REVIEW Small-Angle Scattering for Structural Biology—Expanding the Frontier While Avoiding the Pitfalls

REVIEW

Small-angle scattering for structural biology—Expanding the frontier while avoiding the pitfalls

David A. Jacques and Jill Trewhella*

School of Molecular and Microbial Biosciences, The University of Sydney, Sydney, New South Wales 2006, Australia

Received 23 December 2009; Revised 17 January 2010; Accepted 19 January 2010 DOI: 10.1002/pro.351 Published online 21 January 2010 proteinscience.org

Abstract: The last decade has seen a dramatic increase in the use of small-angle scattering for the study of biological macromolecules in solution. The drive for more complete structural characterization of proteins and their interactions, coupled with the increasing availability of instrumentation and easy-to-use software for data analysis and interpretation, is expanding the utility of the technique beyond the domain of the biophysicist and into the realm of the protein scientist. However, the absence of publication standards and the ease with which 3D models can be calculated against the inherently 1D scattering data means that an understanding of sample quality, data quality, and modeling assumptions is essential to have confidence in the results. This review is intended to provide a road map through the small-angle scattering experiment, while also providing a set of guidelines for the critical evaluation of scattering data. Examples of current best practice are given that also demonstrate the power of the technique to advance our understanding of protein structure and function. Keywords: Small-angle scattering; neutron scattering; X-ray scattering; protein structure; protein complexes; structural modeling; SAXS; SANS; contrast variation

Introduction information has been understood for over 80 years.1 The small-angle scattering of X-rays from macromo- The earliest biological small-angle X-ray scattering lecules in solution and its relationship to basic shape experiments, performed in the 1950s, necessarily used easily purified proteins such as hemoglobin and ovalbumin. Although data interpretation at that Abbreviations BME, b-mercaptoethanol; CD, circular dichroism time was restricted to relatively simple parameters, spectropolarimetry; Dmax, maximum linear dimension; DTT, dithi- othreitol; EM, electron microscopy; HSQC, heteronuclear single such as radius of gyration, it was believed even then quantum coherence; NMR, nuclear magnetic resonance; Rg, ra- that the most important application of small-angle dius of gyration; SDS-PAGE, sodium dodecyl sulfate polyacryl- scattering would be to the study of biological macro- amide gel electrophoresis; TCEP, tris(carboxyethyl) phosphine. molecules.2 In the 1970s and 1980s, the molecular *Correspondence to: Jill Trewhella, Building G08, Butlin Ave, biology revolution and advances in instrumentation University of Sydney, Sydney, NSW 2006, Australia. E-mail: jill. saw some growth in applications of the technique. A [email protected]. significant advance in this period was in the use of Grant sponsor: Australian Research Council (ARC) Discovery small-angle neutron scattering with contrast varia- Project; Grant number: DP09984536; Grant sponsor: Australian Institute of Nuclear Science and Engineering (AINSE) tion to characterize the shapes and dispositions of Postgraduate Research Award. components within bimolecular complexes. Neutron

642 PROTEIN SCIENCE 2010 Published by Wiley-Blackwell. VC 2010 The Protein Society contrast variation revealed that DNA was wrapped scattering experimenter, so that they may avoid around the outside of nucleosome core particles pro- potential pitfalls as the biological applications con- viding an understanding of how DNA was packaged tinue to expand into new territory. in chromosomes3 22 years before the first high-resolution crystal structure of the nucleosome appeared.4 The Basics of Small-Angle Scattering Through the 1970s and 1980s, two groups, Engel- It is important for the small-angle scattering experi- man and Moore and coworkers, and May et al., used menter to have a basic understanding of the under- neutron contrast variation to systematically map the lying physics of the technique to avoid being misled. positions of protein and RNA subunits within the We therefore provide a short description of the ribosome leading to a comprehensive map of the 30S essential elements here. subunit5 and a partial map of the larger 50S subu- X-rays and neutrons have properties of plane nit.6 It would take another 8 years before the first waves, that is, amplitude and wavelength, and as high-resolution crystal structure of the large subunit they pass through matter, secondary wavelets are of the ribosome would appear.7 generated by interactions with individual atoms, With the sophistication and, at the time, unique and the resulting coherent scattering can construc- nature of these experiments, the main challenge lay tively or destructively interfere. The diffraction pat- in data interpretation, and experts in theoretical and terns from proteins in crystals that are exploited in computational methods were required for data analy- crystallography are the result of such interference, sis and modeling. These difficulties have largely been between wavelets scattered by atoms within protein overcome by the ready availability of powerful desk molecules that are regularly spaced in the crystal top computers and the development and continual lattice. Small-angle scattering arises from the coher- improvement of data interpretation and modeling ent secondary wavelets that are scattered by atoms tools; today the most widely used is the ATSAS suite within a single molecule, and as a result it is of programs from the Hamburg EMBL (European Mo- observed for molecules in crystals or in solution. lecular Biology Laboratory) group led by Svergun and Although small-angle solution scattering is often coworkers8 as it has been developed explicitly for described as a low-resolution technique (as it does structural biology applications and is readily down- not provide information on atomic coordinates), it is loaded from the web complete with user manuals. more appropriate to describe it as a technique capa- These developments have made small-angle scatter- ble of providing high-precision information with ing accessible to the broader structural biology com- respect to size and shape.9 It is the rotational aver- munity. Consequently, the scope of questions that can aging of the molecules in solution that limits the in- now be answered by small-angle scattering is growing formation content of small-angle scattering more rapidly, and its potential application to biology has than the resolution limits of the experiment. Indeed, never been greater. although crystallographers refer to resolution in As yet, no community-accepted criteria or stand- terms of the highest angle data measured, as it is a ards have been agreed to for the publication of measure of the smallest distances between scatter- small-angle scattering data. In the case of crystallog- ing centers that can be resolved, the small-angle raphy and NMR, the pressure to develop such stand- scattering specialist will refer to the resolution lim- ards grew as the techniques became more widely its more often in terms of the smallest angles for used, and so the development of broadly accepted which data can be measured as it is this resolution standards must also evolve as the use of small-angle limit that determines the longest distances that can scattering continues to grow. As small-angle scatter- be characterized by the data. This effect is a direct ing yields data that are inherently one-dimensional, result of the reciprocal nature of the scattering data and the user invariably is looking to support a with respect to real space dimensions, and the condi- three-dimensional model, overinterpretation of the tion for the minimum angle required to characterize data will always be a risk if not given careful consid- a scattering particle with a given maximum dimen- eration. Importantly, the absence of quality control sion is given below. in sample characterization and data reduction can To interpret scattering data in terms of accurate mislead the experimenter. In this review, we structural parameters, the scattering signal must be describe the small-angle scattering experiment, its measured from a sample of monodisperse, identical range of application, and the necessary quality con- particles. Sample preparation is therefore a critically trol measures. A particular emphasis is given to the important step [Fig. 1(A)] and will be discussed importance of standards for demonstrating sample more completely later. quality, and the power of other biophysical and bio- Although there are several technical challenges chemical methods in providing constraints for mod- associated with the development of small-angle scat- eling that will reduce the likelihood of overinterpre- tering instrumentation, schematically the experi- tation of the scattering data. It is intended that this mental setup is relatively simple [Fig. 1(B)]. A review be a guide to the nonspecialist small-angle highly collimated X-ray or neutron beam is used to

Jacques and Trewhella PROTEIN SCIENCE VOL 19:642—657 643 Figure 1. Roadmap through the small-angle scattering experiment.

644 PROTEINSCIENCE.ORG Small-Angle Scattering for Structural Biology illuminate the sample, usually a protein or macro- protein. The P(r) profile is sensitive to the symme- molecular complex in solution (typically >1mg try and domain structure within proteins and as mL1 in 5–30 lL for X-ray scattering and >3mg such can yield information concerning the shape mL1 in 150–300 lL for neutron scattering). Tradi- and volume occupied by a protein or protein com- tionally, the radiation is of a single wavelength (or plex. An excellent demonstration of the effect of narrow band of wavelengths), although the develop- protein shape on the P(r) curve is reported in Fig- ment of pulsed neutron sources has led to time-of- ure 5, page 1746 of Svergun and Koch.10 Because flight neutron scattering instruments that can use scattering data can only be measured over a finite white radiation to maximize flux. The scattered radi- q range, P(r) calculations depend upon indirect Fou- ation is recorded on a detector, while the direct rier transform methods and as such they depend beam is usually absorbed by a beam stop; the size upon assumptions, such as the fact that P(r) is zero and position of which are key factors determining at r ¼ 0 and at the maximum linear dimension, the minimum angle measured in an experiment. Dmax. As a result, Dmax is a ‘‘soft’’ or model parame- New developments in solid-state devices have led to ter in the interpretation of scattering data, and its detectors that can absorb an intense direct X-ray uncertainty is highly dependent on the quality of beam without incurring damage. the scattering data. Further, data must be meas-

For reasons of mathematical convenience, the ured to q values

(I) as a function of the amplitude of the scattering ally not valid to assign an error to Dmax. vector or momentum transfer, q: From a high-quality small-angle scattering profile, there are two parameters relating to the size 4psin h and shape of the scattering particle that can be q ¼ ; (1) k readily calculated with high precision; the forward (or zero-angle) scattered intensity, I(0), and the ra- where k is the wavelength of the incident radiation, dius of gyration, Rg. I(0) is the intensity of radiation and y is half the angle between the incident and scat- scattered through zero angle (2y ¼ 0). This value tered radiation [Fig. 1(B)]. As k is fixed and y is small cannot be measured, as it cannot be distinguished (typically <3 ), I(q) versus q is essentially the inten- from the radiation that passes through the sample sity as a function of scattering angle. The relationship unscattered (i.e., the direct beam). However, I(0) can between a scattering particle and its contribution to be determined by extrapolation. I(0) is related to the the scattering profile can be mathematically number of scattering particles per unit volume (N) expressed as follows: and the particle volume (V) squared. Alternatively, it Z can be expressed in terms of the mass per unit volume (C), molecular weight (MW), the contrast (Dq), IðqÞ¼ jðqð~rÞq Þei~q~rd~r j2 ; (2) s and the partial specific volume (m) of the particle: where hi refers to the rotational average and qð~rÞq is the difference in scattering density CDq2v2MW s Ið0Þ¼NðDqVÞ2 ¼ ; (3) between the volume element at position ~r within the NA scattering particle and that of the solvent. The mean difference between the particle and solvent scatter- where NA is Avagadro’s number. ing density is termed the ‘‘contrast’’ and is repre- The Rg is defined as the root-mean-squared dis- sented as Dq (Fig. 2, discussed in detail later). tance of all elemental scattering volumes from their Although I(q) versus q is related to the shape centre of mass weighted by their scattering den- of the macromolecule in solution, the profile is not sities. Objects with the same volume but with differ- intuitively informative, and so to interpret a scat- ent shapes have different Rg values. Thus, Rg pro- tering profile in terms of a structure, it is useful to vides information as to the mass distribution within Fourier transform the scattering profile to obtain a particle. the interatomic distance distribution function, P(r), A useful means for quickly estimating values for of the scattering particle [Fig. 1(B)] (P(r) is also Rg and I(0) is the Guinier approximation. In 1939, referred to as the pair distance or vector length dis- Guinier showed that for sufficiently small values of q: tribution function). Just as a diffraction image can be Fourier transformed to obtain the Patterson 2 2 q Rg function that is used to locate heavy atom positions IðqÞ¼Ið0Þe 3 : (4) in X-ray crystallography, so too can an I(q) profile 2 be Fourier transformed to give P(r) (the radial Pat- Thus, a linear fit of ln[I(q)] versus q yields Rg terson function), which describes the probable fre- and I(0) from the slope and y-intercept, respec- quency of interatomic vector lengths (r) within a tively. For globular proteins, this relationship is

Jacques and Trewhella PROTEIN SCIENCE VOL 19:642—657 645 Figure 2.

646 PROTEINSCIENCE.ORG Small-Angle Scattering for Structural Biology true only for qRg < 1.3, while for elongated shapes from a protein in solution is proportional to the the upper limit is smaller, increasingly smaller for square of this contrast, that is, increasingly extended molecules.12 The necessity that a Guinier plot be linear for globular proteins IðqÞ/Dq2; (7) is a rapid and powerful diagnostic of sample quality. where Dq is readily calculated from the atomic com-

A method for determining I(0) and Rg that uses positions of the protein and its solvent. If the mean the entire scattering profile, and which therefore scattering density of the protein is the same as the can be more precise, is to calculate them from the solvent ðqp qs ¼ 0Þ, in practical terms no small- P(r) function. Rg is the second moment of the P(r) angle scattering from the protein is observed, as the function: contributions to the small-angle scattering arising R from the internal density fluctuations are generally 2 2 PR ðrÞr dr insignificant. Contrast variation experiments involv- Rg ¼ ; (5) 2 PðrÞdr ing the systematic manipulation of protein and solvent scattering densities can be used to great while I(0) is the zeroth moment, which corresponds advantage in studies of protein complexes. simply to the area under P(r): As electromagnetic radiation, X-rays interact Z with the electron clouds surrounding each atom. Thus, Dmax Ið0Þ¼4p PðrÞdr: (6) the more electrons about an atom, the more likely it is 0 that X-rays will be scattered. Proteins generally have similar elemental compositions and therefore two different The relative ease with which Rg and I(0) can be proteins will usually have similar X-ray scattering density, calculated provides a rapid means by which struc- and there is no easy and benign way to manipulate the tural information can be obtained from scattering scattering density of the solvent. data. Also, the fact that they can be calculated from Neutrons, on the other hand, are neutral par- several different mathematical models (Guinier or ticles and have no associated electric field. As such P(r)) allows an assessment to be made regarding the they penetrate the electron cloud and are scattered internal consistency and robustness of the data. by atomic nuclei. The scattering powers of nuclei are determined by the properties of the neutron–nucleus Contrast and Contrast Variation interaction and vary in a nonsystematic manner For the purposes of small-angle scattering data anal- with atomic number and isotopes of the same ele- ysis in terms of molecular shape, when the internal ment can exhibit very different neutron scattering density fluctuations within a protein are small with powers. One of the largest differences in neutron respect to the difference between the mean scatter- scattering power is that between naturally abundant 1 2 ing density of the protein ðqpÞ and that of its solvent hydrogen ( H) and its stable isotope deuterium ( H ðqsÞ, one can treat the protein as a uniform scatter- or D). It is therefore possible, in a small-angle neu- ing density object with a mean contrast tron scattering experiment, to have different con-

Dq ¼ qp qs. Equations (2) and (3) then imply that trasts for two interacting proteins if one protein is the intensity of the small-angle scattering signal deuterated. A contrast series is obtained by

Figure 2. Small-angle scattering from a complex between a deuterated and nondeuterated protein: the contrast variation experiment. The figure illustrates contrast variation using a structure (PDB: 3GMR) of T-cell surface glycoprotein CD1d1 in complex with beta-2 microglobulin. Theoretical scattering profiles were generated for the protein complex in which the beta-2 microglobulin component had its nonexchangeable hydrogens deuterated to 60% in silico.66 (A) The proteins each have the same electron density and hence X-ray scattering density and the small-angle X-ray scattering profile therefore yield information on the shape of the entire complex as a uniform contrast (depicted as all black) particle. (B) The neutron scattering contrast for the deuterated (90% gray) and nondeuterated (40% gray) components is distinct, and it is therefore possible to measure scattering from each individual component by solvent matching the scattering density of the other by H/

D substitution in the solvent. The nondeuterated protein will be solvent matched around 40% D2O, whereas the deuterated protein’s solvent match point will be 90% D2O, this value depending upon the deuteration level of the protein (60% in this example). (C) A theoretical set of data acquired for different %D2O in the solvent (a contrast series) yields information on the shapes and dispositions of the deuterated and nondeuterated proteins. From the contrast series, it is possible to extract scattering profiles corresponding to the deuterated and nondeuterated components (red and blue, respectively) and a cross- term (green) that is related to their relative dispositions. Note that because of the smaller size of the deuterated component, the corresponding P(r) needs to be multiplied by a factor of five to observe the curve clearly. Also, the cross-term contains negative values for I(q) and therefore must be plotted on a linear scale.

Jacques and Trewhella PROTEIN SCIENCE VOL 19:642—657 647 recording SANS data in solvents with different must also be strictly avoided. In general, aggrega- ratios of H2O:D2O; in this manner, the contributions tion is not observed by SDS-PAGE and is best moni- of the two components of the complex to the scatter- tored by dynamic light scattering and removed by ing can be systematically varied. Information con- size-exclusion chromatography. A special case of cerning the shape of the individual proteins and aggregation is disulfide-mediated aggregation, which their relative dispositions can then be extracted can appear over time in protein samples carrying from the contrast series (Fig. 2). Greater detail on reduced cysteine residues. The presence of inappro- 13 this subject can be found in Whitten et al., which priate disulfide formation can be detected by SDS- describes MULCh, a useful set of tools for calculat- PAGE run with and without b-mercaptoethanol ing contrasts, extracting component scattering func- (BME). The nonreducing gel will contain higher MW tions, and other analyses for the extraction of struc- species corresponding to dimers, trimers, and so tural information from contrast variation data. forth, of the sample protein if disulfide-mediated aggregation is present. Proteins that contain The Nature of Small-Angle Scattering Data reduced cysteines must be rigorously handled under In other structural techniques, interpretable data are reducing conditions, and the effects of pH carefully usually only obtained when the sample is properly pre- considered as pH can dramatically affect the behav- pared. In crystallography, a diffraction pattern is only ior of SAS linkages. obtained from a good quality crystal, while in NMR a simple inspection of an HSQC can immediately tell the experimenter if the protein is folded and hence if it Importance of protein concentration would be worth while proceeding with further experi- determination ments. Small-angle scattering patterns can always be The small-angle scattering signal is proportional to obtained from any quality of sample, and, as such, ver- the concentration and MW of the macromolecule ification that the scattering particles are monodisperse being measured [Eq. (3)]. If an accurate sample con- and identical is essential before data analysis in terms centration can be measured, then the MW of the of a structural model can proceed. When adequate macromolecule can be estimated from the scattering quality control is not demonstrated, it is not possible to data. This parameter (along with partial specific vol- have confidence in the structural models derived from ume and Dq) can be critical for data evaluation (see small-angle scattering data. later) as an accurate MW determination can be used to demonstrate sample monodispersity. Accurate Preliminary Sample Characterization concentrations are also required if the oligomeriza- The first step in quality control is to ensure that the tion state of the sample is to be investigated. Typi- sample is thoroughly characterized before the scat- cally, concentrations are determined spectrophoto- tering experiment is performed. The stringent criteria metrically by measuring the absorbance at 280 nm, outlined later, and summarized in Figure 1(A), must be using calculated extinction coefficients.14 The accu- met before interpretable scattering data can be expected. racy of this method is related to the extinction coefficient of the protein, its purity, and the absorption Requirements on sample purity properties buffer constituents. Results obtained from The sample to be measured must be highly pure. Mac- proteins carrying no tryptophan residues must be romolecular impurities (protein or nucleic acid) need treated with skepticism as errors significantly to be removed, especially if they are of higher MW greater than 10% have been observed. Inaccuracies than the macromolecule of interest. The scattering in protein concentration can mislead the experi- signal is proportional to the square of the MW [Eq. menter, especially if one is depending on I(0) for the (3)], and therefore small amounts of contamination by determination of the MW or volume of the scattering high-MW species will contribute disproportionately to particle. Great care must be taken to ensure sample the scattering signal and bias the data to larger struc- purity (small amounts of highly absorbing contami- tural parameters than are true for the molecule of in- nants such as nucleic acids can result in overestima- terest. The largest effects will be at the lowest q val- tion of sample concentration). Solvent blanks can ues, but removal of these data from the analysis is not also be a source of error. For example, when using sufficient to ensure accurate structural parameters. DTT to maintain reducing conditions or as a free Purity is best assessed by SDS-PAGE as well as radical absorber to minimize radiation damage (see 280:260 nm absorbance ratio to avoid nucleic acid con- later), one needs to be aware that there can be dif- tamination (where appropriate). ferent rates of DTT oxidation between the protein- containing samples and buffers. These differences Establishing that samples contain monodispere, can result in a net difference in the measured UV identical particles absorbance at 280 nm of a sample against its solvent As stated earlier, contaminant high-MW species blank as DTT absorbs strongly in this region as its must be removed. Similarly, sample aggregation absorbance is dependent on its oxidation state.

648 PROTEINSCIENCE.ORG Small-Angle Scattering for Structural Biology Alternatives to DTT as a reducing agent are BME or cially at synchrotron intensities, to have a free radical TCEP, the latter being preferred as its low volatility absorber, such as DTT or ascorbate, in the solvent. maintains the reducing environment for extended peri- Radiation-induced aggregation must be assessed on a ods of time and does not lead to a UV absorbance mis- case-by-case basis as it depends upon characteristics match between sample and solvent blank. Ascorbate such as molecular mass, composition, and structure of buffers can also be used as free radical absorbers. each individual protein. As the effects are dose-dependent, a useful strategy for X-ray scattering experi- Solvent blank measurements ments is to collect several exposures and compare the The solvent scattering must be subtracted from the resultant scattering profiles. Radiation-induced protein plus solvent scattering to obtain the scatter- aggregation will be evident in increasing Rg and I(0) ing from the protein molecule. Perfectly matched sol- values with time. Multiple exposures allow the exper- vent blanks are important for accurate absorbance imenter to determine how long an exposure the sam- measurements and for scattering data analysis. ple can withstand before the data become unusable. If

Inaccuracies in solvent subtraction manifest mostly no time dependence for the Rg and I(0) values is in the high-q region of the scattering data and can observed, the data from the multiple exposures can be interfere with modeling calculations.15,16 A good test combined into one dataset for analysis. For some labo- for the adequacy of the solvent subtraction is to ratory-based X-ray instruments, it is impractical to col- release the requirement for P(r) to come to zero at r lect data for multiple periods of sufficiently short dura- ¼ 0. If P(0) is positive or negative, then the solvent tion for this approach. In these cases, performing SDS- has been under- or oversubtracted, respectively. PAGE before and after sample irradiation is good prac- It can be difficult to match the solvent perfectly, tice for each new protein under study. Because of the and it is often unavoidable that a small additive cor- low energy of cold neutrons (equivalent to infrared rection to the solvent scattering needs to be made. electromagnetic energies), radiation damage is rarely This effect can be especially problematic in neutron seen in neutron scattering. The term ‘cold neutrons’ scattering experiments because of the large incoher- refers to the fact that the longest wavelength (4–6 A˚ ) ent scattering from 1H that results in an isotropic neutrons are used for small-angle neutron scattering background contribution that can be mismatched as to maximize resolution (qmin) and these wavelengths a result of subtle differences between sample and are obtained by passing thermal neutrons through a solvent measurement, such as very small changes in cold source, such as liquid hydrogen. the path length. Solvent mismatch is often best minimized by using a last step dialysate as the sol- Initial inspection of the scattering data vent blank. Often, samples need to be concentrated Once the scattering data have been reduced to I(q) before the scattering experiment, and it is tempting versus q and solvent subtraction performed to leave to use the filtrate from a centrifugal device as the only the scattering from the molecules of interest, a solvent blank. Our experience suggests that even af- simple and powerful way to initially evaluate the ter extensive prewashing of the membrane, the fil- solvent subtracted scattering data is to view them as trate can be imperfectly matched to the sample (pos- log[I(q)] versus log(q). If the sample contains mono- sibly because of the presence of glycerol on the disperse, identical particles, and the data are meas- membrane). Therefore, concentrated samples are ured to low enough q to reliably characterize their best dialyzed against the appropriate buffer before largest dimensions, then the plot will have a dis- measurement wherever possible. cernable flat region in the lowest q regime.20 The next analysis should be a Guinier plot, Scattering Data Acquisition and Evaluation which is most sensitive to the longest distances pres- Once a ‘‘scattering-quality’’ sample has been ent in the sample. A source of bias for the long-dis- obtained, certain control experiments are required to tance information in the scattering signal is protein assess the validity of the scattering data and exclude aggregation, which can cause an upturn in the Guin- certain sources of interference [Fig. 1(C)]. The fol- ier plot (which can be dramatic or simply appear as lowing describes how to interrogate scattering data a ‘‘smiling’’ Guinier) and associated increases in the and the methods used for demonstrating their observed Rg and I(0) values. A downturn in the robustness. Useful software from the ATSAS suite Guinier plot (the ‘‘frowning’’ Guinier) is symptomatic includes PRIMUS17 for data inspection and GNOM18 of interparticle interference—an effect due to corre- for performing P(r) analysis. lated distances between particles in solution caused by Coulombic repulsion21 (discussed later). Examples Detecting radiation damage of Guinier plots for lysozyme data are shown in Fig- X-ray-induced radiation damage arises from bond ure 3(D–F). Importantly, if aggregation (including breakage and free radical formation in the samples oligomerization) or interparticle interference is suffi- and can be a source of radiation-induced aggrega- ciently subtle, the Guinier plot can be perfectly lin- 19 tion. For this reason, it is often a good idea, espe- ear, but the Rg and I(0) values will not be accurate,

Jacques and Trewhella PROTEIN SCIENCE VOL 19:642—657 649 Figure 3. Effects of interparticle interference and aggregation on small-angle scattering data. It is often difficult to assess sample quality from I(q) plots alone (A–C). Guinier plots (D–F) can be instructive, as deviations from linearity are clear indicators of interparticle interference (E, orange) or aggregation (F, red). The P(r) presented with a single chosen Dmax (G–I) can be deceptive, and it is possible that only severe aggregation is detected (I, red). Behavior of the P(r) at extended Dmax values (J–L) gives the clearest indication of sample quality. It is important to note that the subtle cases (K, dark yellow and L, magenta) may escape detection by these initial data inspection methods, and as such comparison of the data to secondary ˚ standards is essential. In evaluating these differences of around 1 A in Rg, it is important to note that such a difference is well ˚ outside the precision with which Rg can be determined (generally to within a few tenths of A for a small- to medium-sized protein), and that this degree of inaccuracy will significantly bias any 3D modeling performed against the scattering data.

being either too large or too small, respectively, and Another way to detect aggregation is in the thus bias any 3D modeling performed using the scat- behavior of the P(r) function. Proteins do not have tering data.22 A linear Guinier plot is therefore nec- hard surfaces, and as such, the distribution of longest essary, but not sufficient, for the accurate interpre- dimensions is expected to approach zero (at Dmax)ina tation of globular proteins, and good practice is to concave fashion as viewed from above the horizontal always show it along with the secondary standards axis [Fig. 3(G,J)]. An abrupt arrival of P(r) at zero that confirm the scattering particle has the expected suggests that the chosen Dmax is artificially short. volume or mass (see below). Badly aggregated samples may give small peaks in

650 PROTEINSCIENCE.ORG Small-Angle Scattering for Structural Biology P(r) at high r values or the P(r) curve may never interpretation are accurate for the molecule of inter- approach zero appropriately [Fig. 3(I,L)], whereas est. Few published small-angle scattering experi- samples exhibiting interparticle interference will ments report calibrated I(0)s and those that do often reach Dmax at artificially small values [Fig. 3(H,K)]. do not provide sufficient information to demonstrate In some cases, especially where the scattering mole- the accuracy of this calibration. This lack of stand- cules have flexibility, it may be difficult to choose ard practice is a significant issue for those who want

Dmax. In these cases, Guinier-determined Rg and I(0) to assess the reliability of the data interpretation. values may be used as a guide. Importantly, one must Typically, the I(0)s are calibrated in one of two ways: always keep in mind that Dmax is a soft parameter in by comparison with a known particle of similar com- P(r) modeling; for high quality data with accurate position such as a protein standard or by placing the background subtractions Dmax can be chosen with data on an absolute scale using the scattering from reasonable reliability, but confidence in the choice of water. Both methods require accurate protein con-

Dmax depends upon understanding how the P(r) centration determination of the molecule of interest. transform behaves for a range of chosen Dmax values. When the secondary standard is a protein, the The emergence of easy to apply 3D modeling methods standard will typically have a large extinction coeffi- has led to a practice of skipping or failing to report cient at 280 nm and is measured under conditions in P(r) and Guinier analyses, yet these are important which it is known to be monodisperse and free of steps in evaluating data quality and sample integrity. interparticle interference effects (e.g., glucose isom- erase26 or lysozyme27). The measured I(0) values, The importance of measuring data at normalized to concentration (in mg/mL) and multiple concentrations expected MW, should be constant, provided that the As described in Eq. (2), I(0) is proportional to the molecule of interest and the standard are of similar sample concentration (C); however, aggregation or mean contrast and the same partial specific volume interparticle interference effects can complicate this [Eq. (3)]. If the molecule (or complex) has a different relationship. A decrease in I(0)/C with increasing C scattering density than the standard (e.g., proteins is indicative of interparticle interference and will be and polynucleotides), the differences in contrast and accompanied by an apparent decrease in Rg. Such partial specific volume must be accounted for. effects are often linearly dependent on concentration Because I(0) is proportional to the square of the par- and can therefore be eliminated by extrapolation to tial specific volume and contrast, small errors or dif- infinite dilution.23 Alternatively, charge screening ferences in these parameters can result in quite (by increasing the ionic strength of the solvent) or large errors in the MW determinations. Hence, great adjusting the pH to nearer the isoelectric point of care must be taken to understand the assumptions the protein can perturb the Coulombic repulsion and behind these calculations and the accuracy of each reduce the interference effect.24 An increase in I(0)/ parameter.

C, and accompanying increase in Rg with C, indi- The isotropic (q-independent) scattering of water cates concentration-dependent aggregation or oligo- can be exploited to place scattering data on an abso- merization. In the latter case, this can be instruc- lute scale, which allows one to estimate the molecu- tive, as monomer–multimer equilibria may be lar mass of the scattering molecule. The scattering present in solution (an example of such a study is of pure water over a wide range of temperatures is the measurement of the monomer–dimer equilibrium precisely known.28 The ratio between the experimen- constant for the SARS CoV main proteinase25). It tally determined and theoretical water scattering in- may be possible to find a low concentration range tensity is used to apply a multiplicative correction to where the aggregation is eliminated; alternatively, the data, which then describes I in units of cm1. changes in pH or ionic strength may be helpful. A The absolute scaling allows the MW to be calculated concentration series should always be measured to directly by rearranging Eq. (3): demonstrate that the data are free of effects that Ið0ÞN would bias any structural interpretation. The subtle MW ¼ A ; (8) example of interparticle interference shown in Fig- CðDq vÞ2 ure 3 may not have been detected had a concentration series not been performed. where the correct units are essential: C (g cm3), Dq (cm2, which can be calculated using MULCh13), and Standards m (cm3 g1, which can be calculated using NucProt29). Calibrating I(0) to a scattering standard allows the The methods described earlier to determine MW or volume of the scattering molecule to be deter- molecular mass or volume each depend on accurate mined providing its concentration is known. Verifica- measurement of the lowest angle data. Recently, tion that the scattering particle has the expected Fischer et al.15 described a method for determining MW or volume is perhaps the most important mea- molecular volume from the high-angle data, which sure to ensure that the structural parameters and has been shown to be quite powerful and provides

Jacques and Trewhella PROTEIN SCIENCE VOL 19:642—657 651 a way to evaluate data quality independent of sam- terization is indicated by a significant drop in the R ple concentration. The method relies on accurate factor without a concomitant drop in the free-R fac- high-q data and, as such, poor background subtrac- tor.33 In this situation, restraints are applied (such tions and flexible systems can be significant sources as noncrystallographic symmetry and geometric of error. restraints) to reduce the degrees of freedom in the Best practice in scattering experiments is to refined parameters. The limited information content always put the data on an absolute scale (requiring of the small-angle scattering experiment prevents only a water and empty cell measurement), measure the calculation of a free-R factor equivalent, and so a secondary protein standard, and perform the Fi- an understanding of the nature of the modeled pa- scher method. The reason one wants to do all three rameters is essential to avoid overinterpretation. To is that each method has different sources of error that end, an ‘‘Occam’s razor’’ approach is recom- and so agreement between each method combined mended, that is, that additional parameters be intro- with a linear Guinier and a ‘‘well-behaved’’ P(r) func- duced only when simpler models fail to adequately tion can provide confidence that the scattering data explain the data. Additionally, data from complimen- are from samples of monodisperse identical particles tary techniques can be a powerful source of of the expected molecular mass and hence will yield restraints to greatly improve the confidence in the accurate structural parameters. uniqueness of best-fit models. Conversely, inconclu- An example of how one can be misled by inaccu- sive modeling can indicate a need for restraints and rate concentration or partial specific volume infor- hence direct further experimentation. Here, we dis- mation is from our own work that used the NMR cuss some of the applications of small-angle scatter- structure of the bacterial sporulation inhibitor, ing, the type of analyses that are appropriate, and Sda,30 to interpret solution scattering data. We the nature of additional information that can be reported that Sda was dimeric in solution for the used to provide restraints. conditions of our measurements based on an I(0) analysis that turned out to use insufficiently accurate concentration values for Sda.31 Sda is a small High-resolution structure validation and (46-residue) protein with no tryptophan residues refinement and an unusually weak UV extinction coefficient. One of the simplest and most popular uses for small- Subsequent to our scattering experiments, we solved angle scattering data is structure validation. The the crystal structure of Sda and observed a tight theoretical scattering from atomic models of proteins hexamer that caused us to test our earlier conclu- can be easily calculated using CRYSOL34 or CRY- sions from the scattering data.32 Multiangle laser SON35 and evaluated against measured scattering light scattering combined with a reexamination of data. Atomic models for proteins can be obtained by the NMR data suggested that the trimer was weakly crystallography or NMR, or theoretical models can associated and probably an artifact of the high pro- be built by homology modeling (e.g., using SWISS- tein concentration required for structural analysis. MODEL36). X-ray crystallography is the dominant Further reexamination of the scattering data method of protein structure determination but revealed that the trimer was a significantly better because of the nature of crystal packing, the solution fit to the scattering data than the dimer; the v2 for structure or oligomeric state may not be clear. In the the fit dropping to 0.85 (with no steric clashes) from case of release factor 1 (RF1, responsible for termi- 1.08 (with some steric clashes). This example serves nation of translation in E. coli), a more compact as an important cautionary tale demonstrating the form of the protein was observed by crystallography need not only for accurate data evaluation and a compared with that observed in complex with the good understanding of error propagation in the data ribosome by electron microscopy (EM).37 Small-angle but also the value of having multiple techniques X-ray scattering was able to resolve these differen- available for structure analysis. ces by demonstrating that the more extended (EM) form was present in solution, and that the compac- Data Analysis and Complementary Information tion was an artifact of crystallization. The specific analysis undertaken with small-angle Similarly, ambiguities in generated NMR struc- scattering data largely depends on the nature of the tures have been resolved by comparison against problem being investigated and the additional infor- scattering data. NMR provides short distance mation available [Fig. 1(D,E)]. As stated above, rota- restraints, and hence scattering data can provide tional averaging limits the information content in a additional long distance restraints to improve solu- small-angle scattering experiment. As such, the data tion structures. Methods have recently been devel- are susceptible to overinterpretation with the oped to corefine NMR and scattering data, thereby increasing parameterization of any modeling calcula- increasing accuracy of structure determination of tion. This problem is not unique to small-angle scat- large proteins by NMR.38–41 In these corefinement tering. In crystallographic refinement, overparame- methods, it is essential to have precise and accurate

652 PROTEINSCIENCE.ORG Small-Angle Scattering for Structural Biology data if the objective is to increase the accuracy of It is unusual for ab initio structures to be pre- the derived solution structures. sented alone as they are highly parameterized mod- The protein data bank requires that the rele- els and seldom yield biologically relevant informa- vant ‘‘biological assembly’’ be reported during struc- tion. As small-angle scattering provides information ture deposition. Yet, crystallography and NMR fre- on the large-scale features, it is often possible to quently yield ambiguous results as to the oligomeric model multisubunit proteins based on high-resolu- state of the protein. Small-angle scattering can be a tion structures of domains, either of the protein in simple means for determining the biological assem- question or from structural homologues. Although it bly and is becoming increasingly utilized in struc- is possible to superpose the atomic structures on the ture reports. Recent examples include the functional ab initio model using SUPCOMB,48 it is often more dimer of superoxide dismutase from Alvinella pom- useful, and more revealing, to perform rigid-body pejana42 and the autoinhibitory dimer of the human refinement against the scattering data using SAS- MAP kinase, MEK6.43 REF.49 As one or more molecules are free to move in Although scattering data are significantly chal- space, rigid-body refinement can also suffer from lenged in proving any model correct, they can overparameterization, and multiple nonunique solu- unequivocally prove a model wrong or incomplete, tions may be obtained. To reduce this problem, dis- providing that the data are of high quality and dem- tance and symmetry constraints (obtained from mu- onstrated to be from the molecule of interest. A clas- tagenesis, FRET, or residual dipolar coupling from sic example of a case when a single crystal structure NMR) can be included in the modeling calculation. did not tell the complete story is the original scatter- SASREF is also capable of modeling against multiple ing work on calmodulin and troponin C44 that datasets, such as those derived from a neutron con- showed distinct differences between the crystal and trast variation series or X-ray data from subcompo- average solution forms that were subsequently nents of a modular protein or complex. This increase shown to be important in the functioning of these in- in the number of input scattering curves again helps tracellular calcium receptors. in addressing the problem of the uniqueness of possible solutions. Here again, however, care needs to be taken to demonstrate that all the scattering Characterization of multidomain proteins curves relate to the same structure; for example, in One of the major advances in small-angle scattering the case of a neutron contrast series, I(0) analysis is in recent years is the ability to reconstruct a molecu- needed to demonstrate that there is no D2O-induced lar shape from the scattering data alone. Previously aggregation; in the case of X-ray scattering from thought to be impossible, modern ab initio algo- subunits or truncated proteins, one needs to demon- rithms such as DAMMIN,45 DAMMIF,46 and strate that the truncation or disassociation has not MONSA (http://www.embl-hamburg.de/ExternalInfo/ induced conformational changes. Research/Sax/monsa.html) are able to represent the Accurate rigid-body modeling against scattering particle by finite volume elements (or dummy atoms) data requires complete structures. In practice, model and employ simulated annealing to fit the experi- structures are often missing loops and/or interdo- mental data. The calculation is constrained to pro- main linkers that may be disordered. The program duce a ‘‘physically sound’’ model (i.e., compact and BUNCH49 is capable of performing the rigid-body interconnected), and symmetry constraints may also refinement while modeling missing loops as dummy be applied. residues. BUNCH is especially useful for multido- The central problem in ab initio shape restora- main proteins where X-ray scattering has been per- tion is that of uniqueness, that is, there may be sev- formed on various partial constructs, such as poly- eral models with equally good fit to the data. The pyrimidine tract binding protein.50 dummy atom approach allows multiple models to be The use of a combination of ab initio shape res- generated. The program DAMAVER47 may be used toration and rigid-body refinement is demonstrated to place models into structurally similar classes and by the study of the N-terminal domain organization then generate an average structure from each class. of cardiac myosin binding protein C (cMyBP-C).51 It is tempting to use the number of models gener- DAMMIN revealed an elongated structure consistent ated in each class as an assessment of the likelihood with four folded domains. With that information, it that average structure is correct. However, this was possible to construct homology models (consist- probability argument is insufficient grounds for dis- ent with analysis by circular dichroism spectropo- missing a particular class, and additional informa- larimetry) for the two unknown domains. Combined tion (such as structure predictions, domain models, with NMR structures for the known domains, a or EM data) is required. On the other hand, one rigid-body model was refined with BUNCH to yield class of models having a significantly greater good- a model consistent with the original DAMMIN struc- ness-of-fit measure to the experimental data can be ture. This model was then used in a small-angle grounds for favoring that averaged model. neutron scattering study to demonstrate that

Jacques and Trewhella PROTEIN SCIENCE VOL 19:642—657 653 cMyBP-C decorates actin filaments with implications that is, to collect data at multiple %D2O solvent confor the regulation of heart muscle contraction.52 ditions [Figs. 1(D) and 2(C)]. This strategy allows Other demonstrations of ab initio modeling of such the extraction of scattering functions describing modular proteins include the transcriptional regula- each component and the cross-term relating their tor PUR-a53 and the protein filamin,54 which cross- positions in space.13 Neutron contrast variation links the cell membrane with the cytoskeleton. In studies also obviate the need for perfectly matching the latter example, the small-angle scattering the component and solvent scattering densities. A results drove further NMR studies to reveal a previ- good example of such a scenario is the complex ously unseen immunoglobulin domain-pairing formed between the sporulation histidine kinase, interaction. KinA, and its inhibitor, Sda, from Bacillus subtilis.31 By deuterating Sda and performing small-angle Modeling multisubunit complexes neutron scattering with contrast variation on the Small-angle X-ray scattering can be used to study complex, it was possible to extract structural infor- protein complexes and is particularly informative if mation for each component. The binding of the in- it is expected that one component of a complex hibitor caused a compaction of the dimeric KinA undergoes a conformational change upon binding. (seen as a reduction in Rg and Dmax compared with Once again, the dumbbell-shaped calmodulin pro- the X-ray scattering), and an increase in the appa- vides a classic example of small-angle scattering rent dimension of the Sda component resulting from being used to detect the dramatic conformational col- the two Sda molecules binding on opposite sides of lapse of the protein upon binding its target peptide the kinase dimer. A structural homologue of KinA and advancing our understanding of how this cal- and the NMR structure of Sda were used in rigid- cium receptor functions.55 Larger complexes can also body modeling against the entire contrast series be studied by this method, such as that formed data (including X-ray scattering) using SASREF7 between proliferating cell nuclear antigen (PCNA) (which incorporates the contrast information). A and DNA ligase56 where a combination of ab initio similar experiment was performed for the complex and rigid-body modeling was used to model the between KinA and its second inhibitor KipI [pic- complex, which clearly showed a 1:1 ratio of tured in Fig. 1(D), third panel from left].60 The PCNA:DNA ligase, the latter adopting a more open results of these two experiments showed that the conformation. inhibitors bind the base of the KinA dimerization In the calmodulin example, the peptide binding domain and not the flexible hinge between the dime- partner was sufficiently small as to not contribute rization and catalytic domains as had been previ- significantly the scattering, whereas in the PCNA- ously proposed.30 With this information, redirected DNA ligase example, the two proteins are so large, mutagenesis and biochemical studies61 led to new and with such different shapes that determining understanding of the mechanisms involved in bacte- their relative dispositions was possible. However, rial signaling pathways; particularly, that KipI and accurate determination of the shapes and disposi- Sda inhibited not only the autokinase reaction but tions of proteins in complexes generally requires also the phosphotransferase reaction. The crystal using small-angle neutron scattering with contrast structure of a homologous kinase, KinB, from Geo- variation. bacillus stearothermophilus, also was solved in com- As seen in Figure 2(B), one can ‘‘solvent match’’ plex with Sda,62 confirming that the Sda binding a component of a biomolecular complex by adjusting site was correctly predicted by the neutron scatter- the D2O composition of the solvent so that the con- ing model, albeit with a 180 rotation of Sda—infor- trast of one component is zero. If two components of mation that was beyond the resolution of the small- a complex have different scattering densities (e.g., angle scattering experiment. protein–nucleic acid or protein–deuterated protein complexes) solvent matching one component yields Flexible systems neutron scattering only from the other. This As small-angle scattering is a solution technique, approach has been successfully employed for the the data are time and ensemble-averaged. Thus, it is study of protein–detergent complexes such as lipid possible to measure data for flexible systems. If a transport protein apolipoprotein B-10057 and for pro- system cannot be adequately described by simple tein–deuterated protein complexes such as the syn- rigid-body modeling, it is possible to consider confor- aptic proteins neuroligin and neurexin.58 The latter mational flexibility using an ensemble model with case is especially pertinent to demonstrating the the ensemble optimization method63 or BIBLIO- quality of modeling SANS data as it was soon fol- MOD.64 Because of the very high parameterization lowed by a crystal structure,59 which revealed the of ensemble modeling, extreme care must be taken same subunit arrangement. to ensure that data are not being overinterpreted. Although solvent matching is feasible, it is often Ideally, evidence for flexibility should be obtained to better to perform a contrast variation experiment, demonstrate that ensemble modeling is a valid

654 PROTEINSCIENCE.ORG Small-Angle Scattering for Structural Biology approach, such as disorder predictions, EM data, 3. Pardon JF, Worcester DL, Wooley JC, Tatchell K, Van- NMR ensembles, or missing electron density in crys- holde KE, Richards BM (1975) Low-angle neutron-scat- tal structures. tering from chromatin subunit particles. Nucleic Acids Res 2:2163–2176. An excellent example of a flexible system stud- 4. Luger K, Mader AW, Richmond RK, Sargent DF, Rich- ied by small-angle scattering is protein kinase R mond TJ (1997) Crystal structure of the nucleosome (PKR), a key component of the interferon antiviral core particle at 2.8 angstrom resolution. Nature 389: pathway.20 PKR is known to carry three folded 251–260. domains (whose structures have been solved) demon- 5. 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