Active Form of the Protein Kinase CK2 α2β2 Holoenzyme Is a Strong

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Active Form of the Protein Kinase CK2 α2β2 Holoenzyme Is a Strong Complex with Symmetric Architecture Graziano Lolli,*,†,‡ Alessandro Ranchio,†,‡ and Roberto Battistutta*,†,‡ †

Department of Chemical Sciences, University of Padua, via Marzolo 1, 35131 Padova, Italy Venetian Institute for Molecular Medicine (VIMM), via Orus 2, 35129 Padova, Italy

‡

S Supporting Information *

ABSTRACT: CK2 is a protein kinase essential for cell viability whose activity is altered in several cancers. Its mechanisms of regulation differ from those common to other eukaryotic protein kinases and are not entirely established yet. Here we present crystal structures of the monomeric form of the α2β2 holoenzyme that allow refining a formerly proposed structural model for activity regulation by oligomerization. Previous crystal structures of the CK2 holoenzyme show an asymmetric arrangement of the two α catalytic subunits around the obligate β2 regulatory subunits. Asymmetric α2β2 tetramers are organized in trimeric rings that correspond to inactive forms of the enzyme. The new crystal structures presented here reveal the symmetric architecture of the isolated active tetramers. The dimension and the nature of the α/β interfaces configure the holoenzyme as a strong complex that does not spontaneously dissociate in solution, in accordance with the low dissociation constant (∼4 nM). position of the α chains with respect to the central stable β2 dimer, with two different α/β interfaces. In the description of the first CK2 crystallographic structure 1JWH,10 a relative rotation of 16.4° was identified at the two α/β interfaces for the two halves of the tetramer. On one side of the β dimer, one α chain binds through an extended interface (960 Å2), while the corresponding interface on the opposite side is much smaller (771 Å2). On the basis of the relatively small average α/β interface of the first crystal structure of the holoenzyme, it was suggested that α2β2 might be a transient heterocomplex, which could spontaneously dissociate in vivo. The recent 4DGL structure substantially confirms this asymmetry, with identical relative rotation for the two halves of the tetramer. In this improved structure of the holoenzyme, with a better-traced α/β contact region, the two α/β interfaces are larger and similar in size (1009 Å2 and 1011 Å2), although showing substantial differences, generated by the asymmetric assembly, in the contacting area of the interfacing residues. Despite the enhancements, there is still a not complete accordance between the α2β2 structures, in particular the relatively small α/β interfaces, and the well-documented in vitro stability of the heterocomplex.9,12,13 Moreover, the asymmetric holoenzyme is indeed organized in inactive trimeric rings of tetramers, posing the question of whether the free dissociated tetramers, the fully active form of the enzyme, conserve this asymmetry. In general, protein complexes can be divided into obligate and non-obligate oligomers.14,15 In obligate complexes,

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rotein kinase CK2 is an enzyme involved in crucial cellular functions such as gene expression, cell growth and differentiation, and cell cycle.1 In various cancers, deregulation of CK2 is associated with a markedly elevated activity and with conditions favoring the onset of the cancer phenotype, and therefore CK2 is considered a validated drug target.2−4 The mechanisms of regulation of the CK2 catalytic activity at the protein level are atypical among eukaryotic protein kinases and not well established yet.5 The α catalytic subunit of CK2 is a constitutively active enzyme. Its interacting partner CK2β is not a typical protein kinase regulatory subunit since it does not switch on/off the CK2α activity when assembling with it in the tetrameric α2β2 complex. The holoenzyme instead shows increased or decreased activity on different subsets of substrates in comparison with the monomeric CK2α.6,7 It is then particularly relevant to understand whether the holoenzyme could dissociate and coexist in equilibrium with its constituent subunits, since the alteration of such equilibrium could represent a regulatory mechanism for the kinase.7 This is significant also for the attempt to target the α/β interface as a pharmacological approach alternative to the less specific ATPcompetitive inhibitors, exemplified by two recent studies on the 11-mer cyclic peptide Pc, able to effectively interfere with the holoenzyme assembly.8,9 More in general, a better understating of the overall mechanism of CK2 regulation would be particularly important to disclose the bases of the oncogenic potential of this kinase. In the tetrameric α2β2 complex, the obligate β2 dimer binds the two α subunits on opposite surfaces, so that the latter are not in contact with each other (i.e., no α/α interfaces are present). In both the available crystal structures (PDB codes 1JWH10 and 4DGL11), the α2β2 tetramer is asymmetric in the © XXXX American Chemical Society

Received: August 25, 2013 Accepted: October 31, 2013

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Figure 1. Stereo view of superposed symmetric (sym) and asymmetric (asym) CK2 holoenzymes. (a) CK2-PM symmetric α2β2 tetramer (salmon) superposed to 4DGL asymmetric tetramer (cyan). (b) In 4DGL, the assembly of three α2β2 (cyan, green and violet) in trimers of tetramers induces the distortion not present in CK2-PM (salmon). In 4DGL, the acidic loop from a β chain of a tetramer (green) inserts in between the two lobes of a α chain from the neighboring tetramer (cyan). The assembly is not possible without distortion of the symmetric holoenzyme (salmon).

protomers are not stable on their own, i.e., they fold and simultaneously bind to the partner (as many homodimers do, for instance, the regulatory CK2β2 dimer). Another distinction can be made between permanent and transient complexes.14,15 Permanent protein−protein interactions are strong and irreversible and are characterized by dissociation constants in the low or sub nanomolar range. Obligate complexes are always permanent, while non-obligate oligomers can be permanent, usually only perturbed by proteolysis, or transient. Transient complexes can be either weak or strong. The former have dissociation constants in the micromolar range associated with a dynamic oligomeric equilibrium where interaction is formed and broken continuously. In strong transient complexes a powerful molecular trigger, i.e., phosphorylation or effector molecule, is required to shift the oligomeric equilibrium, generally associated with a large conformational change between a high affinity state with Kd in the low or sub nanomolar range and a low affinity state with Kd in the micromolar range.14,15 The CK2 tetramer has dissociation constant around 4 nM9,13 and therefore should be classified either as a permanent or as a strong-transient heterocomplex. Here we present three new crystal structures of variants of the CK2 α2β2 holoenzyme, crystallized in monoclinic space groups instead of the hexagonal P63 as in the case of former 1JWH and 4DGL structures. These new data allow the identification of novel functionally relevant features in the structural organization of the CK2 holoenzyme and constitute the basis for its correct classification as a strong heterocomplex. In particular, the apparent conflict between relatively modest interface areas of previous structures of the holoenzyme and its reported stability is resolved. Importantly, the new structures represent the enzyme in its most likely active form present in

solution, whereas previous structures showed asymmetric CK2 tetramers as part of multimeric inactive assemblies.10,11 The three crystallographic structures of the CK2 holoenzyme presented here are composed by the same dimer of the fulllength β subunit and by either the full-length α subunit phospho-mimetic mutant (CK2-PM with Thr344, Thr360, Ser362 and Ser370 mutated to glutamate) or the full-length point mutant F121E (CK2-F121E) or the deletion mutant at position 336 with the F121E mutation (CK2del-F121E). All three different isoforms of the CK2 holoenzyme crystallized in monoclinic space groups, unlike the previously reported structures that have been determined in the hexagonal space group P63 (1JWH and 4DGL). Resolution ranges from 3.1 to 3.5 Å (Supplementary Table S1), and the quality of the electron density map of the best structure (CK2-PM) (Supplementary Figure S1) is similar to those of the hexagonal holoenzyme with resolutions 3.1 Å and 3.0 Å for 1JWH 10 and 4DGL,11 respectively. Crystallization in monoclinic space groups is most probably due to the different buffer of the crystallization solution, ammonium citrate at pH 6.5 instead of sodium malonate at pH 7.0. CK2-PM and CK2-F121E, carrying the full-length α subunit, are in P21 space group, with two holoenzyme copies per asymmetric unit, while CK2del-F121E, with the C-terminally truncated α subunit, is in C2 space group, with four tetramers per asymmetric unit (Supplementary Table S1). Despite these differences in the unit cells, the crystal packing is very much similar in all structures, with minor differences between the two space groups in the intertetrameric crystallographic contacts (Supplementary Figure S2). These differences are to be entirely ascribed to the additional space required by the CK2α C-terminus in the CK2-PM and CK2F121E structures. However, in none of these structures is any B

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Figure 2. α/β interacting surfaces colored by electrostatic potential (the electrostatic potentials were calculated by solving the Poisson−Boltzmann equation with the CCP4MG program using the default settings). In symmetric 4MD7 (CK2-PM) the two interfaces are very similar in size and nature (Interfaces type 2), whereas in asymmetric 1JWH and 4DGL one of the interfaces (Interface type 1) is different from type 2 due to the formation of trimers of tetramers.

(Figure 2). The same contact is not present on the opposite side of the tetramers, where the interface of the other α subunit with the β dimer is similar to those found in new symmetric tetramers in monoclinic crystals (Interface type 2, Figure 2). The two α/β interfaces are now very similar in size and, most importantly, in nature, due to the symmetric architecture (Figure 2c). This is confirmed by the dissociation pattern predicted by PISA (‘Protein interfaces, surfaces and assemblies’ service at the European Bioinformatics Institute16) in 2α + β2 for monoclinic structures, while for both 1JWH and 4DGL the predicted dissociation is αβ2 + α, due to the asymmetric assembly. The mean interface area for the symmetric tetramer is 1086 Å2 (Figure 2c), a value in accordance with the nonobligate nature of the complex. Obligate heterodimers have in most cases interface areas significantly larger than 1000 Å2.17 The α/β interfaces are, however, more extended than those expected for weak transient complexes (740 Å2 by Nooren and Thornton17 and 810 Å2 by Dey and co-workers18) and indicate that the CK2 holoenzyme is indeed more stable than initially assumed. Furthermore, the new structures confirm the tracing of residues 190−207 of the β-subunit, in particular of Phe190, reported in the 4DGL structure and corrected with respect to the 1JWH structure (Figure 2), with an overall increase in the mean interface area from 865 to 1086 Å2. In both previous 1JWH and 4DGL structures, the truncate form (at position 336) of the α subunits was present, and hence this is the first time that structures of the complete holoenzyme, i.e., with full-length α and β subunits, are presented. The symmetric nature of the new structures is not to be ascribed to the presence of the α-subunit C-terminal tail nor to the phosphomimetic mutations, as demonstrated by the same architecture adopted by the truncated CK2del-F121E variant and by the full-length CK2-F121E variant without Ser/Thr to Glu mutations, respectively. Together, the three structures

appreciable electron density present for the CK2α C-terminus, indicating that it is flexible and disordered in solution. Hence this tail and its phosphorylation do not appear to have any structural role in the holoenzyme assembly. The analysis of the crystal packing of the monoclinic form of the holoenzyme does not support the possibility of stable oligomeric or filamentous forms. Unlike in the hexagonal lattice, where discrete trimeric rings of tetramers are clearly recognizable, in the monoclinic form all contacts between different tetramers have a pure crystallographic nature. Indeed there is one interaction between the acidic loop of the βsubunit and the basic clusters of the α-subunit of a symmetric tetramer with a significant interface area (around 750 Å2). However, this contact is not responsible for the formation of any closed, self-consistent, oligomeric form of tetramers nor of a filament of tetramers, giving raise to an infinite twodimensional bilayer of tetramers. Hence the existence in solution of stable discrete oligomeric or filamentous forms based on this interaction is highly improbable, indicating that these new structures show the real architecture of the holoenzyme in its monomeric active form. The global tetrameric architecture is very similar in all monoclinic structures (average rmsd over all Cα atoms 1.0 Å) but, notably, is different from that of the tetramers in the hexagonal crystal form previously published (average rmsd over all Cα atoms 3.0 Å).10,11 Unlike in space group P63, in monoclinic crystals tetramers show a different, symmetric architecture (Figure 1a), with two very similar α/β interfaces (Interface type 2 in Figure 2). The asymmetry of the holoenzyme seen in the hexagonal space group is caused by the incorporation of tetramers into trimeric rings (Figure 1), with the insertion of the acidic loop of the β subunit of one tetramer (residues 55−64) in between the two lobes of the α chain of another tetramer, generating the Interface type 1 C

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and trypsinogen with bovine pancreatic trypsin inhibitor (BPTI). The size of the interface in the two complexes is very similar, but differently from trypsin, trypsinogen undergoes large conformational changes when it binds to BPTI with the consequence that this complex is far less stable (>6 orders of magnitude) than trypsin-BPTI because of entropic penalties.18 Hence, all parameters characterizing the properties of the α/β interface as found in the monoclinic forms of the CK2 tetramer (summarized in Table 1) concur to specify a strong

demonstrate that the capacity to adopt both the symmetric and asymmetric (in trimers) architecture is a genuine property of the CK2 holoenzyme and not ″artifacts″ of mutations and deletions. Among protein kinases, CK2α displays a unique flexibility in the area encompassing the hinge region and the following helixαD (hinge/αD region).19 The two mutation F121E and Y125R (in 4DGL) in helix-αD, immediately downstream the hinge region, were designed on the residues that undergo the largest movement in the transition from the open to the closed state. Here we observe that in all structures of the holoenzyme containing truncated CK2α, including the new CK2del-F121E, the hinge region is clearly kept open. In CK2-PM, poor electron density defines the hinge/αD region that appears to be highly flexible and possibly oscillating between the two conformations. The F121E mutation in full-length CK2F121E gives back a good electron density for the hinge region that is in the open conformation. We can conclude that in the CK2 holoenzyme the open conformation seems preferred over the closed one, which instead appears more difficult to stabilize and isolate. The interface size, although being the most obvious, cannot be considered the unique parameter to infer the stability of a protein complex, and indeed also its nature must be taken into account.18 For instance, stable protein complexes can have interface areas similar to those of weak transient complexes but with an increased hydrophobic character, which strengthens the association in the aqueous environment. This is the case for CK2. The α/β interface is largely hydrophobic (Figure 2) with f np (nonpolar fraction of interface area) of 70.5%, a value closer to that of the obligate β2 dimer (73.9%) than to the average value expected for weak dimers (62%).18 This is also reflected by the low P-value (0.109) of the solvation energy gain calculated by PISA;16 P-values less than 0.5 indicate interfaces with surprising (higher than would be average for given structures) hydrophobicity, implying that they can be interaction-specific. The role of the α/β interface could also have been initially underestimated in the 1JWH structure where the full insertion of β-F190 inside a deep hydrophobic cavity on the α surface was not determined10,11 (Figure 2). Indeed F190 was proven to be the key CK2β hot spot residue for the functional interaction with CK2α.8 Other parameters highlight the stability of the α/β interaction. The Rp score evaluates the propensities of the amino acids involved in protein−protein interactions for being at an interface versus the protein surface. Large positive values (Rp > 4.5) are indicative of high levels of stability18 as in the case of CK2 with Rp = 9.8 for the α/β interface. Further, strong complexes tend to have close-packed interfaces. The atomic packing at an interface expresses the shape complementarity of the two surfaces, an attribute quantified by several parameters such as the fraction of fully buried atoms (f bu), the shape complementarity score (Sc), the gap volume index (Igap), and the atomic density index (LD).18 The CK2 α/β interface has f bu = 30%, Sc = 0.68, Igap = 1.6, and LD = 38.7. By comparison, the interface of the obligate β dimer shows similar values, f bu = 34%, Sc = 0.68, Igap = 1.6, and LD = 37.5, further supporting the notion of highly stable α/β interfaces. Of particular importance is to note that the α/β binding sites are largely preformed in the CK2 protomers,12 that is, the association of the free subunits proceeds without large conformational rearrangements. The relevance of this aspect is highlighted by the comparison of the complexes of trypsin

Table 1. α/β Interface Parameters in Symmetric α2β2 Holoenzyme mean interface area f np (nonpolar fraction of interface area) P-value (PISA solvation energy gain) Rp (residue propensity score) f bu (fraction of fully buried atoms) Sc (shape complementarity score) Igap (gap volume index) LD (atomic density index)

1086 Å2 70.5% 0.109 9.8 30% 0.68 1.6 38.7

interaction between the β-dimer and each of the α subunits. This is in accordance with the very low dissociation constant of the tetrameric holoenzyme determined in solution by microcalorimetry, KD ≈ 4 nM,9,13 a value typical for strong protein complexes.14 Indeed, the existence of relatively small interfaces in stable kinase complexes is not unusual. We compared CK2 (interface area >1000 Å2) with the closely related Cyclindependent kinase; the interface for the Cdk9/CycT complex is 960 Å2, similar to the Cdk4/CycD complex (1125 Å2).20−22 In conclusion, all of the above configures the CK2 holoenzyme either as a strong transient (molecularly triggered) or as a permanent complex. Because it is impossible to distinguish between the two possibilities solely on the basis of the dissociation constant and the interface parameters,18 in principle both hypotheses are equally conceivable. Instead, our data strongly argue against the possibility that the CK2 holoenzyme is a weak transient complex, excluding that the catalytic and the regulatory subunits can dissociate (resulting free and isolated in solution) when co-localized in time and space, in absence of a powerful regulatory mechanism. The fact that non-interacting α and β subunits have been observed in cells23 cannot be ascribed to the spontaneous dissociation of the complex, which disagrees with the reported Kd value, the stability of the holoenzyme in vitro, and with the crystallographic data reported here. Rather it can be hypothesized that association of the CK2 holoenzyme can be prevented in vivo by different mechanisms,7 such as unbalanced expression, differential α and β localization, or transport mechanisms, or by the intervention of β-competitive-α-interacting or α-competitive-βinteracting proteins. Regarding the latter, a number of kinases including A-Raf, c-Mos, and Chk1 have been reported to interact with the β-subunit of CK2, possibly using surfaces overlapping with those recognizing CK2α. Tetramer dissociation could be also induced by specific strong regulatory mechanisms able to alter the binding affinities of the constituent subunits by orders of magnitude.7 Heretofore, such molecular triggers have never been unambiguously identified. One possibility could be that such kind of regulatory mechanism is linked to phosphorylation events that can occur on both CK2 subunits. Four residues in the CK2α C-terminal tail are phosphorylated by Cdk1 during mitosis, an event that is D

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Figure 3. Previously proposed model of CK2 regulation,11 integrated with new symmetric structures of the CK2 holoenzyme presented here (A). When co-localized in time and space, CK2 α and β subunits readily assemble into symmetric active tetramers (corresponding to the new crystal structures (A) presented here). Activity is switched off through their organization (essentially via electrostatic interaction) in inactive trimers of tetramers and higher-order interactions generating filaments (corresponding to former crystal structures (B) presented in ref 11). Activity is restored upon a depolymerization process triggered by variations in the physical-chemical local environment (pH, ionic strength, etc.), action of substrates or effectors (e.g., polyamines), or other events.

required for the correct cell cycle progression.24 Also CK2β is found extensively phosphorylated in cells, due to the addition of two phosphate groups at Ser2 and Ser3 by CK2α.25 However, our structural data argue against such possibility. The CK2-PM structure shows that the presence of the phosphomimetic full-length CK2α does not alter the organization of the holoenzyme as well as its stability, as confirmed by differential scanning fluorimetry measurements (Supplementary Table S2). This seems to exclude that phosphorylation of the α subunit can trigger significant conformational changes in the CK2 holoenzyme in vivo. Same results have been obtained with the phosphomimetic CK2β with the autophosphorylation sites Ser2 and Ser3 mutated to aspartate (Supplementary Table S2). In the previously published structures 1JWH and 4DGL, asymmetry of the α 2 β 2 holoenzyme derives from its organization into trimers of tetramers, which are inactive forms.11 Symmetric tetramers presented here instead can be assumed as the most likely active form of the isolated tetramers in cells. On the basis of the new structures, we refine the previously discussed mechanism of CK2 regulation11 as follows (Figure 3). When co-localized in time and space, CK2α and CK2β-dimer spontaneously assemble into a stable heterocomplex, with a very low dissociation constant (KD ≈ 4 nM). The α2β2 complex most probably configures as permanent since no molecular triggers able to significantly affect the relative affinity of the protomers have been identified so far. The conformational stability and rigidity of the isolated protomers, which remain substantially unaltered during the formation of the complex, supports this view. On/off catalytic regulation, on the other hand, is exerted through the equilibrium between free active symmetric α2β2 tetramers and distorted asymmetric tetramers organized in inactive trimers

and further supramolecular assemblies.11 The energetic release of the structural tension upon depolimerization, when trimeric asymmetric tetramers dissociate into free isolated symmetric tetramers, plays a favorable role in the ″activation″ process of CK2. The different structures of the holoenzyme known to date and the relative mechanism of regulation do not exclude the possibility of other functional oligomeric forms such as those suggested on the basis of electron microscopy analysis of recombinant Drosophila CK2.26

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METHODS

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ASSOCIATED CONTENT

The CK2 holoenzyme was purified as previously described.11 Crystals were obtained by vapor diffusion at 20 °C in 0.2 M ammonium citrate pH 6.5, 16−20% w/v PEG 3350. Diffraction data were collected at the ID23-2 (ESRF) for CK2-PM and CK2del-F121E and at the XRD1 (Elettra) for CK2-F121E. Structures were solved by molecular replacement using as search models human CK2β (from 4DGL) and human CK2α (4KWP). Full details are given in the Supporting Information online.

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org. Accession Codes

Atomic coordinates and structure factors have been deposited in the PDB with accession codes 4MD7 (CK2-PM), 4MD8 (CK2-F121E), and 4MD9 (CK2del-F121E), with the designation “for immediate release upon publication” (HPUB). E

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(16) Krissinel, E., and Henrick, K. (2007) Inference of macromolecular assemblies from crystalline state. J. Mol. Biol. 372, 774−797. (17) Nooren, I. M., and Thornton, J. M. (2003) Structural characterisation and functional significance of transient protein-protein interactions. J. Mol. Biol. 325, 991−1018. (18) Dey, S., Pal, A., Chakrabarti, P., and Janin, J. (2010) The subunit interfaces of weakly associated homodimeric proteins. J. Mol. Biol. 398, 146−160. (19) Papinutto, E., Ranchio, A., Lolli, G., Pinna, L. A., and Battistutta, R. (2012) Structural and functional analysis of the flexible regions of the catalytic alpha-subunit of protein kinase CK2. J. Struct. Biol. 177, 382−391. (20) Baumli, S., Lolli, G., Lowe, E. D., Troiani, S., Rusconi, L., Bullock, A. N., Debreczeni, J. E., Knapp, S., and Johnson, L. N. (2008) The structure of P-TEFb (CDK9/cyclin T1), its complex with flavopiridol and regulation by phosphorylation. EMBO J. 27, 1907− 1918. (21) Takaki, T., Echalier, A., Brown, N. R., Hunt, T., Endicott, J. A., and Noble, M. E. (2009) The structure of CDK4/cyclin D3 has implications for models of CDK activation. Proc. Natl. Acad. Sci. U.S.A. 106, 4171−4176. (22) Lolli, G. (2010) Structural dissection of cyclin dependent kinases regulation and protein recognition properties. Cell Cycle 9, 1551−1561. (23) Filhol, O., Nueda, A., Martel, V., Gerber-Scokaert, D., Benitez, M. J., Souchier, C., Saoudi, Y., and Cochet, C. (2003) Live-cell fluorescence imaging reveals the dynamics of protein kinase CK2 individual subunits. Mol. Cell. Biol. 23, 975−987. (24) St-Denis, N. A., Derksen, D. R., and Litchfield, D. W. (2009) Evidence for regulation of mitotic progression through temporal phosphorylation and dephosphorylation of CK2alpha. Mol. Cell. Biol. 29, 2068−2081. (25) Litchfield, D. W., Lozeman, F. J., Cicirelli, M. F., Harrylock, M., Ericsson, L. H., Piening, C. J., and Krebs, E. G. (1991) Phosphorylation of the beta subunit of casein kinase II in human A431 cells. Identification of the autophosphorylation site and a site phosphorylated by p34cdc2. J. Biol. Chem. 266, 20380−20389. (26) Valero, E., De Bonis, S., Filhol, O., Wade, R. H., Langowski, J., Chambaz, E. M., and Cochet, C. (1995) Quaternary structure of casein kinase 2. Characterization of multiple oligomeric states and relation with its catalytic activity. J. Biol. Chem. 270, 8345−8352.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors thank the staff at ESRF beamline ID23-2 (Grenoble, France) and at ELETTRA Synchrotron Light Source (Trieste, Italy) beamline XDR1 for on-site assistance in data collection. This work was supported by Italian Miur (PRIN 2008, R.B.) and by University of Padua (Progetto Giovani GRIC101044, G.L.).

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REFERENCES

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NOTE ADDED AFTER ASAP PUBLICATION Some accession codes were incorrect in the version published on November, 11, 2013. This was corrected in the version published on November 13, 2013.

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