dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2017; David & Perez, 2009; Graewert et al. , 2015; Mathew et al. , 2004)  and at SANS beamlines  (Jordan et al. , 2016)  is becoming increasingly popular. These SEC-SAS measurements involve the collection of SAS data as the solution elutes from the SEC column, and thus enable the separation of components of mixtures and polydisperse solutions. In the case of membrane proteins, this allows the separation of encapsulated proteins from empty detergent micelles or nanodiscs  (Berthaud et al. , 2012). This combined SEC-SAS approach has been extremely successful at synchrotron SAXS facilities and has opened up studies of systems that were previously impossible owing to timedependent aggregation. A drawback to the approach is the necessary dilution of the sample on the SEC column. Additionally, as the fluid in the centre of the tubing linking the SEC column to the SAXS cell flows faster than that at the edges of the tube (Poiseuille flow), the SEC peak will broaden before measurement.
Depending on the path length between the measurement cell/capillary and the end of the column, this broadening can be quite significant. Excessive path lengths will not only degrade the resolution of the eluted peaks, but the UV-absorbance measurements of the eluent may not correlate with the SAS measurement frame, which limits the ability to determine sample concentrations. Monitoring UV absorbance immediately prior to SAS measurements with minimal intervening path length and volume, or ultimately with coincident measurement, facilitates increased accuracy in the estimation of M or V from I(0). Excellent descriptions for the preparation of high-quality samples and well matched solvent blanks for SAXS and SANS experiments have recently appeared in Nature Protocols  (Jeffries et al. , 2016; Skou et al.
Data acquisition and reduction In the case of isotropic solution scattering, data reduction refers to the process of converting counts on a detector to the one-dimensional scattered intensity profile arising from the sample, with associated errors, as I(q) versus q (where q = 4 sin /, 2 is the scattering angle and is the wavelength of the radiation). To obtain the SAS profile relating to the structure of the particle of interest, the data-reduction software must take into account detector sensitivity and nonlinearity, sample transmission, incident intensity and accurate and precise subtraction of solvent scattering. Dilute solution measurement places severe requirements on normalizing scattering intensity measurements, which today can be better than 0. 1% and fully satisfactory. All of these procedures are described in detail in  Svergun et al.
(2013). The data-reduction process may also require addressing potential instrumental 'smearing' effects on the SAS profile (see chapter 4 of  Glatter & Kratky, 1982). The theory guiding the interpretation of SAS data in terms of structure generally assumes an effective point source and a single wavelength. The instrument setup used for a SAS experiment may be an excellent approximation to a point source, or may differ significantly from it and thus require corrections to be made to data or to model scattering profiles for comparison with the experiment. The wavelength resolution (Á/) for SAXS (whether synchrotron or laboratory-based) is generally a good approximation to a single wavelength, while for SANS it can be of the order of 10-15% in order to optimize the neutron flux on the sample (for examples, see https://www.
, 2000; Jacrot & Zaccai, 1981). Pure H 2 O is a readily accessible, universal standard whose scattering has been well characterized over a wide range of temperatures. Secondary standards are also available, such as glassy carbon (see the new NIST Standard Reference Material 3600; https:// www-s. nist. gov/srmors/view_detail. cfm?srm=3600;  Allen et al. , 2017). Absolute scaling enables the direct comparison of SAS data from different instruments, including X-ray and neutron sources, without arbitrary scaling and also enables the determination of M or V from I(0) without reference to the scattering from a reference protein. In the case of SANS, it has been routine to place the data on an absolute scale. The more common practice for SAXS experimenters has been to provide data on an arbitrary relative scale, which we do not recommend for reasons that will be addressed further below.
The indirect Fourier transform methods for calculating P(r) include a smoothing parameter that is a complicating factor in assessing the quality of the fit for a given solution. A simple 2 test is straightforward to calculate, although it does have limitations, as will be discussed below (x2. 4). Another approach used by the popular program GNOM for calculating P(r) is to use a quality-of-fit assessment (referred to as the 'total estimate' ) that is based on 2 combined with a number of 'perceptual criteria'  (Svergun, 1992). The molecular mass M in daltons for a scattering particle is readily calculated as M ¼ Ið0ÞN A CðÁ M Þ 2 ; ð1Þ where I(0) is on an absolute scale in units of cm À1 , N A is Avogadro's number, C is the concentration of the scattering particle in g ml À1 and Á M is the scattering mass contrast, which can be calculated as Á , where Á is the average Summary of guidelines for data acquisition and reduction.
Number of sample exposures and exposure times, the normalization method (e. g. time or beam monitor counts), the method used to determine sample transmission and how radiation damage was monitored (in the case of SAXS). In the case of SANS contrast-variation experiments, sample and buffer transmissions referenced to transmissions of pure 1 H 2 O and 2 H 2 O, from which deuteration of the solvent can be checked. Details of the sample environment, including measurement temperature, measurement cell type and path lengths, any special parameters controlled, e. g. pressure, and additional inline purification or characterization capabilities as appropriate. In the case of SEC-SAS experiments, description of (or reference to) system. Standards measured and controls and method for placing SAS data on an absolute scale in cm À1 , e.
Additionally, it is the case that most readily available inexpensive protein standards have some tendency for time-induced and/or radiation-induced aggregation or degradation, which introduces further systematic error in the assessed M value. Nevertheless, it can be useful in practice to measure a known protein standard (such as lysozyme, bovine serum albumin or glucose isomerase) as a check of the overall experimental setup. However, we do not recommend dependence on this approach for the evaluation of M in favour of absolute scaling of the SAS data and using (1), as this method is subject to fewer errors. The total scattered intensity [calculated as the integral from zero to infinity of q 2 I(q)] is referred to as the Porod invariant Q i , which, for uniform scattering density particles with a well defined boundary, depends only on the volume of the scattering particle and not its form  (Porod, 1951).
The particle volume or Porod volume, V P , is then calculated as V P ¼ 2 2 Ið0Þ=Q i : ð2Þ As Q i is an integral from zero to infinity and data are only measured for a finite q range, in practice the integral is generally estimated using a smoothed, regularized scattering profile obtained from P(r) [for example as in the method of  Fischer et al. (2010)  and in the current implementation of GNOM  (Petoukhov et al. , 2012) ]. The GNOM implementation includes a correction to force the high-q data to obey the expected q À4 dependence for a uniform scattering density particle with a well defined boundary (i. e. a globular, folded biomolecule;  Porod, 1951). By interrogating a large set of theoretical scattering profiles calculated from coordinates of proteins in the Protein Data Bank (PDB;  Berman et al.
e. where internal scattering density fluctuations are negligible;  Whitten et al. , 2008). With sufficient measurements in the contrast series it is possible to extract the scattering profiles for individual components along with a cross-term that encodes information on the dispositions of the components. The MULCh suite of programs (ModULes for the analysis of Contrast variation data; available for download and as a web-based tool at http://smb-research. smb. usyd. edu. au/ NCVWeb/index. jsp; Whitten et al. , 2008)  was designed to aid in planning a SANS contrast-variation experiment by providing the dependence of I(0) on contrast for given deuteration levels in biomolecular components and solvent (Contrast module), for Stuhrmann and parallel axis theorem analysis (Rg module), and for extraction of the scattering profiles of individual components of a complex and their cross-term (Compost module).
g. compactness, connectedness, distance restraints etc. ). As solution scattering data reduce to one-dimensional profiles, there are a number of issues regarding the representation and precision of derived three-dimensional models  (Schneidman-Duhovny et al. , 2012). In the case of data that can be adequately fitted by a single average three-dimensional model (either shape or atomistic representations), an evaluation of the inherent ambiguity in the modelling solution is required. Here, a question to answer is whether a single best-fit model or class of very similar models uniquely fits the data, or whether multiple classes of models exist that fit the data equally well. AMBIMETER is a recently released program that provides an a priori assessment as to whether the spherically averaged single-particle scattering can be fitted by a single relatively well-defined shape, or whether it is Table  3  Summary of guidelines for data presentation, analysis and validation.
Any data from the measurement range that was truncated should be displayed and identified by the use of a symbols that distinguish them from data points included in the linear fit. P(r) versus r with associated R g and I(0) (with errors) and d max values is essential for SAXS data and is advised for SANS data [especially at solvent match points for complexes of components with distinct scattering densities where interpretation of P(r) will be the most intuitive as the scattering object has an approximately uniform scattering density]. M or V estimates, preferably from multiple methods; for example, methods based on I(0) in addition to V P or V c. For I(0)-based methods, values and uncertainties in the calculated or experimentally determined concentration and parameters used, such as , Á and solvent and particle scatteringlength densities, along with the methods of calculation or measurement.
Where applied, the magnitude of corrections for solvent subtraction applied to the data as a potential warning that something is not correct if unduly large (say 1% percent of the solvent scattering level). Where relevant, the method of data desmearing to correct for beam geometry and/or polychromaticity and the original smeared data be made available. For a concentration series, note if no change in R g or I(0)/C is observed with increasing concentration [C in (w/v)] and for best practice report M estimates at each concentrations or provide a plot of I(0)/C versus C. A dimensionless Kratky plot as a check on the degree of folding and/or flexibility in the scattering particle. Kratky and/or Porod-Debye plots might alternatively be used to assess potential flexibility. For SEC-SAS data a plot of I(0) and R g as a function of measurement time or measurement frame, and correlated UV traces if used for estimating C, including the leading and trailing edge of elution peaks.
From (4) we see that 2 will be smaller for data with poor statistics and conversely larger for data with vanishingly small statistical errors. Thus, while relative 2 values are most valuable in comparing two models against the same data set, absolute values can be less useful in comparing fits to two independent data sets. Scattering data are acquired as the sum of events on a detector. A model that fits the data within its error estimates will have a 2 value close to 1, providing that the random statistical errors are propagated correctly and there are no systematic errors. Overestimation or underestimation of the statistical errors and potential contributions from systematic errors have led to reported 2 values ranging from a few tenths to quite large values (>5), and yet the fits to the data may be good, even excellent, or claimed to be good based on a 'by-eye' evaluation of a presented plot (see, for example, Supplementary Fig.
2  in  Appolaire et al. , 2014). Generally, SAS intensity decreases rapidly and by orders of magnitude over the measured q range, and depending upon how the data are presented, regions of significant misfitting of the scattering profile may not be apparent. Also, as 2 is a global fit parameter, it is important to present the data and model fit so that systematic deviations that may be present in specific q regimes are evident, for example in the mid-q regime most highly influenced by domain positioning and orientation where SAS data are often most helpful in SAXS/NMR structure refinement  (Grishaev et al. , 2008). A straightforward and intuitive approach to demonstrating the quality of a model fit over the entire measured or modelled q range of a SAS profile that takes into account relative errors across the measured q range is an error-weighted residual difference plot of [I exp (q) À cI mod (q)]/(q) versus q, as is nicely demonstrated in Figs.
, 2011)  and a measurement of the volatility of the ratio between experiment and fit  (Hura et al. , 2013). Rambo and Tainer proposed the use of a resampling-based adaptation of the reduced 2 test and defined a 2 free with the aim of reducing the chance of model misidentification in noisy data and avoiding overfitting  (Rambo & Tainer, 2013b). The 2 free parameter, however, does not solve problems relating to inaccurate error propagation. A recently proposed alternative to 2 that is independent of the amplitude of the statistical errors considers only the statistical likelihood of a run of consecutive points lying systematically above or below the profile generated from the fitted model  (Franke et al. , 2015). The method has proven to be useful for comparing synchrotron SAXS data frames to detect subtle radiation damage or for selecting SEC-SAXS data frames for averaging and subsequent analysis.
A clear benefit of this tool is that it will discourage the over-interpretation of surface bumps and valleys in these models. For a given optimized atomistic model, accuracy will vary substantially for different regions depending on the contributing data. For example, the linker sequences between structured domains from crystallography or NMR that are modelled only by optimizing the fit to the SAS data will not be accurate at the level of coordinate positions. Likewise, interfaces that are not defined experimentally by crystallography or NMR are likely not to be accurate. The disposition of the domains may be relatively well defined; that is, accurate within limits that can be placed on the spatial and orientational parameters  (Kim & Gabel, 2015; Gabel, 2012). The accuracy will depend on the asymmetry of the structure shape and whether there were additional contacts from experiment or bioinformatics analysis used as restraints.
The tabulated results for all three proteins provided the subset of information required for the deposition of metadata, data and models in the SASBDB (deposition IDs are provided in Table  5g ). The SAXS data were acquired using the SAXS/WAXS beamline at the Australian Synchrotron  (Kirby et al. , 2013)  with a sheath-flow sample environment to maximize the X-ray dose on the sample with minimal radiation loss  (Kirby et al. , 2016). All measured intensity values were multiplied by 2. 05 to account for the shortened sample path length in the sheathflow cell (0. 49 mm) with absolute scaling calibrated to 1 mm H 2 O scattering. SAS data reduction used the beamline software ScatterBrain 2. 82, and we note here that this version of ScatterBrain outputs errors that are twice the standard error and were halved before use in analysis programs.
The A 280 measurements associated with the selected SAS measurement frames (Supplementary Fig. S1a ) for analysis were used with calculated extinction coefficients (using ProtParam;  Gasteiger et al. , 2005)  to estimate protein concentrations. Guinier analysis during data acquisition (autogenerated by PRIMUS;  Petoukhov et al. , 2012)  yielded values of R g and I(0) for each 1 s measured data frame. The R g and I(0) traces (Fig. 1a ) as a function of time show that the GI and CaM samples are highly pure, as expected from their sources. GI was originally sourced from Hampton Research, stored in diluted form for some period and subject to repeated freezethaw cycles. CaM was prepared by bacterial expression and high-resolution SEC  (Michie et al. , 2016). The commercially purified BSA powder had aged in the refrigerator for some years and the SEC trace indicated that it was highly heterogeneous, which is consistent with the known tendency of this protein to self-associate and the lack of any steps to remove higher order oligomers prior to loading.
For GI, R g showed a small increase after the peak (by an average of 0. 6 A ˚over 9 Â 1 s measurement frames) starting where the concentration SASDCQ2 † PDB entry 1cll+ is PDB entry 1cll plus the missing ADQ at the N-terminus and the C-terminal K missing in the crystal structure. ‡ In FoXS the adjustable parameters c 1 and c 2 are adjustments for excluded volume and hydration density. c 1 can vary by 5% (0. 95-1. 05) and the maximum hydration adjustment c 2 of 4. 0 corresponds to $0. 388 e A ˚À3 (compared with bulk solvent density = 0. 334 e A ˚À3 ). § In CRYSOL the adjustable parameters are excluded volume (Vol in A ˚3), optimal atomic radius (Ra in A ˚) and Dro (optimal contrast of the hydration shell in e A ˚À3 ). } In MultiFoXS c 1 and c 2 are the same for all states in a set; the scale factor c is then optimized for each state and a relative weight w n for each state n is output.
The R g values for GI and CaM (Table  5d ) are in good agreement with previously published values from SAXS measurements [Guinier R g values of 32. 5 AE 0. 7 A ˚for GI  (Mylonas & Svergun, 2007)  and 21. 0 AE 0. 6 A ˚for CaM  (Heidorn & Trewhella, 1988) ], whereas the value for BSA lies in between a previously published value from SAXS (29. 9 AE 0. 8 A ˚;  Mylonas & Svergun, 2007)  and that predicted from the crystal structure (26. 75-26. 89 A ˚using FoXS or CRYSOL) from the individual monomer chain A in the dimeric crystal structure (Table  5f ). For all three proteins, the ab initio bead-modelling program DAMMIN  (Svergun, 1999)  was better able to fit the data than its speedier cousin DAMMIF (Table  5e ). However, the latter program provides a rapid assessment of the variability of the shapes that fit the data from 20 independent calculations using the normalized spatial discrepancy (NSD) value.
As there are crystal structures for all three proteins, atomistic modelling was undertaken (Table  5f  ). A tetramer based on the crystal structure of GI (PDB entry 1oad;  Ramagopal et al. , 2003)  predicts an I(q) profile that is a reasonable fit to the scattering data (see Fig. 2 ; 2 = 1. 02 from FoXS or 1. 03-1. 00 from CRYSOL depending on whether a constant subtraction is allowed). However, it is noteworthy here that the GI data have the poorest statistics of our three examples owing to a significant portion of the scattering being taken at lower concentrations. Given the indications of interparticle interference that were observed, at this point the experimenter should be questioning whether the data are of sufficient reliability and statistical quality for their purposes. It is reasonable to conclude from the data that GI is a tetramer with a shape and structure that is largely consistent with the crystal structure.
To go beyond making this assessment, repeating the experiment to obtain data with better statistical precision that are clearly devoid of inter-particle interference is called for. In contrast to GI, the crystal structures of BSA (PDB entry 4f5s chain A) and of CaM (PDB entry 1cll) showed very poor fits to their respective data sets ( 2 = 4. 4 and 10. 8, respectively, from FoXS). There are a few missing amino acids in the CaM crystal structure (Ala-Asp-Gln at the N-terminus and a Lys at the C-terminus. These were added to the crystal structure (1cll+) using MODELLER (https://salilab. org/modeller/; Webb & Sali, 2014) , and the FoXS 2 value decreased marginally to 9. 2. Interestingly, in trying to fit the CaM data to the unmodified crystal structure, the FoXS calculation takes c 2 to its limit of 4, which corresponds to the highest permitted hydration-layer scattering density for the program ($0.
(b) BSA DAMMIN model (wheat spheres) overlaid with the crystal structure (PDB entry 4f5s, chain A, blue ribbon) and one-state optimized model (magenta ribbon) and representative structures from the three-state optimized model (cyan ribbon models). (c) Model fits to I(q) versus q for CaM: I(q) versus q (black squares) for one-state (red line) and two-state (cyan line) models assuming flexible residues 1-3 and 77-81; the lower inset shows the error-weighted residual difference plots for the one-state (red squares) and two-state (cyan squares) models. (d) CaM DAMMIN model (wheat spheres) overlaid with the crystal structure (PDB entry 1cll, blue ribbon) and the one-state model (magenta ribbon) with the representative two-state models to the right (pink; calcium ions are depicted as yellow spheres).
3c  and 3d ). There was no improvement in 2 for the three-state model. The alternate ensemble modelling program for flexible systems (EOM;  Bernadoet al. , 2007)  was also used to model CaM with the same flexible residues, yielding a 2 value of 0. 82 (the model fit is shown in Fig. 4a ). As for the multistate fits from FoXS, the residual difference plot between experimental and model I(q) is flat, but 13 representative structures were selected to represent the ensemble (Fig. 4b ) and this greater structural diversity in the model is reflected in very broad distributions for R g and d max  (Figs. 4c and 4d, respectively)  in the optimized ensemble. The atomistic modelling thus supports the conclusions from the dimensionless Kratky plots that BSA and CaM are both mostly folded proteins with some flexibility, which is significantly greater for CaM, and in each case assuming the flexible regions identified by crystallography or NMR improved the model fits to the data.
Conclusions The example SEC-SAXS experiments on GI, BSA and CaM illustrate the value of comprehensive reporting so that data quality and model accuracy are clearly communicated. Supplementary Table  S1  provides a guide for tabulating the recommended information for a general SAXS experiment; such a table will be included in future releases of the IUCr Journals Word template. Some publishers may well require much of the reporting to be included as supplementary material. Eventually, most of it should be made available via the developing SAXS data and model archives. The latter will be increasingly important for managing related data sets, although  Figs. 2, 3, 4 and 5 in Carter et al. (2015)  show how effectively one can assemble the results for multiple data sets. It is evident that the often-ignored adjustable parameters enhance the understanding of potential limitations in models.