## 3 Materials and Methods  
### Computational Methods  
**Protein Preparation. ** Rel\({}_{Seq}\) three-dimensional structure (PDB 1 VJ7, chain A, residues 5-341) was prepared for docking calculations using the 'Protein Preparation Wizard' of Schrodinger\({}^{\circledgtr}\) suite [40] and OPLS 2005 force field [54]. All water molecules were deleted, and the gaps of the HD domain (K110-N123 and K153-D158) were built using Prime [55]. The residues' protonation states were determined according to PROPKA at pH 7. Two models were built considering the two possible protonation states of His312, i.e., the neutral (His312) and the protonated (Hip312) form. According to Epik [41] results at pH 7\(\pm\) 2,  
Figure 5: STD-NMR experiments (fragment:protein ratio 1000:1; fragment concentration 3 mM). (**a**) \({}^{1}\)H-NMR of fragment **A1** in phosphate buffer at 298 K. (**b**) STD-NMR experiment of **A1** with Rel\({}_{Seq}\) (1–385). (**c,d**) STD-NMR experiment of **A1** with Rel\({}_{Seq}\) SYNTH (79–385) and with Rel\({}_{Seq}\) HYD (1–224), respectively. The same binding mode can be observed for full-length Rel\({}_{Seq}\) and Rel\({}_{Seq}\) SYNTH, while no binding can be detected with Rel\({}_{Seq}\) HYD. the GDP molecule is fully deprotonated (total formal charge of \(-3\)). Hydrogen bonds were optimized according to the exhaustive sampling option, and the entire complexes were optimized by using a restrained minimization (root-mean-square deviation on heavy atoms < 0.30 A). The K110-N123 and K153-D158 gaps of the HD domain were built, and the former was further refined using the'refine loops' tool of Prime (OPLS3e [48], VSGB [56]) with default parameters. Five structures were generated, and the model with the lowest Prime energy was selected for the docking calculation. **Docking protocol. ** Grid-Based Ligand Docking With Energetics (Glide) [37] v.8.0 software was used with the OPLS_2005 force field. Receptor grids for HIS312 and HIP312 systems were generated in a cubic region (24.5 A) centered on GDP molecules with an inner cubic box of 10 A. The receptor was considered a rigid body, while the ligands were considered flexible. The standard precision (SP) method was applied with default parameters. No Epik state penalty was added to the Glide score. The docking protocol was validated for the X-ray ligand by saving five poses after a post-minimization of the first 10 poses. The top-ranked poses succeeded in reproducing the experimental binding mode of GDP (RMSD on heavy atoms of 0.78 A and 1.23 A in the HIS312 and HIP312 models, respectively) (Supplementary Figures S1 and S2). **Fragment libraries preparation. ** Seven fragment libraries were downloaded:  
* Maybridge Ro3 Diversity Set (2500 fragments) (www.maybridge.com, accessed on 9 June 2015);
* Asinex-Fragments-21872 (21,872 fragments) (www.asinex.com, accessed on 18 January 2019);
* 'Fragment Libraries with Experimental Solubility Data', two datasets from Life Chemicals (11,667 and 2921 fragments, respectively) (www.lifec chemicals.com, accessed on 1 February 2019);
* OTAVA Solubility Fragment Library (1021 fragments) (www.otavachemicals.com, accessed on 4 February 2019);
* FragmentLibrary_sdf_13808 (13,808 fragments) from CHEMBRIDGE (www.chembridge.com, accessed on 18 April 2019)
* Preplated Fragment-Based Library (4532 fragments) from SPECS (www.specs.net, accessed on 11 February 2019). For each fragment, we generated 3D structures, tautomers, stereoisomers (at most 32 per ligand), and protonation states (Epik at pH = \(7\pm 2\)) using the Ligprep tool [40]. Their energy was minimized using 'MacroModel' [40], implemented with truncated Newton conjugated gradient method [57], and the resulting structures were used as input for docking calculations (see Supplementary Table S1). **Molecular Dynamics simulations.