Semi-Rigid Solution Structures of Heparin by Constrained X-ray Scattering Modelling: New Insight...

doi:10.1016/j.jmb.2009.10.064 J. Mol. Biol. (2010) 395, 504–521

Available online at www.sciencedirect.com

Semi-Rigid Solution Structures of Heparin byConstrained X-ray Scattering Modelling: New Insightinto Heparin–Protein Complexes

Sanaullah Khan1, Jayesh Gor1, Barbara Mulloy2

and Stephen J. Perkins1⁎
1Department of Structural andMolecular Biology, Division ofBiosciences, Darwin Building,University College London,Gower Street, London WC1E6BT, UK2National Institute of BiologicalStandards and Control, BlancheLane, South Mimms, PottersBar, Hertfordshire EN6 3QG,UK
Received 21 September 2009;received in revised form27 October 2009;accepted 28 October 2009Available online3 November 2009

*Corresponding author. E-mail [email protected] used: IdoA, α-L-idu

vaccinia complement control proteinultracentrifugation; GlcNS, N-suphaPDB, Protein Data Bank; FH, factormacrophage inflammatory protein 1complement regulator.

0022-2836/$ - see front matter © 2009 E

The anionic polysaccharides heparin and heparan sulphate play essentialroles in the regulation of many physiological processes. Heparin is oftenused as an analogue for heparan sulphate. Despite knowledge of an NMRsolution structure and 19 crystal structures of heparin–protein complexesfor short heparin fragments, no structures for larger heparin fragments havebeen reported up to now. Here, we show that solution structures for sixpurified heparin fragments dp6–dp36 (where dp stands for degree ofpolymerisation) can be determined by a combination of analyticalultracentrifugation, synchrotron X-ray scattering, and constrained model-ling. Analytical ultracentrifugation velocity data for dp6–dp36 showedsedimentation coefficients that increased linearly from 1.09 S to 1.84 S withsize. X-ray scattering of dp6–dp36 gave radii of gyration RG that rangedfrom 1.33 nm to 3.12 nm and maximum lengths that ranged from 3.0 nm to12.3 nm. The higher resolution of X-ray scattering revealed an increasedbending of heparin with increased size. Constrained molecular modelling of5000 randomised heparin conformers resulted in 9–15 best-fit structures foreach of dp18, dp24, dp30, and dp36 that indicated flexibility and thepresence of short linear segments in mildly bent structures. Comparisons ofthese solution structures with crystal structures of heparin–proteincomplexes revealed similar ranges of phi (φ) and psi (ψ) angles betweeniduronate and glucosamine rings. We conclude that heparin in solution hasa semi-rigid and extended conformation that is preformed for its optimalbinding to protein targets without major conformational changes.

© 2009 Elsevier Ltd. All rights reserved.

Edited by R. Huber
Keywords: heparin; X-ray scattering; modelling; ultracentrifugation
Introduction

Heparin is a highly sulphated linear polysaccharidethat is found in the granules of mast cells andgranulated cells of organs such as the liver andintestine.1 Heparin is an analogue of heparan sulphatethat mediates a wide range of biological and physio-

ress:

ronic acid; VCP,; AUC, analyticalted glucosamine;H; MIP-1α,α; SCR, short

lsevier Ltd. All rights reserve

logical activities through its interactions with pro-teins. These include inhibition of blood coagulation,1

complement activation,2,3 angiogenesis and tumorgrowth,4,5 antiviral activity,6–8 and release of lipopro-tein lipase and hepatic lipase.1,9 The breadth ofheparin–protein interactions offers many potentialstrategies for therapeutic intervention at the cell–tissue–organ interface. The classical example is thefrequent use of heparin in clinics as an anticoagulant.The basic subunit of heparin is a disaccharide (dp2,

where dp stands for degree of polymerisation)composed of uronic acid and D-glucosamine linkedby a (1–4) glycosidic bond (Fig. 1).8 The uronic acidcan be either α-L-iduronic acid (IdoA), whichaccounts for up to 90% of heparin, or β-D-glucuronicacid, which accounts for up to 10% of heparin. Themost commonly occurring heparin disaccharide

d.

Fig. 1. Chemical structures of disaccharide repeats in heparin and heparan sulphate. (a) The major repeatingdisaccharide unit that occurs in 90% of heparin is [4)-a-L-iduronic acid-(1→4)-a-D-glucosamine(2,6 disulphate)-(1→];abbreviated as IdoA-GlcNS. The location of the C1′-O4 and O4-C4 bonds that are monitored to calculate phi (φ) from theO5′-C1′-O4-C4 atoms and psi (ψ) from the C1′-O4-C4-C3 atoms are indicated by two arrows. (b) The major disacchariderepeating unit of heparan sulphate is [4)-b-D-glucuronic acid-(1→4)-a-D-N-acetyl glucosamine-(1→]; abbreviated as GlcA-GlcNAc, and occurs in the remaining 10% of heparin.

505Solution Structure of Heparin

contains three sulphate groups, which are located onthe 2-OH group of IdoA, and on the 2-NH2 groupof D-glucosamine, and on the 6-OH group of D-glucosamine to form N-sulphated glucosamine(GlcNS). The high degree of sulphation and carbox-ylation makes heparin the most negatively chargedmacromolecule known in nature. Like heparin,heparan sulphate is a linear polysaccharide consistingof alternating uronic acid and α-(1–4)-D-glucosamineresidues, but differs in exhibiting a reduced degree ofsulphation (Fig. 1). Unlike heparin, heparan sulphateis less modified and contains a higher proportion ofN-acetylated saccharides.10,11

Structural studies of heparin are essential for theextensive number of reported heparin–protein inter-actions and their involvement in a broad range ofpathophysiological processes. Up to now, molecularstructures for heparin have been limited to smallfragments.8 For free heparin, solution structures byNMR spectroscopy are available for heparin oligo-saccharides12 and synthetic pentasaccharides (dp5).13

These indicated a linear structure. For heparin–proteincomplexes, the current availability of 19 crystalstructures (September 2009) has revealed heparinstructures of sizes dp4–dp10. These include crystalstructures for acidic andbasic fibroblast growth factorsseparately;14,15 the complexes of acidic and basicfibroblast growth factors with their receptors;16,17

thrombin,18 antithrombin, and the complex of anti-thrombin–S195A and coagulation factor Xa;19–22 foot-and-mouth disease virus;23 neurokinin 1 receptor;24

annexins V and A2;25,26 vaccinia complement controlprotein (VCP);27 and protein C inhibitor.28 Many ofthese crystal structures likewise show extendedheparin conformations. At the opposite extreme ofstructural resolution, macroscopic solution structuresfor large polydisperse heparin fractions have beenstudied by X-ray solution scattering and analyticalultracentrifugation (AUC).29,30 No structural informa-tion at themolecular levelwas reported for these largerheparin fractions. Fibre diffraction studies have alsobeen reported for heparin oligosaccharides.31,32

To extend our understanding of heparin structures,we requiremolecular structures for heparin fragmentsranging from dp6 to dp36. These were obtained byapplying small-angle X-ray scattering and AUC, inconjunction with constrained modelling, as a power-ful combination of three techniques to determinemolecular structures.33,34 This multidisciplinary ap-proach is well-established for solution structuredeterminations of large multidomain complementand antibody proteins,35,36 but is novel for oligosac-charides or related macromolecules such as polynu-cleotides. We show that heparin fragments startingfrom dp18 onwards become progressively more bentwith increase in size. In solution, heparin structuresare essentially extended, but possess enough flexibil-ity in terms of bending to facilitate binding to proteinsin essentially preformed conformations. The resultsprovide new insight onhowheparinbinds toproteins,and the outcome will facilitate more detailed studiesof heparin–protein complexes.

Results and Discussion

Sedimentation velocity data analysis for heparinfragments

Following purification of the six heparin frag-ments dp6–dp36, Fig. 2 shows that the dp6 and dp12fractions eluted as well-resolved peaks from theBiogel P-10 column, while the dp18, dp24, dp30, anddp36 fractions became less resolved with increase insize. Analytical high-performance size-exclusionchromatography of the heparin oligosaccharidefractions was performed as described37 to determinethe sizes of the fractions and shows that the sixselected peak fractions were homogenous.AUC studies macromolecular structures in solu-

tion by following their sedimentation behaviourunder a high centrifugal force.38 In sedimentationvelocity experiments, both the shape of dp6–dp36 at

Fig. 2. Purification profile ofheparin disaccharide fragmentsdp2–dp36. The heparin fragmentswere eluted as peaks using a BiogelP-10 column in 2% ammoniumbicarbonate solution at a flow rateof 0.2 ml/min. Fractions of 2 ml/10 min were collected, and theirheparin concentrations were mea-sured spectrophotometrically at234 nm. The purified fractions usedfor this study are shown by opencircles.

506 Solution Structure of Heparin

0.5 mg/ml and their degree of polydispersity wereanalysed by AUC size distribution analyses usingSEDFIT with three rotor speeds. Absorbance analy-ses for each heparin fragment reproducibly resultedin good fits to the sedimentation boundaries withlow residuals. In all cases, a single peak withsedimentation coefficient s20,w values of 1.01 S fordp6, 1.29 S for dp12, 1.43 S for dp18, 1.58 S for dp24,1.62 S for dp30, and 1.77 S for dp36 was observed(Fig. 3a). The corresponding interference analyses fordp6–dp36 also resulted in good boundary fits, and

Fig. 3. Sedimentation velocity size distribution analysesinterference boundary scans were fitted using SEDFIT softabsorbance data using a wavelength of 234 nm and a rotor speedp12, 1.43 S for dp18, 1.58 S for dp24, 1.62 S for dp30, and 1.77fits are shown for dp12 and dp36, in which only every 10th scainterference data using a rotor speed of 50,000 rpm gave s20,w pfor dp24, 1.60 S for dp30, and 1.89 S for dp36. Beneath these pascan of the 280 fitted boundaries for dp6 and dp36.

single major c(s) peaks with s20,w values of 1.19 S fordp6, 1.34 S for dp12, 1.42 S for dp18, 1.47 S for dp24,1.60 S for dp30, and 1.89 S for dp36 were obtained(Fig. 3b). The peaks and their widths were used toassess fragment polydispersity. In this regard,interference optics showed better resolution andsingle narrowmajor peaks. The single peaks indicatethat the six fragments are relatively homogenous insize. The similar peak widths from either absorbanceor interference optics suggest that all six frag-ments showed narrow size distributions and are

c(s) of heparin dp6–dp36. The (a) absorbance and (b)ware for the heparin fragments at 0.5 mg/ml. (a) Thed of 50,000 rpm gave s20,w peaks at 1.01 S for dp6, 1.29 S forS for dp36. Beneath these panels, representative boundaryn of the 210 fitted boundaries is shown for clarity. (b) Theeaks at 1.19 S for dp6, 1.34 S for dp12, 1.42 S for dp18, 1.47 Snels, representative boundary fits are shown for every 14th


relatively homogenous, in agreement with the high--performance size-exclusion chromatography de-scribed above. Although a slight variability in thes20,wvalues of absorbance and interference data wasobserved at different rotor speeds, the six averagedvalues (together with those for dp10, which wasprepared in a similar manner39) showed a linearincrease with heparin length (Fig. 4a and b).Previously, s20,w

0 values of 1.69 S, 1.88 S, 1.99 S, and2.25 S from interference optics were reported forheparin preparations of approximate sizes deducedto be dp26, dp32, dp38, and dp46, in that order, in0.2 M NaCl.29,30 These earlier values agree well withthe more extensive data presented in Fig. 4b.The sedimentation coefficient s20,w

0 values of 16heparin models corresponding to linear dp10–dp40structures were calculated using HYDROPRO soft-ware on the basis of the linear dp12 NMR struc-ture.12 While variability was observed in their calc-ulated values, the overall dependence of s20,w

0 values

Fig. 4. Comparison of the experimental and predicted sedimThe experimental values for dp6–dp36 are shown by six filledare shown by open circles. (a) Comparison with the averaged40,000 rpm and 50,000 rpm using absorbance optics. (b) Cocoefficients at rotor speeds of 40,000 rpm, 50,000 rpm, and 60,linear models for dp6–dp36 that were created from the NMR

on length is linear (Fig. 4) and agrees well with theexperiment (Fig. 3). By AUC, there is no evidence ofstructural bending from the s20,w values for heparinlengths of up to 18 nm in dp36.

X-ray solution scattering data for heparinfragments

Solution scattering is a diffraction technique thatstudies the overall structure of biological macro-molecules in solution.33 In order to obtain moredetailed structural information compared to thatobtained from AUC, the solution structures of thesix heparin fragments dp6–dp36 at 0.5 mg/ml werecharacterised by synchrotron X-ray scattering.Experiments give the scattering curve I(Q) as afunction of Q (where Q=4πsinθ/λ; 2θ is thescattering angle, and λ is the wavelength). Guinieranalyses of lnI(Q) versus Q2 at low Q values give theradius of gyration RG, which measures the degree of

entation coefficients for the dp6–dp36 heparin fragments.circles. The predicted values for linear dp10–dp40 modelsexperimental sedimentation coefficients at rotor speeds ofmparison with the averaged experimental sedimentation000 rpm using interference optics. Beneath the graphs, thestructure of dp12 (PDB code 1HPN) are shown.


macromolecular elongation. Due to differences inthe lengths of the heparin fragments, different Qranges were required for each fragment in order towork within acceptable QRG ranges (Fig. 5a). Thus,the Guinier fit Q range of 0.2–0.7 nm− 1 for dp6 wassuccessively reduced in stages to 0.14–0.40 nm−1 fordp36 (Fig. 5 legend). The mean Guinier RG valuesincreased from 1.33±0.26 nm for dp6 to 3.12±0.10 nm for dp36 (Table 1). The RG values of 16heparin models corresponding to linear dp10–dp40structures were calculated from sphere modelsderived from the linear dp12 NMR structure.12,40

The calculated RG values increased linearly with thesize of heparin (Fig. 5d). In contrast, Fig. 5d showsthat, unlike the linear increase in the s20,w valueswith size, the Guinier RG values of the six heparinfragments do not exhibit a linear increase withheparin size, with deviations being seen for dp24,dp30, and dp36. The difference from the AUC resultsis attributable to the better resolution of the X-rayscattering method. The RG values in Fig. 5d arecomparable with that of 3.2 nm for dp32 measuredat higher concentrations between 6 mg/ml and20 mg/ml in 0.2 M NaCl.29

If the macromolecule is sufficiently elongated inshape, the cross-sectional radius of gyration RXSvalue monitors the degree of bend within the

Fig. 5. Experimental Guinier and P(r) X-ray scattering anadp36 at concentrations of 0.5 mg/ml. Filled circles were used tlines, as shown. TheQ ranges used for RG analyses were 0.2–0.dp18, 0.08–0.44 nm−1 for dp24, 0.08–0.40 nm−1 for dp30, andplots for dp18–dp36 at concentrations of 0.5 mg/ml. The filledbest-fit lines, as shown. The Q ranges used were 0.9–1.5 nm−1

analyses for dp6–dp36. The r values of the maximum atM1 wergreen), 1.30 nm (dp24: cyan), 1.32 nm (dp30: pink), and 1.40 nmM2 were 3.7 nm (dp24), 3.4 nm (dp30), and 4.2 nm (dp36). T(dp12), 7.4 nm (dp18), 9.4 nm (dp24), 10.3 nm (dp30), and 12.3from Guinier plots ( ) and P(r) curves (▴) with the predicted

macromolecular length. Cross-sectional Guinieranalyses of lnI(Q)Q versus Q2 at larger Q valuesshowed the required linearity for dp18–dp36 in a Qrange of 0.9–1.5 nm−1. Fits gave values of 0.50 nmfor dp18 up to 0.53 nm for dp36 (Fig. 5b, Table 1).The dp6 and dp12 fragments were too small for thisanalysis to be carried out. The small increase in theRXS values with heparin fragment size indicates thatthe fragments are indeed elongated but becomeprogressively slightly more bent with increase insize. Combination of the RG and RXS valuesaccording to the relationship L2 =12(RG

2−RXS2) for

an elliptical cylinder41 showed that dp18, dp24,dp30, and dp36 have approximate lengths of 7.0 nm,9.1 nm, 9.6 nm, and 10.7 nm, in that order. Incontrast, larger L values of 14 nm for dp26, 16 nm fordp32 ,and 20 nm for dp38 have been determined onthe basis of a smaller RXS value of 0.43 nm.29,30

Consideration of the relationship L2 =12(RG2 −RXS

2 )shows that the latter set of L values is too large to beconsistent with the measured RG values.The distance distribution function P(r) curve

calculated from the full I(Q) curve (Materials andMethods) provides RG values and model-indepen-dent determinations of overall lengths L followingan assumption of the value of the maximumdimension Dmax (Fig. 5c). The mean RG values

lyses of heparin dp6–dp36. (a) Guinier RG plots for dp6–o determine the radius of gyration RG based on the best-fit7 nm− 1 for dp6, 0.24–0.7 nm−1 for dp12, 0.12–0.52 nm−1 for0.14–0.40 nm−1 for dp36. (b) Guinier cross-sectional RXScircles were used to determine the RXS values based on thein all four cases. (c) The distance distribution function P(r)e 1.05 nm (dp6: black), 1.44 nm (dp12: red), 1.36 nm (dp18:(dp36: blue). The r values of the subsidiary maximum at

he maximum length L values were 3.0 nm (dp6), 6.0 nmnm (dp36). (d) Comparison of the experimental RG valuesRG values calculated from the linear models of Fig. 4 (○).

Table 1. X-ray scattering and sedimentation coefficient modelling fits for the solution structures of heparin fragments

Heparinfragment Filter

Number ofmodels

Hydratedspheresa RG (nm)b RXS (nm) R-factor (%)

Length L(nm)c s20,w

0 (S)d

dp6 Experimental 1.33±0.26;1.03±0.03

3.0 1.09±0.10

dp12 Experimental 1.83±0.13;1.81±0.08

6.0 1.35±0.03

dp18 None 5000 46–74 1.34–2.36 2.22–9.64 2.2–14.1 NA NARG, R-factor 9 55–64 2.07 0.44–0.51 2.2 7.4–8.0 1.02–1.47

Best fit 1 58 2.07 0.50 2.2 8.0, 7.0 1.29Experimental 2.07±0.05;

2.09±0.090.50±0.01 7.4 1.41±0.04

dp24 None 5000 59–94 1.56–3.02 0.26–11.69 1.3–16.6 NA NARG, R-factor 15 69–85 2.59–2.64 0.46–0.53 1.3–1.4 8.15–10.5 1.05–1.71


2.78±0.060.50±0.01 9.4 1.52±0.07



2.92±0.110.52±0.01 10.3 1.63±0.02



3.52±0.120.53±0.01 12.3 1.84±0.06

NA, not available.a The optimal totals of hydrated spheres are 53 for dp18, 71 for dp24, 88 for dp30, and 106 for dp36.b The first experimental value is obtained from Guinier RG analyses, and the second one is obtained from GNOM P(r) analyses.c The lengths L of the 9–15 best-fit models were calculated using HYDROPRO. The length of the best-fit model length was calculated

using HYDROPRO, and the second one was calculated from the modelled P(r) curve. The experimental L values are the model-independent values from the P(r) curve.

d The averaged experimental s20,w value is reported from absorbance (234 nm) and interference data sets, with absorbance data beingrecorded at 40,000 rpm and 50,000 rpm, and with interference data being recorded at 40,000 rpm, 50,000 rpm, and 60,000 rpm.


obtained from the P(r) curves increase from 1.03±0.03 nm for dp6 to 3.52±0.12 nm for dp36 (Table 1).Comparison of the six pairs of mean Guinier andP(r) RG values showed good agreement to within0.01–0.4 nm (Table 1). Again, the RG values do notincrease linearly with size (Fig. 5d). Model-indepen-dent L values are determined from the r value wherethe P(r) curve reaches zero at large r. The experi-mental L values for dp6 and dp12 were 3.0 nm and6.0 nm, respectively, in good agreement with alength of 3.2 nm for an unhydrated linear dp6 modeland a length of 5.9 nm for an unhydrated lineardp12 model, provided that a hydration shell of0.6 nm (= 2×0.3 nm) thickness is added to thesemodel lengths.42 The experimental L values fordp18, dp24, dp30, and dp36 were found to be7.4 nm, 9.4 nm, 10.3 nm, and 12.3 nm, respectively(Fig. 5c). These values show increasing deviationfrom the lengths of linear dp18, dp24, dp30, anddp36 models (i.e., 8.4 nm for dp18, 11.1 nm for dp24,13.6 nm for dp30, and 16.3 nm for dp36), showingthat heparin is not linear in solution. These valuesalso deviate from the L values determined abovefrom the RG and RXS values, and this is attributableto the assumption of an elliptical cylinder shape forthis L calculation. In conclusion, both the RG and theL values from the P(r) curves indicate a measurabledegree of bending from linearity in larger heparinfragments. The P(r) curves also provide the mostfrequently occurring interatomic distance M withinthe heparin structure from the r value of the peak

maximum. The maximum M1 was observed at rvalues that started at 1.05 nm for dp6 and slowlyincreased to 1.41 nm for dp36 (Fig. 5 legend). Asecond subsidiary maximum M2 may be present atabout 3.4–4.2 nm for dp24, dp30, and dp36. Theappearance of this second feature may correspondto a regular structure that becomes more evident inlonger heparin structures.

Constrained modelling of heparin fragments

Solution structures for the four larger heparinfragments dp18, dp24, dp30, and dp36 weredetermined by constrained scattering modelling,using the linear models created from the NMRstructure of dp12 as starting constraint. Modellingwas not performed for dp6 or dp12 becausetheir sizes were too small for this procedure.In the models, the bond connectivity betweenoligosaccharide rings was maintained, while the phi(φ) and psi (ψ) angles at each glycosidic bond (Fig. 1)were varied randomly in a range of up to ±45° fromtheir starting values. Trial calculations showed thatthis range of rotations was sufficient to produce bentstructures that would fit into the X-ray scatteringcurves. In all, 5000 models for each of the fourheparin fragments were generated. X-ray scatteringcurves were calculated from these models and fittedto the experimental curves. The R-factors and RGvalues were calculated for all the models, where R-factor is a measure of goodness-of-fit and RG was


calculated using the same Q range used for theexperimental Guinier fits (Fig. 5). The comparisonsof Fig. 6a–d showed that all the models (yellow

Fig. 6. Constrained modelling analyses of heparin dp18–dheparin dp18 are compared with their RG values. The verticalred circle (arrowed) denotes the best-fit model, and the greenother best-fit models, where visible, are shown in cyan close tois used in Figs. 7, 8, and 10. (b–d) The corresponding RG analysshown in that order. (e) The R factor values for the 5,000 trial m(f–h) The corresponding RXS analyses for each of the 5,000 mo

circles) spanned the experimental RG values (brokenlines), and that the best R-factor values were wellbelow the level of 5% required for excellent curve

p36. (a) The R-factor values for the 5000 trial models ofbroken line corresponds to the experimental RG value. Thecircle (arrowed) denotes the linear model from Fig. 4. Thethe R-factor minimum. The same colour coding for heparines for each of the 5000 models for dp24, dp30, and dp36 areodels of heparin dp18 are compared with their RXS values.dels for dp24, dp30 and dp36 are shown in that order.


fits.33 This showed that 5000 randomised modelswere sufficient to determine the best-fit heparinsolution structures from them. The lowest R-factorshad RG values (red and cyan circles) that agreed wellwith the experimental RG values. In distinction, thelinearmodels for dp18, dp24, dp30, and dp36 showedlarge deviations from the minimum (green circles).For dp18, modelling analyses show that this has a

slightly bent structure that accounts for the X-rayand AUC data. All nine best-fit models gave thesame R factor of 2.2% and the same RG value of 2.07nm that agree with the experimental RG value of2.07±0.05 nm (Fig. 6a, Table 1). The best-fit dp18models show a maximum length L of 7.6–8.0 nm, ingood agreement with the experimental maximumlength of 7.4 nm. In contrast, the linear dp18 modelgave a worsened R-factor of 3.3%, an RG value of2.25 nm, and an L value of 8.4 nm. Visual agreement

Fig. 7. X-ray modelling curve fits for best-fit and poor-fit dand insets show the P(r) distance distribution functions. Trepresented by black circles or lines, respectively; the red linesfrom trial-and-error searches; and the green lines and modelsFig. 4. The best-fit and linear models are shown to the right, ttheir L values in the P(r) curves. (a–d) The four panels show t

between the experimental I(Q) curve and themodelled I(Q) curve, and that between the experi-mental P(r) curve and the modelled P(r) curve wereexcellent (Fig. 7a). The calculation of sedimentationcoefficients from the nine best-fit models gave s20,w

0

values of 1.02 –1.47 S. The best-fit model gave avalue of 1.29 S, which agrees well with theexperimental s20,w

0 value of 1.41±0.04 S, this beingwithin the usual precision of 0.3 S for thesecalculations.34

For dp24, modelling analyses showed similar goodagreements with X-ray and AUC, but correspondedto slightly more bent structures. For the 15 best-fitmodels, the R-factor and RG values ranged from 1.3%to 1.4% and from 2.59 nm to 2.64 nm, respectively,where the latter corresponds well with the experi-mental RG value of 2.67± 0.15 nm (Table 1). Themaximum lengths of the models were 8.2–10.5 nm, in

p18–dp36 models. The main panels depict the I(Q) curves,he experimental I(Q) and P(r) X-ray scattering data areand models correspond to the best-fit dp18–dp36 modelscorrespond to the linear poor-fit dp18–dp36 models fromogether with their maximum lengths for comparison withhe analyses for dp18, dp24, dp30 and dp36 in order.

Fig. 8. Superimposition of the 9–15 best-fit models for dp18–dp36. Each set of best-fit models for the four heparinfragments was superimposed globally using Discovery Studio VISUALISER software, then their non-hydrogen atomswere displayed as shown. The best-fit model from Fig. 7 is shown in red, while the related best-fit structures are shown incyan.


Table 2. Summary ofφ andψ angles in heparin structures

IdoA–GlcNS GlcNS-IdoA

φ (°) ψ (°) φ (°) ψ (°)

Five crystalstructures (2000)a

−75±10 135±13 78±16 103±19

Nineteen crystalstructures(current study)a

−79±20 132±19 84±22 100±19

NMR structure −55 135 108 83dp18 −55±25 138±21 105±26 90±32dp24 −40±24 139±27 97±29 90±29dp30 −55±26 139±26 108±23 73±20dp36 −53±32 131±31 127±21 75±27

a No outliers were included in these averages (see the text).


good accord with an L value of 9.4 nm. The linearmodel again showed a worsened R-factor of 4.8%, anRG value of 2.94 nm, and an L value of 11.1 nm. Theagreement between the experimental and the mod-elled I(Q) and P(r) curves was excellent (Fig. 7b). The15 modelled s20,w

0 values of 1.05–1.71 S are compara-ble with the experimental s20,w value of 1.52± 0.07 S,and the best-fit model gave a value of 1.50 S.For dp30, modelling analyses showed similar

good agreements with X-ray and AUC, in whichdeviation from a linear structure for dp30 becomespronounced. The 14 best-fit dp30 models gave R-factor values of 3.0–3.3%, RG values of 2.76–2.88 nm,and L values of 9.4–11.8 nm. These correspond wellwith the experimental RG value of 2.83± 0.14 nmand an L value of 10.3 nm (Table 1). The deviationsfrom a linear dp30 model are larger, for which theR-factor is 6.3%, the RG value is 3.41 nm, and theL value is 13.6 nm. The agreement between theexperimental and the modelled I(Q) and P(r)curves was again excellent (Fig. 7c). The 14 modelleds20,w0 values of 1.38–1.89 S agree well with theexperimental s20,w value of 1.63± 0.02 S, with thebest-fit model giving a value of 1.71 S.For dp36, similar good agreements between the

models and the X-ray and AUC data were obtained,and the deviation obtained from a linear dp36structure was larger. The 14 best-fit dp36 modelsgave R-factor values of 3.4–3.8%, RG values of 3.18–3.28 nm, and L values of 10.5–12.9 nm. The latteragrees well with the experimental RG value of 3.12±0.10 nm and an L value of 12.3 nm (Table 1), eventhough the availability of 5000 randomised modelsin this case reduced the quality of the fits in Fig. 6dcompared to those in Fig. 6a and b. The best-fitmodels deviate from the parameters for the lineardp36 model, which have an R-factor of 5.3%, an RGvalue of 3.82 nm, and an L value of 16.3 nm. Themaxima M1 and M2 become more noticeable in theP(r) curve for the best-fit model (Fig. 7d), and theirr values agree with those seen experimentally.The 14 modelled sedimentation coefficients calcu-lated from the best-fit dp36 models ranged between1.59 S and 2.00 S, in good agreement with theobserved s20,w value of 1.84± 0.06 S, with the best-fitmodel giving a value of 1.84 S.In conclusion, the best-fit models for dp18, dp24,

dp30, and dp36 show progressively more bentstructures in solution with increase in heparin size.Compared to the lengths of the linear models, thesebeing the most extended ones possible, the fourheparin fragments are reduced in length by 18%,16%, 29%, and 29%, in that order. This overallconclusion applies to all the best-fit models in eachof the four structure determinations. This is illus-trated by the superimposition of the 9–15 best-fitmodels in each fragment (Fig. 8), which showed thatan increase in bending with increase in size iscommon to all of them. In the case of dp30, andmoreso with dp36, the appearance of the minor peak M2in the experimental P(r) curve is consistent with theappearance of more bending in the larger heparinfragments. In all four cases, the bent models showed

s20,w0 values that are similar to those of the linearmodels, indicating that the AUC data are not able todistinguish between slightly bent and linear struc-tures, unlike the X-ray scattering data.

Comparison with heparin conformations incrystal structures

We now survey the heparin linker conformation in19 heparin–protein crystal structures19–33 and theNMR dp12 solution structure.12 The two majorconformations of six-membered iduronate rings inheparin are the 1C4 chair and the 2S0 skewboat.43 Thetwo forms can interconvert with relatively littledisturbance to glycosidic linkages to neighbouringresidues, and the polysaccharide chain need not bendas a consequence, although the relative positions ofsulphate groupswithin the ringwill alter. In terms ofthe glycosidic linkages, information on their confor-mation in heparin is available from analyses of theirφ and ψ angles (Fig. 1). The first survey of fiveheparin–protein crystal structures43 showed thatthe average φ and ψ angles were −75° and 135° (18values for each), respectively, for IdoA-GlcNSglycosidic bonds, whereas these were 78° and 103°(15 values each), respectively, for GlcNS–IdoAglycosidic bonds (standard deviations of 10–19°).These five structures14,15,23 show similar heparingeometries with that of the NMR structure of dp12,where the φ and ψ angles were −55° and 135°,respectively, for IdoA–GlcNS, and 108° and 83°,respectively, for GlcNS–IdoA.12 Thus, the boundconformation is similar to that in solution (Table 2).The current availability of 19 heparin–protein crystalstructures enabled this analysis to be extended(Fig. 9a and b). All five outliers in Fig. 9a and bcorresponded to the first or the last residue of thebound heparin structure. It appears likely that theseterminal residues at the reducing or non-reducingends have greater freedom to reorientate themselvesin the crystal structures, and the outliers are not con-sidered significant. After the removal of five pairs ofoutliers shown in Fig. 9a and b, the average φ and ψangles of IdoA–GlcNS glycosidic bondswere remark-ably similar to previous values of −79° and 132° (65values each), respectively, whereas the averageφ and

Fig. 9. φ and ψ dihedral angles for heparin fragments. The atoms defining the φ and ψ angles are shown in Fig. 1.(a and b) Sixty-seven pairs of IdoA–GlcNS and 62 pairs of GlcNS–IdoA φ–ψ angles found in 19 protein–heparincomplexes are shown as open circles (PDB codes 1AZX, 1AXM, 1BFB, 1BFC, 1E0O, 1EO3, 1FQ9, 1GMN, 1GMO, 1G5N,1RID, 1QQP, 1XMN, 2AXM, 2GD4, 2HYU, 2HYV, 3DY0, and 3EVJ). The corresponding 10 and 12 pairs of φ–ψ anglesfrom two dp12 NMR solution structures are shown as filled circles (PDB code 1HPN). Note that many of the latter φ–ψangles are similar, with values of 10°–10° or 12°–12°. (c and d) The corresponding φ–ψ angles from the best-fit model inFig. 7 for each of dp18 (8–9 values: red), dp24 (11–12 values: green), dp30 (14–15 values: yellow), and dp36 (17–18 values:blue) are shown in the same scale as that in (a) and (b). Beneath the graphs, the superimposition of dp5 fragments found in12 or 13 heparin–protein crystal structures is shown. From left to right, the dp3 fragments are shown centered on thesecond (GlcNS), third (IdoA), and fourth (GlcNS) rings of dp5, each of which is viewed face-on. Gray, carbon; red, oxygen;yellow, sulphur; blue, nitrogen.


ψ angles of GlcNS–IdoA glycosidic bonds weresimilar to previous values of 84° and 100° (58 valueseach), respectively. Here, the standard deviations

have increased to 19–22°. Overall, it is concluded thatheparin has a well-defined and similar extendedconformation when bound to proteins.


Conformational variability was observed in theextended structures of bound heparin. While con-siderations of structural resolution and carbohy-drate refinement parameters may preclude detailedanalyses, such as the existence of skew-boat or chair-ring conformations, it should be possible to inferrelative IdoA and GlcNS ring orientations. Thecommonly occurring dp5 fragment in 12 or 13 of the19 crystallographically observed heparin structureswas superimposed on the second, third, and fourthrings of dp5 (Fig. 9, bottom). The two rings flankingthe central ring were in similar locations, as expectedfrom Fig. 9a and b, with only one instance of a 180°GlcNS ring flip (visible at the top of the centralimage in Fig. 9). The sulphate and carboxylategroups in the two flanking rings were distributed ina range of up to 0.5 nm, while this positionalvariability was reduced to less than 0.1 nm in thecase of the central ring alone. The superimposi-tions showed that six or seven structures of the19 exhibited clear bends in an otherwise extendedheparin structure. For example, the longest-observed crystallised heparin dp10 is found in the2:2 complex of fibroblast growth factor 1 andfibroblast growth factor receptor 2, in which dp10links the four protein subunits together.16 In the fiveIdoA–GlcNS glycosidic bonds, one ψ angle was 78°,in distinction to the average ψ angle of 132°. In thefour GlcNS–IdoA glycosidic bonds, two ψ angles

Fig. 10. Comparison of selected crystal structures for hepsolution structures. Proteins are shown by blue ribbons, whilfollows. (a) The complex of fibroblast growth factor 1 and fibrothe longest cocrystallised heparin dp10 (PDB code 1E0O). Thfibroblast growth factor 2 and fibroblast growth factor receptodp6 and dp8 molecules (PDB code 1FQ9). (c) Two moleculeslinking (PDB code 1RID). (d) Basic fibroblast growth factor (Fbinding sites (PDB code 1BFC). (e and f) Heparin dp18 and dpsolution structures for heparin.

were 141° and 135°, instead of the average ψ angle of84°. Consequently, two significant bends werevisible in the dp10 structure (Fig. 10a). Heparin dp8bound to VCP assists the virus in its infection cycle27

(Fig. 10c). In the four IdoA–GlcNS glycosidic bonds,oneφ value is −106°, in distinction to the mean valueof −79°; one ψ angle was 78°, in distinction to theaverage ψ angle of 132°. In the three GlcNS–IdoAglycosidic bonds, oneψ anglewas 135°, insteadof theaverage ψ angle of 84°. Sometimes, the heparinconformation is not the same when binding to thesame protein. For example, the crystal structure offour thrombin molecules complexed with two dp8molecules showed that the two dp8 molecules aresandwiched between two different thrombin mono-mers in non-equivalent conformations.18

The best-fit solution structures of dp18, dp24,dp30, and dp36 (Fig. 7) can now be compared withthe observed heparin conformations in crystalstructures. The average φ and ψ angles of theIdoA–GlcNS glycosidic bonds were very similar at−55° and 138° (dp18: 9 values), −40° and 139° (dp24:12 values), −55° and 139° (dp30: 15 values), and−53° and 131° (dp36: 18 values) (Fig. 9c). While theirstandard deviations are higher at 20–32° (Table 2),no outliers were present. The φ angles fromscattering may be slightly reduced compared tothe crystal structures, while being more similar tothe NMR structure (Table 2). Likewise, the average

arin–protein complexes with the best-fit dp18 and dp36e heparins are shown in red. The crystal structures are asblast growth factor receptor 2 (FGF1–FGFR2), to illustratee bending in dp10 should be noted. (b) The complex ofr 1 (FGF2–FGFR1), to illustrate the binding of two heparinof VCP and two heparin dp8, to illustrate heparin cross-GF) with dp6, to illustrate the surface location of heparin36 from Fig. 7, to illustrate the similarity of the crystal and


φ and ψ angles of the GlcNS–IdoA glycosidic bondswere very similar at 105° and 90° (dp18: 8 values),97° and 90° (dp24: 11 values), 108° and 73° (dp30: 14values), and 127° and 75° (dp36: 17 values) (Fig. 9d).No outliers were again present. The φ angles fromscattering may be slightly increased compared to thecrystal structures, while being more similar to theNMR structure (Table 2). It is concluded that,despite the additional bending seen in dp36 com-pared to dp18, heparin is well-maintained insolution as a semi-rigid extended structure (Fig. 8).Its conformations are similar to those seen in 19heparin–protein crystal structures, while the dp12NMR structure (Fig. 4) may be too linear tocorrespond to heparin conformations in solution.

Conclusions

In this study, we have here determined the firstmolecular structures in solution for heparin dp18–dp36. These provide new insight into the way thatheparin (and, by analogy, heparan sulphate) inter-acts with its protein ligands.We show that heparin iswell-represented as an extended and semi-rigidstructure in solution. The dp6 and dp12 structuresby both NMR12 and constrained scattering model-ling (here) show comparatively little bending. Start-ing with dp18, the heparin fragments progressivelyshow higher degrees of partial bending up to dp36,while maintaining approximately linear segmentswithin these structures. The coordinate models havebeen deposited in the so-named Protein Data Bank(PDB)†. As far as we are aware, this study is the firstsuccessful application of constrained scatteringmodelling to oligosaccharides, with this methodhaving previously been used to determinemolecularstructures for multidomain antibody and comple-ment proteins.33,34 We envisage that this modellingapproach can be extended to structure determina-tions for other oligosaccharides and polynucleotides.While solution scattering is traditionally a low-

resolution method that generates shape envelopes,its utility to the determination of medium-resolutionheparin solution structures is assisted by con-strained modelling. Constrained modelling deter-mines a three-dimensional molecular structure thatbest accounts for the observed scattering curve. It isreliable in defining the averaged extension andbending of the polysaccharide chains and inderiving information on flexibility. It cannot providethe resolution necessary to provide coordinateswithin the chain, even if averaged φ–ψ values arecalculated from constrained modelling. Eventhough unique structure determinations are notpossible due to random molecular orientationsobserved by scattering, this modelling is able torule out structures that are incompatible with thescattering curves. Hence, the basic premises ofconstrained modelling are twofold: (i) by fixing

†http://www.rcsb.org/pdb/

parts of the structural analyses to what is alreadyknown about the macromolecule, scattering fits aresubjected to significantly fewer modelling variables;and (ii) by identifying poor-fit models and rejectingthese, good-fit models are obtained and ranked inorder of their compatibility with the data. A relatedstrategy resulted in the NMR solution structure ofdp12.12 By NMR, the measurements of 1H–1Hnuclear Overhauser enhancements for heparinpermitted these to be tested against molecularmodels for heparin. Here, for the constrainedscattering modelling of heparin, the only variablesare the φ and ψ angles of each glycosidic bond. Therandomised variation of these angles readilyresulted in the V-shaped graphs of R-factor versusRG values, from which the best-fit models wereidentified at the lowest R-factor values. In fact, thequality of the dp18–dp36 scattering curve fits isbetter than that obtained for other recent examplesof multidomain proteins such as complement factorH (FH) or complement receptors types 1 and 2.44–46

If constrained modelling is not employed, only amacroscopic view of heparin structures in solu-tion analysed using worm-like sphere models ispossible.29,30,47 The two approaches are concep-tually different. In the worm-like model, flexibilityis dynamic (fluctuating) and distributed continu-ously, while constrained modelling presents afamily of static structures that fit the experimentalX-ray data.Our structural study of dp6–dp36 provides new

insights on 19 crystal structures for heparin–proteincomplexes (Materials and Methods). The crystalstructures are notable for the observation of com-paratively small heparin fragments that range insize from dp4 to dp10, with the most common beingdp5. These sizes are sufficient to form well-definedheparin–protein complexes (Fig. 10). The majority ofcontacts between the protein surface and heparin areionic between basic amino acid side chains andanionic sulphate groups. The axial orientations ofsulphate groups in heparin are repeated after everyfour oligosaccharide rings. Thus, dp4 possesses asufficient number of at least six sulphate groupsand two carboxylate groups to generate proteinspecificity for heparin. Within each dp4 fragment,two sulphate groups are located in similar butopposed axial orientations in GlcNS residues, whilethe third sulphate and the carboxylate group arelocated in opposed axial orientations in IdoA resi-dues (Fig. 4). Views of 12–13 superimposed dp3fragments centred on either IdoA or GlcNS residuesconfirm that these axial orientations are largelypreserved and approximately aligned with eachother between IdoA and GlcNS residues (Fig. 9). Thecurrent study shows that the solution structures ofheparin in sizes of up to dp12 in size are generallylinear, although not necessarily maintaining aregular helical repeat. Linearity may be influencedby the repulsion of the sulphate and carboxylategroups, which assist in this regard but are not man-datory.48 We show that, if the heparin fragments aredp18 or larger, bending of its linear structure


becomesmore pronounced, even though the mean φand ψ angles remain unchanged (Table 2). In theconstrained modelling, this bending appears askinks in the heparin structure at a few positions.Thus, heparin appears as a succession of linearregions similar to dp6 or dp12 that are joined bysemi-rigid kinks. The physical basis for the occur-rence of kinks may result from the occasionaloccurrence of GlcA-GlcNAc sequences, and notIdoA–GlcNS sequences (Fig. 1), but the crystalstructures show that kinks also occur in otherregions (Fig. 10). Overall, our X-ray modelling ofdp6–dp36 clarifies that large heparin segments insolution form extended stable and preformed con-formations that are ideal for protein ligation,including the presence of occasional kinks in thesesolution structures.This study opens the way to analysing more

complex heparin–protein interactions, including theoccurrence of two heparin binding sites on the sameprotein. Can the same heparin molecule bindsimultaneously to a double heparin binding site, ordoes heparin cross-link different proteins? Theheparin-binding regulatory chemokine macrophageinflammatory protein 1α (MIP-1α) is one case inpoint.49 Heparin binds strongly to dimeric MIP-1α,in distinction to monomeric or tetrameric MIP-1α.Heparinase III digests, and molecular modellingsuggests that two dp14 fragments joined by aflexible dp6 fragment bind to dimeric MIP-1α. Thisconclusion is explained by our modelling of dp30and dp36, which indicates the existence of linearsegments joined by semi-rigid kinks. Physiologically,multiple interactions of this type will account for thepackaging of heparin–protein complexes withinmastcell granules. The binding of heparin dp26 to thedimer of interferon-γ represents a different case,where the interaction does not necessarily involvebent heparin structures.30 In distinction to these cases,crystal studies show that heparin is able to cross-linkmonomers to form complexes (e.g., the fibroblastgrowth factor family and their receptors).16,17 Thecomplement regulator FH, which is composed of 20short complement regulator (SCR) domains, is adistinct example altogether.50 The heparin–FH inter-action at cell surfaces protects host cells fromattackbythe innate immune system, directing this insteadagainst pathogenic bacteria, which often lack apolyanionic oligosaccharide coating. Two differentheparin binding sites occur at the SCR-7 and SCR-20domains in FH. Up to now, it is not clear whetherflexibility within FH or heparin could permit SCR-7and SCR-20 to bind simultaneously to the sameheparin oligosaccharide. Our new dp18–dp36 struc-tures indicate that heparin has insufficient flexibilityto facilitate the simultaneous binding of two FH siteswith one heparin. It is more likely that FH cross-linksdifferent heparin oligosaccharides to form very largeoligomers.50 At least two different heparin sites mayhave evolvedwithin FH in order to enable FH to bindselectively to host cells showing an appropriateabundance of polyanionic surfaces, in distinction topathogens that lack these FH sites.

A further key question in relation to heparin–protein interactions is whether protein conforma-tional changes occur on heparin binding. Theavailability of 19 heparin–protein crystal structurespartly answers this question, being mainly limitedby the relatively small sizes of the heparin frag-ments. Physiologically, heparin (and heparan sul-phate) exists as long oligosaccharides. The largestcrystallographically observed heparin to date is adecasaccharide.16 Even when a heparin 14-mer wascocrystallised with a protein, the largest crystallo-graphically observed heparin was as small as apentasaccharide dp5.24 Heparin may induce confor-mational changes in proteins in order to alteractivities. The best-known case is that of antithrom-bin, whose β-sheet structure is allosterically activat-ed by heparin in a series of events in order to inhibitthe coagulation factors IXa and Xa and thrombin.22

In most crystal structures, heparin binding sites arefound on surface-exposed positions (Fig. 10d), andconformational changes do not appear required forcomplex formation. The case of FH is distinct fromthese two scenarios. Each SCR domain is stabilisedby two conserved disulphide bridges at each end ofits β-sheet structure and a hydrophobic core thatincludes a conserved Trp residue.51 A single SCRdomain will accommodate heparin dp8 withoutconformational change.27 However, the linker con-formations between SCR domains are variable andnot easily predicted.52 Flexibility in inter-SCRlinker conformations has been demonstrated bythe different solution and crystal structures of SCR-1/2 in complement receptor type 2, in which thetwo SCR domains are joined by a long eight-residue linker.53 If heparin binds to two neighbour-ing SCR domains, heparin will need to be at leastdp18 in size to do so, and its binding may alter theinter-SCR conformation. An initial study of dp10binding to a recombinant SCR-6/8 fragment of FHshowed that either a conformational change oroligomer formation resulted.39 By this presentstudy, the improved understanding of dp18–dp36solution structures opens the way to clarifying howFH binds to heparin, including the consideration ofheparin-induced conformational change in itsdomain structure.50

Materials and Methods

Purification of heparin fragments

Oligosaccharide fragments of heparin were preparedfrom bovine lung heparin, as previously described.16 Insummary, about 80 mg of heparinase-I-digested heparinwas dissolved in 1.5 ml of 2% ammonium bicarbonate, andthen applied to a preparative gel-permeation chroma-tography column (100 cm×1.6 cm, packed with Biogel P-10; Bio-Rad, UK). The heparin fragments were eluted using2% ammoniumbicarbonate at a flow rate of 0.2ml/min in 2-ml fractions. The absorbance of the fractions at 234 nm wasmeasured, and the fractions corresponding to each resolvedpeak were pooled. Heparin oligosaccharides larger than


dp16 were not completely resolved (Fig. 2). Each fractionwas evaporated under reduced pressure and lyophilisedbefore assessment of their size by analytical gel-permeationchromatography.37 This was carried out using two columns(TSK G3000 SW-XL, 30 cm; TSK G2000 SW-XL, 30 cm;Anachem, UK) connected in series. The eluant was 0.1 Mammoniumacetate solutionat a flowrate of 0.5ml/min, andheparin was detected with a refractive index detector (RI-1530; Jasco, UK). The chromatography system was calibrat-ed using the First International Reference Reagent LowMolecular Weight Heparin for Molecular Weight Calibra-tion (NIBSC 90/686). Heparin quantisationwas achieved byintegration of the area under each refractive index peak andcomparison with a standard curve prepared using knownconcentrations of low-molecular-weight standards.

AUC of heparin fragments

Sedimentation velocity experiments were performedusing two Beckman XL-I analytical ultracentrifuges (Beck-man Coulter, Inc., Palo Alto, CA) equipped with bothabsorbance and interference optics. Experiments withdp6–dp36 fragments were performed at concentrationsof 0.5 mg/ml in 10 mMHepes and 137 mMNaCl (pH 7.4).Buffer density (1.00480 g/ml) was measured at 20 °Cusing an Anton-Paar DMA5000 density meter. A partialspecific volume of 0.467 g/ml was used for heparin.29Runs were carried out in an eight-hole AnTi50 rotor withstandard double-sector cells with column heights of12 mm at 20 °C using absorbance optics at 234 nm andinterference optics. Sedimentation velocity data werecollected at 40,000 rpm and 50,000 rpm using absorbanceoptics, and at 40,000 rpm, 50,000 rpm, and 60,000 rpmusing interference optics. The continuous c(s) analysismethod was used to determine the sedimentation coeffi-cients s20,w of heparin fragments using SEDFIT software(version 9.4).54,55 The c(s) analysis directly fits thesedimentation boundaries using the Lamm equation, thealgorithm for which assumes that all species have thesame frictional ratio f/fo in each fit. The final SEDFITanalyses used a fixed resolution of 200 and optimised thec(s) fit by floating the meniscus and cell bottom whenrequired and by holding the f/fo value, baseline, and cellbottom fixed until the overall root-mean-square devia-tions and visual appearance of the fits were satisfactory(Fig. 3). The f/fo values for the heparin fragments werecalculated to be 1.33 for dp6, 1.39 for dp12, 1.64 for dp18,1.78 for dp24, 1.82 for dp30, and 1.88 for dp36, startingfrom the known volume of each fragment.56

X-ray scattering of heparin fragments

X-ray solution scattering of the six heparin fragments(dp6, dp12, dp18, dp24, dp30, and dp36) was performedon beamline ID02 at the European Synchrotron RadiationFacility (Grenoble, France) in two sessions with a ringenergy of 6.0 GeV.57 In the first session, data werecollected for the six fragments in 16-bunch mode usingbeam currents from 79 mA to 86 mA. In the secondsession, data were collected for the six fragments in four-bunch mode using beam currents from 30 mA to 43 mA.Data were acquired using an improved fibre opticallycoupled high-sensitivity and dynamic-range charge-cou-pled device detector (FReLoN) with a smaller beamstop.The sample-to-detector distance was 2.0 m. Experimentsused the same heparin concentration (0.5 mg/ml) andbuffers as used for the sedimentation velocity experi-ments. For each heparin fragment, samples were mea-

sured in a flow cell, whichmoved the sample continuouslyduring beam exposure in 10 time frames with differentexposure times of 0.1 s, 0.2 s, 0.25 s, and 0.5 s to check forthe absence of radiation damage effects. This exposurewas optimised using on-line checks for the absence ofradiation damage to show that this was not detectable,after which the frames for 0.5 s were averaged in order tomaximise signal-to-noise ratios.Guinier analyses give the radius of gyration RG, which

characterises the degree of structural elongation insolution if the internal inhomogeneity of scattering withinthe macromolecules has no effect. Guinier plots at low Qvalues give the RG and the forward scattering at zero angleI(0):41

lnI Qð Þ = lnI 0ð Þ − R 2GQ

2 = 3

This expression is valid in a QRG range of up to 1.5. If thestructure is elongated (i.e., rod-shaped), the radius ofgyration of the cross-sectional structure RXS and the meancross-sectional intensity at zero angle [I(Q)Q]Q→ 0 para-meters are obtained from:

ln I Qð ÞQ½ � = ln I Qð ÞQ½ �QY0 − R 2XS Q

2 = 2

The RG and RXS analyses were performed using aninteractive PERL script program SCTPL7 (J. T. Eaton andS. J. Perkins, unpublished software) on Silicon GraphicsO2 Workstations. Indirect Fourier transformation of thefull scattering curve I(Q) in reciprocal space gives thedistance distribution function P(r) in real space. This yieldsthe maximum dimension of the macromolecule L and itsmost commonly occurring distance vector M:

P rð Þ = 12π2

Z l

0I Qð ÞQr sin Qrð ÞdQ

The transformation was carried out using GNOMsoftware.58 For dp6, the full X-ray I(Q) curves contained506 data points in the Q range between 0.20 nm−1 and0.89 nm−1. For dp12, 171 data points were used in the Qrange between 0.24 nm−1 and 1.40 nm−1. For dp18, 571data points were used in the Q range between 0.12 nm−1

and 2.0 nm−1. For dp24, 280 data points were used in theQ range between 0.08 nm−1 and 1.0 nm−1. For dp30, 600data points were used in the Q range between 0.11 nm−1

and 2.18 nm−1. For dp36, 252 data points were used inthe Q range between 0.11 nm−1 and 1.81 nm−1.

Molecular modelling of heparin oligosaccharides

To analyse the conformation of free and protein-boundheparin oligosaccharides available in the PDB, theglycosidic dihedral angles φ and ψ corresponding to thetorsion angles O5′–C1′–O4–C4 and C1′–O4–C4–C3, re-spectively (Fig. 1), were calculated for all the IdoA–GlcNSand GlcNS–IdoA disaccharides using INSIGHT II 98.0molecular graphic software (Accelrys, San Diego, CA) onSilicon Graphics O2 and OCTANE Workstations. Thesolution NMR structure of free dp12 was used (PDB code1HPN). The following 19 heparin–protein crystal struc-tures were identified from database searches of the PDB†:biologically active dimer of acidic fibroblast growth factor(PDB codes 1AXM and 2AXM), basic fibroblast growthfactor (PDB codes 1BFB and 1BFC), complex of fibroblastgrowth factor 1 and fibroblast growth factor receptor 2(PDB code 1E0O), complex of fibroblast growth factor 2


and fibroblast growth factor receptor 1 (PDB code 1FQ9),antithrombin (PDB codes 1AZX, 1EO3, and 3EYJ),thrombin (PDB code 1XMN), antithrombin–S195A com-plex with factor Xa (PDB code 2GD4), neurokinin 1 (PDBcodes 1GMN and 1GMO), annexin V (PDB code 1G5N),foot-and-mouth disease virus (PDB code 1QQP), VCP(PDB code 1RID), annexin A2 (PDB codes 2HYU and2HYV), and cleaved protein C inhibitor (PDB code 3DY0).The list is not exhaustive, and other PDB files (PDB codes1NQ9, 1SR5, 1TB6, 1XT3, 1ZA4, 2BRS, and 2B5T) alsocorrespond to heparin–protein crystal structures. Themajority of these were not analysed for this studybecause these involve heparin disaccharides or syntheticheparin mimetics.Linear models of heparin dp6–dp36 were constructed

using the NMR structure of dp1212 in the 1S0 configurationwith INSIGHT II 98.0 software. The superimposition offour dp12 molecules was used to create a dp42 oligosac-charide, from which the six heparin fragments dp6–dp36were obtained by removing non-required disaccharides.Here, the φ and ψ angles were −55° and 135°, respectively,for IdoA–GlcNS, and 108° and 83°, respectively, forGlcNS–IdoA (Fig. 9). The totals of 5000 conformationalmodels were created for each of dp18, dp24, dp30, anddp36 starting from these linear models. The φ and ψangles were randomised to take values in the maximumrange of −45° or 45° from their starting values using theTorsionKick function in a PERL script that was modifiedfrom the ExtractAngle.pl script provided with DiscoveryStudio molecular graphics software (version 2.1)(Accelrys). For example, for dp36, a total of 18 φ and ψangles for IdoA–GlcNS and a total of 17 φ and ψ angles forGlcNS–IdoA were modified in this way.

Constrained scattering and sedimentationcoefficient modelling

Each heparin model was used to calculate X-rayscattering curves for comparison with the experimentalcurves using Debye sphere models.44–46 A cube sidelength of 0.513 nm, in combination with a cutoff of fouratoms, was used to create the spheres in the heparinmodels of dp18–dp36. The hydration shell correspondingto 0.3 g/g H2O was created by adding spheres to theunhydrated sphere models using HYPRO,59 where theoptimal total of hydrated spheres is listed in Table 1. TheX-ray scattering curve I(Q) was calculated using the Debyeequation as adapted to spheres and assuming a uniformscattering density for the spheres:40

I Qð ÞI 0ð Þ = g Qð Þ n−1 + 2n−2

Xmj=1

AjsinQrjQrj

0@

1A

g Qð Þ = 3 sinQR−QR cosQRð Þð Þ2 =Q6R6

where g(Q) is the squared form factor for the sphere ofradius r, n is the number of spheres filling the body, Aj isthe number of distances rj for that value of j, rj is thedistance between the spheres, and m is the number ofdifferent distances rj. Other details are given else-where.42,44–46 X-ray curves were calculated withoutinstrumental corrections, as these are considered to benegligible for the pinhole optics used in synchrotron X-ray instruments. First, the number of spheres N in thedry and hydrated models after grid transformation was

used to assess steric overlap between the heparindisaccharides, where models showing less than 95% ofthe optimal totals were discarded (Table 1). Next, themodels were assessed by calculation of the X-ray RGvalues in the same Q ranges used for the experimentalGuinier fits in order to allow for any approximationsinherent in the use of the QRG range of up to 1.5. Modelsthat were filtered using the N and RG filters were thenranked using a goodness-of-fit R-factor in order to iden-tify the best-fit 9–15 models.Sedimentation coefficients s20,w

0 for the best-fit scatteringmodels were calculated directly frommolecular structuresusing the HYDROPRO shell modelling program, with thedefault value of 0.31 nm for the atomic element radius forall atoms in order to represent the hydration shell.60

PDB accession numbers

The best-fit dp18–dp36 models have been deposited inPDB† with accession codes 3IRI (dp18), 3IRJ (dp24), 3IRK(dp30), and 3IRL (dp36).

Acknowledgements

We thank the Higher Education Commission ofPakistan, the Biotechnology and Biological SciencesResearch Council, the Henry Smith Charity, and theMercer Fund of the Fight For Sight Charity for grantsupport. We also thank Dr. Azubuike I. Okemefunafor excellent computational help.

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