1：Experimental Design and Method Selection:

The study implemented time-gated F?rster resonance energy transfer (TG-FRET) with terbium donors and Cy

2：5 dye acceptors into hybridization chain reaction (HCR) for nucleic acid detection. Hairpin probes were designed with specific sequences for miR-20a and miR-21, labeled with Tb or Cy5 to enable FRET upon HCR amplification. Sample Selection and Data Sources:

Synthetic microRNAs (miR-20a, miR-21, miR-20b) and their DNA analogues were used as targets, purchased from Eurogentec. Serum-containing samples were also tested.

3：List of Experimental Equipment and Materials:

Equipment included a clinical immunofluorescence plate reader (KRYPTOR compact plus, Thermo Fisher Scientific), a fluorescence lifetime plate reader (Edinburgh Instruments), a pulsed nitrogen laser (MNL 100, LTB Lasertechnik Berlin), UV/Vis spectrophotometer (Lambda 35, PerkinElmer), fluorometer (Xenius, SAFAS), electrophoresis system (Mini-PROTEAN Tetra, Bio-Rad), and Zeba Spin Desalting Columns (Thermo Fisher Scientific). Materials included Lumi4-Tb-NHS (Lumiphore Inc.), Cyanine

4：5 NHS ester (Lumiprobe), oligonucleotides (Eurogentec), Tris(hydroxymethyl)-aminomethane, bovine serum albumin, HEPES (Sigma-Aldrich), NaCl (Duchefa), and SYBR green II (Thermo Fisher). Experimental Procedures and Operational Workflow:

Hairpin probes were annealed by heating to 95°C and cooling. Targets were incubated with Tb-labeled probes, then Cy

5：5-labeled probes were added to initiate HCR. After incubation, samples were transferred to microtiter plates for TG-FRET measurements using plate readers with specific optical filters. Gel electrophoresis was performed to confirm HCR product formation. Data Analysis Methods:

FRET ratios were calculated from time-gated PL intensities. Calibration curves were used for quantification, and PL decay times were analyzed to determine FRET efficiencies and distances using equations based on F?rster theory.