 1; 293 down-regulated and 9 up-regulated DEGs between cluster 2 and non-cluster 2, and 26 down-regulated and 218 up-regulated DEGs between cluster 3 and non-cluster 3. Thus, a total of 391 DEGs were screened.

Univariate Cox analysis of these 391 DEGs yielded 69 genes with high prognostic significance ( p < 0.05), including 63 “Risk” and six “Protective” genes ( Fig. S3A ). These 69 hub genes were subsequently screened by LASSO regression ( Fig. S3B ). Further, using 10-fold cross-validation, a model was constructed and confidence intervals for each lambda were calculated ( Fig. S3C ). The model was optimum for lambda = 0.0782, whereby four genes were obtained, including MMP28, CT83, ACP5, and KRT6A ; these were selected as the target genes for further analyses.

The four genes’ expression levels were utilized to determine the risk score for each sample using the TCGA dataset as the training set. Then, using ROC analysis, the RiskScore prognostic classification was carried out ( Figure 8A ). The prognostic prediction classification efficiency was analyzed separately for 1–5 years with obtained AUC values 0.91, 0.93, 0.74, 0.83 and 0.84, respectively , and the AUC values reached 0.7, indicating good predictive performance. Samples with RiskScore greater than zero after z-score normalization were classified into the high-risk group, whereas those with Riskscore lesser than zero comprised the low-risk group, with a highly significant ( p < 0.05) difference between them ( Figure 8B ).

To validate the model’s robustness, the GSE58812 dataset was used for verification. Specifically, the risk model was constructed using these four genes and ROC analysis for prognostic classification was performed based on the RiskScore ( Figure 8C ). The prognostic predictive classification efficiency was analyzed for 1–5 years with obtained AUC values 0.98, 0.71, 0.62, 0.66 and 0.65, respectively. All AUC values were over 0.6, displaying good predictive ability. Furthermore, a significant difference in prognosis was found between the risk groups ( p < 0.05) ( Figure 8D ).

In this study, molecular assays revealed that the expression of MMP28 , ACP5 and KRT6A was increased in MDA-MB-468 and MDA-MB-231 cell lines. In contrast, the expression of CT83 was decreased in MDA-MB-468 and MDA-MB-231 cell lines ( Figs. 9A – 9D ). This result is consistent with previous analyses that high expression of prognostic risk factors and low expression of protective factors associated with higher RiskScore. Given that ACP5 is a key gene influencing high RiskScore, we inhibited the expression of ACP5 in MDA-MB-468 and MDA-MB-231 cell lines, and by transwell assay, we could observe the ability of ACP5 to promote the proliferation of triple-negative breast cancer cell lines. After we inhibited the expression of ACP5 in MDA-MB-468 and MDA-MB-231 cell lines, the invasion and migration ability of the cell lines were decreased ( Figs. 9E – 9G ). This study not only confirms the existence of ACP5 as a prognostic risk factor, but also demonstrates that this gene regulates the TNBC malignant phenotype at the cellular level, thereby influencing TNBC malignant progression.

To elucidate differences in the immune microenvironment of patients between the risk groups, differences in the relative cell abundances predicted by “MCPcounter” were compared (wilcox.test) ( Figure 10A ). T cells, cytotoxic lymphocytes, and monocytic lineage differed significantly between the risk groups. Immune cell infiltration was also assessed (wilcox.test) ( Figure 10B ). “ImmuneScore” was higher in the high-risk group relative to the low-risk group, suggesting that patients in the former had high immune cell infiltration. Additionally, TIMER and EPIC analysis also revealed higher immune infiltration status in high risk group ( Figs. 10C – 10D ).

Subsequently, differences in response to immunotherapy between the risk groups were analyzed in TCGA cohort. First, differences in immune checkpoint expression were compared. Most immune checkpoint genes, including TNFRSF14, LAIR1, and CD244 showed differential expression between the risk groups, with high expression in the high-risk group (wilcox.test) ( Figure 10E ).

A significant positive correlation between the Riskscore and T cells, cytotoxic lymphocytes, and monocytic lineage ( Figure 10F ) was observed. Risk scores also correlated positively with “ImmuneScore”, “StromalScore”, and “ESTIMATEScore” ( Figure 10G ). Drug sensitivity prediction revealed that low-risk group showed higher sensitivity to six traditional drugs (MG-132, Sorafenib, A77004, Bortezomib, Shikonin and AZ628) by wilcox.test ( p < 0.05, Figure 10H ).

Univariate regression analysis based on RiskScore and other clinicopathological characteristics suggested that the latter was the most significant prognostic factor ( p -value = 0.007, Figure 11A ) and remained so ( p -value = 0.003, Figure 11B ). A nomogram was constructed to quantify the survival probability of patients and risk assessment by combining RiskScore and other clinicopathological characteristics ( Figure 11C ). The results confirmed the greatest impact of RiskScore on survival prediction. Subsequently, the model’s prediction accuracy was assessed using a calibration curve ( Figure 11D ). The findings indicated that the calibration curves for 1-, 3-, and 5-year predictions nearly overlapped with the standard curves, pointing to the nomogram’s strong predictive ability. Furthermore, decision curve analysis (DCA) was used to evaluate the model’s dependability. DCA results highlighted that both RiskScore and nomogram had significantly more benefits than the extreme curves with strong survival predictive power relative to other clinicopathological features, especially for the 5-year survival ( Figs. 11E – 11F ).