*2.5. Compaction and Hydration are Experimentally Correlated*

Because of their non-compact structures and more solvent-accessible surface area, disordered regions tend to display a higher hydration water density as compared to more ordered regions [31]. The degree of hydration (*h*) of each species was estimated from *θexp* (see experimental section). For compact globular proteins, this value is usually in between 0.2 and 0.4 g water/g protein. Our data suggests that His6 VPg and VPg forms are more solvated than standard folded proteins (1.44 and 1.57 g/g respectively). This is in agreement with previous hydrodynamic experiments on IDPs. For instance, in the absence of calcium, the adenylate cyclase toxin calcium binding domain is intrinsically disordered and displays a high hydration propensity [32]. Moreover, molecular dynamics simulations show that partially disordered proteins like VPg have a higher capacity to bind hydration water as compared to globular proteins [33]. Interestingly, His6 eIF4E and eIF4E, which both include a long disordered N-terminal region, have a rather high hydration degree (0.72 and 1 g/g respectively) although the presence of the His6 tag seems to slightly decrease the hydration degree in accordance to its compacting effect discussed above. Conversely, eIF4E<sup>Δ</sup>1–46, which corresponds to the globular part of eIF4E, possesses a hydration value expected for compact proteins (0.38 g/g). Using the PDB coordinates of eIF4EΔ1–46 from pea (PDB file 2WMC), we calculated the protein rotational diffusion coefficient (*D*) [34] from Equation (12). From this value (1.49 × <sup>10</sup><sup>7</sup> <sup>s</sup><sup>−</sup>1) the rotational coefficient time was deduced and, in turn a *h* value of 0.53 g/g, which is in fairly good agreement with our estimation

(Table 1). Finally, the binary complex formation is not associated with a significant modification of hydration.

### **3. Conclusions**

As opposed to fully disordered proteins, which display a random coil state, VPg possesses a significant content in secondary structure. These more compact intermediates have led to the concept of molten globule (MG) and the somewhat less compact pre-molten globule (PMG) states. A MG is characterized by a large internal flexibility of its side chains and backbone, with a *Rh* 1.5–2.0 times larger than that of globular proteins. As they are usually distributed in solutions between a limited number of conformers, these proteins prove to be more complex to analyze than fully disordered polypeptides. Modern NMR approaches provide an excellent way to study such proteins [35,36]. However the concentrations required [37], usually from 2 to 10 mg/mL, are far beyond what can be stabilized in solution in the present case. Because it enables the development of low-resolution structural models, taking into account the contribution of intrinsically disordered regions, a hydrodynamic analysis can provide useful data. Hydrodynamic parameters are usually assessed using SEC, AUC (analytical ultracentrifugation), and DLS (dynamic light scattering). However, these techniques also require protein concentrations above 1 mg/mL. We propose an elegant way to deal with especially difficult proteins. Although less used, fluorescence anisotropy can prove quite resolutive and especially suitable when protein concentration is the limiting factor. One can argue that this method gives access to the rotational mobility of the reporter fluorophore and not of the macromolecule itself. However, if, as it is the case here, the probe motion displays a low degree of freedom within the macromolecule, the extracted parameters reflect the hydrodynamic properties of the macromolecule well. The data obtained by SEC and fluorescence spectroscopy were in good agreement. Because analytical ultracentrifugation (AUC) is based on equilibrium and non-equilibrium thermodynamics, it is referred as a gold standard for characterizing the hydrodynamic properties. The expected sedimentation coefficients (*s*20,*w*) for the LMV VPg and lettuce eIF4E were derived from their experimentally measured diffusion coefficients (see Equation (13) in the experimental section). They were in agreement with values reported for their homologous counterparts PVY VPg (46.7% identity, 76.4% similar with LMV VPg) and human eIF4E (43.2% identity, 67.6% similarity with lettuce eIF4E), (Table 2). A fine analysis of potyviral VPg conformers distribution on the basis of their sedimentation properties was recently reported [24]. A *s*20,*<sup>w</sup>* value of 3.2 Svedberg was determined for the major VPg molecular species (70%). [10]. This suggests that most of the VPg was present as a dimer. Indeed, this value is in accordance with the value obtained for non-reduced VPg from PVY [10], Table 2.

**Table 2.** VPgs and eIF4E sedimentation coefficients in water at 20 ◦C.


LMV (lettuce mosaic virus), PVY (potato virus Y), PVBV (Pepper vein banding virus). \* theoretical molecular weight. VPg (LMV)-R and VPg (PVY)-R, VPg under reduced conditions.

#### **4. Materials and Methods**
