library_construction_protocol: To measure enhancer activity of individual elements within the pooled recombinant population, HCR-FlowFISH was performed following the published protocol (Reilly et al., 2021) precisely, including all solution volumes and centrifugation parameters, prior to cell sorting. Briefly, 20 million recombinant cells of each biological replicate were fixed with 4% formaldehyde in PBST (1× PBS, 0.1% Tween 20) at room temperature for 1 h and washed with PBST for 4 times. Following 10 min up to 24 h incubation with cold 70% Ethanol at 4°C, cells were washed with PBST twice and incubated with the pre-warmed Probe Hybridization Buffer at 37°C for 30 min. HCR probes for NMU and ACTB were added together to cells to reach a final concentration of 4 nM per probe. The samples were then incubated overnight with agitation in a 37°C hybridization oven. On the next day, cells were washed with the Probe Wash Buffer for 5 times, with 5× SSCT (5× SSC, 0.1% Tween 20) once, and pre-amplified in the Amplification Buffer for 30 min at room temperature. Snap-cooled hairpins were diluted in the Amplification Buffer and then added to the pre-amplified samples to reach a final hairpin concentration of 60 nM. Samples were incubated with rotation in a dark room overnight at room temperature. On the next day, 5× volume of 5× SSCT was added to the samples before centrifugation and removal of the hairpin amplification solution. Cells were then washed with 5× SSCT for 6 times before final resuspension in PBS at a density of 10 million cells/mL. The samples were filtered through a 35 µm Cell Strainer cap into a 5 mL polystyrene tube (Corning) before sorting. Cells were sorted into 8 bins (2 rounds of 4-way sorting) based on the AF647/AF488 ratio at a minimum coverage of 500× barcode coverage per bin to ensure robust representation in the sequencing library. Sorted cells, together with the unsorted background sample, were pelleted and resuspended in 400 µL of ChIP lysis buffer (50 mM Tris-HCl, pH 8, 10 mM EDTA, 1% SDS), and de-crosslinked overnight at 65°C with 1000× rpm shaking. Samples were then treated with RNase A (Thermo Scientific) and Proteinase K (Invitrogen) before phenol-chloroform extraction of genomic DNA (gDNA). Sequencing libraries were prepared by two rounds of PCR using Q5 High-Fidelity 2X Master Mix (NEB). The 1st round PCR was performed on the recovered gDNA corresponding to a minimum of 200× barcode coverage, using primers ZZ145 and ZZ146 (Table S2 of manuscript) to specifically amplify the 8-bp barcodes from the eNMU genomic locus. A maximum of 500 ng gDNA was used as input in a 50 µL PCR reaction. The PCR program was: initial denaturation 98 °C for 3 min; 11 cycles of 98°C for 10 s, 65°C for 30 s, 72°C for 1 min; and final extension 72°C for 5 min. The PCR products were then purified using homebrew SPRI beads (1.5× bead ratio) to remove unused primers, followed by the 2nd round PCR with standard Illumina Nextera primers to append sequencing library indices and flow cell adaptors to the amplicons. The PCR program was: initial denaturation 98°C for 30 s; 11 cycles of 98°C for 10 s, 67°C for 30 s, 72°C for 20 s; and final extension 72°C for 5 min. Final PCR products were purified using the MinElute PCR purification kit (Qiagen) and DNA concentration was measured by the Qubit dsDNA High Sensitivity assay (Thermo Fisher). The libraries were pooled for sequencing on the Element Biosciences AVITI platform (2 × 80 bp paired-end sequencing).