Date Published: December 01, 2016
Publisher: International Union of Crystallography
Author(s): Nigel Kirby, Nathan Cowieson, Adrian M. Hawley, Stephen T. Mudie, Duncan J. McGillivray, Michael Kusel, Vesna Samardzic-Boban, Timothy M. Ryan.
Coflow is a new method for delivering radiation-sensitive biological and other solution-based samples to high-brightness X-ray beamlines that exploits laminar flow to ameliorate radiation-damage limitations and provides a host of practical improvements associated with these types of experiments.
SAXS is a versatile technique for structural biology that is widely applied to confirm high-resolution crystal structures in solution, and provides lower resolution structural and biophysical parameters, particularly for difficult-to-measure protein samples that are not amenable to high-resolution structure determination (for reviews, see Svergun et al., 1995 ▸; Jacques & Trewhella, 2010 ▸). Increasingly, synchrotron SAXS has been advanced through the development of comprehensive data analysis tools, instrumentation and X-ray detectors, and advances in sample presentation and preparation (Graewert & Svergun, 2013 ▸; Bizien et al., 2016 ▸). A major advance in this regard was the development of SEC–SAXS, initially by Mathew et al. (2004 ▸), with subsequent incorporation into many synchrotron beamlines (for examples, see David & Pérez, 2009 ▸; Watanabe & Inoko, 2009 ▸; Kirby, Mudie, Hawley, Mertens et al., 2013 ▸). This technique greatly advanced the field, assisting the analysis of mixtures, complexes and polydisperse samples by in-line fractionation, increasing confidence in the monodisperse nature of protein samples entering the beam and simplifying buffer matching. Recent solution SAXS development work has focused on automated sample changers, which have reduced the tedious work of manually obtaining reproducible measurements (for a review, see Round et al., 2015 ▸). These capabilities increase the throughput of the measurements, reduce minimum sample volumes, facilitate high-throughput approaches to research and have expanded the demand for solution SAXS considerably.
The flow conditions in the capillary were modelled using the simple parabolic radial velocity profile of laminar flow in a smooth-walled cylindrical tube given bywhere v is the linear flow velocity at a point in the capillary, vave is the average linear flow velocity (in m s−1), which is the total volume flow rate (in m3 s−1) divided by the cross-sectional area (in m2), r is the radial distance from the centre of the capillary, R is the internal radius of the capillary wall, Re denotes the Reynolds number, ρ is the density of the fluid (in kg m−3), d is the internal diameter of the capillary (in m) and μ is the dynamic viscosity of the fluid (0.89 × 10−3 Pa s for water at 25°C). The Reynolds number for a 1 µl s−1 flow of water in a 1 mm diameter capillary is 2.4, with an average velocity 2000 times lower than the critical velocity for breakdown of laminar flow (Reynolds, 1883 ▸). Hence the flow regime is laminar, even for flow rates that are one to two orders of magnitude higher than those typically used for static protein and SEC analyses. The flow field in the capillary is highly non-uniform, as under a laminar flow regime there is a parabolic flow velocity distribution, stretching from zero at the interface between the capillary and the solution to a maximum at the centre of the capillary of twice the average velocity (Fig. 1 ▸). The X-ray dose experienced by a protein molecule is proportional to its dwell time in the beam; hence, the flow-velocity distribution has a strong effect on the dose distribution.
Radiation damage is a major limiting factor in the advancement of SAXS analysis of solution samples. Previous studies on radiation damage have focused on a static sample, which removes complexities arising from very wide dose distributions owing to flow profiles (Hopkins & Thorne, 2016 ▸; Jeffries et al., 2015 ▸; Kuwamoto et al., 2004 ▸; Meisburger et al., 2013 ▸). These studies provide important frameworks with which to understand critical dose levels, assess damage and avoid damage (Jeffries et al., 2015 ▸; Hopkins & Thorne, 2016 ▸; Kuwamoto et al., 2004 ▸), including the use of stabilizing additives. A novel cryogenic method to abrogate radiation damage and greatly increase data quality per sample volume has also been reported. However, this approach requires large additions of PEG to prevent ice crystallization on rapid cooling and has been reported to have difficulties with buffer subtraction at high q (Meisburger et al., 2013 ▸). Unfortunately, the study of static conditions provides limited insight into how flow dynamics affect the absorbed radiation dose. Fluid dynamics, and the influence of Navier–Stokes-based modelling of fluid flows in SAXS capillaries, have been investigated by Gillilan and coworkers (Gillilan et al., 2013 ▸; Nielsen et al., 2012 ▸). They postulate that the nonslip boundary indicated by this modelling will result in a layer of radiation damaged material that is impossible to remove under steady-flow conditions (Gillilan et al., 2013 ▸). The solution proposed was an oscillating flow cell, which redistributes radiation-damaged material, allowing the replenishment of undamaged sample (Nielsen et al., 2012 ▸). The results of the pixel-based modelling and experimental measurements of the effect of sheath flow on radiation damage, dose and data quality is an extension of these studies. The pixel-based modelling provides a practical tool for determining the absorbed dose distribution in a flowing solution under cylindrical laminar-flow conditions. This may be of use for designing improved geometries for solution based SAXS measurements.