## 2 Materials and Methods
### Synchrotron Radiation Circular Dichroism (SRCD)  
SRCD measurements were carried out on the DISCO beamline at the SOLEIL synchrotron (proposal 20210003). The synchrotron light source provides intensities of the beam below 190 nm. Such analyses are not trivial due to the strong absorbance of light below 200 nm by air and water. Conventional spectrometers scan with noise below 200 nm and not at all below 190 nm, while references for NA have the most informative region in the 170-220 nm range. Samples (\(\sim\)4 \(\upmu\)L) were loaded into a CaF\({}_{2}\) circular cell of 12.5 \(\upmu\)m pathlength [36]. Spectral acquisitions of 1 nm steps at 1.2 s integration time were recorded in triplicates between 320 and 180 nm. (+)-camphor-10-sulfonic acid (CSA) was used to calibrate amplitudes and wavelength positions of the experiment.  
Note that the beam dimensions have been optimized and set to 4 mm \(\times\) 4 mm at 1 nm bandwidth in order to reduce the eventual radiation damage of the samples [37; 38]. We have also shown that using this setup, no spectral decrease owing to UV radiation could be observed after 50 consecutive scans (\(\sim\)4 h) on Hfq-CTR (Supplementary Figure S1). Therefore, no radiation damage can be assumed. Radiation damage may also induce degradation of the nucleic acid. In a parallel study using primer extension on polynucleotides subsequent to a full SRCD spectral data collection, no cyclobutane dimers had been formed between adjacent pyrimidines on the same DNA strand. This suggests that little if any photochemical modifications due to UV exposure had occurred on the DNA during the accumulation of the spectra.  
Data analyses (averaging, baseline subtraction, smoothing, scaling and spectral summations) were carried out with CDtoolX [39]. Spectra are presented in units of mdeg versus nm, maintaining the same molar ratios for all presented samples. Due to the origin of absorption, spectra of mixed samples (polynucleotides + peptide) could not be standardized to \(\Delta\epsilon\).  
Two types of experiments have been performed: the effect of Hfq or CTR were tested either on individual RNAs/DNAs or on duplexes such as RNA I:RNA II. As they are not negligible, the contribution of the added Hfq or CTR peptide was subtracted from the SRCD spectra of the complex (the SRCD spectra of the free peptide and protein are presented in Supplementary Figure S2). For all experiments, RNA concentrations were in excess compared to Hfq-CTR. The Hfq-CTR (monomeric) concentration was 0.4 mM. RNAI_Astem and RNAII_Astem concentrations were 13 mM (in bp), the RNAII_C-rich_stretch concentration was 11 mM, the DNA_C-stretch_ssCoIE1 concentration was 15 mM, and the DNA_ColE1 oritor concentration was 14 mM (RNA and DNA concentrations were normalized, taking into account the respective size of fragments).  
The effect of Hfq-CTR was analyzed at 15 \({}^{\circ}\)C to minimize spontaneous annealing between nucleic acids that could occur [24]. For kinetic measurements, an apparent catalytic kinetic constant \(\mathrm{k_{cat}}^{\mathrm{app}}\) was determined during initial rate conditions. This constant was expressed in mdeg.M\({}^{-1}\).min\({}^{-1}\) and depends on protein concentration (CD units cannot be normalized to protein concentration as they are not expressed in the same unit, mdeg vs. M).  
For melting curves, triplet SRCD spectra were acquired every 3 \({}^{\circ}\)C between 15 \({}^{\circ}\)C and 96 \({}^{\circ}\)C. Averaged SRCD values of the maximum of the peaks around 180 and 270 nm are presented as a function of temperature to measure the melting point (Tm). A Boltzmann sigmoid equation, which assumes a two-state model, has been used for fitting of melting curves: y = Bottom + (top - bottom)/(1 + e(Tm - x)/slope)).