Structural analysis of flexible proteins in solution by small angle X-ray scattering combined with...

Journal of

ARTICLE IN PRESS

www.elsevier.com/locate/yjsbi

Journal of Structural Biology xxx (2006) xxx–xxx

StructuralBiology

Structural analysis of flexible proteins in solution by small angleX-ray scattering combined with crystallography

Susan E. Tsutakawa a, Greg L. Hura b, Ken A. Frankel c,Priscilla K. Cooper a, John A. Tainer a,d,*

a Life Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USAb Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

c Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USAd Department of Molecular Biology and The Skaggs Institute for Chemical Biology, The Scripps Research Institute, 10550 North Torrey Pines Road,

Mailstop: MB4, La Jolla, CA 92037, USA

Received 26 May 2006; received in revised form 23 September 2006; accepted 25 September 2006

Abstract

In the last few years, SAXS of biological materials has been rapidly evolving and promises to move structural analysis to a new level.Recent innovations in SAXS data analysis allow ab initio shape predictions of proteins in solution. Furthermore, experimental scatteringdata can be compared to calculated scattering curves from the growing data base of solved structures and also identify aggregation andunfolded proteins. Combining SAXS results with atomic resolution structures enables detailed characterizations in solution of mass,radius, conformations, assembly, and shape changes associated with protein folding and functions. SAXS can efficiently reveal the spatialorganization of protein domains, including domains missing from or disordered in known crystal structures, and establish cofactor orsubstrate-induced conformational changes. For flexible domains or unstructured regions that are not amenable for study by many otherstructural techniques, SAXS provides a unique technology. Here, we present SAXS shape predictions for PCNA that accurately predict atrimeric ring assembly and for a full-length DNA repair glycosylase with a large unstructured region. These new results in combinationwith illustrative published data show how SAXS combined with high resolution crystal structures efficiently establishes architectures,assemblies, conformations, and unstructured regions for proteins and protein complexes in solution.� 2006 Elsevier Inc. All rights reserved.

Keywords: Small angle X-ray scattering; Diffraction; Protein conformation; Structural analysis; Crystallography; DNA repair

1. Introduction

Proteins are dynamic flexible molecules in solution, andconformational changes are often as important for proteinfunction as the catalytic active site. Flexibility enables pro-teins (a) to be regulated allosterically either by post-trans-lational modification, by small molecules or by otherproteins; (b) to have multiple functions that can be coordi-nated; (c) to interact with multiple structurally distinct

1047-8477/$ - see front matter � 2006 Elsevier Inc. All rights reserved.

doi:10.1016/j.jsb.2006.09.008

* Corresponding author. Fax: +1 858 784 2289.E-mail address: [email protected] (J.A. Tainer).

Please cite this article in press as: Tsutakawa, S.E. et al., Structural aBiol. (2006), doi:10.1016/j.jsb.2006.09.008

partners through the same region that can mold to differentshapes; (d) to have reversible interactions through entropicdisorder-to-order transitions, (e) to have increased proces-sivity or specificity by molding to the substrate or to theinteracting partner (Dyson and Wright, 2002).

Flexibility, as a characteristic of proteins, may take onmany forms. Flexibility can be conferred through flexiblelinkers connecting rigid domains or through two domainsthat can move relative to each other through a pivot point.It also can include large stretches of sequence that canassume multiple conformations that may or may not havesecondary structure on their own (Dyson and Wright,2002). In this paper, we define these latter regions as

nalysis of flexible proteins in solution by small angle ..., J. Struct.

mailto:[email protected]

2 S.E. Tsutakawa et al. / Journal of Structural Biology xxx (2006) xxx–xxx

ARTICLE IN PRESS

unstructured. These regions become structured upon bind-ing to substrate, post-translational modification or interac-tion with partners. This disorder-to-order transition eitherprovides a structural platform for the catalytic function orpromotes secondary interfaces for interactions with otherproteins and propagation of a signal (Dyson and Wright,2002).

Eukaryotic proteins are more likely than bacterial pro-teins to be predicted to have unstructured regions. Geno-mic analysis by PONDR, a disorder prediction program,predicts that 2–21% of bacterial proteins within a particu-lar genome have long unstructured regions (>50 aa), com-pared to 25–41% of eukaryotic proteins (Dunker et al.,2000, 2005). This increased frequency of eukaryotic pro-teins with disordered regions is likely correlated with themore complex architecture. It has been observed thateukaryotic complexity is not encoded so much in addition-al proteins but in longer gene sequences (Lander et al.,2001; Venter, 2001). Extensions added during evolutiontypically provide platforms for complex protein–proteininteractions and post-translational modification that helpcoordinate enzymatic or signalling pathways. Given theregulatory nature of these regions, they are likely to beintrinsically unstructured or flexible.

Characterization of flexible proteins in solution can pro-vide the structural framework for understanding proteinfunction. However, high resolution techniques are not welladapted for studying flexible proteins, particularly largeprotein complexes, in solution. Protein crystallographyprovides high resolution atomic structures, and if one islucky, conformational changes can be observed throughsubunits not symmetrically related in the asymmetric unit,regions of increased B values, and distinct crystals with dif-ferent cofactors or partners. However, limiting domainmovement by crystal packing is still a major concern formost protein crystals, and regions that are flexible are ofteneither not visible in the electron density or have beenremoved to enable crystallization. Nuclear magnetic reso-nance (NMR) can provide atomic resolution informationof proteins in solution, but it is still limited by the size ofthe proteins that can be routinely studied. Electron micros-copy (EM), in particular cryo-EM, can provide valuablelow resolution information on proteins in solution throughsingle particle analysis. Cryo-EM can be especially power-ful in combination with computational fitting of compo-nent crystal structures so that detailed informationrelevant to biology and function can be obtained, such asin the recent cryo-EM and crystal structures of pathogenicpili and their pilin subunits (Craig et al., 2006). However,cryo-EM requires very large protein or protein complexes(>300 kDa) or unusual symmetry for effective analyses.

Small angle X-ray scattering (SAXS) is more broadlyable to provide low resolution structural information forflexible proteins in solution to complement crystallograph-ic analyses. Although SAXS is not a high resolutionmethod, detailed knowledge about bio-macromolecules,increased computing power and recent developments in


algorithms have enabled extraction of much more detailedinformation from SAXS data analysis (Chacon et al.,1998; Petoukhov and Svergun, 2003, 2005; Takahashiet al., 2003; Zipper and Durchschlag, 2003). SAXS is alsomost powerful as a hybrid method since combination withother structural information can provide significant bio-logical insight into protein conformations in solution.The relative ease and speed of SAXS sample preparationand data collection means that SAXS can readily be usedin conjunction with other methods. In particular, largecomplexes and flexible proteins are not easily amenablefor crystallography, but pieces of complexes and the rigidportions of flexible proteins are. In these cases, SAXS canbe an extremely powerful and complementary method.Recent SAXS programs which allow the incorporationof high resolution structures as a starting point uponwhich further SAXS analysis may be conducted, buildupon the success of protein crystallography. SAXS analy-sis can reveal the structures of flexible proteins, proteincomplexes, induced conformational changes, and unstruc-tured regions that are not amenable to high resolutionprotein crystallographic methods. Furthermore, SAXScan characterize the assembly, architecture, and confor-mational states for reversible molecular complexes thatform in response to environmental stress and cell state.These dynamic or reversible complexes are critical forkey decisions points in cell biology including pathwaycontrols and coordination. Here, we discuss applicationsand new results of SAXS analysis to protein structureanalysis in the context of informative published SAXSresults including several from our own research or fromassociated researchers at the SIBYLS beamline locatedin the Advanced Light Source at Lawrence BerkeleyNational Laboratory.

2. SAXS basics

When matter is irradiated by an X-ray beam, one of theprimary interactions is the elastic scattering of X-rays byelectrons. X-rays thus scattered by spatially correlated elec-tron pairs constructively and destructively interfere inaccordance with Bragg’s law. The longer the electron pairdistance, the smaller the angle at which interference effectsare observable. This is readily apparent by contrasting thescattering profiles of large proteins relative to small pro-teins. Large proteins will scatter more strongly at smallerangles than small proteins and much more strongly thanbuffer. In the last case electrons are exclusively correlatedon small length scales. Traditionally SAXS was definedby scattering at angles where the small angle cosine andsine approximations apply. However, practically SAXSanalysis may use scattering at angles up to the primaryscattering peak of water at a momentum transfer of�2 A�1 which thereafter overwhelms all other signals.(Momentum transfer s = (4p/k)sin (h/2) where k is thewavelength of X-rays and h is the scattering angle relativeto the incident beam.) For proteins randomly oriented in


S.E. Tsutakawa et al. / Journal of Structural Biology xxx (2006) xxx–xxx 3

ARTICLE IN PRESS

solution, all configurations of the macromolecule are sam-pled during the experiment and the scattering profile is azi-muthally symmetric around the primary beam. Because thesignal difference between buffer and protein is small, thescattering profile of the buffer solution must be subtractedfrom that of the protein. This also removes backgrounddue to parasitic scattering of the primary beam; a ‘‘halo’’of X-rays surrounding the primary beam, and ultimatelythe limiting factor on the smallest angles attainable at agiven instrument. The scattering profile is dependent onthe size and shape of the macromolecule and is a unique‘‘signature’’ of the protein. In their study of the proteindata bank, Sokolova and coworkers have shown that notwo unique structures have identical calculated scatteringprofiles (Sokolova et al., 2003a,b).

IðsÞ ¼ 4pZ Dmax

0

hqð~rÞ � qð�~rÞi sinðsrÞsr

r2 dr ð1Þ

pðrÞ ¼ r2hqð~rÞ � qð�~rÞi ð2Þ

The X-ray scattering from proteins is a function of theirelectron density. The scattering profile from a buffer-sub-tracted macromolecular solution is the Fourier transformof the spatially averaged auto-correlation function of theelectron density (Eq. 1) (Feigin and Svergun, 1987) whereI is the intensity, q(r) is the electron density, Dmax is themaximum dimension of the protein and r is the vectordescribing the spatial position. The spatially averagedauto-correlation function of the electron density (alsoknown as the Patterson function) multiplied by r2 is calledthe pair distribution function or p(r) and is shown in Eq.2. For particles with homogeneous electron density thep(r) plot is an electron pair histogram describing the num-ber of electrons within a macromolecule that are a dis-tance r away from one another. For particles withheterogeneous electron density such as DNA–proteincomplexes the p(r) is a histogram of distances, withinthe particle, weighted by the product of the electron den-sities at the two ends of the connecting vector. From thisplot, the maximum intraparticle distance (Dmax), theradius of gyration (Rg) as well as gross features of theshape (globular, elongated, bilobal) can be determined(Svergun and Koch, 2003).

Helpful for determining the stoichiometry of complexcomponents in the solution, the forward scattering is pro-portional to the number of electrons squared and thus alsoproportional to the molar mass squared. Practically, exper-imenters may determine the mass of a particle by compar-ing the forward scattering of a protein whose mass isknown to the forward scattering of the protein in question.The concentration of protein in the solutions must also beknown. This process allows the experimenters to extractthe instrument dependent proportionality constant for anabsolute mass determination. SAXS is less exact if thereis heterogeneity in the complexes formed, but this limita-tion may be overcome through in-line isolation of complex-es by gel filtration chromatography.


3. Practical aspects of SAXS data collection

Multiple beamlines are set up for SAXS of biologicalsamples around the world, and more SAXS beamlinesare in the planning stages. We manage the SIBYLS beam-line at the Advanced Light Source, which is a uniqueresource with two endstations, one for protein crystallogra-phy and one for small angle X-ray scattering (Trame et al.,2003). The purpose of the design was to facilitate synergybetween these two structural techniques, and the rapidexchange between endstations (<1 h) enables users to doboth analyses on the same trip. Another characteristic ofthe SIBYLS beamline for SAXS analysis is that the beamis fairly broad at the sample position (typically4 · 1.5 mm) but is focused at the detector to a300 · 300 lm spot. The benefit for SAXS analysis is thatthe sample area is maximally exposed to the beam butthe beam is narrowly focused at the detector and therecan be a correspondingly small beam stop. The monochro-mator is actually two double crystal monochromators, a setof Si(1 11) single crystals that provides high spectral resolu-tion (dk/k is less than 10�4) and a set of multilayer crystalsthat provides lower spectral resolution (dk/k is less than10�2) but substantially higher flux. The automated mono-chromator allows rapid wavelength tuning without achange in the target position, and the wavelength range isbetween 8 and 14 keV for the Si(1 11) crystal monochroma-tor and 8 and 12 keV for the multilayer. For SAXS studies,the ability to change wavelength enables optimization ofdata collection for protein size. For most proteins between30 and 150 kDa, we routinely use approximately 1.11 Awavelength. There are also four slits arranged from themonochromator to the sample station to collimate thebeam and minimize parasitic scattering that would increasethe background scatter.

The equipment required for measuring SAXS data isvery similar to standard protein crystallography (PX).The predominant difference is that the beam stop anddetector are often a meter or more away from the samplein order to spread the SAXS signal over a larger area fordetection and for separation of the signal from the primarybeam. At the SIBYLS beamline, the sample cell (developedby Hiro Tsuruta) is 1 mm in thickness with mica windowsand holds 12 ll of solution. The two dimensional detectoris a MAR165 CCD detector, and the sample is separatedfrom the detector with a 1.5 m flight tube under vacuumto minimize air scatter. Although scattering quality is highlyprotein dependent, we have obtained accurate shape pre-dictions with protein concentrations as little as 2 mg/ml(see below). Dilution curves are used to make sure that pro-teins remain monodisperse at high protein concentrationsduring data collection. The buffer also significantly scattersthe X-ray, and a buffer blank is used to subtract scatterfrom the buffer solution as well as eliminate any systematicerrors in the data. Although minimization of electron densebuffer components is advised, we generally find that proteinmonodispersity is a more important criterion. Thus, we



ARTICLE IN PRESS

have collected data on samples in high salt buffer (1 MNaCl) and in phosphate-based buffers. We have also beenable to collect data on samples in detergents but havefound not all detergents to be amenable to SAXS studiesdue to high intrinsic scattering of the detergents. Moreinformation about the beamline can be found on our website: http://www.bl1231.als.lbl.gov.

One of the most powerful aspects of SAXS is that datacollection is rapid. We generally take two exposures, ashort exposure of 5–10 s to obtain accurate data close tothe beam stop and a long exposure of 50–100 s for moreaccurate high resolution data. Most samples take between10 min and 1 h, depending on the number of protein con-centrations that are run. Since most of the time is spentin sample handling, addition of sample handling robotswill greatly accelerate the process.

Fig. 1. Ab initio shape prediction by SAXS analysis. SAXS analysis ofOGG1, glucose isomerase, and PCNA collected at the SIBYLS beamline,ALS. (A) Buffer-subtracted scattering profiles and (B) electron pairdistribution plots of OGG1 (blue), glucose iosmerase (purple), and PCNA(green). Human OGG1 (5 mg/ml) was analyzed in 25 mM Tris pH 7,150 mM NaCl, 1 mM TCEP, 10% glycerol, 0.5 mM EDTA. Work wasdone in collaboration with Tapas Hazra and Sankar Mitra (University ofTexas, Medical Branch, Galveston). Streptomyces rubiginosus glucoseisomerase (Hampton Research) at 2 mg/ml was analyzed in 20 mM TrispH 7.5, 1 mM TCEP. Human PCNA (4 mg/ml) was analyzed in 25 mMTris pH 7.6, 150 mM NaCl, 0.1 mM EDTA and 5 mM DTT. Work wasdone in collaboration with John Pascal and Tom Ellenberger (HarvardUniversity Medical School). (C) Averaged and filtered ab initio shapeprediction calculated by GASBOR and aligned using the DAMAVERprogram suite (Volkov and Svergun, 2003). The DAMAVER programsuite was used to overlay the shape predictions onto the crystals structures(ribbon) of, respectively, OGG1 (1KO9.pdb), glucose isomerase(8XIA.pdb), and PCNA (1AXC), (Bjoras et al., 2002; Carrell et al.,1989; Gulbis et al., 1996).

4. Applications of SAXS to structural analysis

4.1. Ab initio shape prediction

Given that no two proteins with unique structures in thePDB have the same calculated SAXS profile (Sokolovaet al., 2003a), the combination of SAXS data and pro-tein-based knowledge may in fact determine unique threedimensional structures at low resolution. However, currentSAXS ab initio shape prediction are more accurately lowresolution (�10 A) envelopes whose calculated scatteringcurves are consistent with the experimental scatteringcurve. Very basic protein properties are used to significant-ly reduces the number of acceptable three dimensionalenvelope that agree with the experimental scattering curve.Comparison of the ab initio shape predictions from exper-imental SAXS data of proteins in solution and their corre-sponding crystal structures demonstrate that ab initioprograms can be surprisingly accurate.

Eq. (1) describes how the scattering profile may be cal-culated from structural models of bio-macromolecules.Several ab initio algorithms have been written to create alow resolution envelope whose calculated scattering curvematches the experimental data (Chacon et al., 1998;Svergun, 1999; Svergun et al., 2001; Walther et al., 2000).For example, one of the most used algorithms, GASBOR,compares calculated scattering profiles from thousands ofconfigurations of a chain of dummy residues to the mea-sured scattering curve (Svergun et al., 2001). Simulatedannealing is used with additional penalties for non-pro-tein-like density. Typically, GASBOR is run multiple(>10) times and the results are averaged for a final shape.A comparison of individual runs may be evaluated for con-vergence on a final model. Often all runs converge on asimilar structure and the final accuracy and precision ofthe experiment is determined by the finer agreementbetween individual runs. GASBOR may also be startedfrom a crystal structure that includes the hydration shellor symmetry may be enforced. The accuracy of the final


model is expected to vary from protein to protein depend-ing on its shape, size and if symmetry is enforced.

We have collected and analyzed a wide variety of pro-teins at the SIBYLS beamline. Fig. 1 shows several exam-ples of shape predictions determined from experimentalSAXS data collected at the SIBYLS beamline using GAS-BOR on proteins with known structure. In these examplesno information from the crystal structure was used as inputto the GASBOR program. The excellent agreement betweenthe SAXS models and the respective crystal structures dem-onstrates that SAXS analysis can generate accurate predic-tions of the overall protein envelope. These proteins differ insize, shape, and symmetry. OGG1 is a monomeric 39 kDaprotein that acts as a glycosylase in DNA repair. The shapeprediction for OGG1 roughly follows the surface of theOGG1 crystal structure and is notably asymmetric. Glucoseisomerase is a tetrameric protein of 173 kDa and is involvedin xylose metabolism in bacteria. This shape prediction wascalculated from scattering of a 2 mg/ml protein solutionand with P4 symmetry enforced. Proliferating cell nuclearantigen (PCNA) is a trimeric 86 kDa protein that is


http://www.bl1231.als.lbl.gov


ARTICLE IN PRESS

involved in a number of DNA transactions such as replica-tion and DNA repair. Information about the symmetry ofthe protein was not used as input to the program. In partic-ular, the shape prediction for PCNA was remarkable in thatit accurately predicted the trimeric ring structure and thehole that is formed. The hole in the crystal structure isapproximately 35–36 A across. In other protein analyses,we have found holes to be generally problematic for GAS-BOR. The differences between the SAXS shape predictionsand the crystal structures reflect a number of parameters,including the SAXS capability of detecting flexible regions,relative increase in flexibility of proteins in solution asopposed to packed in a crystal, and the low resolution nat-ure of the SAXS data. The latter parameter may be partiallydecreased by obtaining SAXS data out to higher angles(Davies et al., 2005), but there is a theoretical limit to theresolution of the SAXS data.

Understandably, there are caveats to ab initio shape pre-dictions and to SAXS analysis in general. One of the areasneeded for development in SAXS analysis is the confidencelevel in the shape reconstruction. It is well appreciated byeveryone in the field that multiple different shape predic-tions can agree to similar extents with an experimental scat-tering curve. Convergence of the majority, if not all, of theshape predictions to a unique shape is indicative of a cor-rect solution. However, the number of runs and the qualitymeasures of the accuracy in shape predictions have variedwidely in different publications involving SAXS data. Amore quantitative measure of the solution uniqueness isneeded. GASBOR is particularly useful when a great dealis already known about the structure, such as the multimer-ization state and symmetry. However, results are less reli-able when Dmax, an input parameter in GASBOR, isdifficult to assign. Both long flexible regions and the cor-ruption of the monodispersed signal due to small amountsof aggregation result in difficult Dmax assignment. Part ofthe overall problem is intrinsic to the nature of flexible pro-teins in solution. Heterogeneity in conformation cannot becurrently identified or accounted for unless structures arealready known or postulated. Ab initio shape predictionsbased on mixed populations give averaged conformationsand can therefore be misleading (Heller, 2005). Thus, anarea for development is the identification and assignmentof multiple conformations that can be input into SAXSprograms such as OLIGOMER (Konarev et al., 2003).The number of amino acids is also a required input forGASBOR and may be difficult to determine for large olig-omeric complexes where the stoichiometry is not known.As with any single technique, conclusions based on SAXSdata analysis need to be carefully considered and should betested and validated with additional experiments.

4.2. Assembly of individually determined structures into a

complex

Successful high resolution structure analysis oftenrequires the divide-and-conquer approach, where individu-


al domains or subunits but not the whole protein or com-plex can be crystallized or studied by NMR. SAXS datacan provide a framework for piecing together individualhigh resolution structures. On a simple but still informativelevel, SAXS can be used to observe complex formationbased on the Rg. For example, a Rg of 50.9 A calculatedby SAXS analysis of an Mre11/Rad50 ATPase complexindicated that the complex formed a heterotetramer withtwo Mre11 subunits and two Rad50 ATPase domains(Hopfner et al., 2001). Addition of ATP to the heterotetr-amer reduced the Rg to 46.3 A, suggesting that ATP con-formationally induced a tighter complex formation.However, a more direct and still powerful approach is tocompare the scattering curves calculated from a rigid bodyrefinement model to the experimental curve.

An example of the utility of comparing scattering curvescomes from auto-inhibited Ca2+/calmodulin-dependentprotein kinase II (CAMKII). The crystal structures of theindividual domains were known, and there were EM struc-tures of the whole protein (Hoelz et al., 2003; Kolodziejet al., 2000; Morris and Torok, 2001; Rosenberg et al.,2005). CAMKII is a dodecameric enzyme with two hexa-meric rings formed by a central association domain com-plex, and the kinase domains are fixed exterior to thecentral rings. However, the EM structures were in disagree-ment as to how the main association domains of the pro-tein were juxtaposed to the kinase domain. Rosenbergand coworkers analyzed the full-length protein by SAXSand used semi-manual rigid body refinement of the kinaseand association domain structures to determine that theinactive kinase domains lie flat in a ring exterior to the cen-tral assembly domains (Rosenberg et al., 2005). Ab initio

shape predictions based on the experimental scatteringcurve agreed with this model. If instead the kinase domainslay above the plane of the association domains, the calcu-lated scattering curve disagreed strongly with the experi-mental one. The SAXS scattering curve of an activatedCAMKII was significantly different, with an apparentincrease in Dmax of 100 A. The authors speculated thatupon activation, the kinase domains are released from theirposition to positions above and below the plane of theassociation domains. A second SAXS example is determin-ing the oligomerization state in solution of the Hollidayjunction motor RuvB protein (Putnam et al., 2001). SAXSdata provided an overall radius of gyration (Rg) for theparticle of 40 A with a Dmax of 120 A, consistent with thecrystal subunit structure and a generated hexamer assem-bly model. The scattering curve calculated from the hexa-mer model was similar to the experimental scatteringcurve, and an ab initio spherical harmonic reconstructionfit the experimental curve with a small number of parame-ters and matched the hexamer model. These results showedhow SAXS data can exclude packing arrangements thatgive different radii of gyration and maximum interparticledistances, such as more globular arrangements or asym-metric hexamers that are more elliptical and would haveincreased maximum intraparticle distances. The SAXS



ARTICLE IN PRESS

generated hexamer model appears likely to be correct as itshowed good agreement with experimentally determinedSAXS data, EM reconstructions, other hexameric AAA-class ATPases, and the crystallographic packing interfaces.

At SIBYLS, we have increasingly found that combin-ing crystal structures of subunits with SAXS characteriza-tions of the complex to be extremely powerful andefficient in the characterizations of reversible complexes.Such dynamic or reversible complexes act in many criticalaspects of cell biology, and are typified by assemblies,such as DNA sliding clamps that encircle DNA and pro-vide binding sites for many DNA replication and repairenzymes, including polymerase, flap endonuclease, andDNA ligase. Recently, we used SAXS in combinationwith crystallography to help elucidate the mechanismsby which sliding clamps like PCNA coordinate multi-stepDNA transactions, which have been mysterious. Besidesthe new PCNA structure noted above (Fig. 1), we deter-mined structures of Sulfolobus solfataricus DNA ligaseand heterotrimeric PCNA separately by X-ray diffraction,and characterized their complex by SAXS experiments(Pascal et al., 2006). In the structure of this heterotrimericDNA sliding clamp, the three distinct subunits assembleinto a protein ring resembling the homotrimeric PCNAof humans, but with three unique protein-binding sitesthat facilitate the assembly of discrete multi-protein com-plexes. In the absence of a nicked DNA, the Sulfolobus

solfataricus DNA ligase has an open, extended conforma-tion by both crystallographic and SAXS studies. In thereversible complex amenable only to SAXS studies, theDNA ligase retains an open, extended conformation andbinds to a single PCNA3 subunit (Fig. 2). Yet, a closed,ring-shaped conformation of ligase catalyzes a DNAend-joining reaction stimulated by PCNA. This open-to-closed switch in the conformation of DNA ligase isaccommodated by a malleable interface with PCNA thatserves as an efficient platform for DNA ligation. SAXScombined with crystallography thus established a flexiblemodel for DNA ligase function that allows an extendedligase to bind the PCNA platform for DNA replicationand repair and then to close into a ring around DNAfor end joining. In essence SAXS was an essential compo-nent to show that ligase in solution can act like a molec-ular watch band that can extend or wrap around DNA asa reversible functional complex.

4.3. Observation of loops or domains whose structure has notbeen determined

In crystallographic studies, flexible loops or disorderedregions are often either not visible in the electron densityor have already been eliminated in the cloning stage to pro-duce a sample that can be crystallized. SAXS can providean effective complementary technique that can build lowresolution models for these regions onto the known struc-ture. Svergun and his coworkers have developed a suiteof programs, including CREDO, based on their ab initio


programs that can build dummy atoms or Ca chains ontothe crystal structure to show the relative location of these‘‘missing’’ regions (Petoukhov et al., 2002). The knownstructure is fixed and then dummy residues are placed ran-domly within the input Dmax region. During the simulatedannealing runs, the fit to the experimental scattering curveis optimized, and a model for the relative positioning of theunknown region is generated.

In their study of the Escherichia coli primase, Corn andcoworkers used this approach to identify the relative posi-tion of two domains which were putatively connected by along flexible linker (Corn et al., 2005). The structure of thepolymerase domain was determined by solving the crystalstructure, and the regulatory domain had strong homologyto a known structure. SAXS data were collected on the full-length protein. The polymerase domain was used as inputto the program CREDO, which built density on the poly-merase structure to best fit the scattering profile (Fig. 3).The homology model of the regulatory domain fit the addi-tional density built by CREDO. The regulatory domainwas positioned tightly against the polymerase domain,though unexpectedly far away from the proposed path ofthe primer/template (indicated by an arrow). By increasingthe MgCl2 concentration they observed increases in Dmax

(Fig. 3). These studies further complemented fluorescenceresonance energy transfer (FRET) experiments. Bothresults suggested that the regulatory domain is bound tothe polymerase domain through polar contacts and saltbridges which may be disrupted for function. SubsequentFRET studies by the authors indicated that the regulatorydomain acts in trans, and they proposed that release of thetwo domains is an essential step toward regulation of thepolymerase.

4.4. Ligand-induced conformational changes

Proteins often function through mechanistic domainmotions that are controlled by binding small moleculessuch as nucleotide triphosphates, and SAXS provides auniquely rapid and effective tool for observing grossdomain movements. SAXS studies can be done with thesame protein preparation under solution conditions thatare identical to optimized biochemical assay conditions.Variables can include nucleotides, salt, buffer type, andpH. Comparison of the scattering curves can identifychanges in flexibility and, with ab initio analysis, determi-nation of domain shifts relative to each other. Time-re-solved studies add another dimension to characterizationof the conformational changes. Furthermore, automationof SAXS sample loading would open the way for mediumthroughput drug studies to identify compounds that inducea conformational change or changes in protein flexibility(Fischetti et al., 2004).

A recent study on an AAA ATPase, p97, illustrates thepower of SAXS to observe conformational changes in largeproteins (Davies et al., 2005). AAA ATPases are a remark-able family of proteins whose functions are controlled by


Fig. 3. Use of SAXS to identify relative positioning of two domains inEscherichia coli primase, with the structure of only one domain used asinput. Work was published in collaboration with Jacob Corn and JamesBerger (Corn et al., 2005). Electron pair distribution function for E. coli

primase under varying salt conditions. Low salt buffer (20 mM HEPES,pH 7.5, 75 mM potassium glutamate) is colored in black, buffersupplemented with 150 mM MgCl2 in red and buffer supplemented with300 mM MgCl2. Consensus shape prediction (transparent spheres) for theregulatory domain of E. coli primase overlaid with the homology model(ribbon). The envelope of the polymerase domain is shown in solidspheres. The arrow indicates the postulated path of the primer/template.Shape prediction was calculated by CREDO and averaged using theDAMAVER program suite.

Fig. 2. Ab initio shape prediction of complex between DNA ligase and PCNA. SAXS analysis of Sulfolobus solfataricus ssLig, PCNA1, PCNA2, andPCNA3. The protein concentration was 4 and 8 mg/ml, and the sample buffer was 25 mM Tris pH 7.5, 50 mM NaCl, and 1 mM TCEP. Averaged andfiltered ab initio shape prediction was calculated by GASBOR and aligned using the DAMAVER program suite (Volkov and Svergun, 2003). The crystalstructures of ssLig and the PCNA heterotrimer were independently solved of one another and placed as shown in complex using the SAXS envelope.


ARTICLE IN PRESS

binding and hydrolysis of ATP. Different nucleotide statesconfer large conformational changes that traverse theentire protein. p97 is a large protein; a single subunit isapproximately 806 residues, and p97 forms a homohex-amer. In the nucleotide-free form, the protein showed anexpanded structure with an increase of Dmax of approxi-mately 25 A. Comparison of structures with bound


AMP-PNP, ADP, or ADP-AIFx suggests that the specificnucleotide state of one set of ATPase domains alters theflexibility and relative position of two other domains andsets up a path for transfer of energy from the ATPasedomain to interacting proteins through these large confor-mational changes. The authors note that there were signif-icant differences from the EM studies, which they attributeto the higher resolution of the SAXS data. The data, col-lected at the Advanced Photon Source, extended to an s

of 0.73 A�1 and provided the higher angle data criticalfor the detailed features observed in the SAXS shape pre-dictions. An exciting development in the field is the useof molecular dynamics to introduce flexibility in crystallo-graphic structures to match SAXS scattering curves (Kar-plus and Kuriyan, 2005; Wu et al., 2005); this techniquecould provide atomic resolution hypotheses on how pro-teins transition from one conformation to another.Although p97 is a relatively large protein for moleculardynamics, improvements in computing power as well asdevelopments in the algorithms will increase the size possi-ble for this type of study.

4.5. Possibility for visualization of flexible regions in

proteins

Although flexible or unstructured domains are especiallyproblematic for crystallographic studies, these regions canbe uniquely characterized by SAXS. On one level, flexibleand unstructured regions can be identified by the shapeof the scattering curve on a Kratky plot (Doniach et al.,1995; Semisotnov et al., 1996). The Kratky plot graphsI(s)*s2 vs. s, where I is the intensity and s is the momentumtransfer. Kratky plots for natively folded proteins areparabolic in appearance and I(s)*s2 rises and falls in a


Fig. 4. Use of SAXS to predict conformation of an unstructured region inNEIL1 glycosylase. (A) Buffer-substracted scattering profile of NEIL1(5 mg/ml) dialyzed in PBS and 1 mM TCEP. Inset: Kratky plot of NEIL1.The non-parabolic nature of the high s region indicates that there isunstructured regions present in the protein. (B) Averaged and filteredab initio shape prediction calculated by GASBOR and aligned using theDAMAVER program suite. The ribbon structure of NEIL1 N-terminus(1TDH.pdb) was manually fit into the envelope (Doublie et al., 2004). Thearrow indicates the C-terminal residue of the crystal structure. Work wasdone in collaboration with Tapas Hazra and Sankar Mitra.


ARTICLE IN PRESS

relatively sharp peak with increasing s. For unfolded pro-teins, the I(s)*s2 approaches a constant maximum value.For proteins with both structured and unstructuredregions, the Kratky plot shows almost an additive naturewith an initial parabolic nature and a tail at high s thatresembles unfolded protein (Moncoq et al., 2004). As anaside for protein crystallographers, we have found thatidentification of flexible regions in constructs by SAXSanalysis has aided in design and selection of crystallizationtargets.

NEIL1 is a protein where one quarter of the protein ispredicted to be unstructured. It is a DNA glycosylase thatremoves oxidized pyrimidines; the catalytic domain islocated in the N-terminus (Bandaru et al., 2002; Hazraet al., 2002). Sequence analysis by PONDR identified theC-terminal residues 282–390 as disordered (Bandaruet al., 2004). A deletion construct (2–342) with part ofthe C-terminus removed was successfully crystallized(Doublie et al., 2004). In the crystallographic model, onlyresidues from the N-terminus to residue 290 were observa-ble in the electron density, indicating that PONDR success-fully predicted the disordered region to within 10 residues.We have done SAXS analysis on full-length NEIL1(Fig. 4). The Kratky plot is typical of a protein with bothfolded and unstructured regions. Ab initio shape predictionfrom the GASBOR program revealed an oblong structure.The crystal structure for NEIL1 fit well in the wider region,with the C-terminus facing the more narrow region. Oneloop which forms a crystallographic contact with anotherNEIL1 molecule in the crystal packing extends from theshape envelope. It is likely that in the full-length protein,this loop makes contact with the C-terminal region. Thispreliminary study indicates the ability of SAXS to visualizeunstructured regions, although more work needs to bedone to verify this conclusion.

5. Perspectives

High resolution structure has transformed biology, rais-ing our understanding of proteins from one-dimensionalamino acid sequences to three-dimensional structures:Identification of the functional importance of a particularamino acid has been greatly facilitated by knowing its loca-tion within the protein and its chemical environment. Sim-ilarly, SAXS promises to raise this understanding to thenext dimension since detailed characterizations of the pro-tein conformational states, architectures, and reversibleassemblies can provide important clues to how proteinscarry out their functions. With advanced computing andthe growing data base of solved structures, SAXS can bethe optimal means to answer questions at many levels ofresolution and to bridge the gaps between high resolutioncrystal structures and the large and dynamic complexesfunctioning in cells.

The SAXS field has been evolving rapidly in recent yearsand is increasingly becoming a critical technique for struc-tural biology. First, SAXS provides useful information


from almost every sample. Second, the minimal nature ofthe sample requirements compared to other structural tech-niques, with no requirement for labeling or for crystals anda large molecular weight range, is enabling SAXS analysisto become an increasingly powerful and important tool forprobing structure in solution. Third, already many proteincrystallography laboratories, which use the SAXS endsta-tion at the SIBYLS beamline, consider SAXS analysis astandard characterization of their samples to characterizestates of folding, aggregation, assembly, and conformation.Access to SAXS endstations at synchrotrons is availablethrough general user proposals, and beamline staff canaid collaborative projects. As more scientists take advan-tage of SAXS analysis, we will gain a greater fundamentalunderstanding of how proteins function and are controlledthrough dynamic features including conformational flexi-bility, reversible assemblies, and dynamic complexes. Theemerging grand challenge of characterizing molecularmachines that control cell biology, including responses toendogenous and exogenous stress, will require the type ofpowerful and efficient analysis in solution that SAXS canprovide.



ARTICLE IN PRESS

Acknowledgments

We thank Sankar Mitra, Tapas Hazra, Jacob Corn, andJames Berger for collaborating on the structural studiesand for helpful discussions. We thank James Holton, JaneTanamachi, Christine Trame, and Hiro Tsuruta for theirhelp during design and commissioning of the beamline.We thank Jill Fuss and Quen Cheng for constructive dis-cussions and comments on the manuscript and VladimirUversky for helpful discussions on unstructured proteins.The SIBLYS beamline at the Advanced Light Source andthese studies on the integration of crystallographic andSAXS analyses and for the characterization of reversiblecomplexes and modified proteins were supported by theNational Institutes of Health (NIH) Structural Cell Biolo-gy of DNA Repair Machines P01 grant CA92584 and RO1GM46312, and by the Office of Science, Office of Biologicaland Environmental Research, U.S. Department of Energy,under Contract Number DE-AC02-05CH11231.

References

Bandaru, V., Sunkara, S., Wallace, S.S., Bond, J.P., 2002. A novel humanDNA glycosylase that removes oxidative DNA damage and ishomologous to Escherichia coli endonuclease VIII. DNA Repair 1,517–529.

Bandaru, V., Cooper, W., Wallace, S.S., Doublie, S., 2004. Overproduc-tion, crystallization and preliminary crystallographic analysis of anovel human DNA-repair enzyme that damage recognizes oxidativeDNA damage. Acta Crystallographica Section D—Biological Crys-tallography 60, 1142–1144.

Bjoras, M., Seeberg, E., Luna, L., Pearl, L.H., Barrett, T.E., 2002.Reciprocal ‘‘flipping’’ underlies substrate recognition and catalyticactivation by the human 8-oxo-guanine DNA glycosylase. Journal ofMolecular Biology 317, 171–177.

Carrell, H.L., Glusker, J.P., Burger, V., Manfre, F., Tritsch, D.,Biellmann, J.F., 1989. X-ray analysis of D-xylose isomerase at 1.9 A:native enzyme in complex with substrate and with a mechanism-designed inactivator. Proceedings of the National Academy of Sciencesof United States of America 86, 4440–4444.

Chacon, P., Moran, F., Diaz, J.F., Pantos, E., Andreu, J.M., 1998. Low-resolution structures of proteins in solution retrieved from X-rayscattering with a genetic algorithm. Biophysical Journal 74, 2760–2775.

Corn, J.E., Pease, P.J., Hura, G.L., Berger, J.M., 2005. Crosstalk betweenprimase subunits can act to regulate primer synthesis in trans.Molecular Cell 20, 391–401.

Craig, L., Volkmann, N., Arvai, A.S., Pique, M.E., Yeager, M., Egelman,E.H., Tainer, J.A., 2006. Type IV pilus structure by cryo-electronmicroscopy and crystallography: implications for pilus assembly andfunctions. Molecular Cell 23, 651–662.

Davies, J.M., Tsuruta, H., May, A.P., Weis, W.I., 2005. Conformationalchanges of p97 during nucleotide hydrolysis determined by small-angleX-ray scattering. Structure 13, 183–195.

Doniach, S., Bascle, J., Garel, T., Orland, H., 1995. Partially folded statesof proteins—characterization by X-ray-scattering. Journal of Molec-ular Biology 254, 960–967.

Doublie, S., Bandaru, V., Bond, J.P., Wallace, S.S., 2004. The crystalstructure of human endonuclease VIII-like 1 (NEIL1) reveals a zinclessfinger motif required for glycosylase activity. Proceedings of theNational Academy of Sciences of the United States of America 101,10284–10289.

Dunker, A.K., Obradovic, Z., Romero, P., Garner, E.C., Brown, C.J.,2000. Intrinsic protein disorder in complete genomes. GenomeInformatics 11, 161–171.


Dunker, A.K., Cortese, M.S., Romero, P., Iakoucheva, L.M., Uversky,V.N., 2005. Flexible nets—The roles of intrinsic disorder in proteininteraction networks. FEBS Journal 272, 5129–5148.

Dyson, H.J., Wright, P.E., 2002. Coupling of folding and binding forunstructured proteins. Current Opinion in Structural Biology 12, 54–60.

Feigin, L.A., Svergun, D.I., 1987. Structure Analysis by Small-Angle X-ray and Neutron Scattering. Plenum Press, New York.

Fischetti, R.F., Rodi, D.J., Gore, D.B., Makowski, L., 2004. Wide-angleX-ray solution scattering as a probe of ligand-induced conformationalchanges in proteins. Chemical Biology 11, 1431–1443.

Gulbis, J.M., Kelman, Z., Hurwitz, J., O’Donnell, M., Kuriyan, J., 1996.Structure of the C-terminal region of p21(WAF1/CIP1) complexedwith human PCNA. Cell 87, 297–306.

Hazra, T.K., Izumi, T., Boldogh, I., Imhoff, B., Kow, Y.W., Jaruga,P., Dizdaroglu, M., Mitra, S., 2002. Identification and charac-terization of a human DNA glycosylase for repair of modifiedbases in oxidatively damaged DNA. Proceedings of the NationalAcademy of Sciences of the United States of America 99, 3523–3528.

Heller, W.T., 2005. Influence of multiple well defined conformations onsmall-angle scattering of proteins in solution. Acta CrystallographicaSection D—Biological Crystallography 61, 33–44.

Hoelz, A., Nairn, A.C., Kuriyan, J., 2003. Crystal structure of atetradecameric assembly of the association domain of Ca2+/calmod-ulin-dependent kinase II. Molecular Cell 11, 1241–1251.

Hopfner, K.P., Karcher, A., Craig, L., Woo, T.T., Carney, J.P., Tainer,J.A., 2001. Structural biochemistry and interaction architecture of theDNA double-strand break repair Mre11 nuclease and Rad50-ATPase.Cell 105, 473–485.

Karplus, M., Kuriyan, J., 2005. Molecular dynamics and protein function.Proceedings of the National Academy of Sciences of the United Statesof America 102, 6679–6685.

Kolodziej, S.J., Hudmon, A., Waxham, M.N., Stoops, J.K., 2000. Three-dimensional reconstructions of calcium/calmodulin-dependent (CaM)kinase IIalpha and truncated CaM kinase IIalpha reveal a uniqueorganization for its structural core and functional domains. Journal ofBiological Chemistry 275, 14354–14359.

Konarev, P.V., Volkov, V.V., Sokolova, A.V., Koch, M.H.J., Svergun,D.I., 2003. PRIMUS: a Windows PC-based system for small-anglescattering data analysis. Journal of Applied Crystallography 36, 1277–1282.

Lander, E.S., Linton, L.M., Birren, B., Nusbaum, C., Zody, M.C.,Baldwin, J., Devon, K., Dewar, K., Doyle, M., FitzHugh, W., Funke,R., Gage, D., Harris, K., Heaford, A., Howland, J., Kann, L.,Lehoczky, J., LeVine, R., McEwan, P., McKernan, K., Meldrim, J.,Mesirov, J.P., Miranda, C., Morris, W., Naylor, J., Raymond, C.,Rosetti, M., Santos, R., Sheridan, A., Sougnez, C., Stange-Thomann,N., Stojanovic, N., Subramanian, A., Wyman, D., Rogers, J., Sulston,J., Ainscough, R., Beck, S., Bentley, D., Burton, J., Clee, C., Carter,N., Coulson, A., Deadman, R., Deloukas, P., Dunham, A., Dunham,I., Durbin, R., French, L., Grafham, D., Humphray, S., Gregory, S.,Hubbard, T., Hunt, A., Jones, M., Lloyd, C., McMurray, A.,Matthews, L., Mercer, S., Milne, S., Mullikin, J.C., Mungall, A.,Plumb, R., Ross, M., Shownkeen, R., Sims, S., Waterston, R.H.,Wilson, R.K., Hillier, L.W., McPherson, J.D., Marra, M.A., Mardis,E.R., Fulton, L.A., Chinwalla, A.T., Pepin, K.H., Gish, W.R.,Chissoe, S.L., Wendl, M.C., Delehaunty, K.D., Miner, T.L., Deleha-unty, A., Kramer, J.B., Cook, L.L., Fulton, R.S., Johnson, D.L.,Minx, P.J., Clifton, S.W., Hawkins, T., Branscomb, E., Predki, P.,Richardson, P., Wenning, S., Slezak, T., Doggett, N., Cheng, J.F.,Olsen, A., Lucas, S., Elkin, C., Uberbacher, E., Frazier, M., et al.,2001. Initial sequencing and analysis of the human genome. Nature409, 860–921.

Moncoq, K., Broutin, I., Craescu, C.T., Vachette, P., Ducruix, A.,Durand, D., 2004. SAXS study of the PIR domain from the Grb14molecular adaptor: A natively unfolded protein with a transientstructure primer? Biophysical Journal 87, 4056–4064.



ARTICLE IN PRESS

Morris, E.P., Torok, K., 2001. Oligomeric structure of alpha-calmodulin-dependent protein kinase II. Journal of Molecular Biology 308, 1–8.

Pascal, J.M., Tsodikov, O.V., Hura, G.L., Song, W., Cotner, E.A.,Classen, S., Tomkinson, A.E., Tainer, J.A., Ellenberger, T., 2006. Aflexible interface between DNA ligase and PCNA supports conforma-tional switching and efficient ligation of DNA. Molecular Cell 24, 279–291.

Petoukhov, M.V., Svergun, D.I., 2003. New methods for domain structuredetermination of proteins from solution scattering data. Journal ofApplied Crystallography 36, 540–544.

Petoukhov, M.V., Svergun, D.I., 2005. Global rigid body modeling ofmacromolecular complexes against small-angle scattering data. Bio-physical Journal 89, 1237–1250.

Petoukhov, M.V., Eady, N.A., Brown, K.A., Svergun, D.I., 2002.Addition of missing loops and domains to protein models by X-raysolution scattering. Biophysical Journal 83, 3113–3125.

Putnam, C.D., Clancy, S.B., Tsuruta, H., Gonzalez, S., Wetmur, J.G.,Tainer, J.A., 2001. Structure and mechanism of the RuvB Hollidayjunction branch migration motor. Journal of Molecular Biology 311,297–310.

Rosenberg, O.S., Deindl, S., Sung, R.J., Nairn, A.C., Kuriyan, J., 2005.Structure of the autoinhibited kinase domain of CaMKII and SAXSanalysis of the holoenzyme. Cell 123, 849–860.

Semisotnov, G.V., Kihara, H., Kotova, N.V., Kimura, K., Amemiya, Y.,Wakabayashi, K., Serdyuk, I.N., Timchenko, A.A., Chiba, K.,Nikaido, K., Ikura, T., Kuwajima, K., 1996. Protein globularizationduring folding. A study by synchrotron small-angle X-ray scattering.Journal of Molecular Biology 262, 559–574.

Sokolova, A.V., Volkov, V.V., Svergun, D.I., 2003a. Prototype of adatabase for rapid protein classification based on solution scatteringdata. Journal of Applied Crystallography 36, 865–868.

Sokolova, A.V., Volkov, V.V., Svergun, D.I., 2003b. Database for rapidprotein classification based on small-angle X-ray scattering data.Crystallography Reports 48, 959–965.


Svergun, D.I., 1999. Restoring low resolution structure of biologicalmacromolecules from solution scattering using simulated annealing.Biophysical Journal 76, 2879–2886.

Svergun, D.I., Koch, M.H.J., 2003. Small-angle scattering studies ofbiological macromolecules in solution. Reports on Progress in Physics66, 1735–1782.

Svergun, D.I., Petoukhov, M.V., Koch, M.H.J., 2001. Determination ofdomain structure of proteins from X-ray solution scattering. Biophys-ical Journal 80, 2946–2953.

Takahashi, Y., Nishikawa, Y., Fujisawa, T., 2003. Evaluation of threealgorithms for ab initio determination of three-dimensional shape fromone-dimensional solution scattering profiles. Journal of AppliedCrystallography 36, 549–552.

Trame, C., MacDowell, A.A., Celestre, R.S., Padmore, H.A., Cambie, D.,Domning, E.E., Duarte, R.M., Kelez, N., Plate, D.W., Holton, J.M.,Frankel, K., Tsutakawa, S., Tsuruta, H., Tainer, J.A., Cooper. P.K.,2003. SIBYLS—A SAXS and protein crystallography beamline at theALS. In: Warwick, T., (Ed.) Synchrotron Radiation Instrumentation,Eighth International Conference. American Institute of Physics, SanFrancisco, pp. 502–505.

Venter, J.C., 2001. The sequence of the human genome (vol 292, pg 1304,2001). Science 292, 1838.

Volkov, V.V., Svergun, D.I., 2003. Uniqueness of ab initio shapedetermination in small-angle scattering. Journal of Applied Crystal-lography 36, 860–864.

Walther, D., Cohen, F.E., Doniach, S., 2000. Reconstruction of low-resolution three-dimensional density maps from one-dimensionalsmall-angle X-ray solution scattering data for biomolecules. Journalof Applied Crystallography 33, 350–363.

Wu, Y.H., Tian, X., Lu, M.Y., Chen, M.Z., Wang, Q.H., Ma, J.P., 2005.Folding of small helical proteins assisted by small-angle X-rayscattering profiles. Structure 13, 1587–1597.

Zipper, P., Durchschlag, H., 2003. Modeling of protein solutionstructures. Journal of Applied Crystallography 36, 509–514.


Structural analysis of flexible proteins in solution by small angle X-ray scattering combined with...

Documents

Transcript of Structural analysis of flexible proteins in solution by small angle X-ray scattering combined with...