METHOD DETAILS

Summary of library designs and complete sequence information is provided in Table S5.

DNA constructs consisting of the PUF library and short constant regions for subsequent PCR assembly (Figure S1D & Table S7; 5′–TGTATGGAAGACGTTCCTGGATCC–[Variable region]–AGATCGGAAGAGCGGTTCAG–3′) were ordered from CustomArray, Inc. as part of a 90,000 oligo pool of 130 nt sequences. Each of the 34,927 unique sequences in the library (including variants not discussed herein) was included at least in duplicate to increase the probability of error-free generation. In cases where the designed sequence was shorter than 130 nt, the construct was “padded” at the 3′ end with a random sequence that was eliminated during PCR assembly. Primers and DNA oligonucleotides used in the RNA-MaP protocol were ordered from Integrated DNA Technologies (IDT).

The oligonucleotide pool was amplified using emulsion PCR (ePCR) (Williams et al., 2006), allowing us to decrease length and other biases during PCR amplification of our highly diverse library (lengths of 64–130 nt, variable structure content). We closely followed a MYcroarray adaptation of the ePCR protocol from (Williams et al., 2006), as detailed below. Flat-bottom glass vials (1 mL) were cleaned with sterile water, dried, covered with parafilm, and frozen in a Petri dish filled with sterile water. The oil phase was prepared from 4% (v/v) ABIL EM-90, 0.05% (v/v) Triton X-100 and 96% (v/v) mineral oil. The 50 μL aqueous phase consisted of 1.45 ng/μL of the CustomArray oligo pool, 0.2 mM dNTPs, 1 μL of Phire Hot Start II DNA Polymerase (Thermo Fisher Scientific), 1x Phire II buffer, 0.5 mg/mL bovine serum albumin (BSA), and 2 μM of each of RNAPstall and Read2 primers (Table S7 and Figure S1D). A 300 μL aliquot of the vortexed, pre-chilled oil phase was added to the glass vial embedded in the ice-filled Petri dish and stirred on a stir plate with a sterile magnetic bar at 1000 rpm for 5 min. The aqueous phase was then added in five 10 μL aliquots and stirred for another 10 min. The emulsion was divided between seven PCR tubes and amplified for 40 cycles of 98°C for 10 s, 65° C for 10 s, and 72° C for 30 s. Completed PCR reactions were pooled in a 1.7 mL Eppendorf tube, and 1 μL of gel loading dye was added to visualize the aqueous phase. Mineral oil (100 μL) was added and the mix was vortexed for 30 s, followed by centrifugation for 10 min at 13,000 g. The oil was discarded and 1 mL diethyl ether was added, the mixture was vortexed in a fume hood for 3 min and centrifuged for 1 min at 13,000 g. Diethyl ether was discarded, 1 mL ethyl acetate was added, and the mixture was vortexed in a fume hood for 3 min and centrifuged for 1 min at 13,000 g. Ethyl acetate was removed and the diethyl ether extraction step was repeated, followed by discarding the diethyl ether. The tube was incubated for 5 min at 37°C with an open cap to allow residual diethyl ether to evaporate. Water (40 μL) and Agencourt AMPure XP beads (Beckman Coulter; 72 μL) were added and incubated for 15 min at room temperature; the supernatant was removed, the beads were washed with 70% ethanol (2 × 100 μL), dried, and the DNA was eluted in 10.5 μL water.

To further prevent bias toward short oligonucleotides during the subsequent PCR assembly steps, the ePCR-amplified library was fractionated by length on an 8% polyacrylamide gel. Following SYBR Green staining (1x; Lonza), the library-containing lane was covered with aluminum foil to prevent UV-induced damage (Gründemann and Schömig, 1996; Sinha and Häder, 2002), and divided into 6 fractions based on UV visualization of marker lanes. The cut-out bands were frozen on dry ice and eluted overnight in TE buffer (10 mM Tris,HCl, pH 8.0, 1 mM Na₂EDTA) on a rotating platform at 8°C. The DNA was purified using the QIAGEN Gel Extraction Kit (using a protocol adapted for PAGE purification: http://www.qiagen.com/kr/resources/resourcedetail?id=1426dbb4-da09-487c-ae01-c587c2be14c3&lang=en, with QIAGEN MinElute columns). To remove residual co-purified short fragments, each fraction was re-purified on an 8% denaturing gel (8 M urea). For denaturing PAGE, the samples and a Low-MW DNA ladder (New England Biolabs; NEB) were heated in loading buffer (84% (v/v) formamide, 50 mM Na₂EDTA, 0.04% Xylene cyanol, 0.04% Bromophenol blue (BPB); 2.8 μL loading buffer per 5 μL sample) at 90°C for 3 min immediately before loading. The gel was stained with SYBR Gold, the library-containing lanes were covered with aluminum foil and fractions were cut out based on UV visualization of marker lanes. (Additional lanes with 83 nt and 129 nt DNA oligonucleotides were used to facilitate alignment of the NEB low-MW marker with desired lengths.) The DNA was extracted from the gel as above and eluted in QIAGEN EB buffer with 0.1% Tween-20. Purified fractions were re-amplified using the Read2 and RNAPstall_adapt primers (Table S7). The PCR reactions (25 μL) consisted of 2.5 μL of the purified library fractions, 0.5 μM of each primer, 0.2 mM dNTPs, 3% DMSO, 0.02 U/μL Phusion HF Polymerase (Thermo Fisher Scientific), and 1x Phusion HF buffer. The reactions proceeded for 15–23 cycles of 98°C for 10 s, 63°C for 20 s, and 72 °C for 20 s and were purified using QIAGEN MinElute PCR Purification Kit. In all cases here and below, the number of PCR cycles was determined by quantitative PCR (qPCR), using the same primer and template concentrations as in preparative PCR, but in the presence of 0.2–0.5x SYBR Green. To prevent accumulation of by-products, cycle numbers corresponding to about one-third saturation (C_t value) were used in preparative PCR reactions. Each library fraction was amplified for two to three different numbers of cycles around the C_t value, and only reactions lacking high-molecular weight byproducts were propagated to the next step.

Each purified length fraction was assembled into the final RNA array construct with the C_read1_bc_RNAP, D_read2, OligoC and OligoD primers, as illustrated in Figure S1D (see Table S7 for primer sequences). The C_read1_bc_RNAP primer contained a randomized 15 nt ‘barcode’ region that served as a unique molecular identifier (UMI) and allowed high-confidence sequence mapping during subsequent steps (Buenrostro et al., 2014). The PCR reactions consisted of 0.5 nM of the amplified library fractions, 1.5 nM of C_read1_bc_RNAP primer, 1.5 nM of D_read2 primer, 0.5 μM of Oligo C and Oligo D primers, 0.2 mM dNTPs, 3% DMSO, 1x Phusion HF buffer, and 0.01 U/μL Phusion HF Polymerase. The reactions proceeded for 18 cycles of 98 °C for 10 s, 63° C for 30 s, and 72° C for 30 s, and the PCR products were purified using QIAquick PCR purification kit (QIAGEN).

To ensure that multiple copies of each UMI were present on the RNA array, the library was bottlenecked to ~700,000 total molecules (Buenrostro et al., 2014; Denny et al., 2018; Kivioja et al., 2011). UMI redundancy allows distinguishing between sequencing errors and real sequence differences, as errors are unlikely to co-occur in both the UMI and the variable region (see Computational analyses below). To bottleneck, the PCR products were quantified by qPCR relative to the PhiX standard (Illumina). As noted above, the six ‘sublibraries’, corresponding to the different oligonucleotide lengths in our library, were kept separate during all pre-sequencing PCR steps to minimize bias in the final library assayed by RNA-MaP. Dilutions of 1000-fold and 10,000-fold for each fraction were prepared in 0.1% Tween-20. The PhiX standard (Illumina) was diluted to 200 pM and seven serial dilutions were prepared in 0.1% Tween-20. The DNA was then added to a PCR master mix containing 500 nM OligoC and OligoD primers, 200 μM dNTP mix, 0.5x SYBR Green, 3% DMSO, 0.02 U/μL Phusion DNA Polymerase, and 1x Phusion buffer. The PCR reactions proceeded for 35 cycles of 98° C for 10 s, 63° C for 30° s, and 72° C for 30 s. The library concentrations were determined based on the PhiX standard curve of C_t values over concentration (determined in duplicate). The volumes corresponding to a total of 700,000 molecules across all sublibraries were calculated, and each sublibrary was amplified with OligoC and OligoD primers. The PCR reactions contained1.1–5.3 fM of individual sublibraries (in 0.1% Tween-20), 500 nM OligoC and OligoD primers, 200 μM dNTP mix, 3% DMSO, 1x Phusion buffer, and 0.01 U/μL Phusion DNA Polymerase. The reactions proceeded for 23 cycles of 98° C for 10 s, 63° C for 30 s, and 72° C for 30 s, and the PCR products were purified with QIAquick PCR cleanup kit (QIAGEN). Concentrations of 1000-fold dilutions were quantified by qPCR, and the different sublibraries were combined for sequencing. Due to a short OligoD byproduct detected as dominant species in the initial sequencing of our library, the bottlenecked library fractions were re-purified on a denaturing 8% acrylamide gel and amplified using Phusion Hot Start II DNA Polymerase (Thermo Fisher Scientific) instead of regular Phusion, which eliminated the primer byproduct. This library was sequenced and used in all RNA-MaP experiments reported herein.

To facilitate RNA array image alignment and quantification, we included a fiduciary marker oligonucleotide in our RNA array library sample prior to sequencing (see below). This oligonucleotide resembled the library constructs, except for lacking the barcode, RNAP promoter and RNAP start/stall regions and was PCR-assembled separately using an analogous series of steps. The final sequence of the fiduciary oligo consisted of [C_adapter][Read1] CTT GGG TCC ACA GGA CAC TCG TTG CTT TCC [Read2′][D′_adapter] (Fiducial_chip, Table S7).

The bottlenecked, qPCR–quantified library fractions were combined and sequenced using MiSeq Reagent Kit v3 (150-cycle; 56 nt in Read 1, 96 nt in Read 2). To ensure appropriate density of RNA clusters in the RNA-MaP experiments, our library constituted 9%–15% of the total 6–9.6 fmol DNA. The remaining DNA consisted of 84%–90% PhiX DNA and 1% of the fiduciary marker oligonucleotide (Fiducial_chip, Table S7). The final numbers of transcribable clusters were 3.6 × 10⁵−6.5 × 10⁵ on the sequencing chips used in this study.

The RNA-binding domains of H. sapiens PUM1 (828–1176; isoform 2), PUM2 (706–1059; isoform 1), and mutant PUM1 (MUT3–1 in (Cheong and Hall, 2006)) (828–1176) were cloned into a custom pET28a-based expression vector in frame with an N-terminal Histag and a SNAP tag (New England Biolabs) at either the N- (PUM2) or C terminus (hPUM1 and hPUM1 MUT3–1; primers and plasmid sequences available upon request). Constructs were sequenced and transformed into E. coli protein expression strains BL21 (DE3) or RIPL BL21 CodonPlus (Agilent). Protein expression was induced at an OD600 of between 0.6–0.8 with 0.5–1 mM IPTG at 18–20°C for 18–20 h. Cell pellets were lysed four times using an Emulsiflex (Avestin) in Buffer A containing 20 mM Na-HEPES, pH 7.4, 500 mM potassium acetate (KOAc), 5% glycerol, 0.2% Tween-20, 10 mM imidazole, 2 mM dithiothreitol (DTT), 1 mM phenylmethylsulfonyl fluoride (PMSF) and 2X Complete Mini protease inhibitor cocktail (Roche). The lysate was centrifuged at 20,000 g for 20 min to remove membranes and unlysed cells. Nucleic acids in the lysate were precipitated with dropwise addition of Polyethylene Imine (Sigma) to a final concentration of 0.21% (v:v) with constant stirring at 4° C and pelleted by centrifugation at 20,000 g for 20 min. Cleared lysates were then loaded on a Nickel-chelating HisTrap HP column (GE), washed extensively, and His-tagged proteins were eluted over a 10–500 mM imidazole gradient. Protein fractions were pooled and desalted into Buffer B (20 mM Na-HEPES, pH 7.4, 50 mM KOAc, 5% glycerol, 0.1% Tween-20, 2 mM DTT) using a HiPrep 26/10 desalting column. The His-tag was removed by incubation with TEV protease for 13–16 h at 4°C, and the protein solution was loaded for a second time on the HisTrap HP column. The flow-through containing cleaved protein was collected and subsequently desalted into Buffer B. The protein was then loaded on a Heparin or HiQ column and eluted over a linear gradient of KOAc from 50 to 1000 mM. Fractions were pooled and desalted into Buffer C containing 20 mM Na-HEPES, pH 7.4, 100 mM KOAc, 5% glycerol, 0.1% Tween-20 and 2 mM DTT, concentrated using Amicon Ultra–0.5 10KDa filters and diluted two-fold with Buffer C containing 80% glycerol for final storage at −20°C. SDS-PAGE gels of final purified protein constructs are shown in Figure S7K.

Cy3B-labeled SNAP tag substrate was prepared by coupling Cy3B NHS ester (GE Healthcare, 0.75 μmol) with 1.5-fold excess(1.13 μmol) of amine-terminated benzylguanine (NH2-BG; New England BioLabs) in the presence of 1.13 μmol triethylamine in dimethylformamide. The reaction (103 μL) was incubated overnight on a rotating platform at 30°C. The Cy3B-BG product was purified by reverse phase HPLC on an Agilent ZORBAX Eclipse Plus 95Å column and dried by speed-vac evaporation (46% yield).

SNAP-tagged PUF proteins were labeled by incubating 5–10 μM of purified protein with 20 μM of Cy3B-BG in Buffer C. The tube was covered with aluminum foil and rotated at 4°C for 12–14 h. Unincorporated dye was removed with Zeba Spin Desalting Columns (Thermo Fisher Scientific) equilibrated with Buffer C; the protein was concentrated using Amicon Ultra 10KDa filters and diluted two-fold with Buffer C containing 80% glycerol for final storage at −20°C. The labeling efficiencies (based on total protein concentration and Cy3B absorbance at 559 nm; Cy3B extinction coefficient: 130,000 M⁻¹cm⁻¹) were 60% (PUM2-SNAP), 53% (SNAP-PUM1) and 36% (mutant SNAP-PUM1).

The RNA-MaP imaging platform was built out of a repurposed Illumina GAIIx instrument with custom-designed additions as described in (Buenrostro et al., 2014; Denny et al., 2018; She et al., 2017). Briefly, the custom additions included a fluidics adaptor interface to pump reagents to the MiSeq flow cell, a Peltier-based temperature-controlled platform to house the flow cell, an autosampler with 96-well cooling block for RNA-MaP reagents, and a dual–color laser excitation system. Two lasers were employed: a 660 nm ‘red’ laser with a 664 nm long pass filter and a 530 nm ‘green’ laser with a 590 nm band pass filter. MATLAB scripts developed in-house were used to control the fluidics, temperature, position, and imaging of the flow cell. Flow cell images were acquired with 400 ms exposures at 200 mW laser power. Camera focal distances were determined through iterative rounds of imaging of the flow cell and adjustment of the camera’s z-position.

Using the imaging station fluidics system, the flow cell was washed with 5 mM Na₂EDTA in formamide to remove hybridized DNA (250 μL flowed at 100 μL/min, 55°C), followed by Reducing buffer (100 mM Tris·HCl, 125 mM NaCl, 0.05% Tween-20, 100 mM Tris[2-Carboxyethyl]phosphine-HCl (TCEP), pH 7.4) to remove any residual fluorescence from the sequencing reaction (390 μL, 10 min at 60°C). A fluorescent probe complementary to the RNA Polymerase stall sequence (Fluorescent_stall’; sequences of oligonucleotides used in the RNA-MaP protocol are indicated in Table S7) was then annealed to the library and imaged to determine the efficiency of the cleaning steps (500 nM Fluorescent_stall’ in Annealing buffer: 1x SSC buffer, 7 mM MgCl₂, 0.01% Tween-20; 11 min at 37°C). After imaging, the fluorescent probe was removed by washing with 250 μL of 100% formamide (55° C). The flow cell was washed with Wash buffer between steps (290 μL; 10 mM Tris·HCl, pH 8.0, 5 mM Na₂EDTA, pH 8.0, 0.05% Tween-20). Henceforth, wash steps were performed with a 250 μL volume of the specified buffer, unless otherwise noted.

To prepare double-stranded DNA (dsDNA), 5′–biotinylated primer (Biotin_D_Read2, 500 nM) was annealed to the library in Hybridization buffer (5x SSC buffer, 5 mM Na₂EDTA, 0.05% Tween-20) for 15 min at 60°C followed by a 10 min incubation at 40°C. The fluorescent oligonucleotide complementary to the fiducial marker (Fiducial_flow) was also included in the hybridization mixture at 250 nM. After washing the flow cell with Annealing buffer, an additional 500 nM of Biotin_D_Read2 (and 250 nM Fiducial_flow) was annealed to the library in Annealing buffer at 37°C for 8 min. The flow cell was then washed with Klenow buffer (1x NEB buffer 2 (NEB B7002S), 250 μM each dNTP, 0.01% Tween-20). Double-stranded DNA was generated by pumping 130 μL of 0.1 U/μl Klenow fragment (3′−5′ exo(−); NEB M0212L) into the flow cell in three stages separated by 10 min intervals each. The flow cell was maintained at 37°C for this period. Unextended single-stranded DNA templates were subsequently blocked by annealing a non-fluorescent version of the stall probe (Dark_stall′) in a process identical to the one described above.

After dsDNA generation, 1 μM streptavidin in Annealing buffer was pumped into the flow cell and allowed to bind to the biotinylated primer for 5 min at 37°C. Excess streptavidin was then washed out of the flow cell with Annealing buffer. Unbound biotin binding sites in the streptavidin tetramer were saturated by incubating the flow cell for 5 min with 5 μM free biotin in Annealing buffer. Excess unbound biotin was washed out with Annealing buffer.

RNA transcription proceeded in two stages, initiation/stall and extension. In the initiation/stall phase, 130 μL of 0.06 U/μL E. coli RNA polymerase holoenzyme (RNAP; NEB M0551S) was allowed to initiate transcription for 20 min at 37°C on the dsDNA templates in Initiation buffer, which lacked CTP (20 mM Tris·HCl pH 8.0, 7 mM MgCl₂, 20 mM NaCl, 0.1% 2-Mercaptoethanol (BME), 0.1 mM Na₂EDTA, 1.5% glycerol, 0.02 mg/mL BSA, 0.01% Tween-20, and 2.5 μM each of ATP, GTP, and UTP). Upon encountering the first cytosine (C27), the polymerase stalls, thereby sterically preventing the loading of additional enzymes on the same template (Buenrostro et al., 2014). Excess RNAP was washed out of the flow cell with Initiation buffer. Subsequently, Extension buffer was added, which contained all 4 ribonucleotides (20 mM Tris·HCl pH 8.0, 7 mM MgCl₂, 20 mM NaCl, 0.1% BME, 0.1 mM Na₂EDTA, 1.5% glycerol, 0.02 mg/mL BSA, 0.01% Tween-20, and 1 mM each of ATP, GTP, UTP and CTP). The Extension buffer also contained 500 nM each of Fluorescent_stall′ and Dark_read2 oligonucleotides, which were intended to block the regions flanking the variable region in the nascent RNA transcript (Figure 1C) and to prevent undesired intramolecular interactions, as well as to allow visualization of the transcript. Transcription was allowed to proceed for 10 min at 37°C. RNA polymerase eventually is stalled at the streptavidin roadblock at the end of the DNA template, exposing the nascent RNA molecules for binding experiments (Figure 1C).

To ensure complete blocking of RNA regions flanking the variable sequence, transcription was followed by further hybridization of Fluorescent_stall′ and Dark_read2 oligonucleotides (500 nM) for 10 min at 37°C in Annealing buffer. Finally, the flow cell was washed with Binding buffer (20 mM Na-HEPES, pH 7.4, 100 mM KOAc, 0.1% Tween-20, 5% glycerol, 0.1 mg/ml BSA, 2 mM MgCl₂ and 2 mM DTT), the temperature was lowered to 25°C (except for 37°C experiments), and the flow cell was imaged to quantify the fluorescence from the RNA-annealed Fluorescent_stall′ probe.

To determine PUM1 and PUM2 binding affinities, the RNA library was sequentially equilibrated with increasing concentrations of Cy3B-labeled PUM proteins, and the amount of Cy3B fluorescence colocalized with each RNA cluster was determined at each concentration. Two-fold serial protein dilutions (15–17) were prepared in 1x Binding buffer and were stored in light-protected tubes on ice or in the 4°C autosampler chilling block until the incubation. Protein solution (460 μL) was pumped into the flow cell at each concentration and incubated for times ranging from 33 min for the lowest concentrations to 19 min for the highest protein concentrations (25°C; 15–23 min at 37°C). These incubation times were established to be sufficient for equilibration by association and dissociation time courses (halftime ≤ 5.3 min; see also (Vaidyanathan et al., 2017)). The incubation temperature was 25 or 37°C, as indicated for the individual experiments.

Desalted RNA oligonucleotides were ordered from IDT and purified by reverse-phase HPLC (XBridge Oligonucleotide BEH C18 Prep column or Agilent ZORBAX Eclipse Plus C18 column), using an acetonitrile gradient in the presence of 0.1 M triethylamine acetate. Following purification, the solvent was exchanged into MilliQ water with Amicon Ultra 3KDa concentrators.

RNA oligonucleotides for direct binding measurements were ordered from IDT and 5′ labeled with [γ- ³²P] ATP (Perkin Elmer) using T4 polynucleotide kinase (T4 PNK, Thermo Fisher Scientific). The 5 μL reactions contained 1x PNK buffer (Thermo Fisher Scientific), 5 μM oligonucleotide, 5 μM [γ- ³²P] ATP and 1 μL of T4 PNK. The reactions were incubated at 37°C for 30 min and purified by non-denaturing gel electrophoresis (20% acrylamide).

To obtain PUM2 binding affinities in the absence of potential structure formation and alternative sites, and to compare the affinities determined by different approaches, we performed competition gel shift binding measurements with 8-mer oligonucleotides carrying a subset of single mutations in the UGUAUAUA background. PUM2 (0.68 nM) was combined with trace labeled “S1a” RNA (UCUCUUUGUAUAUAUCUCUU, <0.08 nM) in binding buffer (2 mM DTT, 100 mM KOAc, 0.2% Tween-20, 20 mM sodium HEPES, pH 7.4, 5% glycerol, 0.1 mg/mL BSA, 2 mM MgCl₂), and diluted two-fold into solutions containing varying concentrations of unlabeled competitor RNAs (3-fold serial dilution series; 7–8 concentrations per oligonucleotide; final concentrations were 0.34 nM PUM2, < 0.04 nM labeled S1a RNA, 0.17––3330 nM competitor RNA, depending on the oligonucleotide). Binding reactions were incubated at 25°C for at least 1 h; equilibration was established by measuring binding after 1 h and 4.5 h incubations, which gave consistent results. We also performed controls for titration effects, by incubating the most tightly bound oligonucleotides (consensus, 5G and 7G variants) with 0.16 or 0.32 nM PUM2 (final concentration), giving consistent affinities. Following equilibration, 7.5 μL aliquots were transferred to 7.5 μL ice-cold loading buffer (5% Ficoll PM 400 (Sigma), 0.03% BPB, and 2 μM unlabeled S1a RNA in binding buffer). The low temperature and unlabeled consensus RNA in the loading buffer prevented changes due to potential re-equilibration during sample loading (Vaidyanathan et al., 2017)). The samples were carefully and immediately loaded on a continuously running 20% native acrylamide gel (5°C, 750 V, 0.5x Tris/Borate/EDTA (TBE) running buffer: 44.5 mM Trisborate, 1 mM Na₂EDTA, pH 8.3; DANGER: extreme caution is required in this step due to high voltage; https://ehs.stanford.edu/reference/electrophoresis-safety). Gels were dried, exposed to phosphorimager screens and scanned with a Typhoon 9400 Imager.

Binding affinity for the labeled S1a oligonucleotide was measured in parallel by incubating 0.0038–81 nM PUM2 (3-fold serial dilutions) with trace labeled S1a RNA (<0.04 nM) in binding buffer for at least 1 h at 25°C. Samples were analyzed by gel electrophoresis as above. Measurements with three labeled RNA concentrations across a 9-fold range (upper limits of 13–120 pM) gave consistent results, indicating no titration effects. Sufficient equilibration time was established by measuring the dissociation rate (0.011 s⁻¹, corresponding to 5.25 min upper limit of equilibration time—i.e., five half-lives; see below (Vaidyanathan et al., 2017)).

The gels were quantified with TotalLab Quant and fitting was performed with KaleidaGraph 4.1 (Synergy). The affinity for the labeled S1a RNA was determined by fitting to a single-site binding equation:

where θ is fraction bound RNA, A is amplitude, [P] is PUM2 concentration, K_D is the equilibrium dissociation constant and b is background. Competitor affinities (K_D,comp) were determined using the equation by Lin & Riggs (Lin and Riggs, 1972):

where K_D* is the dissociation constant of the labeled S1a RNA; [R_comp]_1/2, the competitor concentration at which half of the labeled RNA is bound; [P]_total, the protein concentration; and [R*]_total the labeled RNA concentration. To determine the fraction of competitor RNA at which half of labeled RNA was bound, the competition binding curves were normalized by the fraction of labeled S1a RNA bound at saturation with no competitor (0.94). [R*]_total was the upper limit of the labeled RNA concentration based on the total input and elution volume in the labeling reaction (<0.04 nM). Using the lower limit based on scintillation measurements of the ³²P label (~0.004 nM) did not affect relative affinity calculations and affected absolute affinities by <10%. The values shown in Figure 2F, S3F are averages and 95% CIs from two replicate measurements.

For determination of flanking sequence effects, CUUGUAUAUAN oligonucleotides (N = A/C/G/U) were ordered from IDT, 5′ end labeled with [γ - ³²P] ATP, and binding was measured as described for the S1a RNA above.

To compare single mutant effects determined by gel-shift to those determined by RNA-MaP, ΔΔG values for the 8-mer oligonucleotides were calculated relative to the UGUAUAUA consensus. For position 9 variants, ΔΔG values were determined relative to the most tightly bound residue (‘G’; Figure S2D).

PUM2 dissociation rate constant from S1a RNA was measured by incubating 3.8 nM PUM2 with labeled S1a RNA (<0.5 nM) in binding buffer at 25°C for 50 min, followed by addition of 2.5-fold volume excess of unlabeled RNA chase in binding buffer (final concentrations: 1 nM PUM2, <0.14 nM labeled S1a RNA, 1 μM unlabeled S1a RNA). At various time points, 7.5 μL aliquots were moved to 7.5 μL ice-cold loading buffer (5% Ficoll PM 400 (Sigma), 0.03% BPB in binding buffer) and immediately loaded on continuously running 20% native acrylamide gel. The dissociation curve was fit to a single exponential in Kaleidagraph:

where θ is fraction bound RNA, A is the fraction bound before adding the chase (A = 0.90), b is the fraction bound at the completion of the dissociation reaction (b = 0.02), k_off is the dissociation constant, and t is time after adding chase.

Saturating concentration of unlabeled consensus RNA (10–200 nM; S1a or UCUUGUAUAUAUA for wild-type PUM1 and PUM2, UCUUGUAUUUAUA for mutant PUM1) was mixed with trace ³²P-labeled RNA of the same sequence (<0.15 nM) and incubated with protein concentrations at least 4-fold below and above the RNA concentration for 45 min – 1 h (25°C). Following native gel electrophoresis, active protein fraction was determined from the intersection of lines fit through protein concentrations below and above the breakpoint. Throughout, the protein concentrations and absolute affinities reflect active protein concentrations (SNAP-Cy3B-PUM2: 57%, PUM1-SNAP-Cy3B: 61%, mutPUM1-SNAP-Cy3B: 20%, unlabeled SNAP-PUM2 used for gel-shift experiments: 38%–45%).