<table><caption>**Table S2 | Cryo-EM data collection and refinement statistics**</caption><thead><tr><th></th><th>FleN<sup>D48A<sub>2</sub></sup> – FleQ<sup>FL<sub>4</sub></sup></th><th>FleN<sup>D48A<sub>2</sub></sup> – FleQ<sup>RE-AAA<sub>3</sub></sup></th></tr></thead><tbody><tr><td>Protein sample</td><td>FleN<sup>D48A<sub>2</sub></sup> – FleQ<sup>FL<sub>4</sub></sup></td><td>FleN<sup>D48A<sub>2</sub></sup> – FleQ<sup>RE-AAA<sub>3</sub></sup></td></tr><tr><td>Complexed ligand</td><td>ACP/ATP<sub>2</sub>*, Mg<sup>++</sup><sub>2</sub></td><td>ACP/ATP<sub>2</sub>*, c-di-GMP<sub>2</sub></td></tr><tr><td colspan="3"><strong>Data collection</strong></td></tr><tr><td>Microscope</td><td>Titan Krios (CM01 at ESRF)</td><td>Titan Krios (EMBL)</td></tr><tr><td>Voltage</td><td>300</td><td>300</td></tr><tr><td>Camera</td><td>Gatan K3</td><td>Gatan K3</td></tr><tr><td>Energy filter</td><td>Gatan GIF Quantum LS</td><td>Gatan GIF Quantum LS</td></tr><tr><td>Pixel size (Å<sup>2</sup>)</td><td>0.66</td><td>0.645 (collection) / 1.419 (refinement)</td></tr><tr><td>Collection mode</td><td>counting with super-resolution</td><td>counting</td></tr><tr><td>Total electron dose (e<sup>-</sup>/Å<sup>2</sup>)</td><td>51.5</td><td>50.3</td></tr><tr><td>Movies</td><td>17,099</td><td>14,268</td></tr><tr><td>Defocus range (μm)</td><td>0.3 – 2.5</td><td>0.8 – 2</td></tr><tr><td>Single particles</td><td>404,228</td><td>1,283,731</td></tr><tr><td>Map resolution (Å)</td><td>3 Å limit for refinement</td><td>3.3 Å limit for refinement</td></tr><tr><td>FSC 0.143 (masked / unmasked)</td><td>2.7 / 3.3</td><td>2.9 / 3.2</td></tr><tr><td>Imposed symmetry</td><td>C2</td><td>none (C1)</td></tr><tr><td>Sharpening B-factor</td><td>112.6</td><td>135.1</td></tr><tr><td colspan="3"><strong>Atomic model refinement</strong></td></tr><tr><td>Number of protein chains / residues</td><td>6 / 2071</td><td>5 / 1552</td></tr><tr><td>Number of ligands</td><td>ACP: 2 | Mg<sup>++</sup>: 2</td><td>ACP: 2 | C2E: 2</td></tr><tr><td>Number of atoms</td><td>16,305 (hydrogens: 0)</td><td>12,266 (hydrogens: 0)</td></tr><tr><td>B-factors</td><td></td><td></td></tr><tr><td>Protein (min/max/mean)</td><td>10.60 / 151.87 / 69.80</td><td>10.76 / 140.99 / 70.78</td></tr><tr><td>Ligand (min/max/mean)</td><td>26.98 / 59.31 / 47.49</td><td>22.03 / 72.64 / 45.66</td></tr><tr><td>Bonds (R.M.S.D.)</td><td></td><td></td></tr><tr><td>Length (Å) (# > 4σ)</td><td>0.003 (0)</td><td>0.003 (0)</td></tr><tr><td>Angles (deg) (# > 4σ)</td><td>0.632 (4)</td><td>0.613 (0)</td></tr><tr><td>Ramachandran plot</td><td></td><td></td></tr><tr><td>Favored (%)</td><td>96.79</td><td>95.52</td></tr><tr><td>Allowed (%)</td><td>3.21</td><td>4.48</td></tr><tr><td>Outliers (%)</td><td>0.00</td><td>0.00</td></tr><tr><td>Rotamer outliers (%)</td><td>0.11</td><td>0.08</td></tr><tr><td>Cβ outliers (%)</td><td>0.00</td><td>0.00</td></tr><tr><td>CaBLAM outliers (%)</td><td>1.47</td><td>1.83</td></tr><tr><td>Peptide plane (%)</td><td></td><td></td></tr><tr><td>Cis proline / general</td><td>4.3 / 0.0</td><td>1.5 / 0.0</td></tr><tr><td>Twisted proline / general</td><td>0.0 / 0.0</td><td>0.0 / 0.0</td></tr><tr><td>CC (mask)</td><td>0.80</td><td>0.69</td></tr><tr><td>Occupancy</td><td></td><td></td></tr><tr><td>Mean</td><td>1.00</td><td>1.00</td></tr><tr><td>occ = 1 (%)</td><td>100.00</td><td>99.95</td></tr><tr><td>0 < occ < 1 (%)</td><td>0.00</td><td>0.00</td></tr><tr><td>occ > 1 (%)</td><td>0.00</td><td>0.00</td></tr><tr><td>Clash score</td><td>8.17</td><td>13.98</td></tr><tr><td>MolProbity score</td><td>1.64</td><td>1.96</td></tr></tbody></table>