Figure 5.

Solution X-ray scattering data and models of lysozyme. Azimuthally integrated background-subtracted scattering intensity as a function of the magnitude of the scattering vector, q, from solutions of 20 mg ml⁻¹ lysozyme in 50 mM sodium acetate buffer, adjusted to pH 4.5, at ambient room temperature. Measurements were performed at the SWING beamline (Soleil synchrotron). The data at q < 1 nm⁻¹ were taken from measurements performed at the P12 EMBL BioSAXS Beamline of PETRA III (DESY, Hamburg), measured under similar solution conditions but at a lysozyme concentration of 2.5 mg ml⁻¹. The solid black curve represents the scattering data. The other curves were based on PDB ID 1lyz. Hydrogen atoms were either implicitly taken into account or explicitly added to the PDB file by PyMol (Schrödinger, 2015 ▸). The broken scattering curves were computed by CRYSOL (ATSAS 2.8.2) (Svergun et al., 1995 ▸), where the maximum order of harmonics was 50 and the order of the Fibonacci grid was 18. The solid curves were computed by D+. In both D+ and CRYSOL the bulk water electron density was set to 334 e nm⁻³ and the contribution of the solvation layer was taken into account. In D+, the grid size was 80, and the orientation average was computed by Monte Carlo integration, using the Mersenne twister algorithm. The solvent Voxel Size was 0.05 nm, the solvent Probe Radius was 0.14 nm and Dummy Atoms were used to account for the volume of excluded solvent [see Section 5.5 and equation (63)]. The fitting algorithm used the normal residuals cost function and the trivial loss function, with 20 iterations, Step Size of 0.01, Convergence Tolerance of 0.01 and Der eps of 0.1 (see Section 9.1). In the implicit model, the solvation layer thickness was 0.2987 nm and its electron density was 337.6 e nm⁻³. The excluded solvent parameter, c ₁, in equation (60) was 1.014, and R ² = 0.998. In the explicit model, c ₁ was 1.012, the solvation layer thickness was 0.301 nm, its electron density was 337.5 e nm⁻³ and R ² = 0.9977. In CRYSOL, in both models, the solvation layer thickness was 0.3 nm and the electron density of the solvation layer was 339 e nm⁻³. In the implicit model χ² = 33.53 and in the explicit model χ² = 35.96. Figs. S38 and S39 in SOM Section 9.4 show two other examples.