motions of calmodulin characterized using both bragg and ... · the experimental methods of x-ray...

Motions of calmodulin characterized using both Bragg anddiffuse X-ray scatteringMichael E Wall1,2*, James B Clarage1 and George N Phillips, Jr1,2

Background: Calmodulin is a calcium-activated regulatory protein which canbind to many different targets. The protein resembles a highly flexibledumbbell, and bends in the middle as it binds. This and other motions mustbe understood to formulate a realistic model of calmodulin function.

Results: Using the Bragg reflections from X-ray crystallography, a multiple-conformer refinement of a calmodulin–peptide complex shows anisotropicdisplacements, with high variations of dihedral angles in several nonhelicaldomains: the flexible linker; three of the four calcium-binding sites (includingboth of the N-terminal sites); and a turn connecting the C-terminal EF-handcalcium-binding domains. Three-dimensional maps of the large scale diffuseX-ray scattering data show isotropic liquid-like motions with an unusuallysmall correlation length. Three-dimensional maps of the small scale diffusestreaks show highly coupled, anisotropic motions along the head-to-tailmolecular packing direction in the unit cell. There is also weak couplingperpendicular to the head-to-tail packing direction, particularly across a cavityoccupied by the disordered linker domain of the molecule.

Conclusions: Together, the Bragg and diffuse scattering present a self-consistent description of the motions in the flexible linker of calmodulin. Theother mobile regions of the protein are also of great interest. In particular, thehigh variations in the calcium-binding sites are likely to influence how stronglythey bind ions. This is especially important in the N-terminal sites, whichregulate the activity of the molecule.

IntroductionCalmodulin enables intracellular calcium levels to influ-ence many biological processes [1]. In the presence ofCa2+, the protein assumes the shape of a dumbbell, theN-terminal and C-terminal globular domains being teth-ered together by a flexible α-helical linker. In this form,calmodulin can activate an acceptor protein: the linkerbends in the middle, which allows the globular ends toengulf a target peptide sequence in a hydrophobicchannel (Figure 1).

There are four calcium-binding sites in calmodulin: two inthe N-terminal domain and two in the C-terminal domain.The two sites in the C-terminal domain bind calciumstrongly. The two sites in the N-terminal domain bindcalcium weakly, and regulate the activity of the protein.Terbium fluorescence decay studies of calmodulin haveshown that the calcium-binding sites are capable of adopt-ing many distinguishable conformations [2].

Nuclear magnetic resonance (NMR) studies of solution-state Ca2+–calmodulin show backbone motions in linkerresidues 77–81 [3]. In addition, X-ray crystallographystudies of Ca2+–calmodulin in complex with the calmodulinbinding domain peptide of the brain calmodulin-dependent

protein kinase IIα (CαMKIIα) showed missing electrondensity in the linker residues 74–83 of calmodulin [4]. Asthis suggests especially high mobility in the linker, wechose this complex to study the motions of crystallinecalmodulin.

X-ray diffraction experiments can be used to characterizethe motions of crystalline proteins. Atomic temperaturefactors in traditional structural models, for instance, will behigh in regions of the protein which are highly mobile. Inaddition, a structural model can be improved by super-imposing several independent structures in a crystallo-graphic refinement. The models are varied to find thebest fit to the data, and, at the end of refinement, the dif-ferences among the structures can be related to motions ofthe crystalline protein.

This technique is known as ‘multiple-conformer refine-ment’ [5,6]. Another way to characterize the internaldynamics of protein molecules comes from an extension ofthe experimental methods of X-ray crystallography.Protein motions give rise to disorder in protein crystals,which causes X-rays to be diffracted into angles that donot satisfy the Bragg condition: this is known as ‘diffusescattering’ [7]. Analysis of this diffuse scattering yields an

Addresses: 1Department of Biochemistry and CellBiology, Rice University, Houston, TX 77005-1892,USA and 2The WM Keck Center for ComputationalBiology, Rice University, Houston, TX 77005-1892,USA.

*Corresponding author.E-mail: [email protected]

Key words: calmodulin, CaMKII, diffuse scattering,multiple-conformer refinement, protein dynamics

Received: 8 September 1997Revisions requested: 1 October 1997Revisions received: 15 October 1997Accepted: 16 October 1997

Structure 15 December 1997, 5:1599–1612http://biomednet.com/elecref/0969212600501599

© Current Biology Ltd ISSN 0969-2126

Research Article 1599

overall description of the character of protein motions[8–10]: how much atoms are moving, in what directionthey are moving, and — something not generally visibleusing Bragg reflections — to what extent the motions ofan atom are influenced by those of its neighbors.

From a purely empirical point of view, diffuse scatteringcomes in two varieties: big and small. ‘Large scale diffusefeatures’ vary on length scales larger than the separationbetween Bragg reflections in reciprocal space, and ‘smallscale diffuse features’ vary on length scales smaller thanthe Bragg peak separation. The large-scale features corre-spond to motions which are only correlated on lengthscales smaller than the unit cell, while the small-scale fea-tures correspond to motions which are correlated onlength scales larger than the unit cell.

Many studies have shown that reasonable models ofprotein dynamics can be used to calculate diffractionpatterns which mimic diffuse scattering in X-ray exposures.Such studies have not only revealed characteristics ofcrystalline protein motions [11–18], but also have beenused to experimentally check the results of single-moleculemolecular dynamics simulations [19]. These same studies,however, rely on visual inspection to evaluate the agree-ment between models and data. In addition, the lack of anobjective measure of agreement between the calculatedand experimental scattering has, in some cases, causedargument about the interpretation of results.

Recently, Wall et al. [20] used X-ray exposures to measurethe three-dimensional reciprocal-space distribution ofdiffuse scattering from crystals of Staphylococcal nuclease.Then, in a manner analogous to ordinary refinement ofstructural models against Bragg reflections, these mapswere used to manually refine simple models of proteindynamics, using familiar R factors and correlation coeffi-cients (see Materials and methods section) as objective

measures of goodness-of-fit. Of all of the simple, analyticmodels evaluated, the ‘liquid-like motions’ model of Casparet al. [14] showed the highest correlation with the data.

Here, we apply similar techniques to study diffuse scat-tering from a crystalline calmodulin–peptide complex.The large scale diffuse features are mapped in an almostidentical fashion to those in the study of Staphylococcalnuclease, and are used to describe the isotropic, liquid-like internal motions of the protein. In addition, thesame techniques are extended and improved in order toresolve the three-dimensional distribution of small scalediffuse features. We use the small-scale data to study amore complex model of protein dynamics — anisotropicliquid-like motions (see Clarage et al. [15]) — and showthat the refinement is sensitive to the particular form ofthe displacement correlations in the model. We presentthese results in terms of the flexibility of the molecule,and its packing in the crystal lattice. We also point outconsistencies with the results of the multiple-conformerrefinement.

All of these studies taken together describe a picture ofcalmodulin protein dynamics on many length scales.Refined atomic temperature factors yield the amplitudesof motion of individual atoms. A multiple-conformerrefinement shows high variations not only in the flexiblelinker, but also in other nonhelical domains, includingthree of the four calcium-binding sites. Large scalediffuse features reveal isotropic atomic displacementswhich weakly influence the motions of neighboringatoms. Finally, small scale, streaked diffuse featuresshow motions which are confined to the same plane asthose in the multiple-conformer refinement. The motionsare strongly coupled in some directions, appearing rigidon the unit cell length scale, and weakly coupled in otherdirections, appearing rigid only over distances smallerthan the unit cell.

1600 Structure 1997, Vol 5 No 12

Figure 1

Dynamics in calmodulin binding. The linker ofcalmodulin (white) bends as the ends of theprotein engulf the target (red stick model);there are also significant motions within theglobular ends. Experiments to characterizethese motions are necessary to understandhow calmodulin works (see text for details).Within the globular ends, helices are shown incyan, β strands in green and loops in orange;Ca2+ ions are depicted as white spheres. (Thefigure was made using the programRIBBONS [41].)

ResultsStructural modelUsing the 1CDM Protein Data Bank (PDB) coordinates[4] as a starting point, a structural model was refined from10 Å to 2.0 Å for the complex of calmodulin, the CaMKIIαpeptide fragment, and Ca2+ ions. The PDB coordinateswere modified to include residues 74–83 of the flexiblelinker, which are missing in the 1CDM structure. Thisfragment was included by extracting starting coordinatesfrom the 1CDL PDB structure [21], manually positioningit with respect to the 1CDM structure using the programCHAIN [22], and incorporating it into the backbone whenrefining the X-PLOR structural model.

The final refined structure was very similar to the 1CDMstructure. The model included 58 water molecules, and anextra Ca2+ ion was found between symmetry-related pairsof molecules. This Ca2+ ion was coordinated to four atoms:an oxygen of the carboxylic acid group of Asp133; the car-bonyl oxygen in the amide group of Gln135; and the sametwo atoms on the symmetry partner. The structure refinedto an Rfree = 0.302 [23], R = 0.234. Our observationsconfirm those of Meador et al. [4] that residues 74–83 ofthe ‘expansion joint,’ or linker, do not show connectedelectron density at the level of 1σ, suggesting that thisregion of the protein is essentially ‘melted’. There are,however, some 1σ features where the linker would lie.The model has extremely high temperature factors in thelinker, reflecting the fact that the electron density is weak.

Multiple-conformer refinementUsing the Bragg reflections from 10.0 Å to 2.0 Å resolution,multiple-conformer refinements were performed using two,three, four and eight copies of the calmodulin–peptidecomplex. The values of (Rfree, R) for each of these were(0.293, 0.200), (0.276, 0.184), (0.262, 0.166), and (0.269,0.152), respectively. An improvement in Rfree was observedin each step between one and four conformers. The eight-conformer refinement showed a decrease in R, but anincrease in Rfree over the four-conformer refinement.

The temperature factors in the multiple-conformer modelswere generally lower than those of the original structuralmodel. This is expected, as the differences in the conform-ers absorb some of the motions accounted for by the tem-perature factors in the single-conformer model. Forinstance, the modeled thermal displacement of Cα posi-tions averaged over the whole protein dropped from 0.69 Åto 0.59 Å, while that averaged over the linker dropped from1.3 Å to 0.85 Å.

In order to look for anisotropic variations in atomic posi-tions, an average atomic variance matrix, analogous to anoverall anisotropic temperature factor, was calculated forthe protein, peptide, and four bound Ca2+ ions (Table 1).The most strikingly anisotropic displacements were seen

in the Ca2+ ions, most of whose motion was basically con-fined to the crystallographic a–b plane, primarily alongthe b axis. The protein and the peptide also both havehigher displacements in the a–b plane than along the caxis. The protein has larger displacements than thepeptide, which is not surprising given that the peptide isalmost completely buried.

As is easily seen by overlaying backbone renderings of theconformers (Figure 2), and plotting the root mean square(rms) deviation of backbone Cα atoms (Figure 3), thegreatest variation among conformers is in the flexiblelinker. This was expected from the lack of continuityobserved in the electron density of the linker region.

The plot in Figure 2 also shows five nonhelical regionswith notably high variations in dihedral angles. The great-est variations are in the neighborhood of the linker(residues 73–84). Four other regions of strong variation areobserved: both N-terminal calcium-binding sites (17–28and 55–64); one of the C-terminal calcium-binding sites(92–101); and a turn linking the C-terminal EF-handcalcium-binding domains (110–116). The N-terminalcalcium-binding sites have particularly strong variations,comparable to those in the flexible linker.

Large scale diffuse featuresAlthough the multiple-conformer refinement gives a clearpicture of motions, the molecular dynamics simulation inthe refinement algorithm determines the correlations inthe atomic displacements among the conformers. Thepatterns in the diffuse scattering, however, are directlycaused by correlations in atomic motions (see below).Therefore, in order to further experimentally characterizethe motions of calmodulin, we analyzed the diffuse scat-tering from crystals of the calmodulin–peptide complex.

As outlined in the Materials and methods section, ourmeasurements were divided into two parts: first, the largescale diffuse scattering; and second, the small scale, orstreaked, diffuse scattering. We will first describe theanalysis of the large scale diffuse scattering.

Research Article Motions of calmodulin Wall, Clarage and Phillips 1601

Table 1

Atomic variance matrices from the four-conformer refinement.

Vxx Vyy Vzz Vxy Vyz Vzx

Protein 0.40 0.41 0.31 0.00 –0.03 0.00Peptide 0.28 0.32 0.19 0.01 0.04 0.02Ions 0.22 0.43 0.09 0.05 0.15 0.01

Unique components of the atomic variance matrices for protein,peptide, and Ca2+ ions, calculated using the structures from the four-conformer refinement. Units are in Å2. Refined atomic temperaturefactors are not included in calculating these matrices. The matrices aresymmetric, so that Vij = Vji.

As with many derivations of expressions for thermal diffusescattering (e.g., Warren [24] and James [25]), the model weuse is in a class where both the displacements of atomsfrom equilibrium and the variation in the distance betweenany two atoms in the crystal are either small or Gaussian-distributed. In this class of models, the total mean scatteredintensity I (q) at scattering vector q = 2πs has the form:

where Fi and Fj are the structure factors of atoms i and j, uiand uj are the vector displacements from equilibrium of

atoms i and j, ⟨⟩ indicates a time average, * indicates thecomplex conjugate, and both i and j index all of the atomsin the crystal. Thus, the exact distribution of large scalediffuse features depends upon all of the N(N–1)/2 uniqueelements of the atomic displacement correlation matrixCij = ⟨uiuj⟩ , where N is the total number of atoms in thecrystal. This matrix can be greatly simplified using theisotropic liquid-like motions model [14], which assumesnot only that each atom has an equal probability to movein any direction, but also that the correlation Cij onlydepends on the average distance between atoms i and j. Inorder to avoid dealing with an unmanageable number offree parameters, therefore, we chose this model todescribe the motions which give rise to the large scalediffuse features in X-ray diffraction from calmodulin.

There are two free parameters in the isotropic liquid-likemotions model: an atomic displacement σ, which describeshow much the atoms move; and a correlation length γ,which roughly describes the distance within which an atominfluences the motions of other atoms. The diffuse scatter-ing predicted in this model has the following form:

where I0(q) is the point-like intensity distribution for theunperturbed crystal, * indicates a convolution, and thesmoothing function Γγ(q) is the Fourier representation ofthe atomic displacement correlations.

Two different functional forms of Γγ(q) were consideredin this study, both of which describe liquid-like motions.The first was one described in Clarage et al. [15], and cor-responds to real-space correlations which decay as e –xγ

1–1:

The second functional form corresponds to real-space cor-relations which decay as x –1e –xγ

2–1:

In both cases, γ describes a length scale over which atomicdisplacements are correlated. Atoms which are furtherapart than a distance γ move essentially independently,while the motions of those that are closer than γ arecoupled. Note that, for large values of q, the second,Lorentzian form resembles a Debye solid with thermallyexcited sound waves. Using diffuse scattering measure-ments of σ and γ in this model, one can derive a dispersion

Γ πγγ

( )( )2 23

222

41

(4)q =+ q

( )Γ πγγ

( )( )1 13

212 2

81

(3)q =+ q

[ ]I e Id 2 2 0 *( ) ( ) ( ) (2)2 2q q q= −q qσ σ Γγ

( )I ei j

ij

i i j j i j( ) ( ) ( ) (1)* – 12 2

q q q

q u u u u u u q= ⋅ ⋅+ +∑F F


Figure 2

Superposition of conformers from the multiple-conformer refinement, andthe packing in the a–b plane of the crystal. Lattice vectors are indicatedby the grey box. The molecules are oriented with the N-terminal domainon the right. The peptide (red) lies almost entirely in the b–c plane, andpoints mainly along the b axis. As can be seen in the figure, the multiple-conformer refinement shows relatively high displacements in the a–bplane. It also shows high variations in dihedral angles for the linker (lightgreen) and four other nonhelical domains (light blue). Three of these fourdomains are calcium-binding sites, including both N-terminal sites. Theproteins pack head-to-tail, with the left most C-terminal calcium bindingsite loop sitting in a ridge between the right most N-terminal α helices.The motions measured from the diffuse streaks are confined to thesame plane as those in the multiple-conformer refinement. They liealong (1, 1, 0), the head-to-tail packing direction indicated in the figure.There is strong coupling along this same direction and weak couplingperpendicular to this direction, especially in the a–b plane through theflexible linker (light green). Ca2+ ions are shown as spheres. The figurewas made using the program RASMOL (R Sayle, Glaxo Research andDevelopment, Greenford, Middlesex, UK).

relation for these waves, and calculate their effects on theentropy and the specific heat of the crystal.

It has been previously shown [20] that σ and γ can beobjectively refined against three-dimensional diffuse data,simply by varying them until the correlation coefficient Cbetween the model and the data is maximized. The sametechniques were used in this study to obtain the best fit toσ and γ for crystalline calmodulin.

In order to calculate the diffuse scattering usingEquation 2, the distribution I0(q) must first be calculated.This distribution is just a point-like sampling of thesquared structure factor F(q) 2 of the unit cell, calcu-lated without any temperature factors using the programX-PLOR [26]. In order to be able to calculate diffuse scat-tering to a resolution as high as 2 Å, I0(q) was calculated to1 Å resolution, as large-scale features are influenced byBragg peaks which are far away in reciprocal space.

Once I0(q) was obtained, the diffuse scattering was calcu-lated, using either Equation 3 or Equation 4 as a functionalform for Γγ(q). As with the experimental data, the sphericalaverage was subtracted from the calculated map and a cor-relation coefficient was then calculated between the dataand the simulation. In addition, a scale factor was adjustedbetween the two to find the best agreement by the R factor.Both models yield an R factor of 0.41 in the 7.5 Å–2.1 Å res-olution range, while the correlation coefficient using Γ(1)

(0.55) is slightly better than that using Γ(2) (0.54). The dataand simulation are compared for both models in Figure 4.

The refined value of the atomic displacement using bothmodels was σ = 0.38 ± 0.08 Å (the error indicates by howmuch the parameter must be changed in order to changethe correlation coefficient by 0.01). The correlation lengthfound using Γ(1) was γ1 = 4.8 ± 1.0 Å. This is a small corre-lation length compared with the results of other diffusescattering studies, such as ones involving insulin [14] (6 Å)or Staphylococcal nuclease (10 Å) [20]. The correlationlength found using Γ(2) was γ2 = 12 ± 3.5 Å, which is signif-icantly higher than γ1.

The different values of the correlation length are due tothe difference in the functional form of the correlations.One can predict that γ1 will be lower than γ2 by comparingthe radial distributions of the correlations. These have theform:

and

where each is normalized such that ∫0∞

c(x) dx = 1. Onemethod of obtaining a correspondence between γ1 and γ2is by constraining the position of the maximum in c(1)

(xmax = 2γ1) to be equal to the position of the maximum in

c(2)

22

( ) 1

(6)21

x dx x e dxx= − −

γγ

c(1) 13

2( ) 1

2 (5)1

1

x dx x dx= − −

γγe x


Figure 3

Root mean square (rms) deviations ofbackbone Cα positions and dihedral angles inthe four-conformer refinement. Largevariations are confined to nonhelical domains(as defined by RIBBONS). There are highvariations in the linker, in three of the calcium-binding sites, and in a turn linking the C-terminal EF-hands.

-50

0

50

100

150

200

250

300

350

400

0 20 40 60 80 100 120 140 160Residue number

Rmsd (phi [º])Rmsd (psi [º])

Rmsd(Cα position [Å x 100])nonhelical regions

Structure

c(2) (xmax = γ2). This produces the relation γ2 = 2γ1, whichwould account for most of the observed difference.

Another way to approach this is illustrated in Figure 5.The distribution c(1)(x) is used to calculate data points forthe value γ1 = 4.8 Å. The distribution c(2)(x) is then fit tothe data points using a nonlinear least squares algorithm,yielding γ2 = 7.7 Å. This fit predicts the relation

for any values of γ1 and γ 2.

Streaked diffuse featuresThe methods used to map the smaller scale streaked fea-tures in three dimensions are similar to those used for thelarge scale diffuse scattering. Rather than being measuredon the same lattice as the Bragg peaks, however, in orderto be resolved these features are measured on a higher res-olution lattice, called a Gibbs lattice. For this study, weused a 64 × 64 × 64 Gibbs lattice, which spanned eightBragg peaks in each direction at eight times the resolutionof the Bragg lattice.

The C2221 space group of the unit cell was used toaverage together all symmetry-related intensity, providingeightfold redundancy in the data. Despite the relativelyweak data, therefore, the streaks appear as beautifullyclear features, as is seen in the map of diffuse intensitycentered on the (2, 20, –4) Bragg reflection (Figure 6).

Without referring to specific models, we first mentionsome salient features in the small scale diffuse scattering.First, diffuse maps clearly show streaks which completelylie within the a*–b* plane. Second, two different kinds ofstreaks are observed: ones which are primarily extendedalong the ± (1, 1, 0) direction in reciprocal space; and

symmetry-related streaks which are extended along the± (–1, 1, 0) direction in reciprocal space. Third, streaks arenever observed to point towards the origin, and theirintensity is strongest when the direction to the origin isperpendicular to the direction of the streak. All of thesecharacteristics of the distribution of diffuse streaks areaccounted for by the models we will now describe.

The streaks were modeled using a three-dimensionalanalog of the model used to describe the large-scale fea-tures (see Clarage et al. [15]):

The variance σ2 of the isotropic model is replaced by avariance matrix V, which can be thought of as a set ofvectors describing the amplitude of atomic motions inthree independent directions.

Two different forms for Γ were used to model the streaks:

and

Equations 9 and 10 are three-dimensional analogs of thepreviously described isotropic models in Equations 3 and4, with the correlation length γ replaced by the correlationmatrix G. In a similar way to the variance matrix, the cor-relation matrix can be thought of as a set of three vectors

Γπ

( )( )det

2 2

2 2

4 G

1 G (10)q

q

=+

[ ]Γπ

(1) 1

12 2

8 G

1 G (9)( )

detq

q

=+

[ ]I e Id ( ) ( ) * ( )q q q q q

q q= − ⋅ ⋅ ⋅ ⋅V V G (8)0 Γ

γ γ2 11.6 (7)=


Figure 4

Comparison of data (left) and simulation(right) for large-scale features. Both aredisplayed using shell images [20], which areMercator projections of the diffuse intensity ina selected resolution shell, in this case onespanning 4.3 Å–3.3 Å. The simulation wasgenerated using exponential correlations, witha displacement σ = 0.38 Å, and a correlationlength γ1 = 4.8 Å. The correlation coefficient(R factor) calculated between the data andsimulation in this shell is 0.71 (0.34). Theazimuthal angle φ varies from –π (left) to π(right), while the polar angle θ varies from 0(top) to π (bottom) in each image. Pixel valuesare displayed on a linear greyscale, rangingfrom 20 counts below (black) to 20 countsabove (white) the mean in the shell.

π−π0

π

−π π φ

θ Structure

which describe the length scale of the decay of correla-tions in three independent directions.

The procedure for modeling the streaks was similar to thatused to model the large scale diffuse scattering (seeabove). The same distribution I0(q) was used inEquation 8 as was used in Equation 2. The elements ofthe matrix G were chosen such that the directions of cou-pling, and hence the directions along which the streakswere smeared, pointed along ± (a*, b*, 0), ± (–b*, a*, 0),and ± (0, 0, c*) (in orthogonal coordinates). The elementsof the matrix V were chosen such that the directions ofmotion were the same as the principle axes of the streaks.All directions were chosen based on the observations ofsalient features described above. This left a total of sixfree parameters in the refinement: γ1, γ2 and γ3, which arethe correlation lengths along each of the defined direc-tions; and σ1, σ2 and σ3, which are the amplitudes ofmotion along each of the same directions. Symmetry-related streaks were generated using the same parameters.

The elements of G and V were given initial values based onestimates of the strength of coupling and amplitude ofmotion along each of the defined directions. A diffuse mapwas then calculated according to Equation 8, using eitherEquation 9 or Equation 10 to describe the correlations.The background was subtracted in a manner identical tothat used to remove large scale diffuse features from thedata, and the same mask was used to ignore lattice pointswhich were too close to a Bragg peak position. A correlation


Figure 5

Comparison of the two functional forms ofcorrelations. As explained in the text, the radialdistribution c(1)(x) is used to generate datapoints for γ1 = 4.8 Å, and the best fit of c(2)(x)to these points is found for γ2 = 7.7 Å. Thisfitting procedure generally predicts therelation γ2 = 1.60 γ1.

0

0.01

0.02

0.03

0.04

0.05

0.06

0 5 10 15 20 25 30 35 40 45 50

Distance (Å)

c (1) Datac (2) Fit

Structure

Figure 6

Comparison of isosurface streaks in the data (a) and the anisotropicliquid-like motions model using a Lorentzian distribution (b). This viewis centered on (h,k,l) = (2, 20, –4), and spans eight Bragg peaks at asampling of eight points per reciprocal-lattice spacing along eachdirection. The surfaces are interpolated at a level about 35 countsabove the background. There is more streaking in the model than in thedata, but the overall agreement is quite good (correlation coefficientwith the data is 0.81). Reciprocal axes are labeled (offset) in the figure.(The figure was made using the program EXPLORER, NumericalAlgorithms Group, Inc., Downers Grove, IL, USA.)

coefficient was calculated between the maps to measuretheir agreement. The six free parameters of G and V wereiteratively varied by hand to maximize the correlation coef-ficient, at which time the refinement was complete.

The results are summarized in Table 2 and are viewed inFigure 6. Despite the poor quality of the second data set,the model parameters refined to values very similar tothose using the data from the first crystal. The refine-ment using Γ(2) produced a better correlation with thedata (0.81) than that using Γ(1) (0.77); visualization of themaps also confirmed that the one calculated using thebest fit to Γ(2) looked more like the data. Using thevalues in the table, γ1

(2)/γ1(1) = 1.4, and γ2

(2)/γ2(1) = 1.6. Equa-

tion 7 thus appears to hold fairly well for the anisotropiccorrelations. The values for γ3 are not unreasonable, butthe short c* axis in the reciprocal unit cell makes it diffi-cult to obtain an accurate measurement of the correlationlength in that direction.

Using the program XCADS (JBC and GNP, first used inits present form in [18], and described at websitehttp://www.bioc.rice.edu/clarage/science/xcads/index.html),the refined model parameters were used to simulate dif-fraction images. A typical result is shown in Figure 7,which compares a simulation with a diffraction image.Whereas past methods required that the model parametersbe adjusted in order to obtain the best visual agreement,this study has shown that objectively refined model para-meters also yield the best visual agreement.

The diffuse streaks can be understood by viewing thepacking of calmodulin in the crystal (see Figure 2). The0.4 Å motions which give rise to the streaked features areentirely along the ± (1, 1, 0) direction in direct space, whichpoints along the end-to-end packing direction in the unitcell. This is also the direction along which the coupling wasthe strongest (γ = 135 Å). The weakest coupling is perpen-dicular to this packing direction in the plane of the figure(γ = 50 Å). That the coupling is so weak in this direction isperhaps not so surprising, as a large solvent cavity contain-ing the melted flexible linker lies between the stacks ofcalmodulin in this direction. Motions are also relativelyweakly coupled into the page (γ = 85 Å, which is smallerthan the unit cell in this direction).

DiscussionEven though Bragg reflections only yield the average elec-tron density, information about motions can be learnedboth from atomic temperature factors and multiple-con-former refinement. There are problems with both of thesemethods, however. Temperature factors are likely to over-simplify the picture, and contain no information about cor-relations in atomic displacements. For instance, using Braggreflections alone, it is difficult to tell whether higher tem-perature factors on surface residues are due to rigid-bodyrotations or increased mobility due to solvent exposure.

Correlations can be inferred by studying the differencesamong structures in a multiple-conformer refinement. Forinstance, in this study, large variations in dihedral angleswere observed in nonhelical domains of the protein. Anatural interpretation would be that the multiple-con-former refinement predicts motions of rigid, α-helical rodstethered together by flexible coils. This is very similar tothe picture obtained from molecular dynamics studies ofmyoglobin [19,27], another primarily α-helical protein.

There is a caveat in the above reasoning. Even if anensemble of structures accurately describes the possiblelocations of individual atoms, the correlations in a multi-ple-conformer refinement generally come from the detailsof molecular dynamics simulations and chemical restraintsrather than diffraction data. In some cases, such as iscommon with alternate sidechain configurations, the elec-tron density can clearly indicate which atoms must movetogether. In cases where the electron density is more con-tinuously smeared, however, the correlations may becomeessentially arbitrary, especially between pairs of atoms ondifferent residues. Although local variations may be clearlyindicated, large-scale motions may be difficult to provewithout further experiments.

Here we compare the results of our multiple-conformerrefinement to a solution NMR study of calmodulin back-bone dynamics by Barbato et al. [3]. The NMR study usesa free recombinant Ca2+–calmodulin from Drosophilamelanogaster, but the comparison is nonetheless interest-ing. Both studies find motions in the linker, and in theturn connecting the C-terminal EF-hand calcium-bindingdomains. Only the NMR study, however, finds motions


Table 2

Results from the analysis of the diffuse streaks.

γ1 γ2 γ3 σ1 σ2 σ3 C

Crystal 1; Γ(1) 35 85 80 0.0 0.5 0.0 0.77Crystal 1; Γ(2) 50 135 85 0.0 0.4 0.0 0.81Crystal 2; Γ(2) 60 145 90 0.0 0.5 0.0 0.42

Two different forms of correlations, Γ(1) and Γ(2) (described in the text), were used to model the streaks. Values for σ and γ are in Å.

in the turn connecting the N-terminal EF-hand calcium-binding domains and only the multiple-conformer refine-ment finds motions in three of the calcium-binding sites.Neither experiment finds large-amplitude motions in anyof the α helices (with the exception of the central portionof the linker), or in the second calcium-binding site in theC-terminal domain. In addition, NMR studies of Ca2+-free calmodulin have shown significant backbonemotions in nonhelical regions, including the calcium-binding sites [28,29,30].

Despite its simplicity, the isotropic liquid-like motionsmodel accurately describes the large-scale features indiffuse scattering from protein crystals. Experimentswith insulin [14], lysozyme [15], tropomyosin [16], tRNA[18], Staphylococcal nuclease [20], and now calmodulinall show diffuse patterns characteristic of liquid-likemotions. There is ample evidence that the correlationlength γ and the mean atomic displacement σ are not justuseful for describing the motions of a small number ofproteins, but are parameters which can be used to charac-terize the motions of many proteins, and to generate ahierarchy of flexibility.

There are some interesting connections between thestreaked diffuse features and the internal motions ofcalmodulin. The analysis of streaked diffuse features, forinstance, implies motions which are confined to the sameplane as the preferred displacements in the multiple-conformer refinement. As the two studies were done inde-pendently, this result shows a measure of self-consistencybetween the Bragg and diffuse scattering analysis.

Analysis of the packing of calmodulin in the crystal (seeFigure 2) shows the important role of the linker in defining

the plane of motion, and the resulting distribution of thestreaks: because the loosely-structured linker lies betweenend-to-end ‘rods’ of calmodulin, there is weak couplingcausing streaks to broaden along the direction of contactbetween the rods, which lies in the a–b plane. If the linkerwere not as mobile, not only would the correlation lengthof 50 Å along this direction be likely to increase, but thecrystalline packing would also be likely to change, as itwould not require as much free energy to bring the linkerout of the solvent and into a more restrained environment.A solvated linker also appears to be electrostaticallyfavorable: among residues 74–84, eight have chargedsidechains, two have polar sidechains, and only one has anonpolar sidechain.

The large scale diffuse scattering does not distinguishbetween the different forms of correlations. Careful analy-sis of the small-scale streaks, however, shows that they aremore consistent with a Lorentzian profile than the formpreviously used to describe liquid-like motions. Furtherexperiments will need to be done to determine whetherthis is solely a property of calmodulin, or whether proteinsare generally better described using the Lorentzian form.

The atomic motions which give rise to the diffuse featuresaccount for most of the motions described by the tem-perature factors from the structural model. Combiningthe results of both diffuse scattering studies yieldsσ = √(0.38 Å)2 + (0.4 Å)2 = 0.6 Å, compared to a value of0.7 Å calculated from the mean temperature factor in thesingle-conformer refinement. A statistically significant dif-ference either could be due to an inaccuracy in themodels, or could be due to the presence of independentatomic fluctuations, which give rise to spherically symmet-ric diffuse features that were not considered in this study.


Figure 7

Diffuse features in X-ray exposures. (a) Imageof X-ray exposure from calmodulin (30 s still atroom temperature and pressure).Measurements of the intensities of the sharpBragg peaks were used to refine bothstandard and multiple-conformer structuralmodels. Note the streaked, small-scalefeatures in the solvent ring (see inset), and thebroader, large scale background features. Weused all 190 diffraction images to obtainthree-dimensional maps of both types ofdiffuse scattering, and used the maps to refineliquid-like motions models of protein dynamics.(b) A simulated exposure calculated using ananisotropic liquid-like motions model inXCADS. The parameters obtained from thediffuse-scattering refinement not only yieldedthe best correlation coefficient with the data,but also produced the best simulateddiffraction images.

Structure

(a) (b)

This study has shown that much of the disorder in crystalsof calmodulin comes about as a result of the internalmotions of the molecule. While the high-resolution featuresof the more rigid domains of the protein may be blurred bythese motions, crystals with disorder can provide insightinto important characteristics of the molecule. For instance,proteins with smaller correlation lengths would be predictedto have higher configurational entropy than those with largecorrelation lengths. In the calmodulin–peptide complex, forexample, the small correlation length and high mobility ofthe linker certainly influences the free energy differencebetween the open and closed states. More generally, itwould be interesting to compare the correlation length witha measure of the stability to denaturation of various pro-teins, to see how the two are related to each other.

Studies using two different crystal forms of lysozyme showthat the short range correlated motions, which give rise tolarge scale diffuse features, do not change in differentcrystal environments [15]. This is not surprising, as thelength scale of correlations (6 Å) is smaller than the size ofthe protein. The values of σ and γ which are obtainedfrom large scale diffuse scattering are therefore likely tobe relevant even in the solution state.

The most locally mobile parts of calmodulin, such as thelinker, do not make crystal contacts. It is possible thatthese parts are mobile simply because they are not con-strained by contacts. Proteins are known, however, to crys-tallize in space groups which allow a high number ofrigid-body degrees of freedom [31]. The important influ-ence of configurational entropy also makes it likely that, inorder to avoid increases in free energy, the protein crystal-lizes in such a way as to preserve the disorder of the mostmobile parts of the protein. This gives additional confi-dence not only in identifying mobile parts of the proteinusing crystallography, but also in guessing at which partsof the protein are relatively rigid.

Large-scale motions, on the other hand, are generally sen-sitive to the particulars of the crystal lattice. Proteins tendto push up against each other in the crystal, so that thepacking is most likely too dense for independent rigid-body motions of entire proteins. For instance, this studyhas shown that in calmodulin crystals, the proteins do nothave independent large-scale motions. Motions are pri-marily along the head-to-tail packing directions of the unitcell, and strongly influence the movements of neighboringproteins along these same directions.

Schomaker and Trueblood’s ‘TLS’ model of rigid-bodytranslations and rotations [32] (where ‘T’ is the translationtensor, ‘L’ is the libration tensor and ‘S’ is the tensor ofcorrelation of translation and rotation) can account formuch of the amplitude of individual atomic temperaturefactors in structural models of proteins [33,34]. Diffuse

scattering should reveal whether the TLS model worksbecause it is accurate, or whether it works because it is aconcise way to account for a general increase in the mobil-ity of residues near the surface of proteins. In fact, Pérez etal. [35] have recently reported that diffuse scattering fromlysozyme has some features which are consistent withindependent rigid-body motions of protein molecules.

Lysozyme, however, has been something of a test case fordiffuse scattering studies, and other models have beenproposed to describe the diffuse scattering [13,15,17]. Forinstance, an early experiment by Doucet and Benoit [13](in a spirit similar to this calmodulin study) showed that amodel based on the motions of rigid clusters of moleculesproduced diffuse streaks similar to those in P212121lysozyme diffraction images. It would be very interestingto perform a careful analysis of the lysozyme diffuse scat-tering using three-dimensional measurements like thosedescribed here and in a previous study of Staphylococcalnuclease [20]. Such a study should compare all relevantmodels to date, and should also include a description ofcoupled rigid-body motions, which would also be consis-tent with the TLS model.

Structural biology can benefit from improvements indiffuse scattering methods in several ways. With increas-ingly good data and three-dimensional representations, itmay be possible to use more complex models to describethe motions. One natural way to extend the liquid-likemotions model would be to break up the protein intodomains j, assigning a different correlation length γj toeach of the domains. Although one could not reasonablymeasure all of the atomic correlations ⟨uiuj⟩ , one couldtune the level of detail, and thus the number of free para-meters, in such a model to accurately reflect the amount ofinformation in the diffuse data. Such improvements areespecially important both in light of the evidence thatmolecular dynamics simulations do not sample enoughconfigurations to precisely measure these atomic correla-tions [19], and in light of the key role that correlations playin determining the thermodynamic properties of proteins.

As the methods improve, it will be possible to revisit aproblem pointed out long ago by Cochran [36]: in order toaccurately measure Bragg peaks, one must effectively sub-tract the diffuse scattering. Although current techniquesare likely to be adequate for subtracting large scale diffusefeatures, streaked features are more difficult to deal within integration algorithms. One possible solution lies in aniterative integration scheme, where Bragg and diffuse dataare measured separately in a first pass, but where Braggpeaks are measured again after the streaks have been char-acterized. Such an iterative scheme would not onlyproduce improved diffuse scattering data, but also yieldbetter Bragg peak measurements improving the quality ofelectron-density maps.


Eventually Bragg and diffuse data could be combined intoa complete X-ray diffraction data set, allowing for a moreaccurate refinement of models of protein dynamics. Thiswould not only be important for obtaining informationabout correlated motions, but would also most likelyimprove the overall quality of structural models by allow-ing a more sophisticated treatment of molecular motions.

Biological implicationsCalmodulin is capable of binding to many different pro-teins and regulating their activities. If the molecularbasis of its function were known, one would be able topredict the influence of calcium on a great number ofbiological processes.

The wide-spread influence of calmodulin can largely beattributed to the flexible linker, which allows the globularends of the protein to reposition themselves when theybind to a target. The detailed properties of the linker willin part determine the binding affinity of calmodulin for itsmany targets. For instance, the linker appears to losecoherent structure when it binds to a target, which nodoubt affects the enthalpy of binding. Understandingmotions such as those observed in this study may prove tobe useful in estimating such effects quantitatively.

We have studied motions in a calmodulin–peptidecomplex using both Bragg and diffuse scattering in X-raydiffraction experiments. Bragg data were used toperform a multiple-conformer refinement, which pro-duced an ensemble of protein structures whose differ-ences were analyzed. Diffuse scattering data were usedto study the correlated motions of the crystalline protein.The results of these studies are complementary, andshow consistencies.

We find two interesting results related to the linker. Asevidence that there are many configurations present in thecrystal, the ensemble of structures from the multiple-conformer refinement both improves the fit to the X-raydata, and lowers the temperature factors. The ensembleshows great variations in the linker. The diffuse scatteringalso shows that atomic motions are only weakly coupledthrough the linker, with a correlation length of 50 Å.

We also find that other parts of the molecule besides thelinker are highly mobile. Most notable are the two regula-tory N-terminal calcium-binding sites. The mobility inthese sites may be related to their relatively weak affinityfor calcium. One of the C-terminal calcium-binding sitesalso shows relatively high variations, as does a turn con-necting the C-terminal EF-hand calcium-binding domains.

This study yields a couple of more general observationsabout motions in crystalline calmodulin. First, the diffusescattering shows that the whole molecule is relatively soft,

having an overall correlation length which is relativelysmall. Compared to insulin and Staphylococcal nuclease,for instance, different parts of the protein move relativelyindependently of each other. Second, the overall motionsof the atoms are anisotropic. Both the distribution ofatomic displacements in the multiple-conformer refine-ment and the streaks in the diffuse scattering show thatatoms move primarily in the a–b plane, and with higheramplitude along the b axis than along the a axis.

Finally, recent improvements in diffuse scatteringmethods have some general implications for structuralbiology. It is not difficult to imagine algorithms for mea-suring Bragg reflections and diffuse scattering simulta-neously, and for including diffuse data in automatedrefinement. Both Bragg reflections and diffuse scatteringwill almost certainly be more accurately measured whenmeasured together, especially when small scale diffusestreaks are present. Also, by combining Bragg anddiffuse data during refinement, one can more accuratelymodel protein motions, improving the quality of struc-tural models and possibly lowering R factors.

Materials and methodsSpecimensDiffraction-quality crystals were microseeded in hanging drops over100 mM sodium acetate at pH 5.2, with 20% polyethylene glycol6000 (PEG 6000), 10 mM calcium chloride and 0.02% sodiumazide. Stock solutions of 24 mg/ml bovine brain calmodulin (SigmaLot 54H9558), 14 mg/ml CaMKIIα peptide (gift of the lab of FQuiocho, Howard Hughes Medical Institute, Baylor College of Medi-cine, Houston, TX), and 30% PEG were mixed into hanging drops inabout a 4:2:1 ratio.

Crystals had an orthorhombic unit cell with space group C2221. Usingthe program DENZO [37], the unit cell parameters were measured tobe a = 38.8 Å, b = 75.2 Å, c = 120 Å, α = β = γ =90°, with a mosaicityof 0.3°. Crystals were mounted in glass capillaries, with the buffertouching the crystal kept to a minimum.

Data collectionData were collected at the F2 station at the Cornell High-Energy Syn-chrotron Source (CHESS), using the Princeton 2K CCD detector (asuccessor to that described in Tate et al. [38]). The beam was tuned to0.98 Å, had a measured polarization of 0.9, and was collimated to a100 µm diameter.

A sequence of 30 s still exposures (see Figure 7), where the gonio-meter position remained fixed, was used to obtain three-dimensionalmeasurements of diffuse intensity. Stills were taken every 1° in spindlerotation, with interleaved 10 s 1° oscillation exposures for obtaining acrystal orientation and Bragg peak measurements. Exposures weretaken at 190 different spindle positions.

Data processingBragg reflections were indexed and measured from oscillation expo-sures using DENZO and SCALEPACK [37] (Zbyszek Otwinowski andWladek Minor). The data were 96% complete from 20 Å–2 Å, with a‘linear R factor’ (Rsym) of 0.06.

In addition to the Bragg reflections, striking diffuse features were visiblein X-ray exposures (see Figure 7). Notably prominent were streaks ema-nating from Bragg reflections, especially in the neighborhood of 3.5 Å


resolution. In addition, broader features, with length scales larger than thedistance between Bragg reflections, were visible.

Before using diffraction images to measure diffuse intensity, someexperimental effects which cause background intensity variations hadto be accounted for. Two effects are significant: the polarization ofthe X-ray beam causes azimuthal variations which are especiallystrong at high resolution; and pixels at high-scattering angles span asmaller solid angle about the specimen than do pixels at low scatter-ing angles, causing an effective decrease in intensity at high resolu-tion. Previously described methods [20,39] were used to correct forboth of these effects.

Large scale diffuse featuresTo isolate the large scale diffuse features, it is necessary to eliminatethe sharp Bragg reflections from diffraction images. A ‘mode filter’image processing technique can be used to successfully eliminateBragg peaks from X-ray diffraction images [20]. This technique wasfound to have some limitations, however: the streaked features incalmodulin diffraction images left traces of intensity in mode-filtered dif-fraction images. A different method was therefore sought to eliminateBragg reflections.

A simple solution was suggested by a symmetry property of theC2221 unit cell space group. In this space group, all Bragg reflec-tions where h + k is odd are identically zero. In addition, as isdescribed below, the streaks emanating from Bragg reflections wereoriented along the (± 1, 1, 0) directions, so that no streaks were everobserved near these systematic absences. To eliminate Bragg reflec-tions from calmodulin diffraction images, therefore, intensity measure-ments were made only in the neighborhood of systematic absences.This meant that reciprocal space was sampled at only every otherMiller index in the a* and b* directions. In addition, due to the rela-tively long c axis of the unit cell, reciprocal space was sampled atonly every fourth Bragg peak in the c* direction. Even with thereduced resolution, however, this sampling was sufficiently detailedto resolve the large scale diffuse features, whose smallest variationswere larger than many reciprocal-lattice spacings.

As is the case with ordinary diffraction data, when diffuse data aremerged to create a three-dimensional data set, variations in beamintensity and the change in the thickness of the specimen with differentcrystal orientations require scaling of intensities. In order to calculate ascale factor for diffuse intensity in a diffraction image, measurementswere taken of the diffuse scattering at high resolution, where coherentscattering is very weak. Using the methods described in Wall [39],these measurements were then used to scale values of diffuse intensityand map them to a three-dimensional lattice of diffuse scattering Id (s),called a ‘diffuse map’. This map is essentially the same as a sparselysampled Bragg lattice, where, instead of being Bragg peak intensities,the values are measurements of the diffuse intensity in the neighbor-hood of the corresponding Bragg peak.

In order to increase signal-to-noise, at the time they were created,the maps Id (s) were symmetry-averaged according to the predic-tions of the C2221 space group of the unit cell. The symmetry aver-aging was crucial to the success of the experiment, as it madeotherwise weak features strong enough to visualize: eight indepen-dent measurements were made for each lattice point, substantiallyenhancing the signal-to-noise.

To eliminate the effects of scattering from disordered solvent, air, andother spherically symmetric sources, the spherically averaged intensitywas subtracted from each intensity value in the diffuse map. Reciprocalspace was sectioned into spherical shells, each of thickness 0.0669Å–1 (the length of the reciprocal unit cell diagonal), and the averageintensity was calculated in each of these resolution shells, producing amap Id

sph(s) of the spherically averaged diffuse intensity. A residualmap, ∆Id(s) = Id(s) – Id

sph(s), was then calculated.

In order to check reproducibility, two independent data sets wereobtained using different crystals in different orientations. After eachmap had its spherical average subtracted, a correlation coefficient, C,was calculated between the resulting residual maps:

where X and Y are two maps being compared (in this case, the twoexperimentally obtained maps of ∆Id(s)), and {s} spans the scatteringvectors in the resolution shells over which the comparison is to takeplace. The result was a correlation of 0.59 in the 7.5 Å–2.1 Å resolu-tion range (for comparison, the correlation in the same range is 0.998before the spherical average is subtracted). In addition, the R factor,defined as

was calculated between the residual maps, giving a value of 0.40 in the7.5–2.1 Å resolution range. This R factor does not compare well withthe Rsym of 0.06 calculated from the Bragg data, which is attributedboth to the relatively weak signal after the spherical average is sub-tracted, and to the fact that the data from the second crystal weremuch weaker than those from the first crystal.

Streaked diffuse featuresWhen he conducted the first thorough experiments to verify the Debyetheory, Laval [40] mapped the distribution of diffuse intensity in theneighborhood of Bragg reflections from diamond crystals completelyby hand. Fortunately, we were able to develop automated methods tomap the three-dimensional distribution of streaked diffuse features incalmodulin diffraction.

The methods were similar to those used in mapping the large-scale fea-tures. As the streaks have structure on length scales smaller than thereciprocal unit cell, however, a lattice which samples reciprocal spaceat a finer scale than the Bragg lattice was required. A Gibbs lattice(described in, e.g., Clarage and Phillips [10]), which subdivides recip-rocal unit cells into equal-sized blocks, is a natural choice. Eight voxelsper Bragg peak spacing, amounting to 512 voxels per reciprocal unitcell, was found to be sufficiently detailed to resolve the streaks, yet wasnot so fine that the 1° spindle sampling left voids in the map. Using theNyquist condition, at this sampling frequency, we estimate that we canobserve motions which are correlated on length scales of up to fourlattice spacings along each unit cell axis.

We now estimate the smallest diffraction feature which can beresolved, given the experimental constraints. Roughly speaking, fea-tures are smeared over a reciprocal space distance of

when the scattering angle θscatt is broadened by δθscatt. The mosaicity,an angular parameter which strictly measures how much the orientationof identical Bragg planes varies throughout the crystal, is commonlyused as a fudge-factor to absorb all kinds of experimental peak broad-ening (including some small scale diffuse scattering, which technicallyshould be separated to measure Bragg peak intensities accurately).The mosaicity thus gives an estimated upper limit on δθscatt: when thevalue of 0.3° (5 × 10–3 rad) for calmodulin is substituted into Equation13 at a resolution of 3.5 Å, where we map the streaked features (see

δ δθ δθs s s≈ Bragg scatt= 12

(13)

{ }

{ }R (12)=

−Σ

Σ

s

s

s s

s

X Y

X

( ) ( )

( )

{ }

{ }( ) { }( )C =

Σ

Σ Σs

s s

s s

s s

X Y

X Y

( ) ( )2 2( ) ( )

(11)


below), the result is δs ≈ 7 × 10–4 Å–1, which means that our experi-ment is sensitive to real-space correlations over distances up to alimit of about (2π × 7 × 10–4 Å–1)–1 = 200 Å at 3.5 Å resolution. Thisestimate indicates that we may be needlessly oversampling the dataat eight measurements per reciprocal lattice spacing, especiallyalong the b* and c* axis. A harder limit is given by the beam divergenceof 1.7 × 10–3 rad at the F2 station reported by CHESS (websitehttp://www.chess.cornell.edu/Facility/F2_station.html), which yields anupper limit of about 600 Å for the largest detectable real-space correla-tions, in which case little, if any, oversampling occurs.

Computer memory limitations prevented the mapping of all of recipro-cal space at this resolution, so diffuse data were only mapped inselected regions of interest. For this study, a strongly streaked regionof reciprocal space, centered on (h,k,l) = (2, 20, –4), and spanningeight Miller indices along each reciprocal axis, was selected. A visual-ization of the resulting map clearly shows the structure of the streakedfeatures observed in diffraction images (see Figure 6). This is the firstreported measurement of such a map using X-ray diffraction from aprotein crystal.

In order to isolate the streaked features, it was necessary to removeboth the Bragg peaks and the large scale diffuse features from theGibbs lattice. As previously described, the large scale diffuse featureswere obtained by averaging pixel values in the neighborhood of system-atic absences. The large scale diffuse intensity at the nearest system-atic absence was then subtracted from each value in the Gibbs lattice.The Bragg peaks were eliminated by masking out the Gibbs latticepoints within an ellipsoid whose axes spanned 1/5 of the latticespacing along each reciprocal axis. The ellipsoid was chosen to belarger than the width of the Bragg peaks, and small enough so as tokeep enough data for refining model parameters.

As was done for the large scale diffuse scattering, we determined the thereproducibility of the streaks by comparing diffuse maps obtained fromexperiments using different crystals. Without background subtraction, thecorrelation coefficient between the two was 0.72. When the backgroundwas subtracted from each of the maps, however, the correlation coeffi-cient was just 0.47. The poor correlation is explained by photon noise:the intensities were much lower in the second data set (the problem wasnot as severe with the large scale diffuse data, as many pixel values wereaveraged together to give the intensities in the large scale diffuse map,substantially increasing the signal-to-noise). Despite the low correlationbetween the two maps, however, they both produced very similar para-meters in the model refinement (see Results section).

Accession numbersCoordinates for the single- and four-conformer refinements have beendeposited in the Brookhaven Protein Data Bank with accession codes1CM1 and 1CM4, respectively.

AcknowledgementsMany thanks to S Gruner, S Ealick, J Ekstrom, CHESS staff, W Meador, FQuiocho, D Caspar, F Yang, and T Romo for their contributions. This workwas supported by the Keck Center for Computational Biology, the Robert AWelch foundation, the Keck Laboratory for Molecular Structure at CornellUniversity, and the National Science Foundation.

References1. Crivici, A. & Ikura, M. (1995). Molecular and structural basis of target

recognition by calmodulin. Annu. Rev. Biophys. Biomol. Struct. 24,85–116.

2. Austin, R.H., Stein, D.L. & Wang, J. (1987). Terbium luminescence-lifetime heterogeneity and protein equilibrium conformationaldynamics. Proc. Natl. Acad. Sci. USA 84, 1541–1545.

3. Barbato, G., Ikura, M., Kay, L.E., Pastor, R.W. & Bax, A. (1992).Backbone dynamics of calmodulin studies by 15N relaxation usinginverse detected two-dimensional NMR spectroscopy: the centralhelix is flexible. Biochemistry 31, 5269–5278.

4. Meador, W.E., Means, A.R. & Quiocho, F.A. (1993). Modulation ofcalmodulin plasticity in molecular recognition on the basis of X-raystructures. Science 262, 1718–1721.

5. Kuriyan, J., Osapay, K., Burley, S., Brünger, A., Hendrickson, W. &Karplus, M. (1991). Exploration of disorder in protein structures by X-ray restrained molecular dynamics. Proteins 10, 340–358.

6. Burling, F.T. & Brünger, A.T. (1994). Thermal motions andconformational disorder in protein crystal structures: comparison ofmulti-conformer and time-averaging models. Israel J. Chem. 34,165–175.

7. Lonsdale, K. (1942). X-ray study of crystal dynamics: an historical andcritical survey of experiment and theory. Proc. Phys. Soc. 54,314–353.

8. Thüne, T. & Badger, J. (1995). Thermal diffuse X-ray scattering and itscontribution to understanding protein dynamics. Prog. Biophys.Molec. Biol. 63, 251–276.

9. Benoit, J.P. & Doucet, J. (1995). Diffuse scattering in proteincrystallography. Quart. Rev. Biophys. 28, 131–169.

10. Clarage, J.B. & Phillips, G.N., Jr. (1997). Analysis of diffuse scatteringand relation to molecular motion. In Methods in Enzymology Vol. 277.Macromolecular Crystallography, Part B. (Carter, C.W., Jr. & Sweet,R.M., eds), pp. 407–432, Academic Press.

11. Phillips, G.N., Jr., Fillers, J.P. & Cohen, C. (1980). Motions oftropomyosin. Biophys. J. 32, 485–502.

12. Boylan, D. & Phillips, G.N., Jr. (1986). Motions of tropomyosin.Biophys. J. 49, 76–78.

13. Doucet, J. & Benoit, J.P. (1987). Molecular dynamics studied byanalysis of the X-ray diffuse scattering from lysozyme crystals. Nature325, 643–646.

14. Caspar, D.L.D., Clarage, J., Salunke, D.M. & Clarage, M. (1988).Liquid-like movements in crystalline insulin. Nature 332, 659–662.

15. Clarage, J.B., Clarage, M.S., Phillips, W.C., Sweet, R.M. & Caspar,D.L.D. (1992). Correlations of atomic movements in lysozyme crystals.Proteins 12, 145–157.

16. Chacko, S. & Phillips G.N., Jr. (1992). Diffuse X-ray scattering fromtropomyosin crystals. Biophys. J. 61, 1256–1266.

17. Fauré, P., Micu, A., Perahia, D., Doucet, J., Smith, J.C. & Benoit, J.P.(1994). Correlated intramolecular motions and diffuse X-ray scatteringin lysozyme. Nat. Struct. Biol. 1, 124–128.

18. Kolatkar, A.R., Clarage, J.B. & Phillips, G.N., Jr. (1994). Analysis ofdiffuse scattering from yeast initiator tRNA crystals. Acta Cryst. D 50,210–218.

19. Clarage, J.B., Romo, T., Andrews, B.K., Pettitt, B.M. & Phillips, G.N., Jr.(1995). A sampling problem in molecular dynamics simulations ofmacromolecules. Proc. Natl. Acad. Sci. USA 92, 3288–3292.

20. Wall, M.E., Ealick, S.E. & Gruner, S.M. (1997). Three-dimensionaldiffuse X-ray scattering from Staphylococcal nuclease. Proc. Natl.Acad. Sci. USA 94, 6180–6184.

21. Meador, W.E., Means, A.R. & Quiocho, F.A. (1992). Target enzymerecognition by calmodulin: 2.4 Å structure of a calmodulin–peptidecomplex. Science 257, 1251–1255.

22. Sack, J.S. (1988). CHAIN — a crystallographic modeling program. J.Mol. Graph. 6, 244–245.

23. Brünger, A.T. (1992). The free R-value: a novel statistical quantity forassessing the accuracy of crystal structures. Nature 355, 472–475.

24. Warren, B.E. (1963). X-ray Diffraction. Dover Publications, Inc., NewYork, NY.

25. James, R.W. (1962). The Optical Principles of the Diffraction of X-Rays. Ox Bow Press, Woodbridge, CT.

26. Brünger, A. (1987). X-PLOR: a System for X-ray Crystallography,Version 3.1 Edition. Yale University Press, New Haven, CT.

27. Elber, R. & Karplus, M. (1987). Multiple conformational states ofproteins: a molecular dynamics analysis of myoglobin. Science 235,318–321.

28. Zhang, M., Tanaka, T. & Ikura, M. (1995). Calcium-inducedconformational transition revealed by the solution structure of apocalmodulin. Nat. Struct. Biol. 2, 758–767.

29. Kuboniwa, H., Tjandra, N., Grzesiek, S., Ren, H., Klee, C.B. & Bax, A.(1995). Solution structure of calcium-free calmodulin. Nat. Struct. Biol.2, 768–776.

30. Finn, B.E., Evenäs, J., Drakengerg, T., Waltho, J.P., Thulin, E. & Forsén,S. (1995). Calcium-induced structural changes and domain autonomyin calmodulin. Nat. Struct. Biol. 2, 777–783.

31. Wukavitz, S.W. & Yeates, T.O. (1995). Why protein crystals favorsome space-groups over others. Nat. Struct. Biol. 2, 1062–1067.

32. Schomaker, V. & Trueblood, K.N. (1968). On the rigid-body motion ofmolecules in crystals. Acta Cryst. B 24, 63–76.


33. Sternberg, M.J.E., Grace, D.E.P. & Phillips, D.C. (1979). Dynamicinformation from protein crystallography. J. Mol. Biol. 130, 231–253.

34. Kuriyan, J. & Weis, W.I. (1991). Rigid protein motion as a model forcrystallographic temperature factors. Proc. Natl. Acad. Sci. USA 88,2773–2777.

35. Pérez, J., Faure, P. & Benoit, J. (1996). Molecular rigid-bodydisplacements in a tetragonal lysozyme crystal confirmed by X-raydiffuse scattering. Acta Cryst. D 52, 722–729.

36. Cochran, W. (1969). The correction of measured structure factors forthermal diffuse scattering. Acta Cryst. A 25, 95–101.

37. Otwinowski, Z. & Minor, W. (1996). Processing of X-ray diffractiondata collected in oscillation mode. In Methods in enzymology Vol. 276Macromolecular Crystallography, Part A. (Carter, C.W., Jr. & Sweet,R.M., eds), pp. 307–326, Academic Press.

38. Tate, M.W., Eikenberry, E.F., Barna, S.L., Wall, M.E., Lowrance, J.L. &Gruner, S.M. (1995). A large-format high-resolution area X-raydetector based on a fiber-optically bonded charge-coupled device(CCD). J. Appl. Cryst. 28, 196–205.

39. Wall, M.E. (1995). Diffuse Features in X-ray Diffraction from ProteinCrystals. PhD thesis, Princeton University, Princeton, NJ.

40. Laval, J. (1939). Étude expérimentale de la diffusion des rayons X parles cristaux. Bull. Soc. Franc. Min. 62, 137–253.

41. Carson, M. (1987). Ribbon models of macromolecules. J. Mol. Graph.5, 103–106.


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