Nuclear magnetic resonance (NMR) studies of solutionstate Ca 2+ calmodulin show backbone motions in linker

Transcription

1 Reearch Article 1599 Motion of calmodulin characterized uing both Bragg and diffue X-ray cattering Michael E Wall 1,2 *, Jame B Clarage 1 and George N Phillip, Jr 1,2 Background: Calmodulin i a calcium-activated regulatory protein which can bind to many different target. The protein reemble a highly flexible dumbbell, and bend in the middle a it bind. Thi and other motion mut be undertood to formulate a realitic model of calmodulin function. Reult: Uing the Bragg reflection from X-ray crytallography, a multipleconformer refinement of a calmodulin peptide complex how aniotropic diplacement, with high variation of dihedral angle in everal nonhelical domain: the flexible linker; three of the four calcium-binding ite (including both of the N-terminal ite); and a turn connecting the C-terminal EF-hand calcium-binding domain. Three-dimenional map of the large cale diffue X-ray cattering data how iotropic liquid-like motion with an unuually mall correlation length. Three-dimenional map of the mall cale diffue treak how highly coupled, aniotropic motion along the head-to-tail molecular packing direction in the unit cell. There i alo weak coupling perpendicular to the head-to-tail packing direction, particularly acro a cavity occupied by the diordered linker domain of the molecule. Addree: 1 Department of Biochemitry and Cell Biology, Rice Univerity, Houton, TX , USA and 2 The WM Keck Center for Computational Biology, Rice Univerity, Houton, TX , USA. *Correponding author. mewall@bioc.rice.edu Key word: calmodulin, CaMKII, diffue cattering, multiple-conformer refinement, protein dynamic Received: 8 September 1997 Reviion requeted: 1 October 1997 Reviion received: 15 October 1997 Accepted: 16 October 1997 Structure 15 December 1997, 5: Current Biology Ltd ISSN Concluion: Together, the Bragg and diffue cattering preent a elfconitent decription of the motion in the flexible linker of calmodulin. The other mobile region of the protein are alo of great interet. In particular, the high variation in the calcium-binding ite are likely to influence how trongly they bind ion. Thi i epecially important in the N-terminal ite, which regulate the activity of the molecule. Introduction Calmodulin enable intracellular calcium level to influence many biological procee [1]. In the preence of Ca 2+, the protein aume the hape of a dumbbell, the N-terminal and C-terminal globular domain being tethered together by a flexible α-helical linker. In thi form, calmodulin can activate an acceptor protein: the linker bend in the middle, which allow the globular end to engulf a target peptide equence in a hydrophobic channel (Figure 1). There are four calcium-binding ite in calmodulin: two in the N-terminal domain and two in the C-terminal domain. The two ite in the C-terminal domain bind calcium trongly. The two ite in the N-terminal domain bind calcium weakly, and regulate the activity of the protein. Terbium fluorecence decay tudie of calmodulin have hown that the calcium-binding ite are capable of adopting many ditinguihable conformation [2]. Nuclear magnetic reonance (NMR) tudie of olutiontate Ca 2+ calmodulin how backbone motion in linker reidue [3]. In addition, X-ray crytallography tudie of Ca 2+ calmodulin in complex with the calmodulin binding domain peptide of the brain calmodulin-dependent protein kinae IIα (CαMKIIα) howed miing electron denity in the linker reidue of calmodulin [4]. A thi ugget epecially high mobility in the linker, we choe thi complex to tudy the motion of crytalline calmodulin. X-ray diffraction experiment can be ued to characterize the motion of crytalline protein. Atomic temperature factor in traditional tructural model, for intance, will be high in region of the protein which are highly mobile. In addition, a tructural model can be improved by uperimpoing everal independent tructure in a crytallographic refinement. The model are varied to find the bet fit to the data, and, at the end of refinement, the difference among the tructure can be related to motion of the crytalline protein. Thi technique i known a multiple-conformer refinement [5,6]. Another way to characterize the internal dynamic of protein molecule come from an extenion of the experimental method of X-ray crytallography. Protein motion give rie to diorder in protein crytal, which caue X-ray to be diffracted into angle that do not atify the Bragg condition: thi i known a diffue cattering [7]. Analyi of thi diffue cattering yield an

2 1600 Structure 1997, Vol 5 No 12 Figure 1 Dynamic in calmodulin binding. The linker of calmodulin (white) bend a the end of the protein engulf the target (red tick model); there are alo ignificant motion within the globular end. Experiment to characterize thee motion are neceary to undertand how calmodulin work (ee text for detail). Within the globular end, helice are hown in cyan, β trand in green and loop in orange; Ca 2+ ion are depicted a white phere. (The figure wa made uing the program RIBBONS [41].) overall decription of the character of protein motion [8 10]: how much atom are moving, in what direction they are moving, and omething not generally viible uing Bragg reflection to what extent the motion of an atom are influenced by thoe of it neighbor. From a purely empirical point of view, diffue cattering come in two varietie: big and mall. Large cale diffue feature vary on length cale larger than the eparation between Bragg reflection in reciprocal pace, and mall cale diffue feature vary on length cale maller than the Bragg peak eparation. The large-cale feature correpond to motion which are only correlated on length cale maller than the unit cell, while the mall-cale feature correpond to motion which are correlated on length cale larger than the unit cell. Many tudie have hown that reaonable model of protein dynamic can be ued to calculate diffraction pattern which mimic diffue cattering in X-ray expoure. Such tudie have not only revealed characteritic of crytalline protein motion [11 18], but alo have been ued to experimentally check the reult of ingle-molecule molecular dynamic imulation [19]. Thee ame tudie, however, rely on viual inpection to evaluate the agreement between model and data. In addition, the lack of an objective meaure of agreement between the calculated and experimental cattering ha, in ome cae, caued argument about the interpretation of reult. Recently, Wall et al. [20] ued X-ray expoure to meaure the three-dimenional reciprocal-pace ditribution of diffue cattering from crytal of Staphylococcal nucleae. Then, in a manner analogou to ordinary refinement of tructural model againt Bragg reflection, thee map were ued to manually refine imple model of protein dynamic, uing familiar R factor and correlation coefficient (ee Material and method ection) a objective meaure of goodne-of-fit. Of all of the imple, analytic model evaluated, the liquid-like motion model of Capar et al. [14] howed the highet correlation with the data. Here, we apply imilar technique to tudy diffue cattering from a crytalline calmodulin peptide complex. The large cale diffue feature are mapped in an almot identical fahion to thoe in the tudy of Staphylococcal nucleae, and are ued to decribe the iotropic, liquidlike internal motion of the protein. In addition, the ame technique are extended and improved in order to reolve the three-dimenional ditribution of mall cale diffue feature. We ue the mall-cale data to tudy a more complex model of protein dynamic aniotropic liquid-like motion (ee Clarage et al. [15]) and how that the refinement i enitive to the particular form of the diplacement correlation in the model. We preent thee reult in term of the flexibility of the molecule, and it packing in the crytal lattice. We alo point out conitencie with the reult of the multiple-conformer refinement. All of thee tudie taken together decribe a picture of calmodulin protein dynamic on many length cale. Refined atomic temperature factor yield the amplitude of motion of individual atom. A multiple-conformer refinement how high variation not only in the flexible linker, but alo in other nonhelical domain, including three of the four calcium-binding ite. Large cale diffue feature reveal iotropic atomic diplacement which weakly influence the motion of neighboring atom. Finally, mall cale, treaked diffue feature how motion which are confined to the ame plane a thoe in the multiple-conformer refinement. The motion are trongly coupled in ome direction, appearing rigid on the unit cell length cale, and weakly coupled in other direction, appearing rigid only over ditance maller than the unit cell.

3 Reearch Article Motion of calmodulin Wall, Clarage and Phillip 1601 Reult Structural model Uing the 1CDM Protein Data Bank (PDB) coordinate [4] a a tarting point, a tructural model wa refined from 10 Å to 2.0 Å for the complex of calmodulin, the CaMKIIα peptide fragment, and Ca 2+ ion. The PDB coordinate were modified to include reidue of the flexible linker, which are miing in the 1CDM tructure. Thi fragment wa included by extracting tarting coordinate from the 1CDL PDB tructure [21], manually poitioning it with repect to the 1CDM tructure uing the program CHAIN [22], and incorporating it into the backbone when refining the X-PLOR tructural model. The final refined tructure wa very imilar to the 1CDM tructure. The model included 58 water molecule, and an extra Ca 2+ ion wa found between ymmetry-related pair of molecule. Thi Ca 2+ ion wa coordinated to four atom: an oxygen of the carboxylic acid group of Ap133; the carbonyl oxygen in the amide group of Gln135; and the ame two atom on the ymmetry partner. The tructure refined to an R free = [23], R = Our obervation confirm thoe of Meador et al. [4] that reidue of the expanion joint, or linker, do not how connected electron denity at the level of 1σ, uggeting that thi region of the protein i eentially melted. There are, however, ome 1σ feature where the linker would lie. The model ha extremely high temperature factor in the linker, reflecting the fact that the electron denity i weak. Multiple-conformer refinement Uing the Bragg reflection from 10.0 Å to 2.0 Å reolution, multiple-conformer refinement were performed uing two, three, four and eight copie of the calmodulin peptide complex. The value of (R free, R) for each of thee were (0.293, 0.200), (0.276, 0.184), (0.262, 0.166), and (0.269, 0.152), repectively. An improvement in R free wa oberved in each tep between one and four conformer. The eightconformer refinement howed a decreae in R, but an increae in R free over the four-conformer refinement. The temperature factor in the multiple-conformer model were generally lower than thoe of the original tructural model. Thi i expected, a the difference in the conformer aborb ome of the motion accounted for by the temperature factor in the ingle-conformer model. For intance, the modeled thermal diplacement of Cα poition averaged over the whole protein dropped from 0.69 Å to 0.59 Å, while that averaged over the linker dropped from 1.3 Å to 0.85 Å. In order to look for aniotropic variation in atomic poition, an average atomic variance matrix, analogou to an overall aniotropic temperature factor, wa calculated for the protein, peptide, and four bound Ca 2+ ion (Table 1). The mot trikingly aniotropic diplacement were een Table 1 Atomic variance matrice from the four-conformer refinement. V xx V yy V zz V xy V yz V zx Protein Peptide Ion Unique component of the atomic variance matrice for protein, peptide, and Ca 2+ ion, calculated uing the tructure from the fourconformer refinement. Unit are in Å 2. Refined atomic temperature factor are not included in calculating thee matrice. The matrice are ymmetric, o that V ij = V ji. in the Ca 2+ ion, mot of whoe motion wa baically confined to the crytallographic a b plane, primarily along the b axi. The protein and the peptide alo both have higher diplacement in the a b plane than along the c axi. The protein ha larger diplacement than the peptide, which i not urpriing given that the peptide i almot completely buried. A i eaily een by overlaying backbone rendering of the conformer (Figure 2), and plotting the root mean quare (rm) deviation of backbone Cα atom (Figure 3), the greatet variation among conformer i in the flexible linker. Thi wa expected from the lack of continuity oberved in the electron denity of the linker region. The plot in Figure 2 alo how five nonhelical region with notably high variation in dihedral angle. The greatet variation are in the neighborhood of the linker (reidue 73 84). Four other region of trong variation are oberved: both N-terminal calcium-binding ite (17 28 and 55 64); one of the C-terminal calcium-binding ite (92 101); and a turn linking the C-terminal EF-hand calcium-binding domain ( ). The N-terminal calcium-binding ite have particularly trong variation, comparable to thoe in the flexible linker. Large cale diffue feature Although the multiple-conformer refinement give a clear picture of motion, the molecular dynamic imulation in the refinement algorithm determine the correlation in the atomic diplacement among the conformer. The pattern in the diffue cattering, however, are directly caued by correlation in atomic motion (ee below). Therefore, in order to further experimentally characterize the motion of calmodulin, we analyzed the diffue cattering from crytal of the calmodulin peptide complex. A outlined in the Material and method ection, our meaurement were divided into two part: firt, the large cale diffue cattering; and econd, the mall cale, or treaked, diffue cattering. We will firt decribe the analyi of the large cale diffue cattering.

4 1602 Structure 1997, Vol 5 No 12 Figure 2 atom i and j, indicate a time average, * indicate the complex conjugate, and both i and j index all of the atom in the crytal. Thu, the exact ditribution of large cale diffue feature depend upon all of the N(N 1)/2 unique element of the atomic diplacement correlation matrix C ij = u i u j, where N i the total number of atom in the crytal. Thi matrix can be greatly implified uing the iotropic liquid-like motion model [14], which aume not only that each atom ha an equal probability to move in any direction, but alo that the correlation C ij only depend on the average ditance between atom i and j. In order to avoid dealing with an unmanageable number of free parameter, therefore, we choe thi model to decribe the motion which give rie to the large cale diffue feature in X-ray diffraction from calmodulin. There are two free parameter in the iotropic liquid-like motion model: an atomic diplacement σ, which decribe how much the atom move; and a correlation length γ, which roughly decribe the ditance within which an atom influence the motion of other atom. The diffue cattering predicted in thi model ha the following form: Superpoition of conformer from the multiple-conformer refinement, and the packing in the a b plane of the crytal. Lattice vector are indicated by the grey box. The molecule are oriented with the N-terminal domain on the right. The peptide (red) lie almot entirely in the b c plane, and point mainly along the b axi. A can be een in the figure, the multipleconformer refinement how relatively high diplacement in the a b plane. It alo how high variation in dihedral angle for the linker (light green) and four other nonhelical domain (light blue). Three of thee four domain are calcium-binding ite, including both N-terminal ite. The protein pack head-to-tail, with the left mot C-terminal calcium binding ite loop itting in a ridge between the right mot N-terminal α helice. The motion meaured from the diffue treak are confined to the ame plane a thoe in the multiple-conformer refinement. They lie along (1, 1, 0), the head-to-tail packing direction indicated in the figure. There i trong coupling along thi ame direction and weak coupling perpendicular to thi direction, epecially in the a b plane through the flexible linker (light green). Ca 2+ ion are hown a phere. The figure wa made uing the program RASMOL (R Sayle, Glaxo Reearch and Development, Greenford, Middleex, UK). A with many derivation of expreion for thermal diffue cattering (e.g., Warren [24] and Jame [25]), the model we ue i in a cla where both the diplacement of atom from equilibrium and the variation in the ditance between any two atom in the crytal are either mall or Gauianditributed. In thi cla of model, the total mean cattered intenity I (q) at cattering vector q =2πha the form: * I( ) i( ) j ( ) e 2 q = q q F F ( u u i i + u u j j + 2 u u i j) (1) q q ij where F i and F j are the tructure factor of atom i and j, u i and u j are the vector diplacement from equilibrium of where I 0 (q) i the point-like intenity ditribution for the unperturbed crytal, * indicate a convolution, and the moothing function Γ γ (q) i the Fourier repreentation of the atomic diplacement correlation. Two different functional form of Γ γ (q) were conidered in thi tudy, both of which decribe liquid-like motion. The firt wa one decribed in Clarage et al. [15], and correpond to real-pace correlation which decay a e xγ 1 1 : Γ() ( ) [ 0 * ] Id( q) = e q2 σ 2 q2σ2 I ( q) Γ γ ( q) (2) 8πγ q = ( 1+ q γ ) The econd functional form correpond to real-pace correlation which decay a x 1 e x γ 2 1 : πγ Γ( ) ( ) 3 q = 1 + q γ In both cae, γ decribe a length cale over which atomic diplacement are correlated. Atom which are further apart than a ditance γ move eentially independently, while the motion of thoe that are cloer than γ are coupled. Note that, for large value of q, the econd, Lorentzian form reemble a Debye olid with thermally excited ound wave. Uing diffue cattering meaurement of σ and γ in thi model, one can derive a diperion (3) (4)

5 Reearch Article Motion of calmodulin Wall, Clarage and Phillip 1603 Figure 3 Root mean quare (rm) deviation of backbone Cα poition and dihedral angle in the four-conformer refinement. Large variation are confined to nonhelical domain (a defined by RIBBONS). There are high variation in the linker, in three of the calciumbinding ite, and in a turn linking the C- terminal EF-hand Rmd (phi [º]) Rmd (pi [º]) Rmd(Cα poition [Å x 100]) nonhelical region Reidue number Structure relation for thee wave, and calculate their effect on the entropy and the pecific heat of the crytal. It ha been previouly hown [20] that σ and γ can be objectively refined againt three-dimenional diffue data, imply by varying them until the correlation coefficient C between the model and the data i maximized. The ame technique were ued in thi tudy to obtain the bet fit to σ and γ for crytalline calmodulin. In order to calculate the diffue cattering uing Equation 2, the ditribution I 0 (q) mut firt be calculated. Thi ditribution i jut a point-like ampling of the quared tructure factor F(q) 2 of the unit cell, calculated without any temperature factor uing the program X-PLOR [26]. In order to be able to calculate diffue cattering to a reolution a high a 2 Å, I 0 (q) wa calculated to 1 Å reolution, a large-cale feature are influenced by Bragg peak which are far away in reciprocal pace. Once I 0 (q) wa obtained, the diffue cattering wa calculated, uing either Equation 3 or Equation 4 a a functional form for Γ γ (q). A with the experimental data, the pherical average wa ubtracted from the calculated map and a correlation coefficient wa then calculated between the data and the imulation. In addition, a cale factor wa adjuted between the two to find the bet agreement by the R factor. Both model yield an R factor of 0.41 in the 7.5 Å 2.1 Å reolution range, while the correlation coefficient uing Γ (1) (0.55) i lightly better than that uing Γ (2) (0.54). The data and imulation are compared for both model in Figure 4. The refined value of the atomic diplacement uing both model wa σ = 0.38 ± 0.08 Å (the error indicate by how much the parameter mut be changed in order to change the correlation coefficient by 0.01). The correlation length found uing Γ (1) wa γ 1 = 4.8 ± 1.0 Å. Thi i a mall correlation length compared with the reult of other diffue cattering tudie, uch a one involving inulin [14] (6 Å) or Staphylococcal nucleae (10 Å) [20]. The correlation length found uing Γ (2) wa γ 2 =12±3.5 Å, which i ignificantly higher than γ 1. The different value of the correlation length are due to the difference in the functional form of the correlation. One can predict that γ 1 will be lower than γ 2 by comparing the radial ditribution of the correlation. Thee have the form: and c (1) c (2) 1 ( x) dx = x dx 2γ 1 2 e xγ xγ 1 ( x) dx = xe 2 dx γ where each i normalized uch that 0 c(x) dx = 1. One method of obtaining a correpondence between γ 1 and γ 2 i by contraining the poition of the maximum in c (1) (x max =2γ 1 ) to be equal to the poition of the maximum in 2 2 (5) (6)

6 1604 Structure 1997, Vol 5 No 12 Figure 4 π 0 π θ π π π φ Structure Comparion of data (left) and imulation (right) for large-cale feature. Both are diplayed uing hell image [20], which are Mercator projection of the diffue intenity in a elected reolution hell, in thi cae one panning 4.3 Å 3.3 Å. The imulation wa generated uing exponential correlation, with a diplacement σ = 0.38 Å, and a correlation length γ 1 = 4.8 Å. The correlation coefficient (R factor) calculated between the data and imulation in thi hell i 0.71 (0.34). The azimuthal angle φ varie from π (left) to π (right), while the polar angle θ varie from 0 (top) to π (bottom) in each image. Pixel value are diplayed on a linear greycale, ranging from 20 count below (black) to 20 count above (white) the mean in the hell. c (2) (x max = γ 2 ). Thi produce the relation γ 2 =2γ 1, which would account for mot of the oberved difference. Another way to approach thi i illutrated in Figure 5. The ditribution c (1) (x) i ued to calculate data point for the value γ 1 = 4.8 Å. The ditribution c (2) (x) i then fit to the data point uing a nonlinear leat quare algorithm, yielding γ 2 = 7.7 Å. Thi fit predict the relation for any value of γ 1 and γ 2. γ = 1.6 γ (7) 2 1 Streaked diffue feature The method ued to map the maller cale treaked feature in three dimenion are imilar to thoe ued for the large cale diffue cattering. Rather than being meaured on the ame lattice a the Bragg peak, however, in order to be reolved thee feature are meaured on a higher reolution lattice, called a Gibb lattice. For thi tudy, we ued a Gibb lattice, which panned eight Bragg peak in each direction at eight time the reolution of the Bragg lattice. The C222 1 pace group of the unit cell wa ued to average together all ymmetry-related intenity, providing eightfold redundancy in the data. Depite the relatively weak data, therefore, the treak appear a beautifully clear feature, a i een in the map of diffue intenity centered on the (2, 20, 4) Bragg reflection (Figure 6). Without referring to pecific model, we firt mention ome alient feature in the mall cale diffue cattering. Firt, diffue map clearly how treak which completely lie within the a* b* plane. Second, two different kind of treak are oberved: one which are primarily extended along the ± (1, 1, 0) direction in reciprocal pace; and ymmetry-related treak which are extended along the ± ( 1, 1, 0) direction in reciprocal pace. Third, treak are never oberved to point toward the origin, and their intenity i tronget when the direction to the origin i perpendicular to the direction of the treak. All of thee characteritic of the ditribution of diffue treak are accounted for by the model we will now decribe. The treak were modeled uing a three-dimenional analog of the model ued to decribe the large-cale feature (ee Clarage et al. [15]): The variance σ 2 of the iotropic model i replaced by a variance matrix V, which can be thought of a a et of vector decribing the amplitude of atomic motion in three independent direction. Two different form for Γ were ued to model the treak: and Γ 8πdet G ( q) = (1) [ 1+ G q ] 4πdet G Γ() 2 ( q) = 1+ G q [ 0 Γ ] Id( q) = e V q V q I ( q)* G ( q) (8) q Equation 9 and 10 are three-dimenional analog of the previouly decribed iotropic model in Equation 3 and 4, with the correlation length γ replaced by the correlation matrix G. In a imilar way to the variance matrix, the correlation matrix can be thought of a a et of three vector (9) (10)

7 Reearch Article Motion of calmodulin Wall, Clarage and Phillip 1605 Figure 5 Comparion of the two functional form of correlation. A explained in the text, the radial ditribution c (1) (x) i ued to generate data point for γ 1 = 4.8 Å, and the bet fit of c (2) (x) to thee point i found for γ 2 = 7.7 Å. Thi fitting procedure generally predict the relation γ 2 = 1.60 γ c (1) Data c (2) Fit Ditance (Å) Structure which decribe the length cale of the decay of correlation in three independent direction. Figure 6 The procedure for modeling the treak wa imilar to that ued to model the large cale diffue cattering (ee above). The ame ditribution I 0 (q) wa ued in Equation 8 a wa ued in Equation 2. The element of the matrix G were choen uch that the direction of coupling, and hence the direction along which the treak were meared, pointed along ± (a*, b*, 0), ± ( b*, a*, 0), and ± (0, 0, c*) (in orthogonal coordinate). The element of the matrix V were choen uch that the direction of motion were the ame a the principle axe of the treak. All direction were choen baed on the obervation of alient feature decribed above. Thi left a total of ix free parameter in the refinement: γ 1, γ 2 and γ 3, which are the correlation length along each of the defined direction; and σ 1, σ 2 and σ 3, which are the amplitude of motion along each of the ame direction. Symmetryrelated treak were generated uing the ame parameter. The element of G and V were given initial value baed on etimate of the trength of coupling and amplitude of motion along each of the defined direction. A diffue map wa then calculated according to Equation 8, uing either Equation 9 or Equation 10 to decribe the correlation. The background wa ubtracted in a manner identical to that ued to remove large cale diffue feature from the data, and the ame mak wa ued to ignore lattice point which were too cloe to a Bragg peak poition. A correlation Comparion of iourface treak in the data (a) and the aniotropic liquid-like motion model uing a Lorentzian ditribution (b). Thi view i centered on (h,k,l) = (2, 20, 4), and pan eight Bragg peak at a ampling of eight point per reciprocal-lattice pacing along each direction. The urface are interpolated at a level about 35 count above the background. There i more treaking in the model than in the data, but the overall agreement i quite good (correlation coefficient with the data i 0.81). Reciprocal axe are labeled (offet) in the figure. (The figure wa made uing the program EXPLORER, Numerical Algorithm Group, Inc., Downer Grove, IL, USA.)

8 1606 Structure 1997, Vol 5 No 12 coefficient wa calculated between the map to meaure their agreement. The ix free parameter of G and V were iteratively varied by hand to maximize the correlation coefficient, at which time the refinement wa complete. The reult are ummarized in Table 2 and are viewed in Figure 6. Depite the poor quality of the econd data et, the model parameter refined to value very imilar to thoe uing the data from the firt crytal. The refinement uing Γ (2) produced a better correlation with the data (0.81) than that uing Γ (1) (0.77); viualization of the map alo confirmed that the one calculated uing the bet fit to Γ (2) looked more like the data. Uing the (2) (1) (2) (1) value in the table, γ 1 /γ 1 = 1.4, and γ 2 /γ 2 = 1.6. Equation 7 thu appear to hold fairly well for the aniotropic correlation. The value for γ 3 are not unreaonable, but the hort c* axi in the reciprocal unit cell make it difficult to obtain an accurate meaurement of the correlation length in that direction. Uing the program XCADS (JBC and GNP, firt ued in it preent form in [18], and decribed at webite the refined model parameter were ued to imulate diffraction image. A typical reult i hown in Figure 7, which compare a imulation with a diffraction image. Wherea pat method required that the model parameter be adjuted in order to obtain the bet viual agreement, thi tudy ha hown that objectively refined model parameter alo yield the bet viual agreement. The diffue treak can be undertood by viewing the packing of calmodulin in the crytal (ee Figure 2). The 0.4 Å motion which give rie to the treaked feature are entirely along the ± (1, 1, 0) direction in direct pace, which point along the end-to-end packing direction in the unit cell. Thi i alo the direction along which the coupling wa the tronget (γ = 135 Å). The weaket coupling i perpendicular to thi packing direction in the plane of the figure (γ = 50 Å). That the coupling i o weak in thi direction i perhap not o urpriing, a a large olvent cavity containing the melted flexible linker lie between the tack of calmodulin in thi direction. Motion are alo relatively weakly coupled into the page (γ = 85 Å, which i maller than the unit cell in thi direction). Dicuion Even though Bragg reflection only yield the average electron denity, information about motion can be learned both from atomic temperature factor and multiple-conformer refinement. There are problem with both of thee method, however. Temperature factor are likely to overimplify the picture, and contain no information about correlation in atomic diplacement. For intance, uing Bragg reflection alone, it i difficult to tell whether higher temperature factor on urface reidue are due to rigid-body rotation or increaed mobility due to olvent expoure. Correlation can be inferred by tudying the difference among tructure in a multiple-conformer refinement. For intance, in thi tudy, large variation in dihedral angle were oberved in nonhelical domain of the protein. A natural interpretation would be that the multiple-conformer refinement predict motion of rigid, α-helical rod tethered together by flexible coil. Thi i very imilar to the picture obtained from molecular dynamic tudie of myoglobin [19,27], another primarily α-helical protein. There i a caveat in the above reaoning. Even if an enemble of tructure accurately decribe the poible location of individual atom, the correlation in a multiple-conformer refinement generally come from the detail of molecular dynamic imulation and chemical retraint rather than diffraction data. In ome cae, uch a i common with alternate idechain configuration, the electron denity can clearly indicate which atom mut move together. In cae where the electron denity i more continuouly meared, however, the correlation may become eentially arbitrary, epecially between pair of atom on different reidue. Although local variation may be clearly indicated, large-cale motion may be difficult to prove without further experiment. Here we compare the reult of our multiple-conformer refinement to a olution NMR tudy of calmodulin backbone dynamic by Barbato et al. [3]. The NMR tudy ue a free recombinant Ca 2+ calmodulin from Droophila melanogater, but the comparion i nonethele intereting. Both tudie find motion in the linker, and in the turn connecting the C-terminal EF-hand calcium-binding domain. Only the NMR tudy, however, find motion Table 2 Reult from the analyi of the diffue treak. γ 1 γ 2 γ 3 σ 1 σ 2 σ 3 C Crytal 1; Γ (1) Crytal 1; Γ (2) Crytal 2; Γ (2) Two different form of correlation, Γ (1) and Γ (2) (decribed in the text), were ued to model the treak. Value for σ and γ are in Å.

9 Reearch Article Motion of calmodulin Wall, Clarage and Phillip 1607 Figure 7 Diffue feature in X-ray expoure. (a) Image of X-ray expoure from calmodulin (30 till at room temperature and preure). Meaurement of the intenitie of the harp Bragg peak were ued to refine both tandard and multiple-conformer tructural model. Note the treaked, mall-cale feature in the olvent ring (ee inet), and the broader, large cale background feature. We ued all 190 diffraction image to obtain three-dimenional map of both type of diffue cattering, and ued the map to refine liquid-like motion model of protein dynamic. (b) A imulated expoure calculated uing an aniotropic liquid-like motion model in XCADS. The parameter obtained from the diffue-cattering refinement not only yielded the bet correlation coefficient with the data, but alo produced the bet imulated diffraction image. (a) (b) Structure in the turn connecting the N-terminal EF-hand calciumbinding domain and only the multiple-conformer refinement find motion in three of the calcium-binding ite. Neither experiment find large-amplitude motion in any of the α helice (with the exception of the central portion of the linker), or in the econd calcium-binding ite in the C-terminal domain. In addition, NMR tudie of Ca 2+ - free calmodulin have hown ignificant backbone motion in nonhelical region, including the calciumbinding ite [28,29,30]. Depite it implicity, the iotropic liquid-like motion model accurately decribe the large-cale feature in diffue cattering from protein crytal. Experiment with inulin [14], lyozyme [15], tropomyoin [16], trna [18], Staphylococcal nucleae [20], and now calmodulin all how diffue pattern characteritic of liquid-like motion. There i ample evidence that the correlation length γ and the mean atomic diplacement σ are not jut ueful for decribing the motion of a mall number of protein, but are parameter which can be ued to characterize the motion of many protein, and to generate a hierarchy of flexibility. There are ome intereting connection between the treaked diffue feature and the internal motion of calmodulin. The analyi of treaked diffue feature, for intance, implie motion which are confined to the ame plane a the preferred diplacement in the multipleconformer refinement. A the two tudie were done independently, thi reult how a meaure of elf-conitency between the Bragg and diffue cattering analyi. Analyi of the packing of calmodulin in the crytal (ee Figure 2) how the important role of the linker in defining the plane of motion, and the reulting ditribution of the treak: becaue the looely-tructured linker lie between end-to-end rod of calmodulin, there i weak coupling cauing treak to broaden along the direction of contact between the rod, which lie in the a b plane. If the linker were not a mobile, not only would the correlation length of 50 Å along thi direction be likely to increae, but the crytalline packing would alo be likely to change, a it would not require a much free energy to bring the linker out of the olvent and into a more retrained environment. A olvated linker alo appear to be electrotatically favorable: among reidue 74 84, eight have charged idechain, two have polar idechain, and only one ha a nonpolar idechain. The large cale diffue cattering doe not ditinguih between the different form of correlation. Careful analyi of the mall-cale treak, however, how that they are more conitent with a Lorentzian profile than the form previouly ued to decribe liquid-like motion. Further experiment will need to be done to determine whether thi i olely a property of calmodulin, or whether protein are generally better decribed uing the Lorentzian form. The atomic motion which give rie to the diffue feature account for mot of the motion decribed by the temperature factor from the tructural model. Combining the reult of both diffue cattering tudie yield σ = (0.38 Å) 2 + (0.4 Å) 2 = 0.6 Å, compared to a value of 0.7 Å calculated from the mean temperature factor in the ingle-conformer refinement. A tatitically ignificant difference either could be due to an inaccuracy in the model, or could be due to the preence of independent atomic fluctuation, which give rie to pherically ymmetric diffue feature that were not conidered in thi tudy.

10 1608 Structure 1997, Vol 5 No 12 Thi tudy ha hown that much of the diorder in crytal of calmodulin come about a a reult of the internal motion of the molecule. While the high-reolution feature of the more rigid domain of the protein may be blurred by thee motion, crytal with diorder can provide inight into important characteritic of the molecule. For intance, protein with maller correlation length would be predicted to have higher configurational entropy than thoe with large correlation length. In the calmodulin peptide complex, for example, the mall correlation length and high mobility of the linker certainly influence the free energy difference between the open and cloed tate. More generally, it would be intereting to compare the correlation length with a meaure of the tability to denaturation of variou protein, to ee how the two are related to each other. Studie uing two different crytal form of lyozyme how that the hort range correlated motion, which give rie to large cale diffue feature, do not change in different crytal environment [15]. Thi i not urpriing, a the length cale of correlation (6 Å) i maller than the ize of the protein. The value of σ and γ which are obtained from large cale diffue cattering are therefore likely to be relevant even in the olution tate. The mot locally mobile part of calmodulin, uch a the linker, do not make crytal contact. It i poible that thee part are mobile imply becaue they are not contrained by contact. Protein are known, however, to crytallize in pace group which allow a high number of rigid-body degree of freedom [31]. The important influence of configurational entropy alo make it likely that, in order to avoid increae in free energy, the protein crytallize in uch a way a to preerve the diorder of the mot mobile part of the protein. Thi give additional confidence not only in identifying mobile part of the protein uing crytallography, but alo in gueing at which part of the protein are relatively rigid. Large-cale motion, on the other hand, are generally enitive to the particular of the crytal lattice. Protein tend to puh up againt each other in the crytal, o that the packing i mot likely too dene for independent rigidbody motion of entire protein. For intance, thi tudy ha hown that in calmodulin crytal, the protein do not have independent large-cale motion. Motion are primarily along the head-to-tail packing direction of the unit cell, and trongly influence the movement of neighboring protein along thee ame direction. Schomaker and Trueblood TLS model of rigid-body tranlation and rotation [32] (where T i the tranlation tenor, L i the libration tenor and S i the tenor of correlation of tranlation and rotation) can account for much of the amplitude of individual atomic temperature factor in tructural model of protein [33,34]. Diffue cattering hould reveal whether the TLS model work becaue it i accurate, or whether it work becaue it i a concie way to account for a general increae in the mobility of reidue near the urface of protein. In fact, Pérez et al. [35] have recently reported that diffue cattering from lyozyme ha ome feature which are conitent with independent rigid-body motion of protein molecule. Lyozyme, however, ha been omething of a tet cae for diffue cattering tudie, and other model have been propoed to decribe the diffue cattering [13,15,17]. For intance, an early experiment by Doucet and Benoit [13] (in a pirit imilar to thi calmodulin tudy) howed that a model baed on the motion of rigid cluter of molecule produced diffue treak imilar to thoe in P lyozyme diffraction image. It would be very intereting to perform a careful analyi of the lyozyme diffue cattering uing three-dimenional meaurement like thoe decribed here and in a previou tudy of Staphylococcal nucleae [20]. Such a tudy hould compare all relevant model to date, and hould alo include a decription of coupled rigid-body motion, which would alo be conitent with the TLS model. Structural biology can benefit from improvement in diffue cattering method in everal way. With increaingly good data and three-dimenional repreentation, it may be poible to ue more complex model to decribe the motion. One natural way to extend the liquid-like motion model would be to break up the protein into domain j, aigning a different correlation length γ j to each of the domain. Although one could not reaonably meaure all of the atomic correlation u i u j, one could tune the level of detail, and thu the number of free parameter, in uch a model to accurately reflect the amount of information in the diffue data. Such improvement are epecially important both in light of the evidence that molecular dynamic imulation do not ample enough configuration to preciely meaure thee atomic correlation [19], and in light of the key role that correlation play in determining the thermodynamic propertie of protein. A the method improve, it will be poible to reviit a problem pointed out long ago by Cochran [36]: in order to accurately meaure Bragg peak, one mut effectively ubtract the diffue cattering. Although current technique are likely to be adequate for ubtracting large cale diffue feature, treaked feature are more difficult to deal with in integration algorithm. One poible olution lie in an iterative integration cheme, where Bragg and diffue data are meaured eparately in a firt pa, but where Bragg peak are meaured again after the treak have been characterized. Such an iterative cheme would not only produce improved diffue cattering data, but alo yield better Bragg peak meaurement improving the quality of electron-denity map.

11 Reearch Article Motion of calmodulin Wall, Clarage and Phillip 1609 Eventually Bragg and diffue data could be combined into a complete X-ray diffraction data et, allowing for a more accurate refinement of model of protein dynamic. Thi would not only be important for obtaining information about correlated motion, but would alo mot likely improve the overall quality of tructural model by allowing a more ophiticated treatment of molecular motion. Biological implication Calmodulin i capable of binding to many different protein and regulating their activitie. If the molecular bai of it function were known, one would be able to predict the influence of calcium on a great number of biological procee. The wide-pread influence of calmodulin can largely be attributed to the flexible linker, which allow the globular end of the protein to repoition themelve when they bind to a target. The detailed propertie of the linker will in part determine the binding affinity of calmodulin for it many target. For intance, the linker appear to loe coherent tructure when it bind to a target, which no doubt affect the enthalpy of binding. Undertanding motion uch a thoe oberved in thi tudy may prove to be ueful in etimating uch effect quantitatively. We have tudied motion in a calmodulin peptide complex uing both Bragg and diffue cattering in X-ray diffraction experiment. Bragg data were ued to perform a multiple-conformer refinement, which produced an enemble of protein tructure whoe difference were analyzed. Diffue cattering data were ued to tudy the correlated motion of the crytalline protein. The reult of thee tudie are complementary, and how conitencie. We find two intereting reult related to the linker. A evidence that there are many configuration preent in the crytal, the enemble of tructure from the multipleconformer refinement both improve the fit to the X-ray data, and lower the temperature factor. The enemble how great variation in the linker. The diffue cattering alo how that atomic motion are only weakly coupled through the linker, with a correlation length of 50 Å. We alo find that other part of the molecule beide the linker are highly mobile. Mot notable are the two regulatory N-terminal calcium-binding ite. The mobility in thee ite may be related to their relatively weak affinity for calcium. One of the C-terminal calcium-binding ite alo how relatively high variation, a doe a turn connecting the C-terminal EF-hand calcium-binding domain. Thi tudy yield a couple of more general obervation about motion in crytalline calmodulin. Firt, the diffue cattering how that the whole molecule i relatively oft, having an overall correlation length which i relatively mall. Compared to inulin and Staphylococcal nucleae, for intance, different part of the protein move relatively independently of each other. Second, the overall motion of the atom are aniotropic. Both the ditribution of atomic diplacement in the multiple-conformer refinement and the treak in the diffue cattering how that atom move primarily in the a b plane, and with higher amplitude along the b axi than along the a axi. Finally, recent improvement in diffue cattering method have ome general implication for tructural biology. It i not difficult to imagine algorithm for meauring Bragg reflection and diffue cattering imultaneouly, and for including diffue data in automated refinement. Both Bragg reflection and diffue cattering will almot certainly be more accurately meaured when meaured together, epecially when mall cale diffue treak are preent. Alo, by combining Bragg and diffue data during refinement, one can more accurately model protein motion, improving the quality of tructural model and poibly lowering R factor. Material and method Specimen Diffraction-quality crytal were microeeded in hanging drop over 100 mm odium acetate at ph 5.2, with 20% polyethylene glycol 6000 (PEG 6000), 10 mm calcium chloride and 0.02% odium azide. Stock olution of 24 mg/ml bovine brain calmodulin (Sigma Lot 54H9558), 14 mg/ml CaMKIIα peptide (gift of the lab of F Quiocho, Howard Hughe Medical Intitute, Baylor College of Medicine, Houton, TX), and 30% PEG were mixed into hanging drop in about a 4:2:1 ratio. Crytal had an orthorhombic unit cell with pace group C Uing the program DENZO [37], the unit cell parameter were meaured to be a = 38.8 Å, b = 75.2 Å, c = 120 Å, α = β = γ =90, with a moaicity of 0.3. Crytal were mounted in gla capillarie, with the buffer touching the crytal kept to a minimum. Data collection Data were collected at the F2 tation at the Cornell High-Energy Synchrotron Source (CHESS), uing the Princeton 2K CCD detector (a ucceor to that decribed in Tate et al. [38]). The beam wa tuned to 0.98 Å, had a meaured polarization of 0.9, and wa collimated to a 100 µm diameter. A equence of 30 till expoure (ee Figure 7), where the goniometer poition remained fixed, wa ued to obtain three-dimenional meaurement of diffue intenity. Still were taken every 1 in pindle rotation, with interleaved 10 1 ocillation expoure for obtaining a crytal orientation and Bragg peak meaurement. Expoure were taken at 190 different pindle poition. Data proceing Bragg reflection were indexed and meaured from ocillation expoure uing DENZO and SCALEPACK [37] (Zbyzek Otwinowki and Wladek Minor). The data were 96% complete from 20 Å 2 Å, with a linear R factor (R ym ) of In addition to the Bragg reflection, triking diffue feature were viible in X-ray expoure (ee Figure 7). Notably prominent were treak emanating from Bragg reflection, epecially in the neighborhood of 3.5 Å

12 1610 Structure 1997, Vol 5 No 12 reolution. In addition, broader feature, with length cale larger than the ditance between Bragg reflection, were viible. Before uing diffraction image to meaure diffue intenity, ome experimental effect which caue background intenity variation had to be accounted for. Two effect are ignificant: the polarization of the X-ray beam caue azimuthal variation which are epecially trong at high reolution; and pixel at high-cattering angle pan a maller olid angle about the pecimen than do pixel at low cattering angle, cauing an effective decreae in intenity at high reolution. Previouly decribed method [20,39] were ued to correct for both of thee effect. Large cale diffue feature To iolate the large cale diffue feature, it i neceary to eliminate the harp Bragg reflection from diffraction image. A mode filter image proceing technique can be ued to uccefully eliminate Bragg peak from X-ray diffraction image [20]. Thi technique wa found to have ome limitation, however: the treaked feature in calmodulin diffraction image left trace of intenity in mode-filtered diffraction image. A different method wa therefore ought to eliminate Bragg reflection. A imple olution wa uggeted by a ymmetry property of the C222 1 unit cell pace group. In thi pace group, all Bragg reflection where h + k i odd are identically zero. In addition, a i decribed below, the treak emanating from Bragg reflection were oriented along the (± 1, 1, 0) direction, o that no treak were ever oberved near thee ytematic abence. To eliminate Bragg reflection from calmodulin diffraction image, therefore, intenity meaurement were made only in the neighborhood of ytematic abence. Thi meant that reciprocal pace wa ampled at only every other Miller index in the a* and b* direction. In addition, due to the relatively long c axi of the unit cell, reciprocal pace wa ampled at only every fourth Bragg peak in the c* direction. Even with the reduced reolution, however, thi ampling wa ufficiently detailed to reolve the large cale diffue feature, whoe mallet variation were larger than many reciprocal-lattice pacing. A i the cae with ordinary diffraction data, when diffue data are merged to create a three-dimenional data et, variation in beam intenity and the change in the thickne of the pecimen with different crytal orientation require caling of intenitie. In order to calculate a cale factor for diffue intenity in a diffraction image, meaurement were taken of the diffue cattering at high reolution, where coherent cattering i very weak. Uing the method decribed in Wall [39], thee meaurement were then ued to cale value of diffue intenity and map them to a three-dimenional lattice of diffue cattering I d (), called a diffue map. Thi map i eentially the ame a a parely ampled Bragg lattice, where, intead of being Bragg peak intenitie, the value are meaurement of the diffue intenity in the neighborhood of the correponding Bragg peak. In order to increae ignal-to-noie, at the time they were created, the map I d () were ymmetry-averaged according to the prediction of the C222 1 pace group of the unit cell. The ymmetry averaging wa crucial to the ucce of the experiment, a it made otherwie weak feature trong enough to viualize: eight independent meaurement were made for each lattice point, ubtantially enhancing the ignal-to-noie. To eliminate the effect of cattering from diordered olvent, air, and other pherically ymmetric ource, the pherically averaged intenity wa ubtracted from each intenity value in the diffue map. Reciprocal pace wa ectioned into pherical hell, each of thickne Å 1 (the length of the reciprocal unit cell diagonal), and the average intenity wa calculated in each of thee reolution hell, producing a map I d ph () of the pherically averaged diffue intenity. A reidual map, I d () = I d () I d ph (), wa then calculated. In order to check reproducibility, two independent data et were obtained uing different crytal in different orientation. After each map had it pherical average ubtracted, a correlation coefficient, C, wa calculated between the reulting reidual map: C= Σ{} X() Y() Σ{} X2() Σ Y2() ( )( {} ) where X and Y are two map being compared (in thi cae, the two experimentally obtained map of I d ()), and {} pan the cattering vector in the reolution hell over which the comparion i to take place. The reult wa a correlation of 0.59 in the 7.5 Å 2.1 Å reolution range (for comparion, the correlation in the ame range i before the pherical average i ubtracted). In addition, the R factor, defined a Σ{} X() Y() R = (12) Σ{} X() wa calculated between the reidual map, giving a value of 0.40 in the Å reolution range. Thi R factor doe not compare well with the R ym of 0.06 calculated from the Bragg data, which i attributed both to the relatively weak ignal after the pherical average i ubtracted, and to the fact that the data from the econd crytal were much weaker than thoe from the firt crytal. Streaked diffue feature When he conducted the firt thorough experiment to verify the Debye theory, Laval [40] mapped the ditribution of diffue intenity in the neighborhood of Bragg reflection from diamond crytal completely by hand. Fortunately, we were able to develop automated method to map the three-dimenional ditribution of treaked diffue feature in calmodulin diffraction. The method were imilar to thoe ued in mapping the large-cale feature. A the treak have tructure on length cale maller than the reciprocal unit cell, however, a lattice which ample reciprocal pace at a finer cale than the Bragg lattice wa required. A Gibb lattice (decribed in, e.g., Clarage and Phillip [10]), which ubdivide reciprocal unit cell into equal-ized block, i a natural choice. Eight voxel per Bragg peak pacing, amounting to 512 voxel per reciprocal unit cell, wa found to be ufficiently detailed to reolve the treak, yet wa not o fine that the 1 pindle ampling left void in the map. Uing the Nyquit condition, at thi ampling frequency, we etimate that we can oberve motion which are correlated on length cale of up to four lattice pacing along each unit cell axi. We now etimate the mallet diffraction feature which can be reolved, given the experimental contraint. Roughly peaking, feature are meared over a reciprocal pace ditance of δ δθ δθ Bragg = 1 2 catt (11) (13) when the cattering angle θ catt i broadened by δθ catt. The moaicity, an angular parameter which trictly meaure how much the orientation of identical Bragg plane varie throughout the crytal, i commonly ued a a fudge-factor to aborb all kind of experimental peak broadening (including ome mall cale diffue cattering, which technically hould be eparated to meaure Bragg peak intenitie accurately). The moaicity thu give an etimated upper limit on δθ catt : when the value of 0.3 ( rad) for calmodulin i ubtituted into Equation 13 at a reolution of 3.5 Å, where we map the treaked feature (ee