Medical contrast media as possible tools for SAXS contrast variation

Medical contrast media are presented as possible tools to probe the internal structure of soft-matter and biological systems by small-angle X-ray scattering solvent contrast variation.


Sample preparation
Iohexol (catalogue number D2158) and sucrose (catalogue number S7903) were purchased from Sigma-Aldrich. DDM (n-Dodecyl-β-D-Maltopyranoside) was purchased from Anatrace (catalogue number D310). Gd-HPDO3A was kindly provided by Bracco Imaging S.p.A., Milan, Italy. All SAXS contrast agent stock solutions were prepared by weighing a given amount of contrast agent on a highprecision balance and adding Milli-Q water by pipetting. The final volume of the mixture was measured by pipetting. The stock solutions were sequentially mixed in appropriate volume ratios with Milli-Q water to reach the desired concentration for a final sample volume of 50 μL. An example of a detailed protocol and amounts of material mixed is given in Table S1 for 1 M reference solutions that were used to calculate and calibrate electron densities, including those of other samples (see below).
For samples containing DDM, a high precision balance was used to weigh 1 mg of the detergent powder in an Eppendorf tube. Subsequently, 50 μL of the contrast solution at the respective concentration was added and gently mixed with the DDM powder by pipetting.

Calculation of solvent electron densities
The solvent electron densities (ρ sol ) were calculated from the amounts of sucrose (C 12 H 22 O 11 ; 342.3 Da; 182 e -), Gd-HPDO3A (C17H29GdN4O7; 558.7 Da; 279 e -) and iohexol (C 19 H 26 I 3 N 3 O 9 ; 821.1 Da; 392 e -) weighed, the amount of Milli-Q water (H2O; 18 Da; 10 e -) added, and the measured solvent volumes of the stock solutions according to Eq. S1, and based on the reference values reported in Table S1. The mass of water was calculated from the added volume (assuming 1 mg = 1 μL).

= (
• − + 2 2 • 10 − ) / (Eq. S1) Electron densities of buffers and DDM samples at different concentrations were calculated from the reference values in Table S1 by linear extrapolation (using the real concentrations from

SAXS theory, experiments and data reduction
For isotropically oriented and non-interacting (i.e. ideal) particulate systems, the scattered intensity I(q) can be written as (Lindner & Zemb, 2002): is the modulus of the scattering vector, λ the X-ray wavelength, and 2θ the scattering angle. The brackets indicate an average over all orientations of the solubilized particles.
( ⃗) and ρ sol are the electron densities of solubilized particles (soft matter systems, biomacromolecules) at a position ⃗ and the bulk solvent. The integral runs over the whole particle volume V.
All SAXS experiments were carried out on the SWING beamline (https://www.synchrotronsoleil.fr/en/beamlines/swing) at the synchrotron SOLEIL (Saint Aubin, France) in flow mode, using an X-ray energy of 12.00 keV and a sample-detector (Aviex CCD) distance of 1.790 m, yielding an I before and I after are the measured X-ray direct beam intensities by intensity monitoring devices based on light-sensitive diodes before and after (in the beamstop) the samples. Eq. S3 allowed to retrieve the real concentrations of the medical contrast agents in both the DDM samples and the buffers from the measured transmissions (Table S2). The X-ray transmissions of the sucrose solutions did not display a notable dependence on concentration and no in situ calibration could be carried out.
The one-dimensional curves of the DDM samples and the buffers displayed strong inter-particle effects over the whole q-range, originating from the presence of contrast agents (Fig. S2). In order to align the buffer signal with the respective sample and to carry out the buffer subtraction in the most accurate way, we generated calibrated buffers, I buff,calib (q), by a linear combination of the buffers lying above (I buff,above (q)) and below (I buff,below (q)) the DDM curve of interest ( Fig. S2): C buff,above and C buff,below are the concentrations of the buffers above and below the DDM sample with concentration C DDM . Please note that all concentrations in Eq. S4 are the real concentrations, calibrated as described, and not the nominal concentrations.

SAXS data analysis
Basic parameters (forward scattered intensity I(0), radii of gyration R G, maximum dimensions D max and pair distance distribution functions p(r)) were extracted from the final 1D scattering curves (Fig. 2, S1, Table S4) (Table S1) and assuming a linear dependence of the water and contrast agent masses as a function of concentration, the CMPs of DDM in sucrose, Gd-HPDO3A and iohexol can be expressed as weight/weight fractions: w/w % = mass of contrast agent / total weight. The total weight being the weight of dissolved contrast agent plus water added.
The aggregation numbers N agg of DDM micelles (Table S5)  Ab initio shapes of DDM micelles were calculated by using the multi-phase modeling program MONSA from the ATSAS package (Franke et al., 2017) for a q-range up to 0.25 Å -1 , and by assuming a constant density for the head-and tail-groups within the micelles. All electron densities and contrasts used in the MONSA runs were calculated as detailed above and are reported in Table   S3. The total micellar head-and tail-group volumes (i.e. MONSA phases) were assumed to be 45,500 and 44,200 Å 3 , respectively. MONSA was run in multiple setups (one or multiple contrasts, looseness and contiguity set to 100 or 0%). The models shown (Fig. 2, Fig. S5 and S6) were obtained by using the default values proposed by MONSA based on an initial spherical search volume for a D max from the p(r) analyzes: bead sizes were 2.25 Å, looseness, discontiguity, peripheral and volume fraction penalty weights were 50.00. The initial annealing temperature was 10.00 with an annealing schedule factor of 0.95.

Table S3
Contrast for the core (tail) and shell (head) phases of the DDM micelles in MONSA. C real are real (i.e. calibrated) concentrations in mM, contrast is given in 10 10 m -2 (with 0.335 e -/Å 3 ≈ 9.40·10 10 m -2 (Jacrot, 1976)).  Table S4 Basic fit parameters of the SAXS contrast series in sucrose, Gd-HPDO3A and iohexol. Radii of gyration R G were obtained from Guinier fits and p(r) distributions, and maximum dimensions D max from p(r) distributions by using GNOM from the ATSAS suite (Franke et al., 2017). The errors of the D max are estimated to be about ± 5Å. Please note that some radii of gyration are imaginary, i.e. multiples of the imaginary unit i (with i 2 = -1). They result from a negative value of a squared radius of gyration which can occur when some regions of solubilized particles have positive and others have negative contrast (Appolaire et al., 2014, Jacrot, 1976, Stuhrmann, 1974. The respective SAXS curves and Guinier fits (Fig. 2, Fig. S1 and S5) have negative slopes at the origin.

Figure S2
Example of the buffer correction. The plot shows the DDM data in 1,250 mM Gd-HPDO3A (nominal concentration, real concentration 1,222 mM), and the 1,250 and 750 mM Gd-HPDO3A buffers (nominal concentrations, real concentrations 1,246 and 738 mM, respectively). The real concentrations were calculated from the sample transmissions as described (Fig. S3, Eq. S3). The calibrated buffer (black line) was obtained by a linear combination (interpolation) of the 1,250 and 750 mM buffers (Eq. S4). Inset: zoom at the high angular region. A single, representative error bar is shown for q = 0.52 Å -1 . While all SAXS data were recorded up to 0.545 Å -1 , in most figures and analyses we cut the data at 0.25 Å -1 , since beyond that value the buffer and sample intensities were indistinguishable for most datasets (see below).

Figure S3
Logarithm of transmissions of sucrose, Gd-HPDO3A and iohexol samples as a function of nominal concentrations. The linear fits were used to calibrate the real concentrations. All data points (concentrations) were used in the case of sucrose and Gd-HPDO3A. In the case of iohexol, the highest concentration was considered to be an outlier and was not used for the fit.  (Table S2) and the relative errors of the DDM concentrations (Table S5), we estimate the relative errors of the CMPs to be about 5 %. The corresponding electron densities were calculated according to equation S1.

Figure S5
Three distinct MONSA models in default mode for sucrose, Gd-HPDO3A and iohexol, respectively, and by using all SAXS curves. The fit, including χ-values, is from Run 1 in each case. The 609 mM dataset was not used in the case of iohexol since it had a limited q-range and very poor statistics with respect to the four others (see Fig. S1). The largest deviations between MONSA fits and experimental data are observed for contrast curves with the lowest statistical impact: 1,200 mM sucrose, and 517 mM Gd-HPDO3A. (Please note the logarithmic scale of intensities). In the case of iohexol, the MONSA modeling failed.