2.1. Cloning, expression and purification of Aae Hfq

The Aae hfq gene was cloned via the polymerase incomplete primer extension (PIPE) methodology (Klock & Lesley, 2009) using an A. aeolicus genomic sample as a PCR template. The T7-based expression plasmid pET-28b(+) was used, yielding a recombinant protein construct bearing an N-terminal 6×His tag and a thrombin-cleavable linker preceding the Hfq (Supplementary Fig. S1a, Supplementary Table S1); in all, the affinity tag and linker extend the 80-amino-acid native sequence by 20 residues, giving the full-length sequence in Supplementary Fig. S1(a). Plasmid amplification, and in vivo ligation of the vector and insert, were achieved via transformation of the PIPE products into chemically competent TOP10 E. coli cells. Recombinant Aae Hfq was produced by transforming the plasmid into the E. coli BL21(DE3) expression strain, followed by outgrowth in Luria–Bertani medium at 310 K. Finally, expression of Aae Hfq from the T7 lac-based promoter was induced by the addition of 1 mM isopropyl β-D-1-thiogalactopyranoside (IPTG) when the optical density measured at 600 nm (OD₆₀₀) reached ∼0.8–1.0. The cell cultures were then incubated at 310 K with shaking (∼230 rev min⁻¹) for an additional 4 h, pelleted at 15 000g for 5 min at 277 K and then stored at 253 K overnight.

Cell pellets were resuspended in a solubilization and lysis buffer [50 mM Tris pH 7.5, 750 mM NaCl, 0.4 mM PMSF, 0.01 mg ml⁻¹ chicken egg-white lysozyme (Fisher)] and incubated at 310 K for 30 min. The cells were then mechanically lysed using a microfluidizer. To remove cell debris, the lysate was pelleted via centrifugation at 35 000g for 20 min at 277 K. The supernatant from this step was then incubated at 348 K for 20 min, followed by centrifugation at 35 000g for 20 min; this heat-cut step was performed because most Hfq homologs examined thus far have been thermostable, and because A. aeolicus is a hyperthermophile (with an optimum growth temperature T_opt of ∼360 K; Huber & Eder, 2006). To reduce contamination by any spurious E. coli nucleic acids, which have been known to co-purify with other Hfqs, the clarified supernatant from the heating step was treated with high concentrations (∼6 M) of guanidinium hydrochloride (GndCl). To remove any particulate matter, Gnd-treated samples were then immediately clarified by 0.2 µm syringe filtration.

Recombinant Aae Hfq was then purified via immobilized metal-affinity chromatography (IMAC) using a Ni²⁺-charged iminodiacetic acid Sepharose column with an NGC (Bio-Rad) medium-pressure liquid-chromatography system. After loading the clarified supernatant from the heat-cut and GndCl-treatment steps, the column was treated with four column volumes of wash buffer (50 mM Tris pH 8.5, 150 mM NaCl, 6 M GndCl, 10 mM imidazole). Next, Aae Hfq was eluted by applying a linear gradient, from 0 to 100% over ten column volumes, of elution buffer (identical to the wash buffer but with 600 mM imidazole). Protein-containing fractions, as assessed by the absorbance at 280 nm and chromatogram elution profiles, were then combined and, in order to remove GndCl, dialyzed against a buffer consisting of 25 mM Tris pH 8.0, 1 M arginine. Next, to prepare for the removal of the 6×His tag, the protein was then dialyzed into 50 mM Tris pH 8.0, 500 mM NaCl, 12.5 mM EDTA. The Aae Hfq sample was subjected to proteolysis with thrombin at a 1:600 Hfq:thrombin ratio (by mass) by incubating at 315 K overnight (∼16 h), followed by application to a benzamidine affinity column to remove the thrombin. To improve the sample homogeneity, Aae Hfq was further purified over a preparative-grade HiPrep 16/60 Sephacryl S-300 HR gel-filtration column; Aae Hfq eluted as a single, well defined peak. Chromatographic steps were conducted at room temperature; lengthier incubation steps, such as dialysis, were carried out at 310 or 315 K throughout the purification, as Aae Hfq samples were found to be relatively insoluble over a few hours at room temperature (∼295 K).

Aae Hfq sample purity was generally assayed via SDS–PAGE gels or matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). Samples were prepared for MALDI by diluting them 1:4(v:v) with 0.01%(v/v) trifluoroacetic acid (TFA) and then spotting them onto a steel MALDI plate in a 1:1(v:v) ratio with a matrix solution (15 mg ml⁻¹ sinapinic acid in 50% acetonitrile, 0.05% TFA); this mixture crystallized in situ via solvent evaporation. Mass spectra were acquired on a Bruker MicroFlex instrument operating in linear positive-ion mode (25 kV accelerating voltage; 50–80% grid voltage), and the final spectra were the result of averaging at least 50 laser shots. Two sets of molecular-weight calibrants were used for low (4–20 kDa) and high (20–100 kDa) m/z ranges. Purification progress and sample MALDI spectra are illustrated in Supplementary Fig. S1(b) and Fig. 2, respectively.

Figure 2 Aae Hfq monomers and oligomers, as assayed by cross-linking and mass spectrometry. MALDI-TOF spectra are shown for (a) native, untreated (non-cross-linked) Aae Hfq monomers, with an expected MW of 9482.9 Da based on the recombinant protein sequence (Supplementary Fig. S1), as well as (b) a chemically cross-linked Aae Hfq sample. As detailed in §2.2, cross-linking assays employed a gentle (`indirect') method, using formaldehyde as a cross-linking agent. The main peaks in the cross-linked sample correspond to hexamers and dodecamers, with expected MWs of 56 897.4 and 113 794.8 Da, respectively. The singly-charged molecular ion peaks, [M+H]1+, are accompanied by schematics (blue and orange balls) that indicate the anticipated architecture of the oligomeric states, alongside the MW of the peak as determined from the mass spectrum (cross-linked species are better characterized by a MW range, rather than a single value, because of variability in the number of cross-linker molecules that react).

2.2. Cross-linking assays

Purified Aae Hfq was chemically cross-linked, using formaldehyde, in a so-called `indirect' (vapor-diffusion-based) method (Fadouloglou et al., 2008). Firstly, Aae Hfq samples at 0.6 mg ml⁻¹ were dialyzed into a buffer consisting of 25 mM HEPES pH 8.0, 500 mM NaCl. Reaction solutions were prepared in 24-well Linbro plates using micro-bridges (Hampton Research). Immediately before use, 5 N HCl was added to 25%(w/v) formaldehyde in a 1:40(v:v) ratio. Next, 40 µl of this acidified formaldehyde solution was added to the micro-bridge, and 15 µl of the 0.6 mg ml⁻¹ Aae Hfq was added to a silanized cover slip. Greased wells were then sealed by flipping over the cover slips and the reaction was incubated at 310 K for 40 min. Reactions were quenched by the addition of a primary amine; specifically, 5 µl of 1 M Tris pH 8.0 was mixed into the 15 µl protein droplet. Cross-linked samples were then desalted on a C4 resin (using ZipTip pipette tips) in preparation for analysis via MALDI-TOF MS, as described above.

2.3. Analytical size-exclusion chromatography and multi-angle static light scattering

Analytical size-exclusion chromatography (AnSEC) was performed with a pre-packed Superdex 200 Increase 10/300 GL column and a Bio-Rad NGC medium-pressure liquid-chromatography system. Prior to AnSEC, all protein samples were dialyzed into a running buffer consisting of 50 mM Tris pH 8.0, 200 mM NaCl. In separate experiments, Aae Hfq samples (250 µM protein) were mixed in a 1:1(v:v) ratio with RNA sequences (at 50 µM) denoted `U<sub>6</sub>' [5′-monophos­phate–r(U)<sub>6</sub>–3′-OH] or `A₁₈' [5′-monophosphate–r(A)₁₈–3′-­OH] and equilibrated by incubation at 310 K for 1 h prior to loading onto the AnSEC column. Elution volumes were measured by simultaneously monitoring the absorbance at 260 nm (RNA) and at 280 nm (protein). A standard curve was generated using the Sigma gel-filtration markers kit, with calibrants in the 12–200 kDa molecular-weight range: cytochrome c (12.4 kDa), carbonic anhydrase (29 kDa), bovine serum albumin (66 kDa), alcohol dehydrogenase (150 kDa) and β-amylase (200 kDa); blue dextran was used to calculate the void volume V₀.

To determine absolute molecular masses (i.e. without reference standards and implicit assumptions about spheroidal shapes), and in order to assess potential polydispersity of Aae Hfq in solution, multi-angle static light scattering (MALS) was used in tandem with size-exclusion chromatographic (SEC) separation. A flow-cell-equipped light-scattering (LS) detector was used downstream of the SEC, inline with an absorbance detector (UV) and a differential refractive-index (RI) detector. In our SEC–UV/RI/LS system, (i) the SEC step serves to fractionate a potentially heterogeneous sample (giving the usual chromatogram, recorded at either 280 or 260 nm on a Waters UV–Vis detector), (ii) the differential refractometer (RI) estimates the solute concentration via changes in the solution refractive index (i.e. dn/dc) and (iii) the LS detector measures the excess scattered light. This workflow was executed on a Waters HPLC system equipped with the Wyatt instrumentation noted below, and utilized the same column (Superdex 200) and solution buffer conditions as described immediately above. LS measurements were taken at three detection angles using a Wyatt miniDAWN TREOS (λ = 658 nm), and the differential refractive index was recorded using a Wyatt Optilab T-rEX. This approach enables the molecular mass of the solute in each fraction to be determined because the amount of light scattered (from the LS data) scales with the weight-averaged molecular masses (the desired quantity) and solute concentrations (from the RI data); if multiple species exist in a given (heterogeneous) fraction, the polydispersity can be quantified as the ratio of the weight-averaged (M_w) and number-averaged (M_n) molar masses. Data were processed and analysed using the ASTRA software package (Wyatt), applying the Zimm formalism to extract the weight-averaged molecular masses (Folta-Stogniew, 2009).

2.4. Fluorescence polarization-based binding assays

RNA-binding affinities were determined via fluorescence anisotropy/polarization experiments (FA/FP; Pagano et al., 2011) using fluorescein-labeled oligoribonucleotides. In particular, the RNA probes 5′-FAM–r(U)₆–3′-OH (FAM–U₆) and 5′-FAM–r(A)₁₈–3′-OH (FAM–A₁₈) were used, with 6-carboxyfluorescein amidite (FAM) modification of the 5′ ends; the FAM label features absorption and emission wavelengths, λ_max, of 485 nm (excitation) and 520 nm (detection), respectively. FAM-labeled RNAs at 5 nM were added to a serially diluted concentration series of purified Aae Hfq (in 50 mM Tris pH 8.0, 500 mM NaCl) and allowed to equilibrate for 45 min at room temperature. The highest Hfq concentration was 30 µM (in terms of monomer), and a total of 18 serial dilutions were performed to produce data sets such as that in Fig. 4. For binding assays that were supplemented with Mg²⁺, a 1 M MgCl₂ stock solution was used and the final Mg²⁺ concentration in the binding reaction was 10 mM.

The fluorescence polarization, P, is measured as P = [(I_∥ − I_⊥)/(I_∥ + I_⊥)], where I_∥ and I_⊥ are the emitted light intensities in directions parallel and perpendicular to the excitation plane, respectively. FP data were recorded on a PheraSTAR spectrofluorometer equipped with a plate reader (BMG Labtech), and values from three independent trials were averaged. The effective polarization, in units of millipolarization (mP), was plotted against log[(Hfq)₆]. Binding data were fitted, via nonlinear least-squares regression, to a logistic functional form of the classic sigmoidal curve for saturable binding. Specifically, the four-parameter equation

was used, where the independent variable x is the log of the (Hfq)₆ concentration at a given data point and the fit parameters are (i) A₁, the polarization at the end of the titration (unbound; lower plateau of the binding isotherm); (ii) A₂, the final polarization at the start of the titration (saturated binding; upper plateau); (iii) x₀, the apparent equilibrium dissociation constant (K_d,app) for the binding reaction in terms of log[(Hfq)₆]; and (iv) a parameter, dx, giving the characteristic scale/width over which the slope of the sigmoid changes. In this formulation, dx is essentially the classic Hill coefficient, measuring the steepness of the binding curve; the greater the magnitude of dx, the narrower the transition region. In addition to fitting the binding data with the four-parameter logistic model (1), a simpler, three-parameter model was also applied, with the functional form

where the terms A₁ and A₂ are as above in (1), K_d is the dissociation constant (x₀ above) and the variables and [P]_t are the total concentrations of ligand (FAM-labeled RNA) and receptor (here, taken as an Hfq hexamer), respectively. Although assuming a 1:1 stoichiometry between Aae (Hfq)₆ and RNA, and not capturing potential cooperativity between possibly multiple ligand-binding sites, this second model does account for the effects of receptor depletion on the fitted K_d values. This, in turn, is an important consideration in fitting data points with abscissas near (within ∼10× of) the true K_d, as the assumption that the concentration of ligand·receptor complex, [·P], is far lower than the total concentrations of each species (, [P]_t) is violated if [P]_t ≃ K_d. That is, free [P] ≅ [P]_t no longer holds near the K_d. Despite the advantage of accounting for receptor depletion, note that this treatment implicitly takes the Hill coefficient (the `slope factor' for the transition region) to be 1, rather than letting it vary (as in equation 1); indeed, the only three degrees of freedom with which to describe the binding curve are the upper and lower asymptotes and the midpoint of the transition (i.e. K<sub>d</sub>, or `x₀' in equation 1). Assuming a Hill coefficient of unity and a simple (1:1 stoichiometry) equilibrium, one can show that neglecting to account for receptor-depletion phenomena gives an apparent (fitted) dissociation constant, K_d,app, that exceeds by [P]_t/2 the `true' K_d,app obtained via equation (2). For these reasons, both models, equations (1) and (2), were considered in fitting the data. All calculations described in this section were performed with in-house code written in the R programming language using the RStudio integrated development environment.

2.5. X-ray crystallography

2.5.3. Structure solution, refinement and validation

Initial phases for the diffraction data sets for both crystal forms were obtained via molecular replacement (MR). Specifically, the Phaser (McCoy et al., 2007) software was used, with the P. aeruginosa (Pae) hexamer structure (PDB entry 1u1s; Nikulin et al., 2005) as a search model for the phasing of both crystal forms (Aae and Pae Hfq share high sequence similarity; see Fig. 1). Note that initial phases for the P1 and P6 Aae crystal forms were obtained independently of one another, i.e. via parallel MR efforts. For the P1 (apo) form, with 12 monomers per unit cell (indicative of two hexamers), the calculated Matthews coefficient (V_M) is 2.06 ų Da⁻¹, corresponding to a solvent content of 40.21% by volume. For the P6 (U₆-bound) form, only one monomer per asymmetric unit is feasible, with a V_M of 2.28 ų Da⁻¹ and a solvent content of 46.08%. These and related characteristics of the diffraction data are summarized in Table 1.

Table 1 X-ray diffraction data-collection and processing statistics Values in parentheses are for the highest resolution shell.   Aae Hfq, apo form (`P1') Aae Hfq·U6 RNA (`P6') Diffraction source 24-ID-E, APS NE-CAT 24-ID-C, APS NE-CAT Wavelength (Å) 0.9792 0.9195 Temperature (K) 100 100 Detector ADSC Q315 CCD Dectris PILATUS 6MF Crystal-to-detector distance (mm) 200 300 Rotation range per image (°) 1.0 1.0 Total rotation range (°) 400.0 300.0 Exposure time per image (s) 1.0 1.0 Space group P1 P6 a, b, c (Å) 63.46, 66.06, 66.10 66.19, 66.19, 34.21 α, β, γ (°) 60.05, 83.94, 77.17   Mosaicity (°) 0.143 0.107 Resolution range (Å) 57.27–1.49 (1.53–1.49) 34.21–1.50 (1.55–1.50) Total No. of reflections 299450 46203 No. of unique reflections 138120 13177 Completeness (%) 93.7 (83.7) 94.9 (93.4) Multiplicity 2.2 (2.1) 3.5 (3.5) 〈I/σ(I)〉 14.0 (3.4) 12.3 (3.6) Rmerge† 0.039 (0.258) 0.056 (0.292) Rmeas‡ 0.052 (0.349) 0.065 (0.345) Rp.i.m.‡ 0.035 (0.234) 0.032 (0.179) CC1/2§ 0.998 (0.886) 0.998 (0.942) Overall B value from Wilson plot (Å2) 12.62 15.87 Matthews coefficient VM (Å3 Da–1) 2.06 [12 subunits in asymmetric unit] 2.28 [one subunit in asymmetric unit] Solvent content (%) 40.21 46.08 †Rmerge = , where Ii(hkl) is the intensity of the ith observation of reflection hkl, 〈.〉 denotes the mean of symmetry-related (or Friedel-related) reflections and the coefficient α = 1; the outer summations run over only unique hkl with multiplicities greater than one. ‡Rmeas is defined analogously to Rmerge, save that the prefactor α = [Nhkl/(Nhkl − 1)]1/2 is used; Nhkl is the number of observations of reflection hkl (index i = 1→Nhkl). Similarly, the precision-indicating merging R factor, Rp.i.m., is defined as above but with the prefactor α = [1/(Nhkl − 1)]1/2. §CC1/2 is the correlation coefficient between intensities chosen from random halves of the full data set.

After obtaining initial MR solutions in Phaser, the correct Aae Hfq amino-acid sequence was built and side chains were completed in a largely automated manner using the AutoBuild functionality in the PHENIX suite (Adams et al., 2010). Individual solvent molecules, including H₂O, MPD and Gnd, were added in a semi-automated manner (i.e. with visual inspection and manual adjustment) after the initial stages of refinement. Refinement of atomic positions, occupancies and atomic displacement parameters (ADPs), either as isotropic B factors or as full anisotropic ADPs, proceeded over several rounds in PHENIX. Some early refinement steps included simulated-annealing optimization of coordinates via molecular dynamics in torsion-angle space, as well as refinement of translation–libration–screw (TLS) parameters to account for anisotropic disorder of each subunit chain (one TLS group was defined per monomeric Hfq subunit). These steps yielded R_work and R_free values of 0.194 and 0.212 for the P1 data set and 0.212 and 0.223 for the P6 data set, respectively. The diffraction limits of the P1 and P6 forms, 1.49 and 1.50 Å, respectively, occupy an intermediate zone between the atomic resolution (d 1.4 Å) and medium-resolution (d 1.7 Å) limits whereupon clearer decisions can be made as to the treatment of B factors (Merritt, 2012). For instance, a relatively simple model (fewer parameters/atom), featuring individual isotropic B factors and one TLS group per chain, might be most justifiable at ∼1.6 Å, depending on the quality of the diffraction data, whereas a more complex B-factor model with a greater number of parameters, e.g. full anisotropic ADP tensors, U_ij, one per atom, is likely to be statistically valid (and indeed advised) at resolutions better than ∼1.3 Å.

For both the P1 and P6 forms of Aae Hfq, a final B-factor model was chosen based on analyses of the data-to-parameter ratio (i.e. the number of reflections per atom), Hamilton's generalized residual (Hamilton, 1965) and related criteria, as implemented in the bselect routine of the PDB_REDO code (Joosten et al., 2012). The P1 and P6 data sets contained 16.5 and 17.5 reflections per atom, respectively, making the anisotropic refinement problem nearly twofold overdetermined; the unsupervised decision algorithm in PDB_REDO identified a fully anisotropic, individual B-factor model as being optimal. The structural models resulting from various ADP refinement strategies were assessed using the protein anisotropic refinement validation and analysis tool PARVATI (Zucker et al., 2010). In the final refinement stages for both Aae Hfq crystal forms, P1 (Z = 12) and P6 (Z = 6), full anisotropic B-factor tensors were refined individually for virtually every atom. [A small fraction of atoms in both the P1 and P6 models were treated isotropically, i.e. by refining individual B_iso values; most of these atoms, selected based on per-atom statistical tests in PDB_REDO, were either water or heteroatoms (e.g. Gnd in P1, PEG in P6).] At no point in the refinement were NCS restraints or constraints imposed for the 12 subunits in the P1 cell. All refinement steps involving visual inspection and manual adjustment of the model were performed in Coot (Emsley et al., 2010).

After the correct protein sequence had been built and refined against the P6 data set, at least two complete nucleotides of U₆ RNA, including three phosphate groups, were clearly visible in α_A-weighted difference electron-density maps (mF_o − DF_c). Ribonucleotides were built into electron density using the RCrane utility (Keating & Pyle, 2010), after an initial round of refinement of coordinates, occupancies and individual B factors in PHENIX. Validation of the final structural models included (i) inspection of the Ramachandran plot via PROCHECK (Laskowski et al., 1993), (ii) assessment of nonbonded interactions and geometric packing quality via ERRAT (Colovos & Yeates, 1993), (iii) analysis of sequence/structure compatibility via the profile-based method Verify3D (Eisenberg et al., 1997) and, finally, (iv) detailed stereochemical/quality checks with the MolProbity software (Chen et al., 2010). Final structure-determination and model-refinement statistics are provided in Table 2.

Table 2 Structure determination and model refinement Values in parentheses are for the highest resolution shell.   Aae Hfq, apo form (`P1') Aae Hfq·U6 RNA (`P6') Resolution range (Å) 46.35–1.49 (1.51–1.49) 34.21–1.50 (1.56–1.50) Completeness (%) 93.9 94.9 No. of reflections, working set 138104 (12739) 13171 (1308) No. of reflections, test set 10625 (983) 662 (70) Final Rcryst 0.1323 (0.1531) 0.1443 (0.1499) Final Rfree 0.1696 (0.2108) 0.1719 (0.1933) No. of non-H atoms  Macromolecules 7670 Hfq 598 Hfq, 43 RNA  Ligands 200 MPD, 32 Gnd, 7 Cl−, 28 PEG 8 MPD, 7 PEG  Solvent 413 H2O 36 H2O  Total 8350 692 No. residues of protein, solvent or ligand molecules included in the final, refined structure  Aae Hfq 848 [over 12 subunits] 71 [over 1 subunit]  H2O 413 36  U6 RNA   ∼2–3†  MPD 25 1  Cl− 7    Gnd 8    PEG‡ 4 1 R.m.s. deviations  Bonds (Å) 0.005 0.005  Angles (°) 0.75 0.76 Average B factors (Å2)  Protein 19.32 22.18  Ligand 25.89 30.44 Ramachandran plot  Most favored (%) 98 97  Allowed (%) 1.7 2.9  Outliers (%) 0 0  Rotamer outliers (%) 0.34 1.5 PDB code 5szd 5sze †This value is given as a range because two complete U nucleotides, plus a fragment of a third residue, could be built into the electron-density maps. ‡Fragments of polyethylene glycol could be built in both structures, generally of two to three repeat units [i.e. (O–C–C)2–O, neglecting H atoms].

2.6. Sequence and structure analyses

Sequences of verified Hfq homologs, drawn from diverse bacterial phyla, were selected for alignment and analysis against Aae Hfq. Here, we take `verified' to mean that the putative Hfq homolog from the published literature has been identified via functional analysis or structural similarity (e.g. shown to adopt the Sm fold). Multiple sequence alignments were computed via two progressive-alignment codes: (i) the multiple alignment using fast Fourier transform method (MAFFT; Katoh & Standley, 2013) and (ii) a sequence-comparison approach using log-expectation scores for the profile function (MUSCLE; Edgar, 2004). The Geneious bioinformatics platform (Kearse et al., 2012) was used for some data/project-management steps and tree-visualization purposes. Multiple sequence alignments (Fig. 1) were processed using ESPript (Gouet et al., 1999) run as a command-line tool; the resulting PostScript source was then modified to obtain the final figures. Iterative PSI-BLAST (Camacho et al., 2009) searches against sequences in the PDB were used to identify homologous proteins as trial MR search models. Pae Hfq, with 46% pairwise identity to Aae Hfq (across 97% query coverage), exhibited the greatest sequence similarity (∼63%, at the level of BLOSUM62) and was therefore chosen as the initial MR search model.

Structural alignments were performed using a least-squares fitting algorithm (McLachlan, 1982) implemented in ProFit (Martin & Porter, 2009). Multiple structural alignment of the 12 monomeric subunits in the apo form of Aae Hfq was used to create a mean reference structure, and each monomer was then aligned with this averaged reference. To assess three-dimensional structural similarity between each of the n(n −1)/2 distinct pairs of monomers, a pairwise distance matrix was constructed by computing main-chain r.m.s.d.s between subunits i and j, giving matrix element (i, j). Agglomerative hierarchical clustering was performed on this distance matrix using either the complete-linkage criterion or Ward's variance-minimization algorithm with a Euclidean distance metric (Jain et al., 1999); in-house code was written for these steps in both the R (within RStudio) and Python languages.

Residues were assigned to secondary-structural elements by a consensus approach via visual inspection in PyMOL as well as the automated assignment tools DSSP and Stride; the precise borders can differ between these codes by a residue or two. Normal-mode analyses of the P1 and P6 structures, taken as coarse-grained (C^α-only) representations and treated as anisotropic network models (ANM), were performed with the ProDy/NMWiz (Bakan et al., 2011) plugin to VMD (Humphrey et al., 1996). The Hessian matrix of the ANM was built using default parameters for the force constant (γ = 1) and pairwise interaction cutoff distance (15 Å). Of the 3N − 6 nontrivial modes, displacements along the softest ∼20 vibrational modes, which correspond to low-frequency/high-amplitude collective motions, were visually inspected in VMD. Other structural analyses (e.g. Fig. 6a) entailed computing the principal axes of the moment of inertia tensor and the best-fit plane to three-dimensional structures (in the sense of linear least squares); the latter task utilized a previously described singular value decomposition code (Mura et al., 2010), and all other structural analysis tasks employed in-house code written in Python or as Unix shell scripts. Nucleic acid stereochemical parameters and conformational properties, e.g. the values of glycosidic torsion angles and sugar pucker phase angles of the U₆ RNA, were analysed and calculated with DSSR (Lu et al., 2015). Surface-area properties, such as solvent-accessible surface area (SASA) and buried surface area (BSA or ΔSASA), were calculated as averages from five approaches: (i) Shrake and Rupley's `surface-dot' counting method (Shrake & Rupley, 1973), as implemented in AREAIMOL, (ii) the classic Lee and Richards `rolling-ball' method (Lee & Richards, 1971), available in NACCESS, (iii) the `reduced surface' analytical approach of MSMS (Sanner et al., 1996), and the more approximate (point-counting) methods from the structural analysis routines available in (iv) PyMOL and (v) PyCogent (Cieślik et al., 2011).

All molecular-graphics illustrations in Figs. 5–8 and Supplementary Figs. S3–S6 were created in PyMOL, with the exception of Supplementary Figs. S4(e) and S4(f) (created in VMD and rendered with Tachyon). LigPlot+ (Laskowski & Swindells, 2011) was used in creating schematic diagrams of interatomic contacts, as in Fig. 8. Many of the scientific software tools were used as SBGrid-supported applications (Morin et al., 2013).

3.1. Cloning, expression, purification and initial biochemical examination of Aae Hfq

Recombinant, wild-type Aae Hfq was successfully cloned, overexpressed and purified from E. coli, as confirmed by various biochemical and biophysical data, including SDS–PAGE gels (Supplementary Fig. S1) and MALDI-TOF mass spectra of the native protein (Fig. 2a). The 6×His-tagged Aae Hfq is 100 amino acids in length, with a molecular weight of 11 365.0 Da and a predicted isoelectric point of 9.69; the working Aae Hfq construct, obtained via proteolytic removal of the tag (Supplementary Fig. S1a), is 83 amino acids in length (9482.9 Da, pI = 9.45). The expected mass computed from the amino-acid sequence is in close agreement with that experimentally characterized by MALDI–TOF, indicating successful (complete) removal of the affinity tag (Fig. 2a) at position G⁻² (residue numbering is such that the wild-type methionine is M¹, as indicated in Supplementary Fig. S1a).

Initial Aae Hfq purification efforts were hindered by nucleic acid contaminants. Specifically, purified protein samples exhibited A₂₆₀/A₂₈₀ absorbance ratios of ∼1.65, indicative of co-purifying nucleic acids (De Mey et al., 2006; Patterson & Mura, 2013); this problem is perhaps unsurprising given the known affinity of Hfq for nucleic acids, combined with the particularly high pI of Aae Hfq. By applying systematic colorimetric assays (Patterson & Mura, 2013) to Aae Hfq samples with high A₂₆₀/A₂₈₀ ratios (Supplementary Fig. S2a), we found that the co-purifying nucleic acids are likely to comprise a heterogeneous pool of RNAs with lengths between ∼100 and ∼200 nucleotides (Supplementary Fig. S2b). Early experiments using anion-exchange chromatography revealed that nucleic acid-bound Hfq would elute at three distinct ionic strengths (in a linear salt gradient), and each peak appeared to contain a population of nucleic acids that varied in length, both within one peak and between the three peaks (data not shown). To obtain well defined, well behaved apo Aae Hfq samples for downstream RNA-binding assays, crystallization trials etc., relatively high concentrations (∼6 M) of guanidinium were added to the cell lysates, the aim being to dissociate spurious Hfq-associated nucleic acids. Inclusion of Gnd in the purification workflow (see §2.1) yielded samples with improved A₂₆₀/A₂₈₀ ratios (∼0.8), suggesting that nucleic acid contamination had been at least partly alleviated (pure protein samples generally have an A₂₆₀/A₂₈₀ of ∼0.7, and E. coli Hfq samples with an A₂₅₀/A₂₇₄ of ∼0.8 have been reported to have trace nucleic acid contamination; Updegrove et al., 2010). Notably, the Gnd denaturant did not appear to unfold or disrupt the oligomerization properties of Aae Hfq based on various observations; for instance, a discrete band corresponding to the hexameric assembly persisted in SDS–PAGE gels of Gnd-treated samples (Supplementary Fig. S1b).

As an initial assessment of its self-assembly properties and oligomeric states in solution, purified Aae Hfq was examined by analytical size-exclusion chromatography (Figs. 3a and 3b, black traces). The protein elutes as a single, well shaped peak, with no apparent splitting, broadening, shouldering, tailing etc. However, the location of this peak is unexpected: the elution volume of the peak gives a molecular weight (MW) of ∼37 kDa, rather than the ∼57 kDa expected for an Aae Hfq hexamer. This apparent MW, obtained using a standard curve as described in §2.3, could indicate a tetrameric assembly, for which the MW is calculated to be 37.9 kDa. Shape-dependent deviations from ideal migration properties would be expected to give an (Hfq)₆ species that migrates faster, not slower, than anticipated based purely on MW, given the larger effective hydrodynamic radius of a toroidal hexamer (versus the roughly globular standards used to calibrate our column elution volumes). However, favorable protein–resin inter­actions would tend to retard the migration of an Aae Hfq oligomer, leading to a smaller apparent MW species. Given the highly basic pI, and the resultant charge on Aae Hfq at near-neutral pHs, we suspect that the low MW estimate from AnSEC stems from protein–resin interactions, electrostatic or otherwise; spurious Aae Hfq retention was also observed in experiments with other, unrelated chromatographic resins. Note that nonspecific protein adsorption to SEC resins was first documented long ago (Belew et al., 1978) and has been reviewed by Arakawa et al. (2010).

Figure 3 The solution-state distribution of Aae Hfq oligomers shifts in the presence of short RNAs. Elution profiles are shown for analytical size-exclusion chromatography of Aae Hfq samples incubated with either (a) U6 or (b) A18 RNAs [specifically, 250 µM Aae Hfq was incubated in a 1:1(v:v) ratio with 50 µM of either U6 or A18 RNA]. The elution of Aae Hfq was detected via the absorbance at 280 nm (A280), and RNA and Hfq·RNA complexes were monitored at A260. While putative Hfq⋯U6 interactions do not appear to shift the oligomeric state, as indicated by the close alignment of the black (Hfq alone) and red (Hfq·U6) peaks in (a), Hfq interactions with A18 do shift the oligomeric species towards a higher-order state [blue arrow in (b), denoting apparent dodecamers]. This shift could correspond to the simultaneous binding of A18 to two Hfq hexamers, potentially via two modes: (i) as an (Hfq)6·A18·(Hfq)6 `bridged' complex or (ii) as A18 bound to one of the two distal faces that would be exposed on an independently stable (Hfq6)2 double-ring dodecamer. These two models cannot be distinguished via AnSEC. (c) To verify the molecular weight of the Aae Hfq elution peak, the protein was analysed via SEC fractionation followed by multi-angle static light-scattering and refractive-index measurements. The SEC elution profile (black trace) is taken as the absorbance at 280 nm. Light-scattering and refractive-index data can be used to compute molar masses, and the open circles shown here (semi-transparent green) are the molar-mass distribution data [i.e. masses (in kDa) as a function of elution volume]. The weight-averaged molecular weight, Mw, of the Hfq sample is computed for the entire peak from this distribution, and the scale is given by the vertical axis on the right-hand side (green numbers; note that this scale applies to the main plot, not the inset). The apparent Mw that was computed, 58.75 kDa, corresponds to a hexameric assembly of Aae Hfq.

The aberrant AnSEC elution behavior prompted us to assay the Aae oligomeric state by alternative means. SEC coupled with multi-angle light scattering (MALS) showed that the Aae Hfq eluting at this peak position corresponds to a hexamer, with a weight-averaged molecular weight, M_w, of 58.75 kDa (Fig. 3c). A plot of the molar-mass distribution (Fig. 3c, green circles) exhibits uniform values across this Aae Hfq peak (Fig. 3c, inset), indicating that this region of the eluted sample is monodisperse. Aae Hfq monomers were found to be susceptible to chemical cross-linking with formaldehyde, as analysed by MALDI-TOF MS (Fig. 2). The main peak in the mass spectrum of this sample (Fig. 2b) corresponds to a hexamer (57 498.0 Da from MS versus 56 897.4 Da from the sequence); a second peak, near 115 kDa, corresponds to within 1.5% of the MW of a dodecameric assembly. Some Sm and Hfq orthologs have been found to assemble into stacked double rings and other higher-order species, based on analytical ultracentrifugation and light-scattering data (Mura, Kozhukhovsky et al., 2003; Mura, Phillips et al., 2003; Dimastrogiovanni et al., 2014), electron microscopy (Arluison et al., 2006; Mura, Kozhukhovsky et al., 2003), gel-shift assays and other approaches; however, an integrated experimental analysis, using multiple independent methodologies on the same Hfq system, strongly suggests that the E. coli (Hfq)₆·RNA binding stoichiometry is predominantly 1:1 (Updegrove et al., 2011).

3.2. Characterization of RNA binding by Aae Hfq in solution

To evaluate putative RNA interactions with Aae Hfq, solution-state binding interactions between Aae Hfq and either U₆ or A₁₈ (unlabeled) RNAs were examined via analytical size-exclusion chromatography. RNAs that are U-rich (e.g. U₆) or A-rich [e.g. harboring an (A–A–N)_n motif] are known to bind at the proximal and distal faces, respectively, of Hfq homologs from Gram-negative species. We found that U₆ RNA binds Aae Hfq in solution, based on comparisons of the following elution profiles (Fig. 3a): (i) Hfq only (black trace, detected via absorbance at 280 nm), (ii) U₆ only (gray, monitored at 260 nm) and (iii) an Hfq and U₆ mixture (red, 260 nm). In sample (iii), the Hfq + U₆ mixture, note the absence of a U₆ RNA peak near 19.5 ml (Fig. 3a, gray) and a concomitant peak shift to a position centered at the Hfq-only trace, indicating saturated binding of the RNA. Properties of the elution profiles for samples (i) and (iii), specifically, no shift in the peak position and no alteration of the bilateral symmetry of the peak (no tailing, shouldering etc.), suggest that the addition of U₆ does not alter the distribution of the apparent oligomeric states of Aae Hfq.

In contrast to the U₆ behavior, adding A₁₈ RNA to an Aae Hfq sample does appear to shift the Hfq oligomeric state to a higher-order species (Fig. 3b, blue trace, major peak) that coexists with the usual hexamer (blue trace, minor peak). This newly appearing, A₁₈-induced species is hydrodynamically larger than (Hfq)₆, as it elutes far earlier than does Hfq in the Hfq-only sample (black trace); the higher-order entity appears to correspond to an Aae Hfq dodecamer. This was further verified based on the M_w determined via SEC-MALS experiments performed in parallel, which agrees to within 0.5% with the ideal M_w of an [(Hfq)₆]₂·A₁₈ complex (Supplementary Fig. S3). Also, note that the Hfq+A₁₈ trace is devoid of a peak at the A₁₈-only position (i.e. no peak in the blue trace near the ∼18.5 ml peak location in the gray trace), indicating that binding has saturated with respect to A₁₈.

To further quantify the interactions of Hfq with U-rich and A-rich RNAs, the binding affinities of Aae Hfq for 5′-FAM-labeled RNA oligoribonucleotides were determined via fluorescence polarization (FP) assays (Fig. 4, Supplementary Fig. S4). FAM-U₆ and FAM-A₁₈ probes were taken as proxies for U-rich and A-rich ssRNAs, enabling us to assay the strength of Aae Hfq⋯RNA interactions with these prototypical A/U-rich RNAs (for brevity, we refer to these RNAs as simply `U<sub>6</sub>' and `A₁₈' if the FAM is obvious from the context). Both U₆ and A₁₈ were found to bind Aae Hfq with similarly high affinities: using a full nonlinear (logistic function) treatment of the sigmoidal binding isotherm given by equation (1), the nanomolar-scale apparent dissociation constants (K_d,app) are 21.3 nM for U₆ and 17.4 nM for A₁₈ (Fig. 4, thin, lighter-color traces). The sigmoidal shape of these binding curves indicates positive cooperativity, and the Hill coefficients were calculated to be 1.3 and 2.2 for U₆ and A₁₈, respectively. The inclusion of 10 mM Mg²⁺ in the binding reaction enhanced the U₆-binding affinity by an order of magnitude, yielding a K_d,app of 2.1 nM (Fig. 4; red, thicker trace) with a Hill coefficient of 1.7; the A₁₈-binding affinity also increased in the presence of Mg²⁺, although by only twofold, to a K_d,app of 9.5 nM (blue, thicker trace) with a Hill coefficient of 2.4.

Figure 4 High-affinity binding of Aae Hfq to A-rich and U-rich RNAs, with variable Mg2+ dependencies. Binding was quantified via fluorescence polarization assays using 5 nM FAM-U6 (red) or FAM-A18 (blue) and varying concentrations of Hfq, either in the absence (thin lines) or presence (thick lines) of 10 mM MgCl2. For each binding reaction, data from three replicates (standard errors given by vertical bars) were fitted using a four-parameter logistic function to model the sigmoidal binding isotherm; nonlinear fits were also performed with an alternative model, accounting for receptor depletion but neglecting cooperativity (§2.4 and Supplementary Fig. S4). The computed binding constants are given (inset) in terms of the (Hfq)6 concentration, as the stoichiometry of all characterized Hfq·RNA complexes, as well as the structural results reported here, suggest that a hexamer is the active/functional unit. The addition of Mg2+ increases the binding affinity for both FAM-U6 and FAM-A18, albeit with a greater influence for the U-rich (proximal site-binding) RNA. Significant binding was not detected for a shorter A-rich (FAM-A6) or C-rich (FAM-C6) ssRNA.

Because the apparent K_d values for U₆ and A₁₈ binding were found to be in the low nanomolar range, depletion of the Hfq receptor must be accounted for near the lower Hfq concentration range sampled in our binding assays (approximately, the nanomolar range; Fig. 4). Receptor-depletion phenomena can lead to spuriously high values of K_d,app as computed from nonlinear regression against FP data, as detailed in §2.4. Thus, to assess the impact of receptor depletion, we also performed a nonlinear least-squares fit of a three-parameter form of the classic binding isotherm (§2.4) against the FP binding data. This model [equation (2) in §2.4] yielded the results shown in Supplementary Fig. S4, with K_d values that were indeed ∼20–40% lower in magnitude than those calculated by fitting with the full sigmoidal/logistical model (i.e. using equation 1). Note, however, that this three-parameter model assumes a Hill coefficient fixed at unity and does not account for the aforementioned positive cooperativity that we detect in Aae Hfq⋯RNA binding (see the discussion of the dx parameter in §2.4). Also, note that the U₆^Mg2+ and A₁₈^Mg2+ Hfq-binding reactions, which had the lowest K_d values (2.1 and 9.5 nM, respectively) of the four systems shown in Fig. 4 and Supplementary Fig. S4, were also the two systems that featured the greatest discrepancy in the K_d,app computed via equation (1) (includes cooperativity, neglects depletion) versus equation (2) (neglects cooperativity, accounts for depletion); this is a reassuring finding in terms of a depletion model for our Aae Hfq·RNA system, as the discrepancies that arise from receptor depletion become disproportionately greater at lower K_d values. Finally, we note that no significant binding was detected between Aae Hfq and either FAM-A₆ or FAM-C₆ (data not shown).

3.3. Crystal structures of Aae Hfq monomers and oligomers, and their lattice packing

Crystals of Aae Hfq were readily obtained in multiple forms, including hexagonal plates and small, birefringent parallelepiped habits (Supplementary Fig. S1c). At least three distinct morphologies could be identified, which we denote (i) a `P1 form' (apo Hfq, without RNA), (ii) a `P6 form' (with RNA; see §3.5) and (iii) a third form that is likely to belong to space group P3₁ or P6₂. Forms (i) and (ii) were well diffracting (Supplementary Fig. S1d), leading to the P1 and P6 structures reported here; the third form yielded diffraction data with potential pathologies, including translational pseudosymmetry or tetartohedral twinning, and its structure will be the subject of future work (K. A. Stanek & C. Mura, unpublished work). Initial Aae Hfq crystals were obtained with a crystallization reagent comprised of 0.1 M sodium cacodylate, 5%(w/v) PEG 8000, 40%(v/v) MPD; inclusion of the additive [Co(NH₃)₆]Cl₃ at ∼10 mM in the final crystallization drop improved the specimen size and quality. These apo Aae Hfq crystals formed in space group P1, with unit-cell parameters a = 63.46, b = 66.06, c = 66.10 Å, α = 60.05, β = 83.94, γ = 77.17°. These dimensions are most consistent with Z = 10–12 monomers per cell, and a resolution-dependent probabilistic estimator for the Matthews coefficient (Kantardjieff & Rupp, 2003) gives a 12-mer as the second-highest peak; also, the a ≃ b ≃ c geometry is consistent with a model in which two Hfq hexameric rings, which generally measure ∼65 Å in diameter, stack atop one another in the cell.

The P1 Aae Hfq structure was refined to 1.49 Å resolution, with initial phases obtained by molecular replacement with a Pae Hfq hexamer search model (PDB entry 1u1s; Nikulin et al., 2005). The Pae homolog was used because sequence analysis (Fig. 1) showed it to have the greatest sequence identity (>40%) to Aae Hfq. A promising molecular-replacement solution was readily identified, and side chains for the Aae Hfq sequence were initially built in an automated manner using PHENIX. As detailed in §2.5.3, the number of reflections per atom, as well as other diffraction data-quality statistics, prompted us to refine the atomic displacement parameters (ADPs) via treatment of the full, anisotropic B-factor tensor for essentially all non-H atoms (most of the isotropically treated exceptions were atoms of solvent molecules or small-molecule components of the crystallization buffer). Anisotropic treatment of individual ADPs began at a relatively late stage in the overall refinement workflow, and doing so noticeably improved the R_work and R_free residuals from 13.6 and 17.2%, respectively, before anisotropic treatment to 13.2 and 16.9%, respectively, after anisotropic treatment (Table 2). The final, refined P1 model was subjected to extensive validation and quality assessment, in terms of both the three-dimensional structure itself (i.e. atomic coordinates) as well as the patterns of B factors (i.e. anisotropic ADPs), as described in §2.5.3.

In addition to >400 solvent (H₂O) molecules, the final P1 model also includes four PEG fragments, eight Gnd molecules, seven Cl⁻ ions and 25 MPD molecules (Table 2). Six each of the Gnd cations and chloride anions bind between the two Hfq rings, in identical positions with respect to the nearest protein subunit (i.e. in a sixfold-symmetric arrangement; Fig. 5); the other Gnd and Cl⁻ species occur at unremarkable locations. The PEG fragments bind in a concave region on the exposed face of the DE ring, i.e. on the distal surface of Aae Hfq (not shown in Fig. 5 for clarity). Notably, this moderately apolar pocket corresponds to the second A site in the (A–A–N)_n recognition motif described above (§1). The cleft is formed between adjacent subunits (at the interfaces of chains I/J, J/K, K/L and L/G), and is well defined in Aae Hfq, with one of its walls formed by the phenolic ring of Tyr23 (homologous to E. coli Tyr25, which is crucial for A-rich RNA binding). The PEG fragments bind with similar poses in each of the four sites. Of the 25 MPD molecules, 24 occupy sixfold-symmetric positions near the proximal face of Aae Hfq (the remaining MPD is near the distal face of the DE ring). These 24 MPDs bind in a 2 × (6 + 6′) arrangement. Here, the `2' denotes that a set of 12 MPDs binds identically to each of the two Hfq hexamers (i.e. the PE and DE rings in Fig. 5), and the prime in `6 + 6′' indicates two distinct subsets of MPDs: one binds at the proximal RNA site of Hfq (below, and Fig. 7), while the other MPD is disposed near the α-helix on the proximal site, not far from the lateral rim.

Figure 5 Crystal structure of Aae Hfq in the apo form, with head→tail stacking of hexameric rings. The apo form of Aae Hfq crystallized in space group P1 as a dodecameric assembly of hexamers stacked in a proximal→distal orientation in the lattice. Ribbon diagrams of the final, refined structure are shown here from perpendicular viewpoints. The proximal-exposed (PE) hexamer is colored blue and cyan, and subunits in the distal-exposed (DE) hexamer are colored alternatingly yellow and orange. Co-crystallizing molecules of MPD (gray C atoms) and Gnd (green C atoms) are shown in ball-and-stick representation, and Cl− ions are rendered as yellow spheres scaled to the van der Waals radius. Note that many of the Gnd cations and Cl− anions are coplanar, where they form a `salty' layer at the ring interface (this is most clearly seen in the transverse view). Contacts between hexamers are mediated by the N-termini of the DE hexamer (top) and the loop L2/strand β2 regions of the PE hexamer (bottom); the approximate location of one of the lateral rim RNA-binding sites is labeled on the DE ring.

The overall three-dimensional structure of the Aae Hfq monomer (Fig. 5) is that of the Sm fold, as anticipated based on sequence similarity and the efficacy of MR in phasing the diffraction data. In particular, the N-terminal α-helix is followed by five highly curved β-strands arranged as an antiparallel β-sheet. The secondary-structural elements (SSEs), shown schematically in Fig. 1, are labeled in the three-dimensional structure of Fig. 6(b). The precise SSE boundaries in Aae Hfq, computed with Stride, are residues 5–16 (α1), 19–24 (β1), 29–38 (β2), 41–46 (β3), 49–54 (β4) and 58–63 (β5); the same ranges are obtained with DSSP, save that the DSSP criteria make Phe37 (not Asp38) the end of the most curved strand (β2). Most of the β-strands in Aae Hfq are delimited by loops that adopt various β-turn geometries (including types I, II′, IV and VIII), with the exception of a short 3₁₀-helix (residues 55–57) between β4 and β5. These loops contain many of the RNA-contacting residues of Hfq (see below) and, as labeled in Figs. 1, 5, 6 and 9, we denote these linker regions as L1→L5. Noncovalent interactions between Hfq monomers include van der Waals contacts and hydrogen bonds between the backbones of strand β4 of one subunit and β5* of the adjacent subunit, effectively extending the β-sheet across the entire toroid; these enthalpically favorable interatomic contacts are likely to facilitate self-assembly of the hexamer. (Unless otherwise stated, asterisks denote an adjacent Hfq subunit, be it related by crystallographic symmetry or otherwise.) Residues 1→68 of the native Aae Hfq sequence could be readily built into electron-density maps for each monomer in the asymmetric unit, thus providing a structure of the N-terminal region of Hfq as well as the entire Sm domain; note that the N-terminal tail, illustrated for the apo/P1 structure in Fig. 5 (bottom right) and Fig. 6(b), was unresolved in many previous Hfq structures. Most of the Aae Hfq C-terminal residues 70→80 were not discernible in electron density and are presumably disordered.

Figure 6 Structural variation across the Aae Hfq monomer (P6) and dodecamer (P1) crystal forms. At a gross structural level, the two Hfq rings in the head-to-tail dodecamer of the P1 crystal form (Fig. 5, axial view) appear to be related by a rigid-body rotation. The two rings, the proximal-exposed (PE) and distal-exposed (DE) hexamers, were brought, via pure rigid-body translation, to a common origin, indicated by the blue sphere in (a). Best-fit planes to each ring were then computed as described in §2.6 and shown here as semi-transparent hexagonal plates of either orange (DE ring) or cyan (PE ring) color. For clarity, the DE ring (orange/yellow in Fig. 5) is omitted in (a), and a couple of the L2 loops are labeled (in the PE ring) simply as a structural landmark. The three principal axes of the moment of inertia tensor are shown in either orange (DE ring) or blue (PE ring); large differences in the orientation of these principal axes are marked by green and red `Δ' symbols, while a `δ' symbol (blue) denotes smaller-scale differences. The rotation between the rings is clear from the relative disposition (Δ) of two of the principal axes. Furthermore, a small, but discernable, difference (δ) in the directions of the normal axes indicates a slight tilt between the rings; this direction would correspond to the sixfold axis in a perfectly symmetric double hexamer. A multiple structural alignment of the 12 subunits in the P1 cell (b) reveals little structural variation of the Sm core (shown as Cα backbone traces), while there are many examples of side-chain variability (as noted in the panel). The defining secondary-structural elements of the Sm fold (L1 loop, β1 strand etc.), as well as the termini, are labeled. The two regions of Aae Hfq that most extensively engage in interactions between rings (hexamer–hexamer contacts in Fig. 5), and in forming crystal contacts, are the L4 loops and the irregularly structured ∼5 residues at the N-terminus (preceding α1). These also are the two most variable regions in Hfq, both in terms of sequence length (and composition) as well as three-dimensional structure, as seen in (b). The side-chain variability shown in (b) takes two forms: (i) alternate conformers that could be built for a single residue, such as the Gln52 example highlighted to the left, and (ii) rotameric variation for a single residue across the 12 subunits, such as the groups of three residues shown as sticks near the top of (b). In many instances of the latter case, the 12 residue states clustered into two groups, corresponding to the DE or PE hexamer. In the diagram in (c), the Hfq subunits in P1, labeled by chain ID, are evenly spaced about a circle; arcs are drawn between the most structurally similar pairs of subunits, with the line thickness inversely scaled by the r.m.s.d. for the given pair. For clarity, not all ∼n2 edges are shown here, but rather only at the levels of subunit pairs and triples (i.e. the deepest and second-deepest levels of leaf-nodes in the full dendrogram of Supplementary Fig. S5c). This result, from hierarchical clustering on backbone r.m.s.d.s, shows that pairs of monomers within a given hexamer are structurally more similar to each other than are pairs between hexamers (chains A→F comprise the PE ring and chains G→L comprise the DE ring).

3.4. The apo form of Aae Hfq

While neither NCS averaging, nor any NCS constraints or restraints, were applied at any point during the phasing and refinement of Aae Hfq in the apo form, the 12 monomers in the P1 cell are virtually indistinguishable from one another (Figs. 6a and 6b, Supplementary Fig. S5), at least at the level of protein backbone structure (there are side-chain variations). The mean pairwise main-chain r.m.s.d. averaged over all monomer pairs in the P1 cell lies below 0.3 Å; this low value is also evident in the magnitude of the ordinate scale of the structural clustering dendrogram in Supplementary Fig. S5(c). To systematically compare structures, a matrix of r.m.s.d.s was constructed from all pairwise subunit alignments. Agglomerative hierarchical clustering on this distance matrix (Supplementary Fig. S5c) reveals that the subunits partition into two low-level (root-level) clusters so as to recapitulate the natural (structural) ordering found in the crystal: that is, chains A→F cluster together (as the proximal-exposed, or PE, ring in Fig. 5), and likewise chains G→L form a second group (the distal-exposed, or DE, ring). This finding is illustrated in Fig. 6(c), which conveys the degree of three-dimensional structural similarity as a circular graph wherein the width of an edge between two chains is inversely scaled by their pairwise r.m.s.d.

At the Aae Hfq monomer level, the greatest structural variation occurs among the N-termini and the L4 loop region between β3→β4; apart from the termini, loop L4 (Fig. 6b) is the most variable region in most known protein structures from the Sm superfamily. The conformational heterogeneity in the termini and loops of Aae Hfq stems, at least partly, from differing patterns of interatomic contacts for different sub­units at the levels of monomers, hexamers and dodecamers in the overall P1 lattice. The patterns of conformational heterogeneity are clear when the dodecameric structure is visualized as a cartoon, with the diameter of the backbone tube scaled by the magnitude of per-atom B_eq values (this derived quantity, computed from the trace of the full anisotropic ADP tensor, is taken as an estimate of the true B_iso values that would result from refinement of an isotropic model); such renditions are shown in Supplementary Figs. S6(a) and S6(b) for the P1 and P6 structures, respectively. Analogously, Supplementary Figs. S6(c) and S6(d) provide thermal ellipsoid representations of the patterns of variation in anisotropic ADPs across the P1 dodecamer and the P6 monomer. In both sets of depictions, Supplementary Figs. S6(a) and S6(b), and Figs. S6(c) and S6(d), colors are graded by the magnitude of per-atom B_eq values from low (blue) to medium (white) to high (red). To initially assess the relative contributions of static disorder (e.g. variation in rotameric states across subunits) and dynamic disorder (e.g. harmonic breathing modes and other collective/global motions) in variable regions such as loop L4 and the termini, a normal-mode analysis was performed on a coarse-grained representation of the Aae Hfq structures, using an anisotropic network model of residue interactions (see §2.6). Illustrative results for the dodecamer and monomer are shown in Supplementary Figs. S6(e) and S6(f), respectively. The pattern of normal-mode displacements for both the dodecamer and monomer do not implicate loop L4 in any especially high-amplitude, low-frequency modes (Supplementary Fig. S6f), suggesting that the increased ADPs (elevated B_eq values) of L4 stem more from static disorder rather than any particular dynamical process involving this loop region (although anharmonic dynamics remain possible). The dodecamer calculation does reveal a significant harmonic mode corresponding to antisymmetric rotation of the two Hfq rings with respect to one another (PE ↺, DE ↻; Supplementary Fig. S6e). This result is consistent with our observation that the only large-scale (dodecamer-scale) structural difference between the two rings is a slight rotation of one relative to the other (Fig. 5, left) versus, for instance, a rigid-body tilt (Fig. 6a, Supplementary Figs. S5a and S5b).

At the Hfq ring and supra-ring levels, the refined P1 structure reveals an Aae Hfq dodecamer consisting of two hexameric rings stacked in a head→tail orientation (Fig. 5). Propagated across the lattice, this arrangement gives cylindrical tubes with a defined polarity. The tubes run along the crystallographic a axis, and their lateral packing yields near-sixfold symmetry along this direction; a slight translational shift of the dodecamers in adjacent unit cells, in the plane perpendicular to a, causes the rings to be slightly offset with respect to the lattice tubes (the tubes are not perfectly cylindrical, insofar as the sixfold axis of an individual Hfq ring is not coaxial with the principal axis of its parent tube). In the dodecamer, the distal face of one Hfq ring is exposed (termed the DE ring), while the other ring features a proximal-exposed face (the PE ring; Fig. 5, right). The N-termini of the DE hexamer contact the L2-loop/β2-strand region of the PE ring, as illustrated in Fig. 5 (the L2 loops mark the beginning of strand β2; see the label in Fig. 6a). As is apparent in the axial view of Fig. 5 (left), one ring is slightly rotated relative to the other. Geometric analysis of this rotation (denoted `Δ' in Fig. 6a), as well as other rigid-body transformations relating the two rings (Supplementary Figs. S5a and S5b), shows that the sixfold symmetry axes of the rings in the dodecamer are not perfectly parallel: a slight tilt occurs between the rings (`δ' in Fig. 6a). This tilt appears to stem largely from structural differences in the N-terminal regions (Supplementary Fig. S5). Consistent with these observations, the set of six N-terminal regions of the DE ring (which mediate ring–ring interactions within a dodecamer) exhibit slightly higher B_eq values and greater conformational variability than do the six N-termini of the PE ring (which mediate dodecamer⋯dodecamer contacts between unit cells), as can be seen in Supplementary Fig. S6(a).

Noncovalent molecular interactions between the proximal⋯distal faces mediate the association of Hfq rings into a dodecamer, and a slightly altered (translationally shifted) version of these same energetically favorable interactions stitches together the dodecamers into a set of crystal lattice contacts in the P1 form of Aae Hfq. Notably, a proximal→distal stacking geometry is also the chief mode of ring association in the Aae Hfq P6 lattice. Aae Hfq dodecamers clearly occur in the P1 lattice, with a substantial amount of buried surface area (BSA) defining the ring–ring interface (Fig. 5). Specifically, 3663 ± 244 Ų of SASA is occluded between the PE and DE hexamers in the PE–DE complex. Note that this quantity is reported as a total BSA = ASA_PE + ASA_DE − ASA_PE–DE, where ASA_i is the ASA of species i, rather than as the per-subunit value (which would be given by half of the above expression, were we to assume a perfectly twofold symmetric interface); also, note that this mean ± standard deviation is reported from the results of five different surface-area calculation approaches, as described in §2.6.

3.5. Crystal structure of Aae Hfq bound to U₆ RNA

Upon co-crystallization with U₆ RNA, a second, distinct Aae Hfq crystal form was discovered. These crystals could be indexed in space group P6, with unit-cell parameters a = b = 66.19, c = 34.21 Å. In this form, the cell geometry, solvent content and molecular mass of Aae Hfq are only compatible with a single Hfq monomer per asymmetric unit; based on known Hfq structures, the crystallographic sixfold axis was presumed to generate intact hexamers, such as that shown in Fig. 7(a). Specifically, co-crystallization of Aae Hfq with this model uridine-rich RNA was achieved by incubating purified Hfq samples with 500 µM U₆ RNA prior to crystallization trials. The complex crystallized in 0.1 M sodium cacodylate, 5%(w/v) PEG 8000, 40%(v/v) MPD, and the denaturant compound Gnd was found to be an effective additive (Supplementary Table S2). The crystal structure of the Aae Hfq·U₆ RNA complex was refined to 1.50 Å resolution (Fig. 7); we emphasize that the initial solution of this structure was achieved independently of the apo P1 form, via molecular replacement, using P. aeruginosa Hfq as a search model.

Figure 7 Crystal structure of Aae Hfq with U-rich RNA bound at the lateral rim. The asymmetric unit of the P6 form contains a single Hfq subunit, shown as a tan-colored ribbon diagram (a), in addition to 36 H2O molecules (red spheres), a molecule of PEG (lime-colored C atoms), a molecule of MPD (gray C atoms) and one molecule of U6 RNA (green C atoms). Nonprotein atoms are shown in ball-and-stick representation using CPK colors (except as noted above for C atoms). Expansion of the asymmetric unit to the full P6 cell gives an intact Hfq hexamer, shown on the proximal face in (a). The meshes delimit the 2mFo − DFc electron-density map, contoured at 1.5σ and shown only in the regions of RNA (dark blue) or MPD (light blue). The fragment of U6 that could be unambiguously built into electron density contained two complete uridines and the 5′ phosphate moiety of the next residue; the path of this RNA strand is denoted by a red-circled 1 and 3 for the ribonucleotides, from 5′ to 3′. Unexpectedly, U6 nucleotides were found on the outer rim of Aae Hfq, in a position analogous to the lateral site of other Hfqs (b), while a molecule of MPD occupied the U-rich binding pore as shown in (c). This magnified view (b) of the lateral site [same color scheme as (a)] shows the RNA-contacting residues (labeled) in greater detail; asterisks distinguish residues from the N-termini of a neighboring subunit, as also indicated in (a). Electron-density maps such as this one were readily interpretable as RNA (see also Supplementary Fig. S7). The magenta dashed lines (hydrogen bonds) and semi-transparent green cylinders (π-stacking interactions) indicate enthalpically favorable Hfq⋯RNA contacts. Most such contacts are mediated by both backbone and side-chain atoms of Aae Hfq, as well as the nucleobase and phosphodiester groups of the RNA; the ribose rings project outward from the cleft and interact with Hfq more sparsely. (c) MPD binds at the pore and mimics the Hfq⋯uridine contacts found at the proximal RNA-binding site in some Hfq homologs. Contacts denoted by magenta dashed lines identically match the contacts to a uridine nucleotide in other Hfq structures containing U-rich RNA (see also Supplementary Fig. S8). The green line indicates a van der Waals contact between Leu39 and MPD, and the green cylinder denotes another apolar interaction between Aae Hfq and MPD; this latter contact would presumably be replaced by a π-stacking interaction between Phe40 and a U base, were a U-rich RNA (rather than MPD) bound at the proximal site.

Those residues that are crucial in forming the proximal (U-rich) RNA-binding pocket in E. coli Hfq and other Hfq orthologs, i.e. E. coli Hfq residues Gln8, Phe42, Lys56 and His57, are conserved in the Aae Hfq sequence (Fig. 1). This observation led us to anticipate that any bound U₆ would be localized to the proximal pore region. Instead, a molecule of MPD, which served as a precipitant and cryoprotectant in our crystallization experiments (Supplementary Table S2), was found to occupy the proximal site of the hexamer, with the MPD hydroxyl groups hydrogen-bonded to the side chains of the His56 and *Gln6 residues of Aae Hfq (Fig. 7c). In addition, the bound MPD makes van der Waals contacts with other conserved residues that line the proximal site, specifically *Leu39 and Phe40. During refinement of this structure, two nucleotides of the U₆ RNA molecule, including the flanking 5′ and 3′ phosphates (the latter coming from the third U), were readily discernible in mF_o − DF_c difference electron-density maps (Supplementary Fig. S7). Rather than being bound at the proximal site, the uridine residues of U₆ occupied a cleft formed between the N-terminal α-helix and strand β2, in a position located roughly near the outer (`lateral') rim of the Aae Hfq toroid (Figs. 7a and 7b). Notably, processing and reduction of the diffraction data (collected from P6-form crystals) in P1 yielded similar electron density for the RNA at each lateral binding pocket in the hexamer (Supplementary Fig. S7).

3.6. RNA binding at the outer rim of the Aae Hfq hexamer: structural details

The Aae Hfq·U₆ structure reveals a lateral RNA-binding pocket that accommodates two uridine nucleotides. The N-terminal α-helix primarily contacts the phosphodiester and ribose groups, and the β2 strand interacts mostly with the uracil bases (Figs. 7a, 7b and 8a). As a consequence of this RNA-binding geometry, both nucleotides that were fully built into electron density (U1 and U2) are held in a bridging, anti conformation (χ = −165.2° for U1, χ = −116.8° for U2), with the ribose moieties extending outward from the pocket (Fig. 7b). Interestingly, while the U1 ribose is in the 3′-endo conformation typically seen in canonical (A-form) RNA structures, with a pseudo-rotation phase angle (P) of 17.5° for this North sugar pucker, the U2 ribose adopts a less typical 2′-endo conformation (P = 163.2°).

Figure 8 Conserved pattern of interatomic contacts at the lateral RNA-binding site of Hfq hexamers. In this schematic diagram of the interatomic contacts between the lateral site of Aae Hfq, U6 RNA and nearby H2O molecules (a), protein atoms are shown as ball-and-stick representations (CPK coloring, light gray C atoms) and covalent bonds in the nucleotides are drawn as thicker, orange-colored lines. For clarity, only a subset of H2O molecules is drawn (green, labeled `W#'). Here, asterisks denote another Hfq chain in the same unit cell and the prime symbol denotes a neighboring cell. Hydrogen bonds are magenta for protein⋯RNA interactions, while those to H2O are shown in green. Stacking interactions between the aromatic entities φ1 and φ2 are indicated by green circles from φ1⋯φ2. Two nucleotides of uridine (labeled) appear in an open, bridging conformation with the α-helix and β2 strand of an Hfq monomer (gray flanking regions). The phosphate groups are hydrogen-bonded to Asn11 and Arg14 of the N-terminal α-helix, while the nucleobase hydrogen bonds to the backbone atoms of strand β2 (specifically, Ser36 and Phe37), thus imparting specificity for uridine. Note that additional π-stacking interactions are present between the side chain of Phe37 and RNA base U2, as well as within the RNA (between U2⋯U1; not shown for clarity). The lateral pocket of Eco Hfq is shown in (b), complexed with the sRNA RydC [same coloring scheme and conventions as in (a)]. The U46 and U47 bases adopt conformations similar to those seen in (a), with the phosphate groups contacting residues of the α-helix. Phe39 π-stacks with U47, analogous to the interaction seen in Aae Hfq. Note that the adjacent G45 and A48 bases are flipped away from the pocket and are shown here to offer context in the overall sequence of the sRNA. While not strictly conserved in terms of precise amino-acid sequence, the N-terminal regions of the Aae and Eco Hfq homologs do provide similar backbone interactions with U1 and U46, respectively. Note also the directionality of the RNA backbone, which follows the same 5′→3′ path along the lateral site on the surface of the Aae and Eco Hfq rings (see also Figs. 7a and 7b).

Protein⋯RNA interactions are mediated by both side-chain and backbone atoms of Aae Hfq. The full set of interactions is shown in three dimensions in Figs. 7(a) and 7(b), and schematically in Fig. 8(a). Two side chains in the N-terminal α-helix of Aae Hfq, Asn11 and Arg14, contact the phosphodiester groups, and another cationic residue (Lys15) is 3.6 Å from the phosphodiester group linking the two uridines. Backbone and side-chain atoms from strand β2 hydrogen-bond to the bases, ensuring uridine specificity (Figs. 7b, 8 and 9). In particular, both the carbonyl O atom and amide N atom of Phe37 interact with N3 and O4 of U2, respectively, while the hydroxyl side chain of Ser36 contacts the exocyclic O4 of the U1 nucleobase. Ser36 also helps position a pivotal H₂O that directly hydrogen bonds to both the N3 atom of U1 and the Ser36 hydroxyl (Fig. 8a); this well ordered (ice-like) water molecule engages in a network of hydrogen bonds in a distorted tetrahedral geometry (additional structural waters also contact the uracil and phosphodiester moieties, as shown in Fig. 8). Other interactions at the lateral site include a series of three π-stacking interactions (Fig. 8a): between the phenyl ring of Phe37⋯U2, between the U1⋯U2 bases and between the phenolic ring of *Tyr3⋯U1. RNA binding at the lateral site is composite in nature, involving not just residues of strand β2 and helix α1 of one Hfq subunit, but also the N-terminal tail of an adjacent subunit in the ring. The irregularly structured N-terminal tail of one Hfq monomer extends into the neighboring lateral site, where the N-terminal sequence H⁰M¹P²Y³K⁴ nearly `covers' this rim site and supplies additional contacts with RNA. For instance, *Tyr3 engages in the π-stacking mentioned above, as well as a hydrogen bond between its amide N atom and the O2 of U1 (an interaction that does not select between uracil and cytidine). Also in this region, the backbone carbonyl O atom of *Met1 hydrogen-bonds to the ribose O2′ of U1, thus contributing to discrimination between RNA and DNA. Finally, we note that two contacts in this region may be spurious: (i) the *His0⋯phosphodiester group interaction, where residue *His0 is from the recombinant construct (not wild-type Aae Hfq; see the numbering in Supplementary Fig. S1), and (ii) the Arg29′⋯phosphodiester group interaction, which is a crystal lattice contact (the prime symbol on Arg29′ indicates an adjacent unit cell).

Figure 9 The lateral site of Aae Hfq is pre-structured for RNA binding. The three-dimensional structure of the single, unique monomer from the Hfq-U6 co-crystal structure (teal backbone) was superimposed with the 12 subunits of the apo Hfq structure (grey). Residues that contact RNA, to within ∼3.6 Å in the P6 Hfq·U6 structure, are shown as sticks for both the P6 and P1 structures. Apart from residue Glu7, which sterically occludes the binding pocket and thus is likely to adopt a different conformation upon RNA binding, note that the side chains in the apo structure adopt rotameric states quite similar to those in the three-dimensional structure of U6-bound Aae Hfq. This finding suggests pre-organization of the RNA-binding site of Aae Hfq.

Comparison of the Aae Hfq·U₆ structure with the independently refined apo Aae Hfq structure suggests that the lateral RNA-binding site is essentially pre-structured for RNA complexation (Fig. 9). In terms of comparative structural analysis, note that the apo/P1 and RNA-bound/P6 structures (i) are at equally high resolutions (1.49 and 1.50 Å, respectively; Table 1), (ii) were refined in similar manners (e.g. using anisotropic ADPs), albeit independently of one another, and (iii) are of comparable quality in terms of R_work/R_free, stereochemical descriptors etc. (Table 2). Residues Asn11, Arg14, Ser36 and Phe37, which are phylogenetically conserved to varying degrees (Fig. 1), largely define the structural and chemical topography of the lateral site (Fig. 7a). As shown in Fig. 9, these crucial residues adopt nearly identical rotameric states in the apo and U₆-bound forms of Aae Hfq. The two principal RNA-related structural differences on going from the apo to the U₆-bound forms are (i) a shift in the Glu7 rotamer (Fig. 9, red label), positioning this side chain away from the pocket and thus enabling the U2 base to be accommodated, and (ii) the precise path of the N-terminal tail (i.e. the ∼5 residues preceding helix α1), which varies with respect to the lateral site. In the dodecameric apo structure, six of the N-termini mediate ring⋯ring contacts (Fig. 5, DE ring) while the other half (from the PE ring) mediate lattice contacts, giving rise to one source of structural heterogeneity in this region. In terms of intrinsic conformational flexibility, normal-mode calculations (Supplementary Fig. S6 and §2.6) indicate that the N-terminal regions in the hexamer are highly flexible when free in solution, but rigidified (as much as any other part of the Sm fold) when sandwiched between the Hfq rings.