Methods and materials
The GSE99795 dataset containing raw data from 144 PRAD cells treated with androgen at 0 and 12 h was downloaded from the Gene Expression Omnibus (GEO) dataset ( https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE99795 ). In this project, the researchers conducted transcriptome profiling of 144 single LNCaP PCa cells, both treated and untreated with androgen, following cell cycle synchronization.

For additional data, we downloaded the RNA-seq and clinical information of The Cancer Genome Atlas (TCGA)-PRAD samples via Genomic Data Commons (GDC) portal ( https://portal.gdc.cancer.gov/ ). The normalization of transcriptome count was conducted using the edgeR package (Version 3.26.8). The expression data and clinical information of other PRAD samples were obtained from GSE116918 , GSE70769 , and the MSKCC-PRAD cohort ( https://www.cbioportal.org/study/summary?id=prad_pik3r1_msk_2021 ) for more intensive analysis.

We collected scRNA-seq data of 144 tumor cells using the GRCh38 reference genome, which contain three types of cells: 0-h untreated cells, 12-h untreated cells and 12-h androgen-treated cells. We utilized the Seurat package to construct the object and applied quality control filters to remove cells with poor quality ( Yip, Sham & Wang, 2019 ). The scRNA-seq was performed using the 10× Genomics platform and the Illumina HiSeq 2500 sequencing technology. We assessed the percentage of gene counts, cell counts, and mitochondria sequencing counts to ensure data integrity. In addition, we performed principal component analysis (PCA) as a linear dimensionality reduction technique. This allowed us to identify the most significant dimensions of dataset based on an estimated P value.

We extracted the expression data of essential genes from the TGCA-PRAD patients and obtained their corresponding clinical information. The least absolute shrinkage and selection operator (LASSO) regression analysis was conducted by the glmnet package to identify the essential targets. Survival analysis was conducted using the survival package, specifically employing the Kaplan-Meier method. To visualize the differential distributions of the ARGs signature, we utilized bubble plots and scatter graphs. Additionally, the multigene activity (MAG) signature was calculated using the formula: MAGs = Σ (βi * Expi), where βi represents the weight of each identified target. In the training TCGA-PRAD cohort, we performed receiver operating characteristic (ROC) curve to evaluate the predictive significance of ARGs. The difference in progression-free outcomes was assessed through Kaplan-Meier analysis with the log-rank test. Furthermore, the ggDCA package was utilized to conduct the decision curve analysis (DCA).

The tumor mutation burden (TMB) calculation in the TGCA-PRAD dataset was performed using the following formula: TMB = (total variant count)/(total length of exons). A Perl script was developed to handle the mutational data from PRAD patients, which included deletions, insertions, and substitutions across bases. The Maftools package was utilized to visually represent the mutation profiles of the two risk levels using a waterfall plot. Subsequently, the chi-square test was employed to detect and compare the differential mutation frequencies of mutants between the two groups of ARGs. Additionally, TMB was determined for each sample, and the potential associations between ARGs and TMB levels were assessed through the estimation of P values.

Consensus clustering ( Wu & Liang, 2021 ) was conducted using the R package “Consensus Cluster Plus.” The optimal number of subgroups was evaluated using the cumulative distribution function (CDF) and consensus matrix. Furthermore, PCA analysis was employed to identify two distinct groups characterized by different molecular processes and prognostic outcomes.

Since we have already divided the TCGA-PRAD cohort into two groups with high and low ARGs levels, we further conducted gene set enrichment analysis (GSEA) using the ARGs score as the phenotype. Using the GSEA software and the Java platform, we utilized the “c2.cp.kegg.v6.2.symbols.gmt gene sets” from the MSigDB database ( http://software.broadinstitute.org/gsea/msigdb ) as the reference set. The enriched crosstalk with false discovery rate < 0.05 were regarded to be statistically significant.

The 293 T cells and human PRAD cell lines (22Rv1 and C42-B) were acquired from the American Type Culture Collection (ATCC). The 22Rv1 and C42-B cells were cultured in Roswell Park Memorial Institute-1640 medium (Invitrogen, Waltham, MA, USA) supplemented with 10% fetal bovine serum (FBS, HyClone, Logan, UT, USA). Authentication of all cell lines was performed through short tandem repeat (STR) profiling. The cells were maintained in a humidified incubator at 37 °C with 5% CO 2 . Regular testing for mycoplasma contamination was conducted using the LookOut Mycoplasma PCR Detection Kit (Sigma-Aldrich, St. Louis, Mo, USA).

The full-length cDNA encoding human ORC1 was amplified through polymerase chain reaction (PCR) and inserted into a pMSCV-puro-retro vector (TaKaRa, Kusatsu, Shiga, Japan) by cloning. Subsequently, two short hairpin RNAs (shRNAs) targeting ORC1 were cloned into the pLKO.1-puro vector (Invitrogen, Waltham, MA, USA). Specific regions of ORC1 promoter sequences were amplified using PCR and cloned into a luciferase reporter plasmid. The transfection of the plasmids into the designated cells was performed using Lipofectamine 3000 (Invitrogen, Waltham, MA, USA). To establish stable cell lines, retroviral or lentiviral infection was employed to express Flag-ORC1 or ORC1-shRNA, respectively. Following a 10-day culture period, the cells were selected using 0.5 μg/mL puromycin. Double-strand oligos of sh-ORC1: 5′-CACCAGTTTTCGATCCAACAAGGGCCGAAGCCCTTGTTGGATCGAAAAC-3′.

Cell viability was assessed using the cell counting kit-8 (CCK-8) kit (Dojindo Molecular Technologies, Mashikimachi, Japan). Following the transfection of C4-2B and 22RV-1 cells with shORC1 lentivirus for 48 h, the cells were seeded in 96-well plates with 1,000 cells per well and five replicate wells. CCK8 reagent was added to the wells, mixed with the cell culture medium, and incubated for 3 h. The optical density (OD) at 450 nm was measured using a microplate reader (ELX-800; BioTek, Winooski, VT, USA) to generate a growth curve.

For the soft agar assay, cells from each group were trypsinized to obtain a single-cell suspension. After cell counting, the cell concentration was adjusted to 5 × 10 2 cells/ml, and 2 ml of the suspension was seeded into each well of a six-well plate. Three parallel wells were set up for each group. The six-well plate was placed in a 37 °C, 5% CO 2 incubator for regular culture, with the medium changed every 2 days. On the 14th day, the six-well plate was removed, and the medium was discarded. The plates were rinsed three times with physiological saline, and the cells were fixed with 1 ml of 4% paraformaldehyde for 30 min. After removing the fixative, each well was stained with 1 ml of 5% crystal violet dye for 1 h. Cell colonies containing ≥50 cells were counted as individual colonies under a microscope.

The cells were plated in either a six-well plate coated with poly-HEMA (Sigma, Burlington, MA, USA) or an ultra-low-attachment plate (Corning, Corning, NY, USA). They were then incubated in serum-free medium supplemented with 1× N2 supplement, 20 ng/mL bovine fibroblast growth factor, and 20 ng/mL epidermal growth factor for a duration of 10 days. The number of spheres formed was counted under a microscope, specifically focusing on spheres with a diameter greater than 100 μm.

Male NOG mice, aged 4 weeks and weighing 20 ± 2.0 g, were utilized as transplant recipients. All procedures involving animals were conducted in accordance with the institutional ethical requirements and were approved by the Institutional Animal Care and Use Committee of Wenzhou Medical University (Approval No. WMU2071357-AC-03). The sample size for the animal experiment was determined as five nude mice in both the shCtrl group and shORC1 group, and the mice were randomly assigned. A cell suspension of approximately 5 × 10 6 C42-B cells in PBS (200 microliters) was injected into 4-week-old NOG nude mice, with five mice in each group. Simultaneously, the mice were treated with enzalutamide at a dosage of 2.5 mg/kg/d. Tumor size was measured every 3 days using calipers, and tumor volume was calculated using the formula: V (mm 3 ) = a × b 2/2 , where “a” and “b” represent the long and short diameters, respectively. At 28 days, the mice were sacrificed, and the subcutaneous tumors were excised and preserved at −80 °C.

The differences between two groups were assessed using the Student’s t-test, while the log-rank test was employed to analyze survival differences. All experimental data were presented as mean ± standard deviation (SD). Statistical analysis was performed using GraphPad Prism 7.0 software. A P -value less than 0.05 was considered statistically significant.