## Introduction

In eukaryotic cells, the expression of tens of thousands of RNAs is regulated by thousands of diverse RNA-binding proteins (RBPs) that interact with RNA in a carefully orchestrated manner1,2. A pivotal aspect in this choreography of regulation is the specificity of RBPs for their target sites1,2,3,4,5,6,7; that is, the degree to which an RBP discriminates between cognate and non-cognate RNAs1,2,4. Specificity of RBPs varies considerably; some RBPs are highly selective for certain RNA sites, others bind degenerate sites, and yet other RBPs interact with RNAs broadly, with little sequence discrimination8,9,10,11,12,13,14. Defining the molecular mechanisms through which RBPs acquire their specificity is critical for understanding the rules of RNA biology and for devising therapeutic strategies against diseases associated with RBP- and RNA-related processes1,2,15.

Among RBPs with the greatest specificity are the three closely related human RbFox proteins (RbFox 1-3), which function in pre-mRNA splicing, miRNA processing and other RNA metabolic steps16. The three RbFox proteins contain divergent N- and C-terminal regions that are likely unstructured but all share a highly conserved RNA-binding domain that belongs to the RNA Recognition Motif (RRM) superfamily16,17. The RbFox RRM binds RNAs with a consensus 5’-GCAUG motif with low nanomolar affinity in vitro18,19,20,21. Even minor changes in the consensus motif decrease the RNA affinity by orders of magnitude19,21, indicating an inherent specificity of RbFox proteins for their consensus sequence that is markedly higher than for most other RBPs8,10,11. In the cell, however, biological effects by RbFox proteins are also exerted by binding to non-consensus sites characterized by lower affinity, when expression levels of RbFox increase22.

How RbFox proteins accomplish higher specificity than most other RBPs is not understood. Even the existing NMR structures, which provide detailed views of the RNA-binding interface, fail to provide a cogent reason for this extraordinary specificity19,20. Therefore, we set out to systematically examine the basis for the high specificity of the RbFox proteins through a combination of high throughput biochemical techniques followed by NMR structure determination. We first determined the affinity of the RRM of RbFox for all possible 16,384 7-mer RNA sequence variants. The resulting affinity distribution reveals two distinct binding modes, one associated with binding to the consensus 5’-GCAUG and a second mode for binding to all other sequences. Mutations in RbFox only have a small effect on the binding of the consensus sequence, but markedly increase affinity for all other variants, thereby diminishing specificity. The results indicate that the binding mode for the non-consensus sequences imposes a large thermodynamic penalty on these sequence variants, thereby enabling exquisite discrimination between consensus and non-consensus RNAs. Comparison of the NMR structures with a non-consensus and the consensus sequence reveals that the two binding modes are associated with substantial structural differences within the RRM. Remarkably, the structural rearrangement extends to protein regions distant from the RNA-binding interface, suggesting that the distinct binding modes can transmit RNA sequence information to potential protein binding partners of RbFox.

Thus, our data show that RbFox employs a previously undescribed mechanism to accomplish its extraordinary specificity - structurally distinct binding modes that enable the imposition of large thermodynamic penalties on non-consensus sequences and transmit RNA sequence information to distant regions of the RRM. The results reveal another layer of biological complexity in RNA-protein interactions and post-transcriptional regulation of gene expression.

## Results

### The affinity distribution of RbFox is bimodal

To examine how RbFox achieves high specificity, we first measured the affinity of the RNA-binding domain (RRM) of RbFox for two RNAs that differ by a single nucleotide (Fig. 1a). The apparent equilibrium binding constant (K1/2) for the RbFox cognate sequence (5’-GCAUG) was reduced by orders of magnitude by this single nucleotide substitution (Fig. 1a, b), consistent with previous data19,20,21. This result highlights the remarkable ability of RbFox to discriminate effectively between RNA substrates that differ by only small sequence variations.

Next, we comprehensively characterized the specificity landscape of the RbFox RRM by employing High Throughput Sequencing Equilibrium Binding (HiTS-Eq)12,13,23,24. This approach allows the simultaneous determination of apparent affinities for large numbers of sequence variants within an RNA pool12,13,23. We constructed a pool of 16,384 unique RNAs encoding all possible 7-mer sequences in a segment with 7 randomized nucleotides (Fig. 1c). This segment was flanked on each side by a 3 nt linker with fixed sequence and an adaptor to facilitate conversion of the RNA into cDNA for subsequent Illumina sequencing (Fig. 1c and Supplementary Fig. 1). To prevent base pairing between adapter regions and complementary sequences in the randomized RNA regions, which would bias the available substrate pool23,24, we annealed DNAs complementary to the adapter regions to mask the corresponding sequences (Fig. 1c).

The RNA pool was incubated in separate reactions with increasing concentrations of RbFox. Upon reaching equilibrium, samples were transferred to non-denaturing PAGE to separate RbFox-bound and -unbound substrates (Supplementary Fig. 1). Unbound substrates were isolated, converted to cDNA, and sequenced on the Illumina platform (Fig. 1d). The preparation of the cDNA libraries included unique molecular identifiers (UMIs), to identify and correct for PCR overamplification artifacts9,23,24 (Supplementary Fig. 1). As expected, the addition of RbFox caused depletion of variants in the unbound RNA pool, compared to the control pool without RbFox (Fig. 1e).

We calculated apparent relative association constants (KA,rel, affinities normalized to the affinity of the sequence 5’-UGCAUGU) for all substrate variants from binding reactions with increasing RbFox concentrations, as previously described19,20,21. Experiments were performed in independent duplicates, which provided highly correlated sequencing read values (R2 > 0.85; Supplementary Fig. 2). Apparent affinities obtained with HiTS-Eq also correlate well with affinities measured for individual substrates by us and others21 (R2 = 0.92, Fig. 1f), indicating that the HiTS-Eq approach faithfully reflects the results of conventional biochemical assays.

The histogram of KA,rel values for all sequence variants represents the global affinity distribution for RbFox (Fig. 1g). Notably, the distribution is bimodal, with a large, broad peak encompassing the vast majority of the 16,384 sequence variants, and a much smaller peak with sequence variants that contain the cognate 5’-GCAUG and the closely related 5’-GCACG (Fig. 1g, small peak marked by triangle). High affinities of RbFox for 5’-GCACG containing variants are consistent with previous observations8,11,18. Accordingly, the sequence logo for sequence variants with the highest affinities is identical to that obtained with the RNA Bind-n-Seq (RBNS), RNACompete and HTR-SELEX approaches8,10,11,18 (Fig. 1h). The global affinity distribution also highlights the extraordinary specificity of RbFox, compared to other RBPs (Supplementary Fig. 3).

Our data provide two insights. First, the affinity of RbFox for all sequence variants without 5’-GCA(U/C)G is lower by orders of magnitude, compared to its cognate 5-mer. To our knowledge, this extraordinary ability to discriminate against all but two closely related sequence variants has not been reported for other RBPs. Second, the bimodal affinity distribution of RbFox differs from the unimodal distributions seen for other RBPs8,9,12,13.

### Quantitative binding models indicate two distinct binding modes

To understand the determinants of these unique features of RbFox specificity, we applied quantitative binding models, focusing on the minimal 5 nt RbFox consensus9,12,24. To account for variations in the register of each possible 5-mers in our RNA pool with 7 randomized nucleotides, we plotted affinity values for all 48 5-mers for each of the 1,024 5-mer variants and determined the median relative affinity for each 5-mer (Fig. 2a and Supplementary Fig. 4a). The obtained values correlate well with corresponding 5-mer affinity scores calculated from the RBNS approach22 (Supplementary Fig. 4b), a high throughput approach designed to delineate preferred binding motifs for RBPs8,18.

Comparison of the HiTS-Eq 5-mer and 7-mer affinities show how nucleotides flanking the core 5-mer affect RbFox binding (Supplementary Fig. 4c). Comparable affinities of 5’-GCAUG and 5’-GCACG variants depend on nucleotides flanking the core 5-mer, as previously noted8,11,18. Our data reveal that the impact of flanking nucleotides depends also on the 5-mer sequence. For example, a 5’-U flanking 5’-GCACG enhances the affinity, compared to a 5’-G, but for most other 5-mers, a 5’-U decreases the affinity, compared to 5’-G (Supplementary Fig. 4c).

To better understand the rules governing the binding of RbFox to the core 5-mer, we analyzed the median affinity values with a Position Weight Matrix (PWM) model (Fig. 2b), the simplest model to describe the binding of a protein to all RNA sequence variants. Although a PWM considers only the position of each nucleotide in isolation9,12,24, the model accounts for 75% of the data variance among the 5-mers (Fig. 2b). However, the PWM bears no resemblance to the cognate 5-mer, indicating instead a preference for G at all positions (Fig. 2c). Most interestingly, the model reveals a single outlier—the cognate 5’-GCAUG sequence (Fig. 2b). These observations indicate that a PWM can describe affinities for almost all sequence variants to a considerable degree, except for the cognate variant.

To examine whether the inherent limitations of the PWM cause the striking divergence between cognate and non-cognate RNAs, we applied a binding model that considers pairwise coupling (PWC) between all nucleotides7,9,12,24. Considering coupled contributions from multiple positions within the binding sites often improves the description of the experimental variance2. We analyzed the binding profiles to RbFox for 5’-GCNUG sequences (Supplementary Fig. 5), and found that substituting the G2-A4 base-pairing interaction lowers the binding affinity dramatically, highlighting the importance of couplings involving even non-adjacent nucleotides. The PWC model accounts for 90% of the data variance (Fig. 2d), an excellent result for experimental high-throughput data9,12,13. Yet, the cognate 5-mer remains a clear outlier, even though the PWC model highlights favorable base couplings contributions in the cognate variant (Fig. 2e, highlighted fields). PWM and PWC models for all 7-mer RNA variants, which do not consider the binding register of the minimal 5-mer, also identify variants with the cognate 5’-GCAUG as outliers (Supplementary Fig. 6). Collectively, our analyses of the RbFox-RNA interaction with quantitative binding models suggest that the bimodal affinity distribution of RbFox cannot be explained by a single binding mode. Therefore, we conclude that RbFox employs distinct binding modes—one for its cognate 5-mer and one or more other modes for non-cognate sequence variants. To our knowledge, multiple binding modes have been reported for multi-domain RBPs, but not for a single RRM.

### Protein mutations affect the two binding modes differently

To probe the notion of two distinct binding modes, we measured the affinity distribution of an RbFox variant containing four amino acid changes (RbFoxmut, Fig. 3a). These mutations were introduced to improve binding to a pri-miRNA comprising a near-consensus sequence20. We hypothesized that mutations in the RRM should affect the two distinct binding modes differently. We first measured the binding of RbFoxmut to the individual RNAs examined above with wild type (wt) RbFox (Fig. 3b). RbFoxmut bound an RNA with the cognate 5-mer with slightly reduced affinity, compared to wt RbFox (Fig. 3b, c). However, RbFoxmut bound to an RNA with a single base change only slightly less well than to the cognate sequence. In contrast, the binding of wt RbFox to this RNA was barely detectable (Fig. 1a, b). This observation indicates that the mutations in RbFoxmut markedly increase the affinity for non-cognate RNAs, compared to the wt protein, while impacting binding to the cognate sequence much less.

We next examined RbFoxmut with HiTS-Eq using the RNA pool employed above for wt RbFox (Supplementary Fig. 7). Apparent affinities obtained with HiTS-Eq correlate well with corresponding data measured for individual RNAs (R2 = 0.83, Fig. 3d). However, the affinity distribution for RbFoxmut does not display the pronounced bimodal shape observed with wt RbFox. Rather, the RbFoxmut distribution shows a tail corresponding to high affinity variants (Fig. 3e and Supplementary Fig. 8a). In addition, the RbFoxmut distribution narrows and is shifted towards higher relative affinities compared to the wt RbFox distribution (Fig. 3e). The global increase in relative affinities for non-cognate sequences, compared to wt RbFox, coincides with a pronounced decrease in specificity for RbFoxmut (Fig. 3e and Supplementary Fig. 8a); that is, the mutant protein does not discriminate against non-cognate sequences as strongly as the wt protein. In addition, the base preference of wt RbFox at position 2 of the cognate 5-mer is essentially lost in RbFoxmut (Figs. 3f and 1h); a possible reason for the slightly lower affinity of RbFoxmut for the cognate sequence, compared to wt RbFox (Fig. 3b). The loss of stringency at position 2 also allows RbFoxmut to accommodate more diverse 5-mer variants in the binding mode reserved for the cognate sequence in wt RbFox.

The opposite effects of RbFox mutations on the affinities for cognate and non-cognate RNAs, strongly support the notion of distinct binding modes of RbFox. In addition, our data reveal that wt RbFox accomplishes high specificity by thermodynamically penalizing all sequences, except the cognate and near-cognate variant with a specific flanking nucleotide. RbFoxmut is unable to impose a similar thermodynamic penalty. The affinities for non-cognate sequence variants increase relative to the cognate sequence and specificity is reduced, compared to wt RbFox. The apparent need to impose a thermodynamic penalty on all but the cognate sequence provides an additional rationale for the two distinct binding modes observed for wt RbFox (Fig. 2).

We next probed how the binding mode for the non-cognate RNA variants differed between wt and mutant RbFox. To this end, we analyzed the affinity distribution of RbFoxmut with the PWM and the PWC models, as described for wt RbFox (Fig. 4 and Supplementary Figs. 8b, 9). The PWM model for RbFoxmut accounted for 35% of the data variance and differed from the PWM for wt RbFox, most notably by a preference for U, instead of G (Supplementary Fig. 9c). The PWC model accounted for 66% of the data variance for RbFoxmut (Fig. 4a, b) and revealed numerous differences with wt RbFox (Fig. 4c), highlighting a significant specificity shift by only 4 mutations of RbFox. Collectively, these data indicate substantial differences in the binding mode for the non-cognate variants between RbFoxmut and wt protein, thereby supporting the notion of distinct binding modes.

### Cognate and non-cognate RNAs induce distinct structures in the RbFox RRM

The existence of two distinct binding modes of RbFox raised the question of whether these binding modes also differ structurally. To examine this possibility, we performed NMR studies with a 7-nt cognate (5’-UGCAUGU) and two non-cognate RNAs, which differ from the cognate variant at a single nucleotide (5’-UGCAUAU) or (5’-UUCAUGU), designated as RNA1 and RNA2. RNA1 and RNA2 both represent examples for non-cognate sequence binding modes, and rank in the 17.4 and 37.6 percentile, respectively, among the 16,384 sequence variants. We titrated each RNA into the wt RbFox RRM until saturation, while monitoring 1H-15N HSQC (Supplementary Fig. 10). We observed slow-exchange binding kinetics with the cognate RNA and intermediate-exchange binding kinetics with the non-cognate variants (Supplementary Fig. 10), consistent with the nanomolar affinity of the cognate RNA and the markedly lower association constants of the non-cognate variants observed in the HiTS-Eq data (Fig. 2).

Next we collected 3D NMR spectra at saturating RNA concentrations and calculated the chemical shift difference (CSD) between the RbFox complexes bound to the consensus RNA and to RNA1 and RNA2 (Fig. 5a, d). For RNA1, mapping of these differences onto the structure of wt RbFox identified changes in four regions of the protein: β1(R118-V121), β2 and the following loop (I143-E152), β3 (G159-E164) and the C-terminal tail (A191-A193) (Fig. 5c). In the structure of RbFox RRM complexed with its cognate RNA, the AUG (nucleotides 4 to 6) element is bound in a canonical manner through π-π stacking with the β-sheet surface, while UGC (nucleotides 1 to 3) is recognized by loop residues19. Accordingly, similar chemical shifts for the region of RbFox interacting with UGC were observed in the two complexes, indicating that the UGC nucleotides in both structures maintain the same contacts within the RNA-binding cleft of RbFox. In contrast, the G- > A substitution at position 6 causes marked changes in the β-sheet region that binds to the AUG element (0.2–0.7 ppm, Fig. 5a). We also observed significant chemical shift changes (>0.1 ppm) in the α1/β2 and β3/α2 loops (highlighted and labeled in blue in Fig. 5a, b), which are distant from the RNA-binding surface (Fig. 5c). For RNA2, where G2 is mutated to U, we observed a similar pattern of CSDs, not only in the direct RNA-binding cleft, but also on the distal α1/β2 and β3/α2 loops (Fig. 5d–f). Mapping of these differences onto the structure of wt RbFox protein revealed three major regions directly contacting G2 and its base paring partner A4: β1 and its following loop (L119-R129), β3 and its preceding loop (I149-F160), and β4 and its preceding loop (G178-V188). Compared to the G6- > A mutation, the distal α1/β2 and β3/α2 loops of RbFox are affected by the G2- > U mutation to a similar extent, although the overall changes induced by the G2- > U mutation are much smaller.

To gain detailed insight into the structural differences between the RbFox RRM structures with cognate and non-cognate RNAs, we determined the structure of the RbFox RRM with the RNA1 substrate. The 1H-15N HSQC and NOESY spectra changed during data collection, suggesting multiple binding orientations that are most likely due to the weak binding of the non-cognate RNA. These characteristics made unambiguous NOE identification difficult. To overcome this problem, when collecting spectra for the protein, we oversaturated the protein with RNA and changed the sample frequently during data collection to ensure RbFox was consistently in the fully bound conformation. For the RNA, we used some NOEs for the GCA sequence from our previous NMR dataset within the pre-miR20b stem loop in complex with RbFox25. Since chemical shifts are very similar for both proteins and RNAs, we obtained a dataset that converged to a reliable structural ensemble (Supplementary Table 1). RNA2 binds even more weakly, as demonstrated by highly inhomogeneous peak intensities (Fig. 5e) and the loss of multiple HN signals in the 1H-15N HSQC (highlighted in gray in Fig. 5d); because of the poor spectral quality resulting from reduced affinity, the structure of RbFox bound to RNA2 could not be determined.

A 2.0 Å rmsd difference was observed for RbFox in complex with the cognate and non-cognate RNAs, with large differences in protein regions distant from the RNA-binding site as well (Fig. 6). In the NMR structure with the cognate sequence, G6 forms the most extensive contacts with the protein (Fig. 6a, left panel). In our structure with the non-cognate RNA, the G6- > A substitution abolishes the hydrogen-bonding interactions with R118 and T192. Our structure also reveals increased dynamics for A6 and stacking interactions between the aromatic chain of F160 and the aliphatic chain of R194 (Fig. 6a, right panel). The hydrogen bonding network of U5 is also rearranged due to loosened interactions between A6 and the protein. With the non-cognate RNA, the stacking between the imidazole ring of H120 and U5 is lost or weakened, because the side chain of H120 is flexible, as revealed by line broadening in the NMR spectra. The hydrogen-bonding interactions with N190 are completely lost, and those with T192 can only be observed for less than half of the models in the structural ensemble (Fig. 6a). For a large majority of the converged structures, the aromatic ring of F160 tilts to stack with the base of A6. The RNA-binding strands β1 and β3 float away from the RNA, due to the loss of close contacts with A6 and U5, and the β2 β3 loop reorients to better accommodate the non-cognate RNA (Fig. 6b).

Collectively, these structural features indicate that RbFox employs structurally distinct binding modes for the cognate and the non-cognate RNA, sacrificing the binding energy of multiple hydrogen bonds and π–π stacking interactions in order to accommodate a non-cognate sequence. These observations provide structural evidence for the thermodynamic penalty model.

Equally intriguingly, the non-cognate RNA induces a distinct long-range conformational rearrangement in RbFox, which remodels the surface on the protein distant from the RNA-binding site (Fig. 6b, c). The side chain of R118 rotates almost 90 degrees to interact with the Watson-Crick face of A6, thereby losing a hydrogen bond with the Hoogsteen face of G6, that can only be formed with the cognate RNA (Fig. 6c). The rotation of R118 leads to a reorientation of the side chain of K117. These rearrangements, together with the reoriented side chain of N190 and flipping out of the side chain of E164, are necessary to relieve steric clashes (Fig. 6c). This domino-like effect causes the movement of the N-terminal loop, β3-α2 loop and the α2 helix, propagating the conformational change to peripheral structural elements α1 and β2 and the connecting loop. A new surface is created by the above rearrangements, exemplified by the negative-charged residue E164 flipping out and altering the protein surface electrostatics (Supplementary Fig. 11). Thus, a single nucleotide change in the RNA triggers not just binding mode alterations at the RNA-binding site, as would be expected, but also at a distal surface, where other factors potentially interact with RbFox to modulate its biological activities26.

We carried out an NMR analysis to investigate whether wt RbFox’s divergent binding mode is structurally lost in the mutant. We used two RNAs, a 7-nt cognate RNA 5’-UGAAUGU and a non-cognate RNA 5’-UGAAUCU, to titrate into RbFoxmut and collected 1H-15N HSQC spectra, as was done for wt RbFox (Supplementary Fig. 12a, b). In contrast to wt RbFox, we observe slow-exchange on the chemical shift time scale with both RNAs, indicating both cognate and non-cognate RNAs bind to RbFoxmut with strong affinity, better than µM. Furthermore, taking advantage of the tight binding, we were able to collect high quality 3D NMR spectra to complete the backbone HN assignments for both RbFoxmut complexes and compared the CSDs between them. Compared to wt RbFox, fewer residues in RbFoxmut protein are affected by the single-nucleotide mutation and smaller CSDs are observed, suggesting the chemical shift changes of RbFoxmut originate mainly from differences in the chemical environment caused by the nucleotide change, but not by a structural change (Supplementary Fig. 12c–e). CSDs distal from the RNA-binding surface induced by the G6- > A or G2- > U mutations, as observed with wt RbFox, were not observed for the G6- > C mutation with RbFoxmut. Taken together, these results provide strong evidence that the conformational divergence induced by RNA substrates observed with wt RbFox is weakened in RbFoxmut. This observation supports our notion that a pronounced bimodal binding mode is a unique characteristic of wt RbFox.

## Discussion

Specificity variations are critical determinants of RBP function1,2,5,8,10,11,14. Defining the molecular mechanisms that determine RBP specificity is thus necessary for understanding RNA biology. Here, we have shown that a highly specific RNA-binding module, the RNA recognition motif of the RbFox proteins, accomplishes extraordinary sequence specificity through a previously unknown mechanism, the use of two structurally distinct binding modes. One binding mode exclusively accommodates cognate and near-cognate RNAs with high affinity, while the other binding mode accommodates all other RNAs, but with markedly reduced affinity.

The notion of distinct binding modes for the RRM of RbFox is based on three converging, independent lines of evidence. First, the affinity distribution of RbFox for all 16,384 7-mer RNA sequence variants is bimodal (Fig. 1). In contrast, affinity distributions for other RBPs are unimodal8,9,12, reflecting the gradual incremental effects of protein sequence variations on RNA affinity22. A single binding mode can be modeled by either a position weight matrix or more complex models considering functional coupling between bases24,27 (e.g., pairwise interaction matrix). However, the bimodal affinity distribution of RbFox cannot be described by a single binding model.

Second, mutations in RbFox affect the two binding modes differently. The mutations only slightly decrease the affinity for the cognate RNA variant, but markedly increase affinity for all other variants, thereby reducing overall specificity (Fig. 3). Related observations were reported for the RBP FBF-2, a member of the PUF-protein family, where mutations in the RNA-binding site increased accommodation for multiple sequence variants28.

Third, structural differences between complexes of RbFox with the cognate and a non-cognate sequence are observed (Figs. 5, 6). Beyond expected differences at the RNA-protein interface, we also identify pronounced differences in regions distant from the RNA-binding site. In other RBPs for which structures with different RNA variants have been reported, structural variations are generally concentrated at the RNA-binding sites29,30,31, even where relatively large changes are introduced in the protein30,32. Our data with RbFox reveal instead that structural rearrangements in the RRM can be communicated to a distant surface. While this is not unprecedented, it is also intriguing that the conformational change depends on whether a cognate or non-cognate RNA is bound to the protein. The structural analysis suggests that the different binding modes are accomplished in a switch-like manner: the cognate variant induces one structure while non-cognate variants another. It is possible that additional, but presumably smaller structural differences occur within the non-cognate binding mode, similar to the differences that have been observed for other RBPs bound to multiple different RNAs29,30,31,33. Structural and functionally, the propagation of the conformational rearrangements to sites distant from the RNA interface reveals that RNA can act as an allosteric effector, potentially regulating the binding of other proteins to RbFox, and altering the composition of multi-component RNP complexes, including the Large Assembly of Splicing Regulators (LASR)34.

The use of distinct binding modes by a single RRM to achieve high sequence specificity is an interesting concept for single protein domains. Distinct binding modes have been reported for proteins with multiple domains, reflecting the differential contributions of each RRM for binding to complex multimodal RNA sites; an important and well-understood advantage of their modular structure31,35,36,37. However, these scenarios differ fundamentally from the multiple binding modes of a single RNA-binding module shown here. The two binding modes of the RbFox RRM enable exceptionally high sequence selectivity by enabling the imposition of a high thermodynamic penalty on the non-cognate sequences. Mutations in the RRM diminish the ability to maintain the high thermodynamic penalty because the affinity for non-cognate variants increases and specificity decreases (Fig. 3).

We speculate that the two binding modes evolved to allow sharp discrimination between small sequence variations within a single RRM, which might be impossible to accomplish within a single binding mode, as reflected by the generally relaxed specificity of many RRMs38. To accomplish an RbFox-like difference between cognate and near-cognate sequences within a single binding mode would require a range in the affinity distribution that might not be physically possible, biologically desirable, or both. Since RNA-protein association is universally limited by diffusion, affinities in the sub-nanomolar range or higher, are necessarily associated with long lifetimes of the RNA-protein complex39, which might be incompatible with RBP functions in pre-mRNA splicing regulation, where remodeling of RNA-protein interactions occurs on the scale of minutes or faster1,2,39. Low affinities for RNA-protein interactions are limited by the electrostatic properties of RNA, which promote “non-specific” interactions with proteins that are usually in the low to mid micromolar range1,2,39. Therefore, we propose that the dual binding modes for RbFox evolved to overcome the physical limits of sequence discrimination imposed by a single binding mode.

It remains an open question why RbFox requires higher specificity than other RBPs. Recent data show that RbFox binds and promotes biological effects also at near-cognate RNA sites in cells, but only at increased cellular RbFox concentrations22. The extraordinary specificity of RbFox might thus be necessary for high fidelity binding to the cognate sequence at low RbFox concentrations, which is likely critical for accurate control of splicing networks in brain, heart, and muscle, and during embryonic development16. In addition, the different conformations of RbFox on cognate and non-cognate sequences described herein, might promote the assembly of distinct regulatory complexes, which allow RbFox to transmit even minute changes in RNA sequence to potential binding partners. The structural differences between the two binding modes thus add a previously unappreciated layer of regulation to RBP biology.

## Methods

### Protein expression and purification

Expression and purification of RbFox RRM and RbFoxmut were performed as previously described20,25. Briefly, the recombinant plasmid was transformed into BL21 (DE3) competent cells. Transformants were grown in LB media at 37 °C to OD600nm = 0.6. The recombinant proteins were overexpressed in E. coli at 18 °C overnight upon induction of 0.5 mM IPTG. The cells were harvested by centrifugation and resuspended in lysis buffer (20 mM Tris at pH 8.0, 150 mM NaCl and 1 mM DTT) and lysed by sonication at 4 °C. The crude extracts were centrifuged at 27,000 × g for 60 min to remove the cell debris. To purify the recombinant proteins, the supernatant was applied onto a HisTrap column (GE Healthcare) and a Heparin column (GE Healthcare) in succession. Protein concentrations were measured by UV absorbance at 280 nm and confirmed by the Bradford assay.

Protein preparation for NMR experiments required complete removal of traces of RNase contaminants, due to the long incubation and weak binding of wt RbFox to the non-cognate RNA. To accomplish this, RbFox was double tagged with both Hisx6 and GST at its N-terminus and purified with HisTrap and GSTrap columns in succession, followed by a Heparin column to remove residual non-specifically bound RNAs. Both affinity tags were then cleaved with TEV protease and removed by Nickel affinity chromatography. The purified protein eluent was concentrated and loaded onto a Superdex 75 10/300 GL column equilibrated with NMR buffer (10 mM sodium phosphate at pH 6.0 with 30 mM NaCl). Aliquoted protein samples were flash-frozen for storage at −80 °C.

### RNA substrates for equilibrium binding and HiTS-Eq measurements

RNA substrates were purchased from Dharmacon (Lafayette, CO) and Sigma-Aldrich (St. Louis, MO). RNA substrates were 5’ end labeled using γ32P-ATP and T4 Polynucleotide Kinase (NEB, MA)40. Uniformly radiolabeled RNA substrates were purified with 20% denaturing PAGE (acrylamide/bis 19:1, 7 M urea, 0.5 × TBE) and concentrations were quantified by scintillation counter.

For the HiTS-Eq randomized RNA pool, 5’ end radiolabeled randomized RNA substrates containing a central segment of 7 randomized (NNNNNNN) nucleotides flanked by illumina sequencing primers (underlined sequences) were annealed with two complementary DNA oligonucleotides (underlined sequences) (Table 1). The RNA–DNA complexes were purified by 15% non-denaturing PAGE (acrylamide/bis 19:1, 0.5 × TBE) and concentrations were quantified by scintillation counting40.

### Equilibrium binding with individual RNAs

RNA-protein binding reactions for wt RbFox with consensus RNA and for RbFoxmut with all RNAs were performed at 30 °C (10 mM Tris, 150 mM NaCl, 3.4 mM EDTA, 0.001% NP-40, pH 7.5, 5’ end radiolabeled RNAs: 1 nM) and protein concentrations as indicated in the Figures (for sequences see Table 2). RNA and protein were incubated for 10 min. Longer incubation times did not change the observed fractions of bound RNA. Samples were then loaded on 8% non-denaturing PAGE. Gels were dried, and radioactivity in bound and free RNA was quantified using Phosphorimager (GE) and ImageQuant 5.2 software (GE Healthcare, IL). Plots of the fraction bound RNA vs. protein concentrations were fitted against the quadratic binding equation using KaleidaGraph (v3.52).

$${{{{{\rm{Fraction}}}}}}\,{{{{{\rm{Bound}}}}}}={{{{{\rm{A}}}}}}\times \frac{({K}_{1/2}+{R}_{0}+{P}_{0})-\sqrt{\{{({K}_{1/2}+{R}_{0}+{P}_{0})}^{2}-4\times {R}_{0}\times {P}_{0}\}}}{2\times {R}_{0}}$$
(1)

(A: reaction amplitude, K1/2: apparent dissociation constant, R0: RNA concentration, P0: protein concentration).

Affinities for wt RbFox for non-consensus RNAs were measured by competition with consensus RNA, due to low affinities of wt RbFox for these RNA variants. Consensus RNA (final concentration 1 nM) was incubated with RbFox for 10 min. Competitor RNAs at increasing concentrations were added and incubated for 10 min. Longer incubation times did not change observed fractions of bound and free RNA. Samples were loaded on 8% non-denaturing PAGE, as above. Gels were dried and radioactivity in bound and free bands were quantified using a Phosphorimager (GE) and ImageQuant 5.2 software (GE Healthcare, IL). Plots of the fraction bound RNA vs. chase RNA concentrations were fitted against the binding equation for competitive inhibition using KaleidaGraph41.

$${{{{{\rm{Fraction}}}}}}\,{{{{{\rm{Bound}}}}}}={A}\times \frac{{R}_{1}}{{R}_{1}+{[{K}_{1/2}]}_{1}\times \left(1+\frac{{R}_{2}}{{[{K}_{1/2}]}_{2}}\right)}$$
(2)

(A: reaction amplitude, R1: Substrate concentration, R2: Competitor concentration, [K1/2]1: apparent dissociation constant for substrate, [K1/2]2: apparent dissociation constant for competitor)

### HiTS-Eq measurements and sequencing library preparation

HiTS-Eq reactions (50 µL) were performed with 1 nM of 5’ end radiolabeled RNA pool with increasing protein concentrations, as indicated in the figures. RNA and protein were equilibrated for 10 min. Longer incubation times did not change the fraction of bound and free RNA. Bound and free RNAs were separated by 8% non-denaturing PAGE. The gel was exposed for 30 min to autoradiography film, free RNA species were located, cut out, and eluted from the gel and RNA was extracted and recovered as previously described40.

The HiTS-Eq libraries for Illumina next generation sequencing (NGS) were generated from the eluted RNA as previously described9,12,13,23. The RNA was reverse transcribed into cDNA with Superscript III Reverse Transcriptase (Invitrogen, CA). The cDNA was PCR amplified into HiTS-Eq libraries using index barcode primers (Table 3). The HiTS-Eq DNA libraries were purified with 8% non-denaturing PAGE. DNAs with 137 bp were cut out and extracted as previously described9,12,23. DNA concentration and quality were analyzed using a DNA Bioanalyzer chip (Agilent, CA). Subsequently, the HiTS-Eq libraries for different protein concentrations were pooled (equimolar) and sequenced using 50 bp single-end reads on Illumina HiSeq 2500.

### Processing of Illumina sequencing data

Raw sequencing reads were quality checked with FastQC v0.11.5 and de-multiplexed based on their corresponding index barcode primers using Novocraft v3.0.8 (http://novocraft.com) or the Fastx-Toolkit v0.0.13 (http://hannonlab.cshl.edu/fastx_toolkit/). The sequencing reads were then aligned to the sequence of nucleotides 6–29 of the single strand randomized substrate, allowing one mismatch but no gaps using Perl scripts. The counts of the individual 7-mer sequences and two degenerative random nucleotides in the index barcode primers were added and exported into excel tables using Perl scripts (https://github.com/hsuanchunlin/HiTS-EQ, https://github.com/xxy103/HiTS-EQ).

### Calculation of binding constants from HiTS-Eq data

Relative equilibrium constants (KA,rel) were calculated from concentration dependent changes of the 7-mer sequence variants analogous to the procedure described previously9,12,23. The ratios of the two RNA substrates S1 and S2 at a given protein concentration (E) was described using a competitive binding scheme according to: S1,0 and S2,0 are initial concentrations of the RNA substrates S1 and S2 at HiTS-Eq control reaction, and equilibrium constants are described as K1 and K2.

$$\frac{{S}_{1}}{{S}_{2}}=\frac{{S}_{1,0}}{{S}_{2,0}}\frac{1+\frac{E}{{K}_{2}}}{1+\frac{E}{{K}_{1}}}$$
(3)

(S1,0 and S2,0: initial concentrations of the RNA substrates S1 and S2 at the HiTS-Eq control reaction, K1 and K2: equilibrium constants)

The association constant (K2) for S2 is:

$${K}_{2}=\frac{E}{\left(\left(\frac{{S}_{1}}{{S}_{2}}\right)\left(\frac{{S}_{1,0}}{{S}_{2,0}}\right)\left(1+\frac{E}{{K}_{1}}\right)\right)-1}$$
(4)

The relative association constant for a given RNA variant (K2,rel) is the value for the given RNA variant (S2), normalized by the value for substrate S1 [UGCAUGU], according to:

$${K}_{2,{{{{{\rm{rel}}}}}}}=\frac{E}{\left(\left(\frac{{S}_{1}}{{S}_{2}}\right)\left(\frac{{S}_{1,0}}{{S}_{2,0}}\right)\left(1+E\right)\right)-1}$$
(5)

KA,rel values for each 7-mer RNA variants were calculated using the sequencing read counts over protein concentrations. The KA,rel values for 5-mer RNA variants were determined by splitting each 7-mer substrates into 3 non-overlapping 5-mer substrates and averaging their KA,rel values.

### Quantitative binding models

The relative association constants were fitted with the Position Weight Matrix (PWM) model as previously described9,12,23. For each sequence variant, the predicted association constant (KA) value is determined by a set of linear coefficients at individual nucleotide positions, according to:

$${{{{\mathrm{ln}}}}}({K}_{A,{{{{{\rm{rel}}}}}}})\sim \mathop{\sum }\limits_{i=1}^{n}{\alpha }_{i}{A}_{i}+{\beta }_{i}{C}_{i}+{\gamma }_{i}{G}_{i}+{\delta }_{i}{U}_{i}$$
(6)

The numbers for Ni (N = A, C, G, U) are based on the nucleotide identity at position i (i = 1 − n, n refers to the length of the sequence motif). Ni was assigned to value 1 for matched nucleotide at position i, and 0 otherwise. The cognate sequence motif UGCAUGU or GCAUG for 5-mers were used as baseline and excluded from the linear regression for the PWM models. Linear coefficients for the PWM model correspond to the parameters αi, βi, γi and δi, i = 1 − n.

The Pairwise Coupling (PWC) model considers all pairwise interactions between two nucleotides9,12. Interaction coefficients between individual nucleotide positions were added to the PWM model to fit the KA,rel data from HiTS-Eq in equation, as previously described9,12,23. Interaction coefficient values (In) with a T value larger than 3.5 were considered statistically significant. Obtained interaction coefficients values were plotted as heatmaps.

$${{{{\mathrm{ln}}}}}({K}_{A,{{{{{\rm{rel}}}}}}})\sim \mathop{\sum }\limits_{i=1}^{n}({\alpha }_{i}{A}_{i}+{\beta }_{i}{C}_{i}+{\gamma }_{i}{G}_{i}+{\delta }_{i}{U}_{i})+\mathop{\sum }\limits_{i=1}^{n}{\alpha }_{n}{I}_{n}$$
(7)

### NMR sample preparation and data collection

RNAs for NMR measurements were purchased from Integrated DNA Technologies. Oligonucleotides were dissolved in RNase-free water, desalted using a PD MiniTrap G-10 and re-suspended in NMR buffer after overnight lyophilization. 13C, 15N labeled RRM of RbFox (residues 109-208) was prepared in minimal M9 medium supplemented with 1 g/L 15NH4Cl and 2 g/L 13C-glucose. The complex was formed by titrating unlabeled RNA into 13C, 15N labeled protein, and monitored by recording the 15N HSQC of the protein. NMR experiments were performed on Bruker Avance 600 and Avance 800 spectrometers equipped with HCN cryo-probes and pulsed field gradients. NMR data were processed with NMRPipe42 and analyzed with CCPNMR43. 2D F1-, F2-filtered NOESYs44 (mixing times 100 and 300 ms) and 2D TOCSY (mixing time 80 ms) were collected on unlabeled RNA in complex with 13C, 15N labeled protein in D2O at 298 K to assign the aromatic and sugar protons of the RNA. 2D 15N/13C HSQCs, 3D HNCACB, CBCA(CO)NH, HNCO, HN(CA)CO, HBHA(CO)NH and HCCH-TOCSY spectra were collected on 15N, 13C labeled protein in complex with unlabeled RNA to assign the backbone and the non-aromatic side-chains of the protein. 2D 13C HSQC with carbon centered at ~125 ppm and 3D 13C NOESY-HSQC (mixing time 150 ms) were also recorded to assign aromatic side chains of the protein.

### NMR resonance assignments and structural calculation

Protein assignments followed the regular protocol using triple resonance spectra listed above. RNA resonance assignments were obtained from 2D NOESY and TOCSY by comparison with chemical shifts of GCAUG motif of pre-miR20b stem loop complexed with RbFox and those reported for UGCAUGU-RbFox complex19,25. Manually assigned intermolecular NOE distance restraints derived from 3D NOESYs at 100 ms mixing time were separated into three ranges based on the cross-peak intensities, strong (1.8–3.5 Å), medium (1.8–4.5 Å) and weak (1.8–5.5 Å). Additional NOEs observed only in 2D NOESY with 300 ms of mixing time were assigned as very weak (1.8–6.5 Å).

The NOE distance restraints for the complex were obtained from the combination of: intra-protein NOEs automatically assigned from 15N and 13C NOESY-HSQCs obtained by CYANA; intra-RNA NOEs manually assigned from 2D F1-, F2-filtered NOESYs spectra; and intermolecular NOEs manually assigned from 2D F1-filtered, F2-edited NOESY and 3D 13C F1-filtered, F3-edited NOESY-HSQC.

Dihedral angle restraints for the conformation of sugar rings (C2’-endo or C3’-endo) were added, based on H1’-H2’ cross-peak intensities in 2D TOCSY spectrum. With all of the restraints above, 100 initial structures were generated in CYANA45, and the 20 structures with the lowest target function were further regularized in an implicit solvent model using the SANDER module of Amber 14.046. We have used ff99bsc0xOL3 force field for RNA and ff14SB force field for protein. The script for the restrained simulated annealing protocol was modified from Tolbert et al.47. Protein torsion angles were obtained by TALOS+48. For the complex, we heated the system to 1500 K during Amber simulated annealing refinement. The 20 lowest-energy structures were analyzed with PROCHECK-NMR49.

### Comparison of inherent specificity of multiple RBPs

We utilized RbFox HiTS-Eq data as well as RNA Bind-n-Seq (RBNS) datasets from the ENCODE consortium to generate affinity distributions. First, we normalized HiTS-Eq RbFox global binding affinity data to a scale of 0 to 1. In addition, for RBNS datasets, we sorted through the RBPs analyzed by the ENCODE consortium to select only the RBPs that had a single RNA binding domain in their structures or; if the RBP had multiple RBDs, then a single RBD was purified and examined. Specifically, we selected 5 RBPs (PUM1, DAZ3, RBM6, SRSF8, and SRSF11) to generate the affinity distributions. Next, the 5-mer RBNS enrichment (R) scores for the selected RBPs were acquired from ENCODE data portal (https://www.encodeproject.org). The R scores were then normalized to a scale of 1-to-Euler’s constant (e), followed by natural log-normalization to fit R scores to a scale of 0 to 1. The normalized affinities for 5-mer sequence variants were then used to generate the affinity distributions for the six selected RBPs. While there is no agreed-upon method to quantitatively define the inherent specificity, we used the ratio between the highest affinity value to the median affinity value.

### Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.