Material and Methods
Single-cell sequencing dataset, GSE176078 , comprising nine samples was extracted from the NCBI data Gene Expression Omnibus (GEO; https://www.ncbi.nlm.nih.gov/geo/ ). The statistical power ( Therneau, Hart & Kocher, 2023 ) of this experimental design, calculated in RNASeqPower is 1.0. Single-cell data were subjected to filtering, quality control, clustering, and dimensionality reduction using the “Seurat” ( Gribov et al., 2010 ) package. Microarray data of GSE58812 was extracted from GEO, and probes were transformed to “symbols” using the annotation file. In total, 107 qualified tumor samples and 16,416 genes were obtained after excluding tumor samples and normal tissues without information on clinical follow-up and overall survival (OS).

Clinical phenotypic data of TNBC were extracted from The Cancer Genome Atlas (TCGA) database. Samples without information on survival time and statuses were removed, and all those with patient survival time >0 days were retained. Subsequently, expression profile data were downloaded from TCGA. Finally, 113 para-cancerous and 113 tumor samples were obtained. The statistical power of this experimental design, calculated in RNASeqPower is 1.0. Furthermore, copy number variations (CNVs) on the Masked Copy Number Segment type of TNBC were obtained from TCGA database and integrated using “gistic2” ( Mermel et al., 2011 ) software. Finally, the single nucleotide variants (SNVs) in TCGA-TNBC dataset processed by “mutect2” software, were obtained from TCGA database. Cellular senescence-related pathways were extracted from the Molecular Signature Database (MSigDB: https://www.gsea-msigdb.org/gsea/index.jsp ). Sangerbox platform ( http://vip.sangerbox.com/ ) was introduced to assist bioinformatics analysis in this study ( Shen et al., 2022 ).

First, 38,582 cells were obtained after filtering the single-cell RNA-seq data matrix according to the cell criterion (<250 transcripts/cell) and gene criterion (<3 cells/gene). The “PercentageFeatureSet” function was then used to determine the percentages of mitochondria and rRNAs. Ultimately, 38,007 cells that met the following inclusion criteria were obtained: One cell could express between 100 and 6,000 genes, the mitochondrial content was less than 25%, and each cell had a unique molecular identifier ( Yasuda et al., 2021 ) of at least 100.

Variance stabilization transformation (VST) was used to identify variable characteristics after the aforementioned data were log-normalized. High-variance genes were then discovered by employing the “FindVariableFeatures” tool. Further, the “FindIntegrationAnchors” function was utilized to remove batch effects using the canonical correspondence analysis (CCA) method for 10 samples. The data were integrated using the “IntegrateData” function. The anchor (dim = 30) was determined by principal component analysis (PCA) and dimensionality reduction after normalization using the “ScaleData” function for all genes. The cells were clustered using “FindNeighbors” and “FindClusters” functions with resolution = 0.1; this yielded 11 subpopulations. Finally, the TSNE dimensionality reduction analysis was performed on 38,582 cells using the “RunTSNE” function.

With threshold parameters of logfc = 0.5 (fold-change), Minpct = 0.35 (minimum percentage of differential gene expression), and adjusted P0.05, marker genes of subpopulations were screened using the “FindAllMarkers” tool. Subsequently, changes in cellular CNVs in single-cell data were predicted using the “copycat” ( Gao et al., 2021 ) package to distinguish tumor cells. Although cancerous and normal tissues were differentiated during sampling, cancerous tissues might contain normal cells. Therefore, a distinction between the two was necessary.

Cellular senescence-related pathways were obtained from the GSEA website ( https://www.gsea-msigdb.org/gsea/index.jsp ). We separately calculated the corresponding scores of non-malignant and malignant cells in cellular senescence-related pathways by ssGSEA using the “GSVA” package and normalized the enrichment scores for each pathway by z-score. The scores of each sample of normal and tumor tissues in the bulk RNA-seq dataset were analyzed by ssGSEA for these senescence-related pathways ( Subramanian et al., 2005 ). Finally, the significance of each senescence-related pathway in cancer and para-cancerous tissues was assessed using “wilcox.test”.

The genes related to the G1/S phase (p15-Cell cycle G1/S, MDM2-p21-Cell cycle G1/S, and p27-Cell cycle G1/S; 27 genes in total) were extracted from the Kyoto Encyclopedia of Genes and Genomes (KEGG) official website. Subsequently, the scores for G1/S genes were calculated for each sample in TCGA dataset by “ssGSEA”. Genes in the HALLMARK_G2M_CHECKPOINT pathway were downloaded from MSigDB via GSEA and the scores of G2 checkpoints were calculated for each sample in TCGA dataset by “ssGSEA”. We downloaded REACTOME_TELOMERE_EXTENSION_BY_TELOMERASE using GSEA and the primary role of this pathway was “Telomere Extension By Telomerase”. Finally, GSEA-derived enrichment scores in TCGA dataset for epithelial-mesenchymal transition (EMT) were computed by ssGSEA for 200 genes in the HALLMARK_EPITHELIAL_MESENCHYMAL_TRANSITION pathway for each sample ( Liberzon et al., 2015 ).

Univariate Cox analysis was conducted using the “coxph” function in the survival package of R to screen the significant ( p < 0.05) prognosis-related genes. LASSO-Cox regression analysis was conducted for prognosis-related genes using the “glmnet” package in R ( Friedman, Hastie & Tibshirani, 2010 ). The changing trajectory of each independent variable was analyzed. Increased lambda was positively related to increased number of independent variable coefficients tending to zero. Finally, by 10-fold cross-validation, a model was constructed; for each lambda, the confidence intervals were calculated.

The risk-related prognostic score (Riskscore) was calculated for each sample according to the equation for the sample risk score: Riskscore = Σβi×Expi, where Expi denotes the level of gene expression of the corresponding gene signature and β is the corresponding Cox regression coefficient. ROC analysis and z-score for RiskScore were computed using the “timeROC” package in R. Samples with RiskScore lower than zero comprised the low-risk group, while those with RiskScore greater than zero after z-score normalization were classified into the high-risk group. Finally, the Kaplan–Meier curves were plotted.

Consensus clustering was conducted using the “ConsensusClusterPlus” package ( Wilkerson & Hayes, 2010 ). In total, 500 bootstraps were conducted using the “hc” algorithm with “canberra” as the metric distance; in the training set, 80% of the patients were in each bootstrap process. After the number of clusters was selected to between 2 and 10, “ConsensusClusterPlus” in the TCGA clustered the 113 TNBC samples dataset. The optimal classification was confirmed based on the consensus matrix and cumulative distribution function (CDF).

Using hg38 as the reference genome, the CNV-related TCGA-TNBC results were integrated by “gistic2″software at a confidence level of 0.9. The downloaded SNV data from TCGA were analyzed using the “maftools” ( Mayakonda et al., 2018 ) package.

The scores of the relevant immune cells were calculated using the “MCPcounter.estimate” function of the “MCPcounter” package ( Becht et al., 2016 ), Tumor Immune Estimation Resource (TIMER) ( Li et al., 2020 ) and Estimating the Proportion of Immune and Cancer cells (EPIC) ( Zhou et al., 2020 ) methods. Significant differences were determined using “kruskal.test”. Immune cell infiltration was assessed using the “Estimation of STromal and Immune cells in MAlignant Tumor tissues using Expression” (ESTIMATE) ( Yoshihara et al., 2013 ) which provides information on tumor purity, scores of immune cell infiltration, and stromal cell levels in tumor tissues. Subsequently, the TIDE ( Jiang et al., 2018 ) software was used to assess the putative immunotherapeutic efficacy in the defined molecular subtypes ( http://tide.dfci.harvard.edu/ ). Higher TIDE score indicates less immunotherapy benefit as it suggests a greater possibility of immune escape. The correlation and significance of the risk score with the immune cell score were separately calculated using the “Hmisc” package’s “rcorr” function based on Pearson’s method.

Differential expression analysis of cluster 1, 2 and 3 was performed in both GSE and Target datasets in “limma” package ( Ritchie et al., 2015 ). Finally, differentially expressed genes (DEGs) were filtered under “—log2 (Fold Change)— > 1 and p < 0.05”.

Using TRIzol reagent (Thermo Fisher, Waltham, MA, USA), total RNA was collected from MDA-MB-468, MDA-MB-231 and MCF10A cell lines with 260/280 the value was between 1.8–2.0. High-Capacity cDNA Reverse Transcription Kit (4368814, ThermoFisher, Waltham, MA, USA) was conducted for reverse transcription. Using a LightCycler 480 PCR System (Roche, Indianapolis, IN, USA), the RNA from each sample (2 µg) was subjected to qRT-PCR with FastStart Universal SYBR ® Green Master (Roche, Indianapolis, IN, USA). The cDNA was a template with a reaction volume of 20 µl (0.5 µl of forward and reverse primers, 2 µl of cDNA template, 10 µl of PCR mixture, and appropriate volume of water). For the PCR reactions, cycling began with an initial DNA denaturation phase for 30 s (s) at 95 °C, then a total of 45 cycles were run for 15 s at 94 °C, for 30 s at 56 °C, and for 20 s at 72 °C. Each sample was performed for three separate analyses. Data from the threshold cycle (CT) were normalized to the level of GAPDH by 2 −ΔΔCT . The mRNA expression was compared in the normal and control tissues. Sequences of primer pairs targeting (Shanghai Gemma Gene Co., LTD, Shanghai, China) the genes are listed as follows:

Breast cancer cell lines MDA-MB-468, MDA-MB-231, and non-tumorigenic epithelial cell lines MCF10A were suspended in serum-free cell freeze and immediately frozen in liquid nitrogen tanks. MDA-MB-468, MDA-MB-231 and MCF10A cell lines were commercially obtained from Beijing Bena Biotechnology Co. (Beijing, China). Cells were cultured in DEME F-12 medium (Gibco, Waltham, MA, USA). Lipofectamine 3000 (Invitrogen, Waltham, MA, USA) was used for transfecting the ACP5 siRNA (Sagon, China) and negative control (NC) into the cells. The target sequences for ACP5 siRNA were TCCTAAATCAAGCATCTTTCTGT (si ACP5).

Migration and invasion of MDA-MB-468 and MDA-MB-231cell lines were detected. Cell (5 × 10 4 ) inoculation onto chambers coated (for invasion) or uncoated with Matrigel (BD Biosciences, USA) (for migration) was performed. The upper layer was added with serum-free medium, while the lower layer was added with complete DMEM medium. After incubation for 24 h, migrated or invaded cells were fixed using 4% paraformaldehyde and dyed by 0.1% crystalline violet. Cell number was counted using a light microscope. The experiment was conducted in our own lab.

All statistical analysis was done with R program (v4.2.0). The Wilcoxon test evaluated two-group difference. Differences among three groups were analyzed by the Kruskal–Wallis test. Cox analysis and survival analysis both used the log-rank test. For Wet experiments, the number of each group was 3 independent experiments. Assay carried out by investigator’s lab. Consumables in experiments we use are RNAase and DNAase free.