Patients and sample collection

The Cancer Genome Atlas (TCGA) prostate adenocarcinoma (TCGA-PRAD) data were downloaded from UCSC Xena. Other datasets, including Memorial Sloan Kettering Cancer Center (MSKCC, GSE21032), GSE116918, GSE70768, and GSE70769, were obtained from the Gene Expression Omnibus (GEO) database. The gene expression profiles of the five datasets were preprocessed as previously described [16]. PCa tissues and adjacent noncancerous tissues were collected from PCa patients for immunohistochemistry analysis after prostatectomy at the First Affiliated Hospital of Anhui Medical University. Our study was approved by the Ethics Committee of the First Affiliated Hospital of Anhui Medical University, and written informed consent was obtained from the participants (Approval No. PJ 2021-12-24).

Gene set variation analysis (GSVA)

Gene set variation analysis (GSVA), a gene set enrichment method, is used to assess variations in pathway activities in a certain population [17]. Fifty hallmark gene sets were obtained from the Gene Set Enrichment Analysis (GSEA) database. We performed GSVA between the recurrence and nonrecurrence groups using the “GSVA” package in R software (Version 3.4.3) [17, 18]. Commonly activated or suppressed signaling pathways were selected and overlapped to identify significant and stable pathway gene sets.

Establishment of the prognostic E2F-related gene signature with LASSO Cox regression using the MSKCC cohort

Based on the results achieved above, we obtained the gene list of the “HALLMARK_E2F_TARGETS” pathway from the GSEA database (https://www.gsea-msigdb.org/gsea/msigdb/cards/HALLMARK_E2F_TARGETS.html), with 420 founder gene sets included. Univariate Cox regression was performed to screen RFS-related gene candidates in the MSKCC cohort. Subsequently, we used LASSO Cox regression analysis to establish an optimal RFS prediction signature for PCa patients based on these candidates using the “glmnet” package in R [19]. Briefly, LASSO regression was used to identify the E2F-related genes associated with the biochemical recurrence of PCa, and Cox regression was performed to obtain the corresponding coefficients of each gene. The risk formula was calculated based on the expression levels of the candidate genes and their corresponding coefficients, which was expressed as follows: = \(_^ (}_\times }_)\), where \(}_\) is the expression level of the candidate gene in patient \(i\), and \(}_\) is the coefficient of gene \(i\). The risk score of the E2F-related gene signature of each patient was obtained based on the risk formula.

Evaluation of the E2F-related gene signature for RFS prediction in PCa patients using the MSKCC cohort

Based on the risk score of the E2F-related gene signature, an equal number of PCa patients from the MSKCC cohort were allocated into low- and high-risk groups. We used Kaplan–Meier (K–M) survival analysis to assess survival differences between PCa patients from different risk groups. A heatmap was generated to visualize the expression of the four E2F-related genes in the low- and high-risk groups using the “pheatmap” package in R software. The “survival” package in R was used to perform a two-sided log-rank test. Moreover, time-dependent receiver operating characteristic (ROC) curve analysis was adopted to obtain the area under the curve (AUC) for 1-year, 3-year, 5-year, and 10-year RFS and to estimate the performance of the E2F-related gene signature in RFS prediction using the “survivalROC” package in R [20].

Validation of the prognostic value of the E2F-related gene signature in the TCGA-PRAD cohort

To determine the clinical application value of the established gene signature derived from the MSKCC cohort, the TCGA-PRAD cohort was utilized to validate the gene signature. Kaplan–Meier analysis, log-rank test, and time-dependent ROC curves were performed to demonstrate the significance and accuracy of RFS prediction using the TCGA-PRAD cohort.

Association of the prognostic signature with other clinicopathological characteristics

The association between the risk score and pathological T stage and Gleason score was analyzed using the t-test. In the MSKCC and TCGA datasets, K-M survival analysis was performed for PCa patients with pathological stages T3 + T4 and Gleason score ≥ 7.

Establishment and validation of the RFS-predicting nomogram based on the E2F-related gene signature

To explore the advantages of our E2F-related gene signature, ROC curve analysis was performed between our E2F gene signature and four previously published PCa-related gene signatures [21,22,23,24]. Among these, Yang et al. constructed a gene signature with 28 hypoxia-related genes to predict BCR in localized PCa [21]; Liu et al. built a cancer stem cell-related gene signature comprising 13 genes to predict early BCR in PCa [22]; Cuzick et al. established a cell cycle progression (CCP) score that integrated 31 CCP genes to predict BCR in PCa [23]. Finally, Zhang et al. established a prostate cancer stemness model (PCS) with 13 genes to predict progression-free survival in PCa [24]. Multivariate Cox regression was performed to identify RFS-related clinicopathological characteristics in the MSKCC cohort, which was used to establish the E2F-related gene signature-based RFS-predicting nomogram using the “Regplot” package in R for application of the E2F-related gene signature in clinical practice. The calibration curve and decision curve analysis (DCA) were used to assess the performance of the RFS-predicting nomogram. Based on our nomogram, each patient in the TCGA cohort obtained a nomogram score, and a Kaplan–Meier analysis was conducted between PCa patients with low and high scores. DCA and time-dependent ROC analysis were used to evaluate the predictive ability of the nomogram scores.

Cell culture, transfection, and antibodies

Human PCa cell lines (PC3 and C4-2) were purchased from the American Type Culture Collection (ATCC, Manassas, VA, USA) and cultured in Dulbecco’s modified Eagle’s medium (DMEM, Gibco, USA) with 10% fetal bovine serum (FBS, Cat# 10270-106, Gibco, UK) and penicillin–streptomycin combination solution (10 kU/mL penicillin and 10 mg/mL streptomycin, Cat# PB180120, Procell, Wuhan, China) at 37 °C and 5% CO2. PCa cells were transfected with small interfering RNAs (siRNAs) (General biological system, Anhui, China) using Lipofectamine 3000 reagent (Lot# 2307436, Invitrogen, USA). The sequences of si-cyclin-dependent kinase inhibitor 2C (si-CDKN2C), si-Rac GTPase-activating protein 1 (si-RACGAP1), and the nontargeting control (NC) are shown in Additional file 1: Table S1. The antibodies used were as follows: anti-CDKN2C (Cat# ab192239, Abcam, Cambridge, UK), anti-RACGAP1 (Cat# ab134972, Abcam, Cambridge, UK), anti-β‐actin (Cat# AF7018; Affinity, OH, USA), and anti-β‐tubulin (Cat# AF7011, Affinity, OH, USA). The secondary antibodies included goat anti‐rabbit for CDKN2C, RACGAP1, and β-actin (Cat# AS014, ABclonal, Wuhan, China) and goat anti-mouse for β-tubulin (Cat# S0002, Affinity, OH, USA).

Immunohistochemistry (IHC) analysis

IHC was performed as described in our previous study [25]. Briefly, after fixing the tissues with 4% formalin for 48 h overnight at 4 °C, the PCa and adjacent noncancerous tissues were embedded in paraffin and then sliced into 5-μm thick sections. Subsequently, the tissue sections were dewaxed and dehydrated with xylene and 100%, 95%, and 75% alcohol solutions. Then, antigen retrieval and endogenous peroxidase blocking with 0.3% hydrogen peroxide were conducted, and sections were incubated with primary antibodies against CDKN2C and RACGAP1 (1:100) overnight. The tissue sections were washed with phosphate-buffered saline (PBS, pH 7.2) and incubated with secondary antibodies (1:400, Cat# PV-6000, Zsbio, Beijing, China) at room temperature. After incubating the sections with horseradish peroxidase and 3,3′-diaminobenzidine (DAB, Cat# ZLI-9018, Zsbio, Beijing, China), the sections were counterstained with hematoxylin. Images were obtained under a light microscope (Product model# CX43, Olympus, Japan).

Western blotting

Western blotting was performed as described in our previous study [26]. Total protein was extracted from cells using RIPA lysis buffer (Sigma, USA), and the concentrations were determined using a BCA assay kit (Cat# P0012S, Beyotime, Shanghai, China). After mixing with loading buffer and boiling for 10 min, samples were loaded onto sodium dodecyl sulfate (SDS) polyacrylamide gels, and then the proteins were transferred onto NC membranes. The membranes were blocked in 5% nonfat milk (Yili Industrial Group, Inner Mongolia, China) for 1 h at room temperature. After incubation with specific primary antibodies overnight at 4 °C, the membranes were incubated with the corresponding secondary antibodies (1:5000) for 1.5 h at room temperature. Immune complexes were visualized using an ECL reagent (Cat# P0018AS, Beyotime, Shanghai, China). The optical density values were quantified using ImageJ software (NIH, Bethesda, USA).

MTT

PC3 cells (3000 cells per well) or C4-2 cells (5000 cells per well) were seeded into 24-well plates and cultured for 24 h. Cell growth was determined at 0, 24, 48, and 72 h after transfection. Briefly, 50 μL of MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium-bromide, 5 mg/mL, Cat# 3580GR001, BioFroxx, Germany) was added to each well and incubated at 37 °C for 1.5 h. After removing the medium, the formazan crystals were dissolved in 1 mL of DMSO for 10 min. Relative cell growth was determined based on the optical density value of each well.

Colony formation

Cells were seeded into 6-cm dishes at a density of 1000 cells per well, and colony formation was assessed on day eight. The cell culture medium was changed regularly, and methanol was used to fix the colonies for 15 min. The colonies were then washed with PBS and stained with 1% crystal violet. The number of colonies was quantified using ImageJ software (NIH, Bethesda, USA). We counted the colony numbers by a deep-learning based counting tool, CFU.Ai (https://www.cfu.ai/), it help us to obtain the exact number for each well.