Biochimica et Biophysica Acta 1817 (2012) 1388–1391
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Low pH induced structural reorganization in thylakoid membranes☆ Anjana Jajoo a, b,⁎, Milán Szabó b, Ottó Zsiros b, Győző Garab b a b
School of Life Science, Devi Ahilya University, Khandwa Road, Indore 452 001, India Institute of Plant Biology, Biological Research Center, Hungarian Academy of Sciences, P.O. Box 521, H-6701 Szeged, Hungary
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Article history: Received 31 October 2011 Received in revised form 22 December 2011 Accepted 2 January 2012 Available online 8 January 2012 Keywords: Acidic pH Circular dichroism Excitonic CD LHCII Psi-type CD Thylakoid membranes
a b s t r a c t By using low temperature fluorescence spectroscopy, it has been shown that exposing chloroplast thylakoid membranes to acidic pH reversibly decreases the fluorescence of photosystem II while the fluorescence of photosystem I increases [P. Singh-Rawal et al. (2010) Evidence that pH can drive state transitions in isolated thylakoid membranes from spinach, Photochem Photobiol Sci, 9 830–837]. In order to shed light on the origin of these changes, we performed circular dichroism (CD) spectroscopy on freshly isolated pea thylakoid membranes. We show that the magnitude of the psi-type CD, which is associated with the presence of chirally ordered macroarrays of the chromophores in intact thylakoid membranes, decreases gradually and reversibly upon gradually lowering the pH of the medium from 7.5 to 4.5 (psi, polymer or salt induced). The same treatment, as shown on thylakoid membranes washed in hypotonic low salt medium possessing no psi-type bands, induces no discernible change in the excitonic CD. These data show that while no change in the pigment–pigment interactions and thus in the molecular organization of the bulk protein complexes can be held responsible for the observed changes in the fluorescence, acidification of the medium significantly alters the macro-organization of the complexes, hence providing an explanation for the pH-induced redistribution of the excitation energy between the two photosystems. This article is part of a Special Issue entitled: Photosynthesis Research for Sustainability: from Natural to Artificial. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The efficiency of photosynthetic light energy conversion depends largely on the molecular architecture of the photosynthetic membranes, which also determines the migration of the excitation energy in the pigment system and its supply to the reaction centers. One of the basic features of the photosynthetic system of chloroplasts is its ability to be regulated by short-term variations in the external environmental conditions [1,2]. Most regulatory functions operate via feedback mechanisms during photosynthesis, which, by adjusting the composition and/or the structure of the pigment system, can fine-tune the photosynthetic functions. For instance, in the case of phosphorylation-dependent state transitions, regulated by redox sensing, redistribution of the excitation energy between the two photosystems is achieved via substantial reorganizations, e.g. the movement of a pool of mobile light-harvesting complex II (LHCII) antenna proteins associated with photosystem II (PSII), and structural changes at the level of supercomplexes and remodeling of the membrane ultrastructure [3–11]. Phosphorylation of LHCII can also be regulated by light at the substrate level via inducing conformational changes [12,13]. LHCII in vivo and in vitro is capable of undergoing
☆ This article is part of a Special Issue entitled: Photosynthesis Research for Sustainability: from Natural to Artificial. ⁎ Corresponding author at: School of Life Science, Devi Ahilya University, Khandwa Road, Indore 452 001, India. Tel.: +91 731 2477166; fax: +91 731 4263453. E-mail address:
[email protected] (A. Jajoo). 0005-2728/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.bbabio.2012.01.002
thermo-optically driven reorganizations, i.e. structural changes induced by the dissipation of excess excitation energy [14–16]. The feedback mechanism operating via the light-induced acidification of the lumen, i.e. via the formation of the light-induced transmembrane proton gradient, is of particular importance since it is involved in the regulation of utilization vs. dissipation of the excitation energy in the light harvesting pigment system. The short-term regulatory mechanism, qE, the energydependent component of the non-photochemical quenching (NPQ) controls the magnitude of dissipation of the singlet excited state of chlorophyll a, and by this means protects plants against processes of photodegradation [17–19]. Although the molecular mechanism of qE is still debated, it is most widely agreed that it requires and relies on the flexibility of the structure and/or composition of the light harvesting apparatus, i.e. it involves some kind of reversible structural changes either at the level of individual light harvesting or auxiliary complexes, such as PsbS, or/and at the level of their macroassembly [20–28]. Excess light leads to formation of a trans-thylakoid pH gradient which in turn stimulates the xanthophyll cycle [29]. In a recent report it has been shown that at low pH (pH 5.5), the fluorescence of PS II decreases with concomitant increase in the fluorescence of PS I, resulting in an increase in the F735/F685 ratio [30]. This study indicated that the distribution of the excitation energy between the two photosystems can be altered by varying the pH, possibly by a rearrangement of the complexes between the stacked and nonstacked regions. This work prompted us to explore further the nature of these putative structural changes, which are thought to bring about
A. Jajoo et al. / Biochimica et Biophysica Acta 1817 (2012) 1388–1391
the low pH induced changes in the fluorescence of higher plant thylakoid membranes. To this end, we used CD spectroscopy, which is a sensitive and non-destructive technique to study the conformation of
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different pigment–protein complexes as well as their chiral macroorganization. Protein complexes and their small aggregates exhibit shortrange, excitonic interactions between the pigment molecules, whereas extended ordered arrays of the pigment–protein complexes display psi-type CD bands due to their densely packed chirally organized pigment systems [30,31]. CD spectra were measured on isolated pea thylakoid membranes exposed to different pH treatments. Our data show that whereas the excitonic CD signals are essentially insensitive to changes in the pH between 4.5 and 7.5, the psi-type CD bands display significant but reversible pH-dependencies, indicating that the longrange chiral order of the complexes is modulated in a reversible manner by relatively small pH variations. 2. Materials and methods 2.1. Isolation of thylakoid membranes Thylakoid membranes were isolated from pea (Pisum sativum L.) leaves grown in the greenhouse for 10–12 days. Leaves were homogenized in buffer A (50 mM Tricine-KOH pH 7.5, 0.4 M sorbitol, 5 mM MgCl2, 5 mM KCl). The homogenate was filtered through 4 layers of cheesecloth and the filtrate was centrifuged for 2 min at 300 ×g. The pellet was discarded and the supernatant was centrifuged at 5000 ×g for 10 min. In order to remove the envelope membrane, the pellet was resuspended in the hypotonic buffer B (50 mM Tricine-KOH pH 7.5, 5 mM MgCl2, 5 mM KCl) and the suspension was centrifuged at 5500 × g for 10 min. The pellet containing intact thylakoid membranes was resuspended to a chlorophyll content of 1–2 mg/ml in buffer A. All steps of the isolation were performed at 4 °C and the isolated thylakoid membranes were stored on ice until further use. 2.2. pH treatment For pH treatment, the membranes at a chlorophyll content of 20 μg/ml were resuspended in 50 mM Tricine buffer with their pH adjusted to 7.5, 7.0, 6.5, 6.0, 5.5, 5.0 and 4.5; the reaction medium also contained 0.4 M sorbitol, 5 mM KCl and 5 mM MgCl2. The membranes were incubated at different pHs for at least 20 min, but the variations in the incubation time, between 10 min and 2 h, had no effect. For obtaining washed thylakoids displaying no psi-type CD bands, the thylakoid membranes were washed twice in 50 mM Tricine buffer, pH 7.5, supplemented with 5 mM EDTA, and were sonicated (Branson
Fig. 1. Dependence of CD spectral features on the pH in the range of 4.5 to 7.5. (A) Effect of lowering pH on the CD spectra of intact thylakoid membranes; the pH was titrated gradually in steps of 0.5 but the results are shown only for selected values. (B) Reversibility of the low pH induced effects; the pH was increased from the indicated pH value to 7.5; the spectra are shown for selected pH values. (C) Variations of the amplitude of the main psi-type CD band at about 690 nm as a function of the pH as in (A), and its reversibility as in (B).The thylakoid membranes were incubated in reaction media containing 0.4 M sorbitol, 50 mM of Tricine-KOH, adjusted to the indicated pH, and 5 mM KCl and 5 mM MgCl2 with a chlorophyll content of 20 μg/ml. Reversibility was measured by titrating the pH back to 7.5 using the same reaction medium.
Fig. 2. CD spectra of washed thylakoid membranes measured at different pHs; spectra are shown for selected treatments only. Thylakoid membranes were washed twice in Tricine buffer supplemented with KOH and 5 mM EDTA followed by sonication (see Materials and methods). Chlorophyll content, 20 μg/ml.
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450 Sonifier) on ice for 20 s using constant duty cycle and output value of 10. This was followed by the pH treatment in the same medium which otherwise was similar as described above. Reversibility of the pH effects was studied by titrating the pre-treated samples with KOH from different pHs (5.0, 5.5, 6.0, 6.5, 7.0) back to pH 7.5. 2.3. CD measurements CD spectra were recorded at room temperature on Jasco J-815 spectropolarimeter. The spectra were measured at room temperature between 400 and 750 nm with an optical pathlength of 1 cm, a bandwidth of 2 nm and data pitch of 0.5 nm. The scan speed was set to 100 nm/min and the integration time was 1 s. The CD spectra are normalized to the maximum absorbance of the samples at around 678 nm. Absorption spectra were recorded at room temperature with Shimadzu UV-3000 spectrophotometer in a double beam mode, with an optical pathlength of 1 cm, the cuvette was placed close to the photomultiplier tube, in front of which a quartz diffuser was placed. 3. Results and discussion As shown in Fig. 1A, the intensity of the two main positive CD bands of freshly isolated intact thylakoid membranes at around (+) 690 and (+)510 nm gradually decreases upon gradually lowering the pH of the medium from 7.5 to 4.5. Since it has been shown that these bands are of psi-type origin and thus originate from chirally organized macro-arrays of the complexes, the observed variations demonstrate that there are well discernible low pH induced changes in the macro-organization of the thylakoid membranes [31,32]. It is interesting to note that while these two bands decrease at about the same extent, the third major psi-type band, a negative band at around (−)675 nm, displays hardly any change. This latter band has been shown to depend mainly on the stacking of granal thylakoid membranes, whereas the positive psi-type bands depend more on the lateral organization of the complexes [16,33,34]. Although the complexity of the psi-type CD bands [32] does not allow us to determine the exact nature of these structural changes, our data, which indicate the decrease in the long-range order of the complexes rather than the stacking of membranes, are in broad terms consistent with literature data showing that lateral reorganizations and the formation of smaller aggregates play a role in qE, which depends on the acidification of the lumen [25,35,36]. It was important to clarify whether these pH induced changes are reversible or irreversible. To test this, the samples—previously pre-treated and measured at different pHs—were titrated back with KOH directly to 7.5 as described in Materials and methods, and the spectra were recorded at pH 7.5 (Fig. 1B). A very clear, almost complete reversal of the pH induced effect was observed in the amplitude of all the major peaks even when the pH was reversed from 4.5. This can be seen also in Fig. 1C, showing the pH-dependence of the main psi-type band. These data thus reveal distinct and significant structural changes in the thylakoid membranes, and also show that the changes are largely reversible. It is to be noted that similar reversible changes have earlier been observed upon illuminating the thylakoid membranes with high light; further, the light-induced reorganizations, detected as CD transients, could be eliminated by uncouplers, showing the role of lumenal acidification in the reorganizations [14]. Later studies have also shown that although the changes in the thylakoid membranes are sensitive to uncouplers, they can also be induced thermo-optically and even in isolated lamellar aggregates of LHCII [15,37]. In order to examine the effect of the pH on the excitonic interactions, which conveniently can only be done in the absence of psi-type bands, thylakoids were washed twice in hypotonic, salt-free medium containing 5 mM EDTA [33] and mildly sonicated. By this means, we could investigate the behavior of the excitonic CD bands of thylakoid membranes,
which is dominated by the bands originating from LHCII (Fig. 2) [38]. It is clearly seen that in these washed thylakoid membranes pH titration did not result in any significant changes in the CD spectra neither upon gradually lowering the pH from 7.5 to 4.5 (Fig. 2), nor upon jumping from 4.5 to 7.5 (not shown). This shows that the decrease in the pH does not affect the short range, excitonic interactions; and in particular the pigment–pigment interactions in the LHCII complexes. The excitonic CD bands remain largely invariant also in thylakoid membranes exposed to illumination with high light [14–16,39]. These data are also fully consistent with earlier CD data on reconstituted complexes, revealing a high stability of the complexes at low pH [40]. This stability has been shown to be warranted by the presence of negatively charged amino acids in the lumenal loop between the transmembrane helices B and C. It has also been shown that acidification of the medium induced only a very small decrease in fluorescence in wild type reconstituted LHCII, but a much stronger quenching in the mutant with lower stability in the lumenal loop [41]. The apparent stability of the individual complexes, either upon lowering the pH or upon illumination of the membranes, explains the largely reversible nature of the macrodomainreorganizations induced by low pH or high light. In other terms, it appears that the arrangement of the complexes in the membrane can be changed, e.g. via reversible dissociation and migration of some of the protein components, without affecting noticeably their molecular architecture. In conclusion, our data provide evidence for significant and specific reorganizations in the thylakoid membranes that are exposed to low pHs. Our data with pH show that these reorganizations, affecting the long range order of the complexes, are essentially fully reversible, a feature that appears to have a role in the mechanism of qE; this structural flexibility and reorganizations induced by acidic pHs may also have a broader significance in the multilevel light adaptational mechanisms, e.g. in repair cycles and redistribution of the excitation energy. Acknowledgments AJ thanks Hungarian State Board (HSB) for scholarship to do research in Hungary. This work was supported by the Hungarian Fund for Basic Research (OTKA CNK 80345, to GG) and by the Photosynthesis “Life from Light” Foundation. References [1] S. Lemeille, J.D. Rochaix, State transitions at the crossroad of thylakoid signalling pathways, Photosynth. Res. 106 (2010) 33–46. [2] J.F. Allen, J. Forsberg, Molecular recognition in thylakoid structure and function, Trends Plant Sci. 6 (2001) 317–326. [3] Z. Varkonyi, G. Nagy, P. Lambrev, A.Z. Kiss, N. Szekely, L. Rosta, G. Garab, Effect of phosphorylation on the thermal and light stability of the thylakoid membranes, Photosynth. Res. 99 (2009) 161–171. [4] M. Iwai, Y. Takahashi, J. Minagawa, Molecular remodeling of photosystem II during state transitions in Chlamydomonas reinhardtii, Plant Cell 20 (2008) 2177–2189. [5] M. Iwai, M. Yokono, N. Inada, J. Minagawa, Live-cell imaging of photosystem II antenna dissociation during state transitions, Proc. Natl. Acad. Sci. U. S. A. 107 (2010) 2337–2342. [6] M. Tikkanen, M. Pippo, M. Suorsa, S. Sirpio, P. Mulo, J. Vainonen, A. Vener, Y. Allahverdiyeva, E.M. Aro, State transitions revisited—a buffering system for dynamic low light acclimation of Arabidopsis, Plant Mol. Biol. 62 (2006) 779–793. [7] S.G. Chuartzman, R. Nevo, E. Shimoni, D. Charuvi, V. Kiss, I. Ohad, V. Brumfeld, Z. Reich, Thylakoid membrane remodeling during state transitions in Arabidopsis, Plant Cell 20 (2008) 1029–1039. [8] G. Finazzi, F. Rappaport, A. Furia, M. Fleischmann, J.D. Rochaix, F. Zito, G. Forti, Involvement of state transitions in the switch between linear and cyclic electron flow in Chlamydomonas reinhardtii, Embo Rep. 3 (2002) 280–285. [9] G.C. Papageorgiou, Govindjee, Slow changes—scaling from the past, J. Photochem. Photobiol., B 104 (2011) 258–270. [10] J.F. Allen, S. Santabarbara, C.A. Allen, S. Puthiyaveetil, Discrete redox signalling pathways regulate photosynthetic light-harvesting and chloroplast gene transcription, PLoS One 6 (10) (2011) 9 pages, e26372. [11] S. Matsubara, Y.C. Chen, R. Caliandro, Govindjee, R.M. Clegg, Photosystem II fluorescence lifetime imaging in avocado leaves: contributions of the lutein epoxide and violaxanthin cycles to fluorescence quenching, J.Photochem. Photobiol. B 104 (2011) 271–284.
A. Jajoo et al. / Biochimica et Biophysica Acta 1817 (2012) 1388–1391 [12] H. Zer, M. Vink, N. Keren, H.G. Dilly-Hartwig, H. Paulsen, R.G. Herrmann, B. Andersson, I. Ohad, Regulation of thylakoid protein phosphorylation at the substrate level: reversible light-induced conformational changes expose the phosphorylation site of the light-harvesting complex II, Proc. Natl. Acad. Sci. USA 96 (1999) 8277–8282. [13] H. Zer, M. Vink, S. Shochat, R.G. Herrmann, B. Andersson, I. Ohad, Light affects the accessibility of the thylakoid light harvesting complex II (LHCII) phosphorylation site to the membrane protein kinase(s), Biochemistry-US 42 (2003) 728–738. [14] G. Garab, R.C. Leegood, D.A. Walker, J.C. Sutherland, G. Hind, Reversible changes in macroorganization of the light-harvesting chlorophyll a/b pigment protein complex detected by circular-dichroism, Biochemistry-US 27 (1988) 2430–2434. [15] V. Barzda, A. Istokovics, I. Simidjiev, G. Garab, Structural flexibility of chiral macroaggregates of light-harvesting chlorophyll a/b pigment–protein complexes. Light-induced reversible structural changes associated with energy dissipation, Biochemistry-US 35 (1996) 8981–8985. [16] A.G. Dobrikova, Z. Varkonyi, S.B. Krumova, L. Kovacs, G.K. Kostov, S.J. Todinova, M.C. Busheva, S.G. Taneva, G. Garab, Structural rearrangements in chloroplast thylakoid membranes revealed by differential scanning calorimetry and circular dichroism spectroscopy. Thermo-optic effect, Biochemistry-US 42 (2003) 11272–11280. [17] C.A. Wraight, A.R. Crofts, Energy-dependent quenching of chlorophyll a fluorescence in isolated chloroplasts, Eur. J. Biochem. 17 (1970) 319–327. [18] J.M. Briantais, C. Vernotte, M. Picaud, G.H. Krause, Quantitative study of the slow decline of chlorophyll a fluorescence in isolated chloroplasts, Biochim. Biophys. Acta 548 (1979) 128–138. [19] P. Horton, A.V. Ruban, R.G. Walters, Regulation of light harvesting in green plants, Annu. Rev. Plant Phys. 47 (1996) 655–684. [20] P. Horton, A. Ruban, Molecular design of the photosystem II light-harvesting antenna: photosynthesis and photoprotection, J. Exp. Bot. 56 (2005) 365–373. [21] Z.R. Li, S. Wakao, B.B. Fischer, K.K. Niyogi, Sensing and responding to excess light, Annu. Rev. Plant Biol. 60 (2009) 239–260. [22] A.A. Pascal, Z.F. Liu, K. Broess, B. van Oort, H. van Amerongen, C. Wang, P. Horton, B. Robert, W.R. Chang, A. Ruban, Molecular basis of photoprotection and control of photosynthetic light-harvesting, Nature 436 (2005) 134–137. [23] R. Goss, G. Garab, Non-photochemical chlorophyll fluorescence quenching and structural rearrangements induced by low pH in intact cells of Chlorella fusca (Chlorophyceae) and Mantoniella squamata (Prasinophyceae), Photosynth. Res. 67 (2001) 185–197. [24] P.H. Lambrev, T. Tsonev, V. Velikova, K. Georgieva, M.D. Lambreva, I. Yordanov, L. Kovacs, G. Garab, Trapping of the quenched conformation associated with nonphotochemical quenching of chlorophyll fluorescence at low temperature, Photosynth. Res. 94 (2007) 321–332. [25] A.R. Holzwarth, Y. Miloslavina, M. Nilkens, P. Jahns, Identification of two quenching sites active in the regulation of photosynthetic light-harvesting studied by time-resolved fluorescence, Chem. Phys. Lett. 483 (2009) 262–267. [26] A.V. Ruban, R. Berera, C. Ilioaia, I.H.M. van Stokkum, J.T.M. Kennis, A.A. Pascal, H. van Amerongen, B. Robert, P. Horton, R. van Grondelle, Identification of a mechanism of photoprotective energy dissipation in higher plants, Nature 450 (2007) 575-U522.
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[27] C. Ilioaia, M.P. Johnson, C.D.P. Duffy, A.A. Pascal, R. van Grondelle, B. Robert, A.V. Ruban, Origin of absorption changes associated with photoprotective energy dissipation in the absence of zeaxanthin, J. Biol. Chem. 286 (2011) 91–98. [28] S. de Bianchi, N. Betterle, R. Kouril, S. Cazzaniga, E. Boekema, R. Bassi, L. Dall'Osto, Arabidopsis mutants deleted in the light-harvesting protein Lhcb4 have a disrupted photosystem II macrostructure and are defective in photoprotection, Plant Cell 23 (2011) 2659–2679. [29] A.M. Gilmore, T.L. Hazlett, Govindjee, Xanthophyll cycle-dependent quenching of photosystem-II chlorophyll-a fluorescence—formation of a quenching complex with a short fluorescence lifetime, Proc Natl Acad Sci USA 92 (1995) 2273–2277. [30] P. Singh-Rawal, A. Jajoo, S. Mathur, P. Mehta, S. Bharti, Evidence that pH can drive state transitions in isolated thylakoid membranes from spinach, Photochem. Photobiol. Sci. 9 (2010) 830–837. [31] G. Garab, Linear and circular dichroism, in: J. Amesz, A.J. Hoff (Eds.), Biophysical Techniques in Photosynthesis, Advances in Photosynthesis, Kluwer, Dordrecht, 1996, pp. 11–40. [32] G. Garab, H. van Amerongen, Linear dichroism and circular dichroism in photosynthesis research, Photosynth. Res. 101 (2009) 135–146. [33] G. Garab, J. Kieleczawa, J.C. Sutherland, C. Bustamante, G. Hind, Organization of pigment protein complexes into macrodomains in the thylakoid membranes of wild-type and chlorophyll-b-less mutant of Barley as revealed by circulardichroism, Photochem. Photobiol. 54 (1991) 273–281. [34] Z. Cseh, S. Rajagopal, T. Tsonev, M. Busheva, E. Papp, G. Garab, Thermooptic effect in chloroplast thylakoid membranes. Thermal and light stability of pigment arrays with different levels of structural complexity, Biochemistry-US 39 (2000) 15250–15257. [35] S. de Bianchi, L. Dall'Osto, G. Tognon, T. Morosinotto, R. Bassi, Minor antenna proteins CP24 and CP26 affect the interactions between photosystem II subunits and the electron transport rate in grana membranes of Arabidopsis, Plant Cell 20 (2008) 1012–1028. [36] A.V. Ruban, M.P. Johnson, C.D. Duffy, The photoprotective molecular switch in the photosystem II antenna, Biochim. Biophys. Acta 1817 (2012) 167–181. [37] A. Istokovics, I. Simidjiev, F. Lajko, G. Garab, Characterization of the light induced reversible changes in the chiral macroorganization of the chromophores in chloroplast thylakoid membranes. Temperature dependence and effect of inhibitors, Photosynth. Res. 54 (1997) 45–53. [38] P.H. Lambrev, Z. Varkonyi, S. Krumova, L. Kovacs, Y. Miloslavina, A.R. Holzwarth, G. Garab, Importance of trimer–trimer interactions for the native state of the plant light-harvesting complex II, Biochim. Biophys. Acta 1767 (2007) 847–853. [39] E.E. Gussakovsky, V. Barzda, Y. Shahak, G. Garab, Irreversible dissambly of chiral macrodomains in thylakoids due to photoinhibition, Photosynth. Res. 51 (1997) 119–126. [40] C.H. Yang, P. Lambrev, Z. Chen, T. Javorfi, A.Z. Kiss, H. Paulsen, G. Garab, The negatively charged amino acids in the lumenal loop influence the pigment binding and conformation of the major light-harvesting chlorophyll a/b complex of photosystem II, Biochim. Biophys. Acta 1777 (2008) 1463–1470. [41] C. Liu, Y. Zhang, D. Cao, Y. He, T. Kuang, C. Yang, Structural and functional analysis of the antiparallel strands in the lumenal loop of the major light-harvesting chlorophyll a/b complex of photosystem II (LHCIIb) by site-directed mutagenesis, J. Biol. Chem. 283 (2008) 487–495.