*4.2. Size Exclusion Chromatography*

A superose 12 HR 10/30 column (GE Healthcare) was calibrated with separate 500 μL injections of the following native globular proteins: γ-globulin (bovine, 158 kDa), Ovalbumin (Chiken) 44 kDa, myoglobin (horse, 17 kDa and vitamin B12 (1.35 kDa). Excluded volume (*V*0, 8.74 mL) was determined with blue dextran. The volume of the column, *V*t was 24 mL. Chromatography conditions were 20 mM HEPES/KOH, 0.4M KCl and 1.4 mM 2-Mercaptoethanol, flowrate 0.5 mL/min.

#### *4.3. Hydrodynamic Radius Measure*

The Stokes radius, also termed *Rh*, is the radius of a hard sphere that diffuses at the same rate as the protein. A commonly used method for measuring *Rh* is SEC. The size exclusion column is calibrated using the elution volume (*Ve*) of standard folded proteins (i.e., Globular) of known molecular weight. The apparent molecular weight of the protein of interest is then deduced from *Ve*. *Rh* is determined as the *Rh* expected for a globular protein of that apparent molecular weight, for which simple relations exist [22,40].

The retention factor *Kav* of the proteins was determined as follows:

$$K\_{av} = \frac{V\_t - V\_0}{V\_t - V\_0} \tag{1}$$

There was a linear relationship between *Kav* and log*Mapp* (Figure 1C):

$$K\_{av} = -0.24 \log M\_{app} + 1.47\tag{2}$$

$$M\_{app} = 10^{\frac{1A\mathcal{T} - \mathcal{K}\_{\text{ann}}}{0.24}} \tag{3}$$

It was assumed that the protein considered has the hydrodynamic behavior of its equivalent rigid sphere of *Rh* and an *Mapp*. A linear relationship exists between log*Mapp* and log*Rh* which, knowing the SEC derived apparent molecular weight of a protein, allows the determination of its *Rh* [22]. For a globular protein, the expression is:

$$
\log(R\_h) = -0.2 + 0.36 \log \left( M\_{app} \right) \tag{4}
$$

#### *4.4. Structural Feature Estimation*

The apparent molecular density or compaction (*ρ*) of a globular protein is:

$$\rho = \frac{M}{4/3\pi R\_h^3} \tag{5}$$

with *M*, the molecular weight calculated from the protein amino acid composition. A plot of log(*ρ*) vs. log(*M*) allowed us to estimate the structural family; ordered globular, molten globule, pre-molten globule, or native coil-like protein (Figure 1D). Straight lines that define the different groups of conformational states were calculated from [41].

*Fluorescence measurements.* All steady state fluorescence acquisitions were obtained at 25 ◦C in 20 mM HEPES pH 7.5, 0.25 mM NaCl and 1 mM DTT using a SAFAS Xenius spectrofluorimeter (Monaco) equipped with a Peltier temperature controller. For optical characteristics of the instrument, see [39]. Affinity constants were deduced from steady state eIF4E tryptophan intrinsic fluorescence decrease upon titration by VPg as previously described [39]. In order to ensure that the system reached an equilibrium before measurements, a thorough mixing (gentle back and forth syringe flushing) of the various molecular species, was followed by a 10 min incubation. Then, an average value was collected during another 10 min, both for the acquisition of eIF4E steady state intrinsic fluorescence and anisotropy measurements.

Fluorescence anisotropy measurement. The fluorescent probe bound to the VPg was chosen so that *τ* its fluorescent lifetime be of the order of magnitude of *θ*, the rotational correlation time of the VPg in solution. *A,* the measured anisotropy is defined as:

$$\frac{A\_0}{A} = 1 + \frac{\pi}{\theta} \tag{6}$$

*A*<sup>0</sup> is the fundamental anisotropy observed in the absence of other depolarizing processes such as rotational diffusion or energy transfer. If *θ τ* then the measured anisotropy is equal to *A*<sup>0</sup> (infinite viscosity, no motion of the macromolecule). If *θ τ* then the anisotropy is zero. For the AEDANS group, a fluorescence lifetime of 15.6 ns was determined by phase-modulation fluorimetry on a SLM 4800 fluorimeter. This value is in the range of *θ* values for proteins (15–70 kDa).

The anisotropy of the AEDANS labelled VPg either free or associated with eIF4E was measured at 25 ◦C in solutions of various viscosity (*η*). The dependency of the anisotropy on viscosity is given by the Perrin equation:

$$\frac{1}{A} = \frac{1}{A\_0} + a\frac{T}{\eta} \tag{7}$$

with

$$
\alpha = \frac{\tau R}{A\_0 V} \tag{8}
$$

Plotting 1/*A* versus T/*η* gives usually a straight line. The viscosity was experimentally increased by addition of sucrose in the buffer. *V* the hydrodynamic molar volume was determined from *α,* the slope value:

$$V = \frac{\tau R}{A\_0 \alpha} \tag{9}$$

The experimental rotational correlation time *θexp* was deduced from *V*:

$$
\theta\_{\exp} = \frac{\eta V}{RT} \tag{10}
$$

The rotational correlation time of an equivalent rigid sphere of the same molecular weight M was calculated as follows:

$$\theta\_{\rm calc} = \frac{\eta M}{RT} (\overline{v} + h) \tag{11}$$

where *v* is the protein partial specific volume (usually 0.73 cm3/g) and h is the degree of hydration (g H2O per g of protein; usually 0.2 < *<sup>h</sup>* < 0.4); *<sup>R</sup>* = 8.31 × 107 erg mol−1·K−1. From Equation (13), replacing the calculated rotational time by rotational correlation times experimentally determined for each molecular species, leads to an estimation of *h* their degree of hydration (Table 1). Alternatively, knowing *D*, the rotational diffusion coefficient of the protein, its rotational correlation time can be obtained:

$$\theta = \frac{1}{6D} \tag{12}$$

The expected sedimentation coefficient can be deduced as follows:

$$s = \frac{MD(1 - \rho\_{20}\overline{\sigma})}{RT} \tag{13}$$

with *M*, molecular weight, *ρ*<sup>20</sup> solvent density (water).

**Supplementary Materials:** Supplementary materials can be found at http://www.mdpi.com/1422-0067/20/7/ 1794/s1.

**Author Contributions:** T.M. and J.W. conceived and designed the experiments. A.B., N.C., B.D., J.C., J.W., and T.M. performed the experiments. T.M. and J.W. analyzed the data. T.M. wrote the manuscript. T.M. and J.W. discussed the results and commented on the manuscript.

**Funding:** This work was partially supported by Le Ministère Français de l'enseignement supérieur et de la Recherche (JC Fellowship).

**Acknowledgments:** We thank Sonia Longhi (CNRS-Marseille, France) for fruitful discussions. We are indebted to Stephane Claverol (centre de genomique fonctionnelle, Bordeaux) for mass spectrometry analysis.

**Conflicts of Interest:** The authors declare that they have no conflicts of interest with the contents of this article.

### **Abbreviations**

