Smaller capillaries improve the small-angle X-ray scattering signal and sample consumption for biomacromolecular solutions

Sample exposure cells of small-angle X-ray scattering instruments often utilize cylindrical capillaries where the diameter, or path length, is typically selected to balance between scattering and absorption. Here it is demonstrated that, for radiation-sensitive solution samples, using capillaries with a diameter smaller than the optimal path length in combination with continuous sample flow improves the quality of the scattering signal for a given quantity of material.


S2. Radiation dose for sample flow
Following the approach of Jeffries et al., 2015, andHopkins &Thorne, 2016, the radiation dose D on the samples is calculated as Here, F is the beam flux (photons s -1 ), E the photon energy (J photon -1 ), t the time the same sample spot is exposed, Xray the beam profile, the mass density of the sample (g cm -3 ), d the path length and the linear absorption coefficient. The factor 1000 converts J g -1 to J kg -1 to obtain Gy.
The path length is given by the respective capillary diameters. For linear capillary flow, the time the same sample is actually exposed to the beam is given by the average dwell time tdwell. The parameters present at P12 are discussed in §2.2 (assuming a Gaussian beam profile)). The values of and for the protein solutions studied are taken from Jeffries et al., 2015, which studied similar protein solutions (lysozyme: = 1.028 g cm -3 , = 5.56 cm -1 ; BSA: = 1.023 g cm -3 , = 5.27 cm -1 ). The transmission TSiO2 of quartz glass wall of the capillaries has to be taken into account in addition (di = 1.7 mm: TSiO2 = 0.81; di = 0.9 mm: TSiO2 = 0.79). The so computed average radiation doses are given in Table S1 and Table S2.
For non-flowing conditions, the average dose is higher for the smaller capillary, whereas with flow the dose is lower than for the larger one.  Supporting information, sup-3

S3. Radial velocity profiles
The radial velocity profiles of a liquid in the linear flow regime can be approximated as (Rogers, 1992) Herein v is the linear flow speed, r the radial distance from the center of the capillary and R = 0.5 di the capillary radius. At the border of the capillary (r = R) the velocity approaches zeros. For the di = 0.9 mm capillary much higher flow velocities are reached over a large part of the profile, which results in a stronger exchange of sample. Only at the lowest flow rate measured at (Q = 10 µl/min), the velocity profile for the di = 0.9 mm capillary is smaller than at for the di = 1.7 mm capillary at the highest flow rate. Especially for the flow rates studied here, nearly all SAXS curves are similar for the smaller capillary. In this situation, the BSA solutions are even partially under-exposed, allowing to collect more SAXS curves before radiation damage sets in and thus yielding lower noise data. Normalized deviation from the AUTOGNOM curves, Δ<I(s)>, for both curves. d) Parameter DEV as a function of the total volume flow rate Q for both capillaries.

S5. Results from beamline BM29
Additional SAXS measurements on both type of capillaries have been performed at beamline BM29, ESRF, Grenoble (Pernot et al., 2015), using at photon energy of E = 12.5 keV (λ = 0.099 nm) with a beam size of 700 µm x 700 µm (v x h, full width half maximum, FWHM) and a flux of 1.4 x 10 12 photons s -1 at a storage ring current of 200 mA. For this X-ray energy, the optimum path length for water is dopt = 3.9 mm. Thus, the diameter for both capillaries are much smaller than dopt. Similar to the measurements at P12, standard batch mode measurements were performed using a robotic sample changer (Round et al., 2015) both with continuous in-capillary sample flow through the beam line under vacuum. At BM29, a constant volume of Vtot = 30 µl was loaded into the capillaries that were maintained at a constant temperature of T = 20 °C.
SAXS data were recorded from lysozyme solutions (concentrations: 2.5 mg/mL; 4.8 mg/mL; 9.7 mg/mL) in a similar buffer as used for the P12 measurements. Data were collected with a PILATUS 1M photon counting detector (DECTRIS, Switzerland) from samples and buffers at several different flow rates and total exposure times. For each run, ten 2D-SAXS data were recorded at different collection times per frame from 0.5 s to 3.6 s resulting in different flow rates (Q = 2 -6 µl/s). (Here, the flow rate Q was given as Q = Vtot / (texp * 10 frames + 10 s)).
For the averaged SAXS curves, the exposure time without radiation damage, tav, as well as the DEV parameter were determined as described in the main text (Fig. S5). In case of the di = 0.9 mm capillary, radiation damage sets in latter than for di = 1.7 mm. The resulting averaged SAXS curves therefore have a lower DEV parameter in case of the smaller capillary. Based on the proposed criterion, the best flow rate is present for Q ≈ 3 µl/s. The data obtained from BM29 using different experimental parameters thus confirm that in case of radiation-damage sensitive samples, the use of capillaries with smaller diameters can yield SAXS curves of higher quality.