*4.10. SAXS*

SAXS experiments were performed on a Rigaku 3-pinhole PSAXS-L instrument, at 45 kV and 0.88 mA. The MicroMax-002+ X-ray Generator Systems includes a module with a microfocus sealed tube source, and an X-ray generator unit producing Cu-Kα transition photons, with λ = 1.54 Å wavelength. Vacuum was maintained both in the flight path and sample chamber. A two-dimensional multiwire X-ray detector (Gabriel design, 2D-2000X) was used as a detector of the scattered X-rays. We obtained the azimuthally averaged scattered intensities as a function of the scattering vector *Q* (where *Q* = 4π(λ) <sup>−</sup>1sinθ, and θ represents half the scattering angle). Silver behenate was used as standard for calibration (reciprocal space). The solutions were filling Boron-rich capillaries with an outside diameter of 2 mm and wall thickness of 0.01 mm. The contribution from the corresponding buffer (measured on the same capillary) was subtracted by applying the proper factors obtained from transmission measurements. The sample-detector distance was 2 m, allowing covering a *Q*-range from 0.008 to 0.2 Å<sup>−</sup>1.

From the intensity scattered at low-*Q* values –in the so-called Guinier regime– we can determine the average gyration radius, *R*g, of the protein under several conditions, by using the Guinier law: *I*(*Q*) = *A* exp( <sup>−</sup>*R*<sup>2</sup> *gQ*<sup>2</sup> <sup>3</sup> ). The pre-exponential factor, *A*, is determined by the molecule concentration, the scattering contrast and the mass of the macromolecules dispersed in the solution. On the other hand, we can estimate the compaction grade through the scaling exponent υ, which relates to *Q* as *<sup>I</sup>*(*Q*) <sup>≈</sup> *<sup>Q</sup>*−1/*υ*, in the high *<sup>Q</sup>*-range here explored. The values of <sup>υ</sup> are 1/3 for a polymeric chain collapsed into a globule; 0.5 for a random-coil polymer (which is the conformation of a linear polymer chain in Θ-conditions); and 0.6 for a swollen chain in a good solvent (self-avoiding-walk conformation). The form factor of a coil, with scaling exponent υ, is described in terms of the so-called generalized Gaussian coil function, given by the expression [52]: *<sup>I</sup>*(*Q*) <sup>≈</sup> <sup>1</sup> *<sup>ν</sup>U*1/2*<sup>ν</sup> γ* 1 <sup>2</sup>*<sup>ν</sup>* , *U* <sup>−</sup> <sup>1</sup> *<sup>ν</sup>U*1/*<sup>ν</sup> γ* 1 *<sup>ν</sup>* , *U* , where *U* = (2*ν* + 1)(2*ν* + 2)*Q*2*R*<sup>2</sup> *<sup>g</sup>*/6 and *<sup>γ</sup>*(*a*, *<sup>x</sup>*) = *<sup>x</sup>* <sup>0</sup> *<sup>t</sup>a*−<sup>1</sup> exp(−*t*)*dt*. From the fits of this function to the experimental data, the value of the radius of gyration can also be obtained.

#### *4.11. Molecular Modelling*

A model of C-LrtA (without the His-tag) was obtained in MD simulations by using a protocol previously adopted for IDPs [23,24]. In brief, simulations were performed with the GROMACS package [53] starting from a protein model built by using VMD [25], and collapsing it in a brute-force run carried out in the isobaric-isothermal ensemble. C-LrtA was initially in an extended conformation, except for backbone turns in correspondence with proline residues. The protein was centered in a rhombic dodecahedron box with a minimum distance of 1 nm from the edge of the simulation box, and surrounded with explicit water molecules. Amino acid residues were adjusted to mimic neutral pH and Na<sup>+</sup> counterions were added to obtain an overall neutral molecular system. The AMBER ff99SB-ILDN force field [54] was used for the protein, and the TIP3P [55] model for water. Other simulation conditions, including modelling of the electrostatics and van der Waals interactions, and reference values and coupling times for the thermostat and barostat, were as previously described [56,57].
