Essential Dynamics of Helices Provide a Functional Classification of EF-Hand Proteins Francesco Capozzi,†,‡ Claudio Luchinat,*,‡,§ Cristian Micheletti,*,| and Francesco Pontiggia| Department of Food Science, University of Bologna, Piazza Goidanich, 60, 47023 Cesena, Italy, Magnetic Resonance Center (CERM), University of Florence, Via L. Sacconi, 6, 50019 Sesto Fiorentino, Italy, Department of Agricultural Biotechnology, Via F. Maragliano, 75-77, 50144 Florence, Italy, and International School for Advanced Studies (SISSA), INFM-Democritos and Italian Institute of Technology, Via Beirut 2-4, 34014 Trieste, Italy Received May 24, 2007
Low energy modes have been calculated for the largest possible number of available representatives (>150) of EF-hand domains belonging to different members of the calcium-binding EF-hand protein superfamily. These proteins are the major actors in signal transduction. The latter, in turn, relies on the dynamical properties of the systems, in particular on the relative movements of the four helices characterizing each EF-hand domain upon calcium binding. The peculiar structural and dynamical features of this protein superfamily are systematically investigated by a novel approach, where the lowest energy (essential) modes are described in the space of the six interhelical angles among the four helices constituting the EF-hand domain. The modes, obtained through a general and transferable coarse-graining scheme, identify the easy directions of helical motions. It is found that, for most proteins, the two lowest energy modes are sufficient to capture most of the helices’ fluctuation dynamics. Strikingly, the comparison of such modes for all possible pairs of EF-hand domain representatives reveals that only few easy directions are preferred within this large protein superfamily. This enables us to introduce a novel dynamics-based classification of EF-hand domains that complements existing structure-based characterizations from an unexplored biological perspective. Keywords: EF-hand proteins • slow dynamics • helix dynamics • calcium • cluster analysis
Introduction Most vital processes, ranging from cellular duplication and apoptosis to contraction and secretion, depend on calcium signaling, in turn, based on a limited number of proteins devoted to signal transduction.1-6 Most of these proteins belong to the EF-hand superfamily. EF-hand proteins share a common structural building block constituted by the so-called EF-hand motif (helix-loop-helix).7 The minimal functional unit, called EF-hand domain, is constituted by a pair of EF-hand motifs connected by a short linker and packed face to face.8 Each EFhand domain is capable of binding two calcium ions through specific interactions with conserved amino acids and backbone carbonyl groups of the two loops. In spite of sharing virtually the same structural topology and architecture,9 EF-hand domains display a multiplicity of arrangement of the four helices typically schematized in three main architectures: antiparallel bundle, orthogonal bundle, and chair bundle.10 This variability is crucial for signal transduction. Upon calcium binding, EF* To whom correspondence should be addressed. C.L.: e-mail, luchinat@ cerm.unifi.it; phone, +39 055 4574262; fax, +39 055 4574253. C.M.: e-mail,
[email protected]; phone, +39 040 3787300; fax, +39 040 3787528. † University of Bologna. ‡ University of Florence. § Department of Agricultural Biotechnology. | SISSA/ISAS. 10.1021/pr070314m CCC: $37.00
2007 American Chemical Society
hand domains undergo different degrees of conformational changes, related to the variety of different functions.1 The large conformational diversity and variety of responses to calcium binding of EF-hand domains has posed major difficulties for their grouping and classification in terms of structural features. Some of us have recently proposed a simplified structural description based on the six angles formed by the 4 helices of the EF-hand domain. It was found that only two linear combinations of the angles suffice to capture most of the observed structural variations and, thus, provide a concise and quantitative framework for representing the structural diversity.10 Yet, owing to the almost continuous spectrum of structures,11,12 no simple unsupervised criterion emerged for partitioning the proteins in neatly separated groups. Here, we undertake a novel investigation of the unifying traits within the EF-hand superfamily by examining and comparing the directions of the concerted interhelical movements that the different EF-hand domains can sustain upon thermal excitation. The collective movements of the helices are established numerically within the elastic network model which is based on a quadratic free-energy approximation.13-22 This transparent framework is computationally inexpensive and, by validation against extensive atomistic molecular dynamics studies, has been previously shown to provide a reliable description of Journal of Proteome Research 2007, 6, 4245-4255
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research articles large-scale concerted movements in various proteins and enzymes.16,20,23-26 Furthermore, several studies have linked the thermal excitation of these concerted movements to the structural changes (e.g., allostery) that assist and facilitate protein function.27-31 At variance with the case of structural classification, a clear and natural grouping of the proteins emerges from this dynamical-based perspective. In particular, we identify four main clusters of dynamic behaviors in which >150 different EF-hand domains fall. EF-hand domains belonging to the same cluster share remarkably similar large-scale movements. At the same time, the typical dynamic behavior of members of different clusters is very different. Interestingly, only a loose relatedness exists between similarity of interhelical angles and dynamical modes for any two EFhand domains. Indeed, the dynamical description is by no means a copy of the structural one, as structures with very different interhelical angles can share similar dynamics and vice versa. The dynamical classification is finally discussed in connection with the known biological function of the various EF-hand members.
Materials and Methods To characterize the large-scale helical movements in distinct EF-hand domains, we followed a strategy articulated over three main steps: (i) creation of a database of viable EF-hand protein domains selected among all nonredundant available structures; (ii) use of suitable mesoscopic models for systematic identification of the essential dynamics of each selected EF-hand domains; (iii) detection of statistically significant similarities of the concerted interhelical movements in distinct EF-hand domains. A self-contained account of each of these steps is provided below (further technical details are covered in the Supporting Information). Construction of the Database. We started from the selection of 308 EF-hand domains analyzed in the structural study of ref 10. This data set was originally compiled from a comprehensive set of X-ray or NMR-resolved structures ensuring the widest representation of the different biological families and the various possible structural/chemical contexts of EF-hand domains. The data set includes both apo and holo forms, both N-terminal and C-terminal domains, and each of them both in the presence or absence of bound ligands. This database was sieved for this study to remove entries (i) with incomplete or ambiguous (alternate locations for CA atoms) structural information or containing nonstandard amino acids, (ii) where any of the EF-hand domain helices was too short to reliably determine its axial orientation (see below) for the purposes of the present calculations, or (iii) where the number of heavy atoms was too large (greater than ∼2000) for an efficient numerical calculation of the model interhelical dynamics. Accordingly, we did not consider PDB entries with missing residues or with helices spanning less than six amino acids (helices defined according to ref 10). This selection procedure singled out 185 EF-hand domains. Their PDB codes and accompanying structural/biological information are provided in Table S1 of the Supporting Information. Concerted Interhelical Fluctuations. The large-scale concerted movements sustained in thermal equilibrium by each of the proteins in the database are identified through a mesoscopic “topological“ model, namely, an elastic network approach.17-20 These models build on the fact that proteins are endowed with a remarkable degree of elasticity32,33 that allows 4246
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them to sustain large-scale conformational fluctuations where, for example, tens of amino acids are concertedly displaced by a few hundred picometers over time spans of about 10 ns. Owing to these large space and time scales, such concerted displacements can be aptly captured and described with simplified models that are oblivious of the fine (atomic) structural and chemical details. The simplified elastic network model that we accordingly adopt introduces anisotropic quadratic couplings, that is, harmonic springs, to penalize the displacement from the native separation, b r0ij, of any pair of contacting heavy atoms, i and j. More specifically, the freeenergy cost associated with changing the separation of a generic atomic pair by δr bij is F)
1 2
∑ ∆ V |br ij ij
0
r ij| ijδb
2
/|b r 0ijb r 0ij|2
i,j
where ∆ is the contact matrix whose element ∆ij is equal to 1 [0] if the native separation, |r b0ij| is smaller [larger] than 500 16,18 The interaction strength V is the same for all contacting pm. ij pairs, with the exception of those involving metal ions for which the interaction is enhanced by a factor of 2 to mimic the local electrostatic effect. Clearly, the change in pairwise distances δr bji results from the displacement of the individual atoms from their reference crystallographic positions, δx bi and δx bj (that is δr bji ) δx bi - δx bj) which can be taken as the fundamental degrees of freedom of the model system. Upon making this change of variables, the free energy takes on the quadratic form: F)
1 2
∑ δxb M δxb i
ij
j
(1)
i,j
where M is the symmetric effective interaction matrix. The eigenvectors of M associated to the smallest nonzero eigenvalues define the generalized directions along which the system can be distorted with minimal free-energy cost. The spatial modulations associated to these collective displacements, also termed slow modes, thus correspond to the large-scale concerted atomic fluctuations that are most easily excited by thermal fluctuations. Within a quadratic approximation of the free energy, the slowly-relaxing low energy modes correspond to the collective coordinates obtained from the essential dynamics analysis. The entailed atomic displacements will tend to cause the least distortion of the native distances of interacting atoms. Equivalently, each atom will tend to be displaced perpendicularly to the bonds with the contacting neighbors. In contrast, the fastest modes in the system (which contribute the least to the overall system fluctuations) will embody precisely the energetically costly distortions of the bonds between contacting atoms. The precise strength of the pairwise harmonic interactions therefore impacts directly on the fast modes and their eigenvalues, while, for the above-mentioned orthogonality property, has a milder effect on the space of slow modes. For example, upon changing the enhancement factor of the interaction between protein heavy atoms and metal ions from 2 to 5, the eigenvalues of M associated to the slowest mode of protein 1qlk change by only 3%. The change approaches 5% if the enhancement factor is set to 20 or more. The traditional description of the slow modes in the space of atomic displacements is not immediately suited for comparing global movements in different EF-hand domains. Because of the differences in length, domain organization, cofactors, and so forth, it is clearly impossible to establish a pervasive
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Essential Helix Dynamics in EF-Hands
one-to-one correspondence of the displacements of all heavy atoms in different proteins. A natural way to overcome this difficulty in this case is to consider the large-scale movements of the axes of the four helices of each EF-hand domain in the space of the six interhelical angles. Denoting with ai,j the angle formed by the ith and jth helices, we shall accordingly summarize the relative orientation of the four helices with the array R b having components:R b ) {a1,2; a1,3; a1,4; a2,3; a2,4; a3,4}. Notice that a nonlinear relationship exists between the six interhelical angles. The slow modes in this six-dimensional space are obtained by a suitable reduction of the degrees of freedom in the system (see Supporting Information). When the linear transformation relating small changes in coordinate space around the native structures, {δx b}, to changes in angle-space, {δR b}, is performed, it is possible to project the free energy of eq 1 in the interhelical angle space: F)
1 2
∑ δR M˜ δR i
ij
j
(2)
i,j
where {δR b} is the deviation from its native value of the ith component of the six-dimensional angular array, R b. The previous equation allows one to express the fluctuations in thermal equilibrium of any pair of angles in terms of the corresponding element of the pseudoinverse of M ˜: -1 〈δRiδRj〉 ∝ M ˜ i,j
(3)
As before, the independent modes of decay of thermal excitations are provided by the six eigenvectors of the M ˜ matrix,v b1, b v2, ..., b v6 (with associated eigenvalues λ1, λ2, ..., λ6). As a consequence of eq 3, the fluctuations along each of the six principal directions will be proportional to the inverse of the corresponding eigenvalues. This fact is conveniently exploited to establish the relative contribution, ωi, of the ith slow mode to the overall square fluctuation dynamics: 6
ωi ) λ-1 i /
∑λ
-1 j
(4)
j)1
Because of the progressive decrease of the weight of the slow modes with their ranking, our results and discussion will be restricted to the top two slow modes which are indeed sufficient to account for most of the angular fluctuations. Comparison of Interhelical Angles and Their Fluctuation Dynamics in Different Proteins. Two different notions of distances will be used to compare the reference crystallographic interhelical angles and their slow modes in all distinct pairs of proteins (distinguished by the superscript a or b). The structural (static) distance used to capture the similar relative orientation of the four EF-hand domain helical axes is naturally defined as the Euclidian distance in the space of angular vectors:
dstruct(a,b) )
x
6
∑ (R
a i
- Rbi )2
(5)
i)1
The above measure cannot be straightforwardly adopted to compare the slowest modes in two proteins. At variance with the previous expression, the dynamical distance should in fact (a) be insensitive to a change of sign of all components of a slow mode, as the free-energy change in eq 2 is unaffected by the choice of the sign, and (b) allow the seamless comparison
of the fluctuation dynamics entailed by several slow modes simultaneously. The simplest of such measure can be constructed, as customary,34 by assuming an equally weighted importance of the top n slow modes (as anticipated, we shall limit the attention to the cases n ) 1 or n ) 2). Indicating with b vai [v bbi ] the ith slowest mode of protein a [b], the dynamical distance is hence defined as ddyn n (a,b) ) 1 -
x ∑∑ 1
n
n
n
|v bai b v bj |2
(6)
i)1 j)1
The above distance ranges from 0 to 1, corresponding to perfect coincidence or complete orthogonality of the space spanned by the top n slow modes. A small value of the dynamical distance does not imply per se a high statistical significance of the slow modes similarity. For example, when the entire dynamical space is considered, n ) 6, the dynamical distance will be necessarily equal to 0 for all pairs of proteins. We have therefore complemented the analysis of the pairwise distances in dynamical space with a control on the likelihood that they could have arisen by chance (i.e., in the absence of any meaningful correlation between the slow modes of two proteins). This was accomplished by comparing the observed distance values against a control distance distribution expected for sets of orthonormalized vectors randomly picked in the six-dimensional space. More precisely, we repeatedly generate random basis sets for the sixdimensional space. The resulting distribution of ddyn values, n thus, provided the required statistical reference. It should be noted that other criteria for choosing the reference distribution could be adopted, possibly also accounting for the nonlinear relationship that ties the six interhelical angles. The one adopted here was chosen for its transparency and simplicity of application. Clustering of Interhelical Dynamics. The inspection of the distribution of dynamical distances for n ) 2 exhibits the distinctive hallmark of the presence of clusters with very similar interhelical angle fluctuations. Of the several available clustering schemes, we adopted the standard K-medoids combinatorial algorithm (suitable also for non-Eucledian metrics) whose only input parameter is the number of desired clusters, K.35 For a given value of K, the algorithm optimizes the choice of cluster representatives and cluster members so that the summed distance of each protein from its cluster representative is the smallest possible. The data set clustering was initially carried out for 2 e K e 15. Inspection of the resulting clusters and the matrix of pairwise distances of intercluster and intracluster members revealed that a balanced subdivision could be achieved for K ) 4. Larger values of K lead to a small intercluster pairwise distance compared to the natural cluster separation indicated by the overall distribution of pairwise distances. On the other hand, smaller values of K yielded excessively large intracluster pairwise distances compared to the natural cluster “radius”, again indicated by the overall distance distribution.
Results and Discussion For each member of the comprehensive structural selection of 185 EF-hand domains, we identified the concerted interhelical angular slow modes that occur in thermal equilibrium and established their relative contribution to the overall angular fluctuation dynamics. In particular, for each considered EFhand domain, we calculated the fraction of angular fluctuation Journal of Proteome Research • Vol. 6, No. 11, 2007 4247
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Figure 1. Normalized distribution of the fraction of angular fluctuations captured by the first mode (a) and by the first plus second modes (b).
dynamics captured by the first slow mode alone and by the combination of the first and second slow modes. The distribution of such fractional dynamical contributions over the whole data set is shown in Figure 1. It is seen that the first mode alone (Figure 1a) is typically sufficient to cover 38% of the total angular fluctuations. As illustrated by Figure 1b, the inclusion of the second mode raises the fraction of captured angular fluctuations whose average is ω j ) 0.671 with dispersion σω ) 0.055. Lower fractional values of the total fluctuation reflect a rather flat free energy landscape where it is hence difficult to have a clear-cut ranking of the different essential dynamical spaces. To avoid these ambiguous situations, we omitted from further analysis the proteins in the leftmost tail of the distribution of Figure 1b. More precisely, we discarded the 31 entries whose weight of the first two modes was smaller than ω j - σω. In the following, we shall thus exclusively consider the 154 proteins that result from this filtering of the original data set (the corresponding PDB codes are highlighted in Table S1 of the Supporting Information). Our first aim is to establish the existence of statistically significant analogies of angular fluctuations in distinct EF-hand domains and, if so, cluster the data set into groups with similar dynamics. We hence started by measuring the dynamical distances of the first slow mode for all distinct pairs of proteins. The resulting distribution of 11 781 pairwise distances is shown in Figure 2a. The distribution shows an increase for distance values smaller than 0.1. This distribution should be compared with the reference distribution of distance values expected from random choices of the slow modes (dotted curve in Figure 2a). It is immediately apparent that the experimental distribution has only a small overlap with the random distribution, thus, indicating the existence of statistically significant correlations among the slowest angular modes of distinct EF-hand domains. The experimental distribution, however, lacks the bimodal signature that should accompany a clear clustering of the domains in distinct groups of comparable population and “diameter”. In the latter case, in fact, the cumulative distribution should present a peak at small distances arising from intracluster pairwise comparisons, and one at larger distances corresponding to the most probable intercluster distance. Conversely, a bimodal character is clearly visible when the angular dynamical distance is calculated over both the first and second slow mode (n ) 2 in eq 6), see Figure 2b. Again, the increase at ddyn values smaller than 0.1, which measures the n dynamical consistency (radius) within the dominant clusters, 4248
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Figure 2. Normalized distributions of the dynamical distance ddyn for n ) 1 (a) and n ) 2 (b) (solid lines), compared with the n random reference distributions (dotted line).
has a good statistical significance, as it does not appreciably overlap with the reference distribution. The good consistency of the fluctuation dynamics within the clusters is further accompanied by the separation of the dominant clusters, denoted by the peak at d ∼ 0.3 (which captures the typical dynamical distance of members of distinct dominant clusters). In conclusion, the distribution obtained including two slow modes indeed indicates the existence of dynamical clusters. A viable partitioning of the dataset into clusters (having sizable populations and typical inter- and intracluster distances consistent with the features of the distribution of Figure 2) was obtained for a K-medoids clustering with K ) 4. The number of members in the four clusters (CL0, CL1, CL2 and CL3) is respectively, 66, 48, 21 and 19. The four representatives are: the holo-form of the rat S100B protein (1qlk_A0) for CL0, the holo-form of the C-terminal human CaM bound to a target peptide (1nwd_A2) for CL1, the holo-form of the N-terminal human nucleobindin 1 (1snl_A2) for CL2, and the apo-form of the C-terminal small subunit of rat calpain (1aj5_A2) for CL3. The quality of the clustering can be visually appreciated through the density plot of Figure 3. It portrays a color-coded distance matrix of all pairs of domains, which were re-indexed so that the first 66 entries are the members of the first cluster, the subsequent 48 belong to the second cluster, and so forth. The analysis of the distances of each entry from the four cluster representatives (see Supporting Information) indicates that the dynamical similarity is striking across members of the two dominant clusters and less marked for the remaining two which, indeed, contain some members that are close to CL0. Nevertheless, the marked block character of the matrix suggests that the distinct character of the clusters should persist upon addition of EF-hand domains unrelated to the ones used here. We have verified this expectation by repeatedly reducing the data set by 20% (that is, by leaving out 31 members) and identifying the four cluster representatives. All members of the nonreduced set (i.e., including entries not used for the identification of the representatives) were then assigned to the cluster of the nearest representative. The resulting clusters were then compared with the reference ones (CL0, CL1, etc.). On average, the random data set reduction results in only ∼16 members out of 154 to be assigned to a cluster different from the reference one. This indicates that (i) the partitioning in four
Essential Helix Dynamics in EF-Hands
Figure 3. Density plot of pairwise dynamical distances ddyn 2 . Proteins have been grouped according the subdivision in four clusters (CL0, ..., CL3).
groups is not labile even when the number of removed items compares with the combined population of the two smallest clusters and (ii) newly available entries unrelated to those used for clustering can be reliably attached to existing clusters using the criterion of minimal dynamical distance to the nearest representative. The partitioning of all examined EF-hand domains into the four CL0-CL3 clusters is reported in Table S1 in Supporting Information. The first feature to notice is the typically high homogeneity of the essential modes within each functional family. By “functional family”, we define here a domain belonging to a specific terminus of a certain protein family in a particular metal and/or target binding state. It appears that each functional family has its own characteristic movements, describable by a couple of slow modes which are shared by other members of the same functional family. In Figure 4, the dynamical distances between domains belonging to families constituted by more than three members are color-coded and reported in matrix form. Visual inspection of this figure confirms that the dynamical distances within each functional family are, on average, very small. It also appears that EF-hand domains containing a bound peptide show a larger variability of behavior, consistent with the structural diversity of the EFhand domains complexed with various ligands. In such a context, the peptide binding imparts to the EF-hand domain a different functional role which accounts for the relatively large distances of dynamics between elements of the same protein family observed in few cases. The following analysis will thus concentrate on EF-hand domains free of bound ligands. The relative information is summarized in Table 1. In summary: • The apo-forms of the N-terminal domains, or of singledomain proteins, are characterized by essential modes clusterized in CL0, CL2, and CL3. CL0 comprises some S100 proteins, most of the skeletal troponins C (skTpCs), the pentaEF-hand (PEF) proteins, including calpains, and the KChIP. The remaining S100 proteins are grouped in CL2, while CL3 collects CaM, MELC, recoverin, and one skeletal troponin C. It is apparent that there is no clear relationship of the partitioning between CL0, CL2, and CL3 with the conformational state of the domains. All domains are in the antiparallel bundle conformation, except KChIP which has an orthogonal bundle conformation despite being an apo-domain. This domain falls
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Figure 4. Density plot of pairwise dynamical distances. Only members of the most populated functional families have been represented. The notation N[C] XCa PY is used to indicate that the domain is in the N[C] terminal part of the protein, bound to X calcium atoms and connected to a peptide interacting to Y EFhands motifs. Keys to the families: (1) calmodulin-N 2Ca P0; (2) calmodulin-N 2Ca P2; (3) myosin regulatory light chain-C 1Mg P2; (4) calmodulin-C 2Ca P0; (5) calmodulin-C 2Ca P2; (6) myosin regulatory light chain-C 0Ca P2; (7) myosin essential light chain-C 0Ca P2; (8) S100-N 2Ca P0; (9) calpain small subunit-C 2Ca P0; (10) skeletal troponin C-N 0Ca P0; (11) S100-N 0Ca P0; (12) calmodulin-C 0CA P0. Further details are provided in the Supporting Information.
in CL0, but together with several other domains with clear antiparallel bundle structure. • The apo-forms of the C-terminal domains fall in CL0, CL2, and CL3. CL0 comprises all PEF protein domains but calpains; CL2 comprises CaM, MELC, and calcium vector proteins, and CL3 comprises calpains (small subunit). • With regards as domains binding only one calcium ion, these are all clustered in CL0, independently of whether they are N- or C-terminal domains or whether the calcium ion is bound in the first or the second loop of the domain. • Finally, the dicalcium (or holo) forms may fall into any of the four clusters. CL0 comprises neurocalcin, calcineurin B, the dimeric S100 proteins, and the N-terminal domains of the PEF calpain (small subunit) and programmed cell death protein; CL1 hosts N- and C-terminal domains of CaM and skeletal troponin C, and the C-terminal domains of KchIP; CL2 contains only the single EF-hand domain of nucleobindin1, and CL3 contains calbindin D9k and the C-terminal domain of the PEF calpain (small subunit). To help appreciate the differences in essential dynamics among the four different clusters, we have selected the representative domain for each of them and visualized the first two essential modes (EM1 and EM2) in the form of schematic animations (see animation set 1 in Supporting Information). In such animations, the four helices H1-H4 are represented as ribbons harboring colored cylinders that oscillate according to their essential dynamics. To better capture the helices’ mobility, all structures in the animations were superimposed by fitting their β-scaffolds. This choice is also in line with a recently proposed model for EF-hand opening upon calcium binding, where the short β-sheet connecting the loops does Journal of Proteome Research • Vol. 6, No. 11, 2007 4249
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Table 1. Structure-Dynamics Clusterization of Functional Domains within the EF-Hand Superfamily
a N-term, N-terminal domain/motif pair; M-pair, middle motif pair; C-term, C-terminal domain/motif pair. b A, antiparallel bundle; O, orthogonal bundle; C, chair bundle. c The number on the right indicates which motif is occupied by Ca within the EF-hand pair. EPS15 has a calcium ion in either motif 1 or motif 2. Entries in the CL column indicate the cluster(s) to which members of a given family are assigned.
not change when the domain opens.36 From H1 to H4, they are colored in red, yellow, green, and blue. Each couple of essential modes, EM1 and EM2, characterizing the essential dynamics of each representative, is describable by looking at the effect of the movement on the interhelical angles. For example, a parallel, in-phase movement of both helices in a pair has a negligible effect on their interhelical angle (e.g., H2H4 in EM1 of the CL0 representative), while a scissor-type, antiphase movement has a large effect on their interhelical angle (e.g., H1-H3 in EM2 of the same CL0 representative). Analogously, a stationary helix determines an intermediate effect on the interhelical angle when the other helix of the pair is oscillating (e.g., H1-H2 in EM2 of the CL0 representative). The slowest modes of the four cluster representatives indicate different mobility for the four helices. For example, in CL0, EM2 shows much wider fluctuations for H1 and H3 than for H2 and H4. A dissimilar behavior of helical displacements is also observed in the other three clusters. In CL1, EM1 shows H2 and H3 more displaceable than H1 and H4, and EM2 shows H3 and H4 more displaceable than H1 and H2. In CL2, EM1 has a practically immobile H2, and H3 is much less moveable than H1 and H4. The last case of dissymmetry in movements of the four helices is encountered in EM2 of CL3, where H3 is the only helix being almost immobile. The description of the slow modes of all representatives is concluded by looking at EM1 of CL0, EM2 of CL2, and EM1 of CL3, 4250
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where all helices are capable of large movements. However, a different combination of in- and out-of-phase fluctuations gives origin to three distinct pairs of modes. EM1 of CL0 has scissortype displacements, mainly for H1-H2 and for H3-H4; EM2 of CL2 has the same type of displacement mainly for H1-H3 and for H2-H4; finally, EM1 of CL3 has a scissor-type displacement mainly for H1-H3 and H3-H4. It is interesting to notice that frequency domain fluorescence anisotropy measurements37 pointed out that CaM helix H1 (red in the animation) undergoes large amplitude nanosecond motions. Following calcium binding, helix H1 becomes immobile and structurally coupled with the overall rotation of CaM. Accordingly, helix H1 shows larger displacement in CL3 (where the N-terminal apo-CaM is located) than in CL1 (which includes both the Nand C-terminal holo-CaMs). Overall, the pairs of slow modes characteristic of each cluster are sizably different from one another. It is therefore surprising that domains with analogous structure (e.g., N- and C-terminal domains of apo-CaM, Table 1) are assigned to different clusters (CL3 and CL2, respectively), and even more surprising that domains that differ sizably in structure, such as, for example, apo- and calcium-bound forms of S100 proteins (Table 1), belong to the same cluster (CL0). In general, domains that undergo a sharp transition between an antiparallel bundle and an orthogonal bundle structure upon calcium binding38 (such as CaM-like proteins) move from either CL2 or CL3 in the apo
Essential Helix Dynamics in EF-Hands
Figure 5. Scatter plot and projected histograms of structural and dynamical distances for all distinct pairings of the 154 proteins.
form to CL1 in the calcium-bound form, while domains that undergo still sizable but more localized conformational rearrangements, such as S100 proteins,39,40 usually belong to CL0 in the apo form and remain in the same cluster in the calciumbound form. Interestingly, those domains that are only capable to bind one calcium ion are also found in CL0. Apparently, the dynamical clustering reflects only to a modest extent the ”structural context“ of the 4 helices under consideration. We recall that the slow modes calculations, though analyzed for the 4 helices only, are performed on the whole domain. In summary, there is no strict correlation of the “dynamical distance” between two functional domains expressed with the ddyn values, which measure the consistency of the space 2 spanned by the two lowest energy modes of both proteins, with the “structural” distance measured as the Euclidian distance of the six interhelical angles. Likewise, there is no obvious relationship among different functional families belonging to the same cluster of slow modes. The relationship between the dynamical and angular distances can be also appreciated in the scatter plot of Figure 5, where we have reported simultaneously both quantities for each of the 11 781 distinct proteins pairs. The overall trend of the distribution indicates a fair degree of correlation between the interhelical dynamics and the helical spatial arrangements, but the dispersion is substantial. As already observed, pairs of proteins with very similar interhelical angles can differ significantly in dynamics, and vice versa. This point is illustrated with another specific set of animated examples in the Supporting Information (animation set 2). The histograms flanking the scatter plot in Figure 5, showing the distribution of the dynamical distances and of the angular distances, prompt further considerations. The dynamical distribution is of course the same as shown in Figure 2b. The presence of several pairs of members of different clusters contributing to the ddyn peak at 0.3 is clearly visible (the values 2 range from 0 to 1). The double peaked attainable by ddyn 2 character of the ddyn histogram in Figure 5 should be com2 pared with the broader distribution of angular distances. Although, as elucidated by previous studies,10 some grouping
research articles of the proteins can also be discerned in terms of angular distances, the distinction among such groups is less pronounced than for the dynamical features. The qualitative difference of the two histograms emphasizes the nonredundancy of the insights offered by comparison of static and dynamic features of the interhelical angles. In particular, it is noteworthy that, despite the almost continuous spectrum of interhelical arrangements, it is possible to identify groups of proteins that have common and distinctive dynamical traits. These features are conveniently illustrated by exploiting a reduced representation for the interhelical angles based on their first two principal components that was introduced10 to account concisely for the observed structural diversity of EFhand domains. Angular movements can be represented as arrows in the 2D space of the principal components described above (due to the near-degeneracy of the first two slow modes, we decided to define for each protein a new orthonormal base (V1 and V2) in the space generated by its first two modes so that the first vector of the base is the one that maximizes the scalar product with the top mode of its cluster representative). In the plot of Figure 6, the interhelical arrangements are represented as points in the PC space, while the segments indicate the new, optimized, basis vectors directions (both orientations are equivalent). For clarity, V1 and V2 are represented in separate graphs. The color code of the points and segments reflects the dynamical cluster of origin: the fainter the color is, the higher its dynamical distance from the cluster representative. These plots provide a vivid illustration of the features emerging from the previous structural/dynamical analysis. In particular, members of the same dynamical cluster may occupy a fairly large region of the PC space, and yet, their intercluster dynamical consistency, perceivable by the projected directions of V1 and V2, is very high (indeed all members of any cluster have mutual dynamical distance typically below 0.2). It is also apparent that, in the absence of the dynamical clues (i.e., the segments in Figure 6), it would be very difficult to introduce any clear-cut objective criterion for grouping the points, given the diffuse repertoire of interhelical angles. The dynamical criterion, on the contrary, leads to a very sharp distinction among the most populated clusters. Though the representation of Figure 6 is in a reduced PC space, it can be appreciated how pairs of proteins with very different dynamics can be close in angle space and vice versa. From the detailed analysis of Figure 6, several interesting structural/dynamical considerations can be made. First, for all members of CL3 (colored in red) and for the large fraction of those of CL0 (colored in orange) that lie in the lower right area of the PCS space (indicated by a dashed ellipse in Figure 6), the two projected directions of motion are almost parallel to one another and oriented along the direction of spreading in the PC space of the corresponding EF-hand family members. As pointed out before, these domains comprise mostly apo domains and dicalcium ones that do not open up completely upon calcium binding, that is, those mainly in the antiparallel bundle form. This fact strongly suggests that the considerable structural variation observed among the individual domains along the major axis of the ellipse in Figure 6 reflect a progressive distortion along the easy directions of motion indicated by the segments. It is appealing to observe that individual domains within this large subgroup are mostly scattered precisely along the common easy axis, thus, covering the space of easily excitable conformational changes available Journal of Proteome Research • Vol. 6, No. 11, 2007 4251
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each particular functional domain within its protein frame. For example, for proteins constituted by a couple of domains tethered by a flexible linker,41 the slow modes of the C-terminal are well-differentiated from the N-terminal counterpart. To evaluate the effect derived from the presence of the other domain, either as a tail of the N-terminus or as a heading of the C-terminus, on the slow modes dynamics of the EF-hand domains, the calculations have been performed also on truncated single domains of CaM and skTpC. For CaM, there are not appreciable differences between the whole protein and the truncated domains; that is, such dynamics are an intrinsic property of the domain. On the contrary, the N-terminal domain of skTpC falls in CL3 when the slow modes are calculated on the whole chain, while it is assigned to CL0 when only the truncated N-terminus is considered for calculation. Thus, for this protein, the inclusion of the C-terminal domain is able to affect the slow modes dynamics of the N-terminal moiety resulting in a crossing of the boundary between the competing clusters CL0 and CL3, as it emerges from inspection of family 10 in Figure 4. The first four elements in this group are NMR structures of isolated N-terminal domains, whereas the fifth domain is the only X-ray structure of the whole protein. Thus, in view of the previous considerations, a clearer picture can be depicted about the dynamics of the tandem domain EF-hand proteins. The apo forms of the C-terminal domain of CaM and MELC are characterized by slow modes found in CL2, probably expressing dynamics optimized for different purposes than those developed by the N-terminus of the same protein, which belongs to CL3. It is largely believed that in these “tandem” proteins the two domains may have two distinct roles,42 for example one regulatory and the other structural. The concept of regulatory and structural domains was first introduced for skTnC, in which the high-affinity, C-terminal (structural) domain always binds Ca2+ in the muscle cell, and the lowaffinity, amino-terminal (regulatory) domain triggers the Ca2+ signal leading to muscle contraction.43 This hypothesis has been extended to other EF-hand proteins.44
Figure 6. Projections of the (a) first and (b) second optimized basis vector of the essential modes, V1 and V2, on the twodimensional PC space. Members of the four clusters are colored orange (CL0), blue (CL1), green (CL2), and red (CL3). Cluster representatives are shown with thick circles.
to the individual members. Conversely, the directions of motion of the members of CL1 and CL2, as projected in the PC space, are both different for the two modes and also different within each cluster. CL1 and CL2 host many dicalcium domains that are in the orthogonal or chair bundle form, that is, those that are ready to recognize and bind target proteins. It is conceivable that their motion is less predictable, being possibly also dictated by the rather broad range of interactions that some of them (e.g., calmodulin) are able to perform. The above considerations hint at a relationship between interhelical dynamics and biological function. This relatedness emerges more clearly if one considers, besides the structural features themselves, also the location of 4252
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From the present observations, it may be hypothesized that different specializations for different domains may also hold for multidomain proteins comprising non-“tandem” EF-hand domains with a regulatory function, such as calpain and calcineurin, a protease and a phosphatase, respectively. Indeed, the cluster analysis captures different essential modes for the N- and the C-terminal moieties of the penta-EF-hand domain (PEF) in the calpain small subunit (falling in CL0 and CL3, respectively, both in the apo- and in the calcium-bound forms). These differences are paralleled by the largely different affinity for Ca2+ displayed by the two pairs of binding loops: the one in the N-terminal domain binds calcium in a canonical way, while the one in the C-terminal binds only one calcium in its first EF-hand at physiological calcium concentrations.45 Ca2+ binding to the two PEF domains in calpain (one in the small, 28 kDa, and the other in the large, 80 kDa, subunit) is the trigger for Ca-induced proteolytic activity of the calpains, starting with a small conformational change in the N-terminal region of the PEF in the small subunit. Ca2+ binding to the two PEF domains also weakens the affinity of these two subunits for each other, causing their dissociation. The motor which drives the large rearrangement in the whole protease is thus a small rearrangement of EF-1 in the small subunit, amplified by the loose contacts between the two PEF domains, whose effect is propagated to the catalytic domain through a “lever” domain.
Essential Helix Dynamics in EF-Hands
The calcium switching in calpain is, therefore, somewhat different from those adopted in other CaM-like systems, mainly performed through the removal of an autoinhibitory moiety associated to an effective target molecule. This difference may be reflected in the essential modes displayed by calpain, which are insensitive to the presence of calcium but maintain a strong differentiation between N- and C-termini. This behavior is in agreement with the fact that calpain is a preassembled machine that has a catalytic function with a regulatory function embedded in it, while, for example, activation of kinases by CaM requires CaM to bind calcium, undergo a conformational transition, and then wrap around the lid kinase peptide and lift it from its blocking the catalytic enzyme site.46-48 At variance with calpain, the slow modes dynamics analysis of other PEF proteins (e.g., sorcin, grancalcin, and the programmed cell death protein) show that also the C-termini of these proteins fall in CL0 as does the N-terminal pair of calpain. These PEF proteins are responsible for different cellular functions, all initiated by changes in the interhelical angles elicited by calcium binding. The coincidence of the slow modes for both domains in PEF may suggest an equal involvement of the two parts in the whole movement responsible for calcium activation, consistent with these PEFs being involved in networking with other cellular components rather than in regulation or signaling, which requires specific recognition. Apparently, it is not sufficient to reside in different parts of the molecule to experience different slow modes, as it might be concluded from the results on CaM-like proteins and calpain. The dimeric S100 proteins, a family of EF-hand proteins with a noncanonical calcium binding loop, are involved in a large variety of cellular cycle functions. They are characterized by a large variety of ways with which they can bind their target peptides. From the static point of view, calcium binding essentially maintains the antiparallel structure of the domain, although a large movement occurs involving mostly helix 3. Dynamically, S100 proteins comprise two groups with distinct dynamical character (that is with dynamical distance ∼0.2). The first group, encompassing both the apo- and the calciumbound forms, neatly falls in CL0 (dynamical distance from the cluster representative, dr ∼ 0.04). The second group is at the border between CL2 (dr ∼ 0.21) and CL0 (dr ∼ 0.25) and are, thus, assigned to the former cluster, although a strong CL0 character can be also associated to the dynamics of this subgroup of dimeric S100 proteins. It is worth noting here that calculations performed on only one subunit of the dimeric protein does not change its dynamics (distance ∼0.07 among each others). Conversely, the only natural monomeric S100 protein, calbindin D9k (which is sequentially and structurally homologous to the other dimeric S100 proteins and undergoes similar conformation changes upon calcium binding), falls into CL3 in its calcium-bound form. Another interesting observation pertains to the tandem domain calcium vector protein, for which the N-terminal domain falls in CL2 rather than in CL3 as in the other tandem proteins. However, in this particular protein, the regulatory domain is the C-terminal rather than the N-terminal domain. In this case, the N-terminal domain is unable to bind calcium, and for this reason, it is assigned a structural role.49 Its belonging to CL2, like the structural C-terminal domains of the other tandem domain proteins, reinforces the idea that the dynamical behavior of the EF-hand domains may reflect their function even more closely than their structural features.
research articles Similar considerations arise from the evaluation of dynamics of other two proteins, namely, nucleobindin and KChIP. Nucleobindin, in the full saturated form, has a floppier and less compact EF-hand domain relative to other proteins in the EF-hand superfamily; the high degree of dynamic or conformational flexibility is a particular feature that facilitates its dual function as a Ca2+-buffer and a Ca2+-sensor, depending on the needs of the cell.50 This particular feature may be the reason nucleobindin is the only holo form being clusterized in CL2, which is a cluster that mainly groups the more flexible apo forms. The calcium binding protein KChIP associates with the Kv4 family K+ channels and modulates their biophysical properties. However, only the C-terminal domain of KChIP is able to bind two calcium ions, whereas the N-terminal domain has lost this ability, thus, determining the absence of calciummediated conformational changes.51 This feature may account for KChIP being the only tandem domain protein whose N-terminal apo form is in CL0, where other proteins with incomplete calcium binding ability are collected. Further comments arise from the inspection of domains of particular biological interest that were nevertheless excluded from the cluster analysis because of the inability of the top two slow modes to represent faithfully the interhelical dynamics (ω1 + ω2 smaller than 0.6175 in Table S1 in Supporting Information). Along with other domains belonging to functional families with members already included in the cluster analysis, such as MELC, CaM, and S100, an interesting case is the calciumbindingproteinfromEntamoebahistolytica(EhCaBP),52-54 which belongs to a family of EF-hand proteins endowed with a strong specificity for target binding, although they share a high sequence homology within the family. The slow modes analysis on the only member with known structure (1jfk) indicates that the holo form of the N-terminal domain is characterized by slow modes that are markedly dissimilar from the representative of CL1 (gathering most of the holo forms) and more alike those of CL2 and CL0 (gathering most of the more flexible apo forms). This may reflect the expected good flexibility of the two CaBP isoforms from E. histolytica which are able to recognize different targets even though only a few mutations distinguish them. Further Considerations and Conclusions. The analysis of the slow modes of motion of the four helices has been performed for 187 domains of the EF-hand protein superfamily, using a novel approach that describes the motions directly in the interhelical angle space. It is found that, for as many as 154 of them, the dynamics is well-described by only a pair of slow motions that by themselves account for more than 65% of the global motions. The formulation of the problem in interhelical angle space provides the common framework for comparing the concerted helical movements sustained in all possible pairs of EF-hand domains, regardless of the degree of structural similarity. This previously unexplored perspective, thus, represents a systematic quantitative attempt to elucidate the connection between the large structural variability with EF-hand domains and largescale concerted movements, which typically shape the conformational changes that assist or accompany the functional activity.55 From a general point of view, it is found that the distance in dynamical space of two EF-hand domains is only loosely related to the spatial (static) difference of the helices orientation. In particular, the analysis of the distribution of both static and dynamic distances shows that the former is essentially a Journal of Proteome Research • Vol. 6, No. 11, 2007 4253
research articles continuum, while the latter is clearly bimodal, indicating that a “natural” clustering of the type of motions of EF-hand domains occurs. This dynamical grouping, which aptly complements previous structurally related subdivisions, appears adequately captured at the level of four dynamical clusters. Within members of the cluster, the dynamical similarity is high and very significant from the statistical point of view. The robust nature of the dynamical grouping, which highlights the presence of highly corresponding interhelical movements in otherwise different domains, hints at the functional relevance of the observed modes. This observation is further supported by the detailed analysis of the findings. First, the dynamical clusters appear compatible with the recently investigated distribution of the domains in the space of structural principal components.10 Second, a certain relatedness exists between the four dynamical clusters (CL0, CL1, CL2, and CL3) and the limited number of possibilities in which the four helices can be arranged (albeit with considerable structural heterogeneity) upon calcium binding/ release. Indeed, with very few exceptions, the so-called antiparallel bundle structures fall in CL0 or CL3, chair bundle structures are assigned either to CL0 or CL2 while orthogonal bundle structures fall in CL1. A clear distinction between dynamics and structural points of view lies in the fact that the former perspective allows the natural emergence of a limited number of protein groups distinguished by well-defined dynamical characteristics. Capturing these groupings through unsupervised clustering schemes is more elusive from the structural (static) perspective. In addition, it is interesting to notice that the dynamical-based partitioning identifies four main clusters at variance with the traditional tripartite subdivision arising from structural inspection (the additional cluster essentially bridging the open and closed conformations). Finally, proteins that are constituted by two tethered domains show different dynamics for their N- and C-terminal domains in the apo form (CL3 and CL2, respectively), while the structural difference among them is only marginal. Thus, the dynamic features provide a clue to the biological distinction between structural and regulatory type of domains proposed for this family of proteins. Both domains fall in the CL1 cluster when in the calcium form. The dynamics in CL1 is more variable from one domain to another than it is, for instance, in CL3, probably reflecting the eclecticism of these domains (recently defined as “the hubs” within the interactome network)56 in binding a variety of target proteins. Finally, proteins that undergo more localized structural variations upon binding of calcium, and whose function is usually associated to binding only one specific partner (“non-hub” domains)56 fall in CL0 both in the apo- and calcium-bound form. Their dynamics mainly occurs along the direction of structural variation within the group, thus, suggesting that these domains are “hardwired” to perform one and the same specific motion to exert their function, and that the structural variability among the members of the group is also confined to a variability along the directions of the hardwired motion. The proposed methodology is applicable also to proteins that contain more than one pair of EF-hand motifs per domain. As an example, we consider the case of calbindin D28k whose structure has been resolved recently. This single domain protein comprises 6 EF-hand motifs and has been described to work both as calcium sensor and calcium buffer.57,58 The motion of its domains can be classified in terms of the previously determined clusters by identifying the closest of the four cluster 4254
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representatives. By doing so, it is found that the central EFhand pair is assigned to CL1, consistently with several other Calcium-loaded transducing proteins. The N- and C-terminal motif pairs, instead, fall in the same cluster (CL0) as all domains able to bind only one Ca ion. In summary, from the comprehensive survey of EF-hand domains, it emerges that the introduction of a transparent framework for comparing proteins’ internal dynamics has allowed identifying unexpected unifying properties, arguably functionally related, among structurally diverse members of the superfamily. The methodology employed in this study is general and, accordingly, ought to be readily applicable to investigate structure-dynamics relationships within other superfamilies where the relevant biological features can be described in terms of the intramolecular orientation of a set of secondary elements.
Acknowledgment. We acknowledge support from COFIN Grant 2006025255 and FIRB 2006 from the Italian Ministry for Education, from Regione Friuli Venezia Giulia (Grant Biocheck, 200501977001), the Italian Institute of Technology, Ente Cassa di Risparmio di Firenze, and EC projects UPMAN, SPINE2, and Nano4Drugs. Supporting Information Available: Methodological details, animated representation of the interhelical movements, and tables containing the data set with a detailed characterization of the interhelical slow modes. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Nelson, M. R.; Chazin, W. J. Structures of EF-hand Ca(2+)-binding proteins: diversity in the organization, packing and response to Ca2+ binding. Biometals 1998, 11 (4), 297-318. (2) Bhattacharya, S.; Bunick, C. G.; Chazin, W. J. Target selectivity in EF-hand calcium binding proteins. Biochim. Biophys. Acta 2004, 1742 (1-3), 69-79. (3) Carafoli, E.; Klee, C. B. Calcium as Cellular Regulator; Oxford University Press: New York, 1999. (4) Carafoli, E.; Santella, L.; Branca, D.; Brini, M. Generation, control, and processing of cellular calcium signals. Crit. Rev. Biochem. Mol. Biol. 2001, 36 (2), 107-260. (5) Evenas, J.; Malmendal, A.; Forsen, S. Calcium. Curr. Opin. Chem. Biol. 1998, 2 (2), 293-302. (6) Berridge, M. J.; Bootman, M. D.; Lipp, P. Calcium-a life and death signal. Nature 1998, 395 (6703), 645-648. (7) Kretsinger, R. H.; Nockolds, C. E. Carp muscle calcium-binding protein. II. Structure determination and general description. J. Biol. Chem. 1973, 248 (9), 3313-3326. (8) Grabarek, Z. Structural basis for diversity of the EF-hand calciumbinding proteins. J. Mol. Biol. 2006, 359 (3), 509-525. (9) Pearl, F. M.; Bennett, C. F.; Bray, J. E.; Harrison, A. P.; Martin, N.; Shepherd, A.; Sillitoe, I.; Thornton, J.; Orengo, C. A. The CATH database: an extended protein family resource for structural and functional genomics. Nucleic Acids Res. 2003, 31 (1), 452-455. (10) Babini, E.; Bertini, I.; Capozzi, F.; Luchinat, C.; Quattrone, A.; Turano, M. Principal component analysis of the conformational freedom within the EF-hand superfamily. J. Proteome. Res. 2005, 4 (6), 1961-1971. (11) Yap, K. L.; Ames, J. B.; Swindells, M. B.; Ikura, M. Diversity of conformational states and changes within the EF-hand protein superfamily. Proteins 1999, 37 (3), 499-507. (12) Theret, I.; Baladi, S.; Cox, J. A.; Gallay, J.; Sakamoto, H.; Craescu, C. T. Solution structure and backbone dynamics of the defunct domain of calcium vector protein. Biochemistry 2001, 40 (46), 13888-13897. (13) Levy, R. M.; Srinivasan, A. R.; Olson, W. K.; McCammon, J. A. Quasi-harmonic method for studying very low frequency modes in proteins. Biopolymers 1984, 23 (6), 1099-1112. (14) Levitt, M.; Sander, C.; Stern, P. S. Protein normal-mode dynamics: Trypsin inhibitor, crambin, ribonuclease and lysozyme. J. Mol. Biol. 1985, 181 (3), 423-447. (15) Horiuchi, T.; Go, N. Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme. Proteins 1991, 10 (2), 106-116.
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PR070314M Journal of Proteome Research • Vol. 6, No. 11, 2007 4255
