Article | Published:

Cyanobacterial photosystem II at 2.9-Å resolution and the role of quinones, lipids, channels and chloride

Nature Structural & Molecular Biology volume 16, pages 334342 (2009) | Download Citation



Photosystem II (PSII) is a large homodimeric protein–cofactor complex located in the photosynthetic thylakoid membrane that acts as light-driven water:plastoquinone oxidoreductase. The crystal structure of PSII from Thermosynechococcus elongatus at 2.9-Å resolution allowed the unambiguous assignment of all 20 protein subunits and complete modeling of all 35 chlorophyll a molecules and 12 carotenoid molecules, 25 integral lipids and 1 chloride ion per monomer. The presence of a third plastoquinone QC and a second plastoquinone-transfer channel, which were not observed before, suggests mechanisms for plastoquinol-plastoquinone exchange, and we calculated other possible water or dioxygen and proton channels. Putative oxygen positions obtained from a Xenon derivative indicate a role for lipids in oxygen diffusion to the cytoplasmic side of PSII. The chloride position suggests a role in proton-transfer reactions because it is bound through a putative water molecule to the Mn4Ca cluster at a distance of 6.5 Å and is close to two possible proton channels.


Oxygenic photosynthesis involves several protein–cofactor complexes embedded in the photosynthetic thylakoid membranes of plants, green algae and cyanobacteria. Among these complexes, PSII has a prominent role because it catalyzes the oxidation of water, leading to the production of four protons, four electrons and dioxygen, which is the prerequisite for all aerobic life1,2.

The membrane-intrinsic part of homodimeric PSII from the cyanobacterium Thermosynechococcus elongatus comprises (in each monomer) the antenna proteins CP47 and CP43, the reaction center subunits D1 and D2, and 13 small subunits, among them cytochrome (cyt) b-559 with two transmembrane α-helices (TMHs), PsbE and PsbF. In addition, there are three membrane-extrinsic subunits (PsbO, PsbU and PsbV) located at the lumenal side. Chlorophyll a (Chl) molecules bound to CP43 and CP47 absorb light and funnel the excitation energy to the reaction center. Charge separation occurs at the reaction center, leading to the oxidation of pigment P680 to a cationic radical P680•+, and the electron that is released travels along the redox-active cofactors of the electron-transfer chain (ETC) across the membrane.

PSII uses two types of plastoquinone-9 (PQ) molecules located close to the cytoplasmic side. One (in the QA site) is fixed and serves as a single-electron carrier. The other (in the QB site) is a substrate that, after accepting two electrons and two protons, leaves the QB site as plastoquinol (PQH2) and enters the PQ pool in the thylakoid membrane. The PQ pool provides a connection between PSII and the cytochrome b6f complex, where PQH2 is reoxidized to PQ; PQ then returns to PSII, whereas the reduction equivalents are further transferred to photosystem I (PSI).

To regain its neutral state, the highly oxidative P680•+ abstracts an electron via the redox-active tyrosine TyrZ (Tyr161 of D1, D1-Y161) from the Mn4Ca cluster located at the lumenal side of PSII. After accumulation of four oxidation equivalents by the Mn4Ca cluster accompanied by stepwise proton release, dioxygen is formed3,4.

Several medium-resolution (3.8–3.0 Å) crystal structures of cyanobacterial PSII have been elucidated5,6,7,8,9. Here we present an improved structural model of PSII from T. elongatus at 2.9-Å resolution, revealing all subunits assigned, additional auxiliary cofactors (among them 25 lipids per monomer), channels connecting the large internal quinone cavity9 with the PQ pool, and the chloride ion known to be necessary for efficient water oxidation at the Mn4Ca cluster.


Diffraction data processing

By reprocessing the X-ray diffraction data of our previously published 3.0-Å structure of PSII9 to a resolution of 2.9 Å, the amount of unique data used in the refinement of the structural model was increased by more than 40%. This led to 94.2% completeness of the data set (see Methods) associated with a distinct improvement in the quality of the electron density (Supplementary Fig. 1 online; for a discussion of the differences from previous structural models of PSII, see Supplementary Discussion online).

Protein subunits

The data at 2.9-Å resolution not only permit refinement of the positions of all 17 protein subunits already assigned at 3.0-Å resolution9, but also allow assignment of the small protein subunits ycf12, PsbY and PsbX (Fig. 1a and Supplementary Fig. 2 online) to the previously unassigned TMHs X1, X2 and X3 (ref. 9), respectively.

Figure 1: The homodimeric PSII complex.
Figure 1

(a) Overview of PSII from the cytoplasmic side (membrane-extrinsic subunits omitted). The monomer-monomer interface is indicated by a black dashed line and the noncrystallographic C2 axis relating the two monomers as a black ellipse (center). Helical parts are shown as cylinders, and the subunits D1 (yellow), D2 (orange), CP43 (magenta), CP47 (red), cyt b-559 (cyan, subunits α and β) and the remaining eleven small subunits (gray) are labeled in monomer I. In monomer II, the five TMHs of D1 and D2 are labeled a to e and the six TMHs in CP43 and CP47 are labeled a to f. Cofactors are shown in stick mode; monomer I shows Chl (green), Car (orange), heme (blue), Pheo (yellow), PQ (red), the Mn4Ca cluster (red and orange spheres; barely visible) and non-heme iron (blue sphere). Monomer II shows lipids and detergents (yellow). (b) Schematic view of the 13 small membrane–intrinsic subunits of PSII, showing locations and post-translational modifications of the N termini. TMHs are indicated by rectangles, with the directions of the polypeptide chains given by arrows. N termini are shown as thin lines with symbols for processing: red ellipse, Met1 removed; yellow triangle, acetylation; blue square, formylation; red line, cleavage of the N-terminal signal sequence. (c) Left, a view of one monomer looking onto the monomer-monomer interface along the membrane plane, with the cytoplasm above and the lumen below. Proteins are shown in cartoon presentation in gray, and subunit PsbM in cyan; lipid and detergent molecules are in space-filling presentation (carbon, yellow; oxygen, red). Right, interactions between PsbM (cyan) of monomer I and PsbM* (gray) of monomer II. The N and C termini are labeled; specific protein-protein interactions are indicated by circles and involve residues highlighted (yellow) in the amino acid sequence of PsbM given below.

Subunit ycf12 (Cyanobase gene tsr1242, is located next to PsbJ, PsbK and PsbZ, with its N terminus pointing toward the lumen. This TMH was erroneously assigned to PsbN7, which is not present in our PSII preparation according to our MS analysis (see below). The distance of 5.8 Å between ycf12 and putative Ca2+ close to PsbK9 (Ca2+-PsbK) could be bridged by water.

PsbY can be assigned unambiguously to electron density because of a characteristic break in the TMH that was predicted from secondary-structure elements10. The poor electron density of PsbY suggests loose association with the main body of PSII, which might be the reason for its absence at 3.5-Å resolution7. PsbY contacts the TMH of PsbE, with residues 14, 17 and 21 pointing toward the heme group of cyt b-559 and partially shielding it from the membrane. The presence of PsbY in PSII was confirmed by MS (see below and Supplementary Table 1 online).

PsbX is located next to PsbH and D2 with its N terminus in the lumen, and the segment PsbX-Gly22 to PsbX-Val29 shields ChlzD2 from the membrane.

The 20 subunits identified were found in all our preparations of dimeric PSII from T. elongatus as shown by N-terminal sequencing, gel electrophoresis and MS, and these data indicate that all of the 13 small subunits except PsbL are post-translationally modified at their N termini (Fig. 1b and Supplementary Table 1). N termini at the lumenal side are either formylated (PsbI, M, T, Y, Z, ycf12) or the N-terminal presequence is cleaved (PsbK, PsbX) or both modifications occur (PbsY). In contrast, N termini exposed on the cytoplasmic side show either cleavage of Met1 (PsbE, PsbH) or both cleavage of Met1 and acetylation (PsbF, PsbJ). The modification asymmetry might be due to different localization of the respective processing enzymes in the lumenal and cytoplasmic compartments.

The two monomers of the PSII homodimer are related by a noncrystallographic two-fold axis (ellipse in center of Figure 1a). There is only one direct protein-protein contact formed between subunits PsbM and PsbM* (*, from the other monomer) (Fig. 1c).

Lipids and the monomer-monomer interface

The 14 lipid (numbered 1–14) and 2 detergent molecules (n-dodecyl-β-D-maltoside; β-DM) previously assigned9,11 were confirmed and 11 new lipids (numbered 15–25; Fig. 2 and Supplementary Fig. 2) were located in each monomer. Within a monomer, there are 11 (44%) monogalactosyl-diacylglycerol (MGDG), 7 (28%) digalactosyl-diacylglycerol (DGDG), 5 (20%) sulfoquinovosyl-diacylglycerol (SQDG) and 2 (8%) phosphatidyl-glycerol (PG) molecules. They reflect the highly conserved lipid composition of cyanobacterial thylakoid membranes (≈45%, ≈25%, 15–25% and 5–15% respectively12). The distribution of lipids is asymmetric, with the head groups of negatively charged PG and SQDG being located exclusively on the cytoplasmic side, those of uncharged DGDG on the lumenal side and those of MGDG on both sides.

Figure 2: Lipids in photosystem II.
Figure 2

(a) Side view of the PSII dimer along the membrane plane, with the cytoplasm above and the lumen below. The 25 lipid and 7 detergent molecules per monomer are shown in space-filling mode (carbon, yellow; oxygen, red), protein subunits in gray, and the three membrane-extrinsic subunits in green (PsbO), violet (PsbU) and blue (PsbV). (b) Location of lipids in the PSII homodimer, viewed as in Figure 1a. Membrane-embedded proteins are shown in gray and lipids in yellow (carbon) and red (oxygen). The red elipses I, II and III encircle the lipid clusters mentioned in the text, and the blue box indicates the region enlarged in c. (c) View along the membrane plane of the eight lipids of the lipid cluster (indicated with blue box in b) forming a bilayer structure in the PQ-PQH2 exchange cavity. The charged PG3, PG22 and SQDG4 and neutral MGDG18 (forming a cork) are on the cytoplasmic (above; carbon, yellow; oxygen, red) side and the neutral MGDG19, DGDG5, DGDG6 and MGDG7 are on the lumenal (below) side (carbon, green). (d) Lipids close to QB (cyan). Shown are negatively charged lipids PG3, PG22 (purple) and SQDG4 (green), neutral MGDG18 (gray), non-heme Fe2+ (blue sphere) and part of subunits D1 (yellow, forming the QB site) and D2 (orange). Conserved D1-Asn266 makes a hydrogen bond with glycerol of PG22.

The electron density of detergent β-DM15 (ref. 9) at the monomer-monomer interface was reassigned to MGDG15. The head group of SQDG16 lies in a positively charged pocket between subunits D2 and CP47. SQDG16 is accompanied by detergent β-DM31, which indicates either the presence of two lipids in this pocket under in vivo conditions or that SQDG16 adopts two alternative positions.

On the cytoplasmic side, MGDG17 is close to SQDG13 (ref. 9) at the monomer-monomer interface, whereas MGDG18 is located near the PQ-PQH2 exchange cavity. The head group of MGDG19 on the lumenal side of PSII is near the putative Ca2+-PsbK ion at a possibly water-mediated distance of 6.7 Å. MGDG19 is close to DGDG5 in a pocket formed by CP43 and the small subunits PsbJ, PsbK and ycf12. MGDG20 is close to PsbI and ChlzD1, and lipid MGDG21 is near the periphery of PSII between CP43 and TMHs ZA and ZB of PsbZ (Supplementary Fig. 2).

PG22, the second PG molecule newly identified in PSII, is on the cytoplasmic side close to QB, SQDG4, MGDG18 and PG3 (Fig. 2d). DGDG23 is on the lumenal side close to PsbI and TMH a of D1, with its head group forming polar contacts with sugars from MGDG20 and β-DM32. SQDG24 is embedded between PsbY, PsbF and PsbX. The DGDG25 head group is in contact with the C-terminal loop of PsbE and the ab loop (connecting TMHs a and b) of D2, with its fatty acid interacting with CarD2. The five newly assigned detergent molecules β-DM28 to β-DM32, except β-DM31 (see above), are at the periphery, close to the membrane.

At the monomer-monomer interface, protein-protein interactions are formed only between subunits PsbM and PsbM* located close to the pseudo two-fold C2 axis relating the monomers in the homodimer (Fig. 1a). Their single TMHs interlock with the heptad motif typical of membrane-spanning leucine zippers13 (Fig. 1c), and the open space between the monomers is filled by 14 lipids, seven from each monomer (Fig. 2b and Supplementary Fig. 2). In addition, there are eight β-DM molecules that may have replaced galactolipids during preparation, suggesting that there may be even more lipids when PSII is in the thylakoid membrane.

Of the 18 lipids per monomer not located at the monomer-monomer interface, three are at the periphery of PSII, and seven form clusters with two to three lipids in the lipid belt around D1 and D2: DGDG1 and DGDG2 (Fig. 2b, ellipse I) between D1 and CP43 and MGDG9, MGDG10 and MGDG11 (Fig. 2b, ellipse II) plus SQDG16 and DGDG8 (Fig. 2b, ellipse III) between D2 and CP47. The remaining eight lipids (PG3, SQDG4, PG22 and MGDG18 on the cytoplasmic side and MGDG19, DGDG5, DGDG6 and MGDG7 on the lumenal side) are arranged as a bilayer island (Fig. 2b, blue box, and Fig. 2c) encircled by protein subunits D1, CP43, PsbE, PsbF, PsbJ and PsbK, forming the PQ-PQH2 exchange cavity.

Carotenoids and chlorophylls

In addition to the 11 carotenoids identified earlier9, there is one more carotenoid (Car15) on the D2 side close to Car11 (CarD2). Car15 is shifted along the membrane normal by 7.5–10.8 Å, with partial overlap of the isoprenoid chain relative to Car53 (ref. 7). Carotenoids CarD2, Car12, Car13, Car15 and Car16 are within van der Waals distance from each other and are possibly coupled for fast electron and/or exciton transfer.

The number of 35 Chl did not change compared to the 3.0-Å structure9; the space assigned to one additional Chl in ref. 7 is instead filled with lipid DGDG2. Our electron density allowed complete modeling of the phytol chains (Supplementary Fig. 1) of all 35 Chl and of the two Pheo, many of them contributing to the hydrophobic binding pockets of other Chls. The orientations of the chlorin rings confirmed those reported in ref. 9, except for Chl11, which had to be flipped 180°.


QA was modeled completely. The double bond of the terminal isoprenoid unit of QA is sandwiched between phenyl rings of conserved D1-Phe52 and PsbT-Phe10, and the QA tail stabilizes ChlD1 by van der Waals contacts (Supplementary Fig. 3a,b online). The tail of QB now shows seven of the nine expected isoprenoid units. It is accommodated in the newly discovered PQ-PQH2 exchange channel II with a portal between PsbF and TMH a of D2 (Fig. 3a,b) that opens toward the PQ pool.

Figure 3: The quinone exchange cavity in PSII.
Figure 3

(a) Schematic view of the PQ-PQH2 exchange cavity and the two entry and exit portals connecting the QB and QC sites to the PQ pool in the thylakoid membrane. Approximate dimensions are given in angstroms; QB and QC are colored cyan and yellow, respectively, the QB site is highlighted in pink, and the three lipids forming the cork (the head groups for PG22, SQDG4 and MGDG18 are shown as red, green and white squares) nearly closing the cavity toward the cytoplasm are indicated. (b) Calculated channels (I and II, gray) for PQ-PQH2 transfer between the PQ pool and the QB and QC sites, viewed from the cytoplasmic side. Shown are the PQs in the QB site (light blue) and QC site (yellow), non-heme Fe2+ (blue sphere), Car15 (orange), Chl37 (green), SQDG4 (gray), cyt b-559 heme (dark blue) and the surrounding proteins (pink). CarD2, ChlD2 and MGDG7 are not shown. (c) Possible mechanisms for the PQ-PQH2 exchange between the QB site of PSII and the PQ pool in the thylakoid membrane, viewed from the cytoplasm. Channels I and II open toward the PQ pool. PQ is shown with a red and PQH2 with a blue head group. The QB site is highlighted pink, the QC site in green and labeled; the yellow patch indicates a hydrophobic region formed by the fatty acids of MGDG7, MGDG18 and the phytol chain of ChlD2. Small arrows symbolize movements of PQ molecules. See text for explanations concerning the alternating, wriggling and single-channel mechanisms.

A third PQ molecule (QC) is located in the PQ-PQH2 exchange cavity (Fig. 3), in agreement with a stoichiometry of at least 2.5 PQ to 35 Chl per monomer of crystalline T. elongatus PSII14,15. Its below-average electron density indicates partial disorder, and it could be modeled only with five isoprenoid units. QC resides in channel I with a portal between PsbJ and cyt b-559 (ref. 9 and Fig. 3b) and forms van der Waals contacts with CarD2, fatty acids of SQDG4, MDGD7, the isoprenoid chain of QB and the phytol chain of ChlD2, but not with the protein. Its head group is 17 Å away from the head group of QB and 15 Å from the heme of cyt b-559 (edge-to-edge distances), in agreement with the presence of a PQ site near cyt b-559 (ref. 16). For possible PQ-PQH2 exchange mechanisms, see Figure 3c and discussion.

Mn4Ca cluster and chloride binding site

There are only insignificant changes in the positions of cations and ligating amino acids of the Mn4Ca cluster, relative to ref. 9, but the electron density revealed a patch at about the 4.3 σ level near the Mn4Ca cluster that was modeled and refined as fully occupied Cl (Fig. 4a).

Figure 4: The Mn4Ca cluster of PSII and the Cl binding site.
Figure 4

(a) Position of Cl (green sphere) located in the native electron density (blue, contoured at 1.2 σ level) close to the Mn4Ca cluster (red and orange spheres; Mn1 is partially hidden behind Mn2). The coordinating amino acids are from D1 (yellow) except for D2-Lys317 (orange). (b) Enlarged view of the neighborhood of Cl showing coordinating amino acids and electron density (blue, contoured at 1.2 σ level) for a putative water molecule (purple sphere) located between Mn4 and Cl. Distances are given in angstroms.

Cl is located 6.5 Å from the Mn4Ca cluster, coordinated by conserved D2-Lys317NZ, D1-Asn181ND and D1-Glu333N (Fig. 4b) and close to the entrance of proton channels C and G (see below; Fig. 5a,b). An additional patch of electron density between the Mn4Ca cluster and the Cl site might arise from a water molecule(s) with Cl·water and water·Mn4 distances of 3.3 Å and 3.5 Å, respectively; water is also ligated by conserved D1-Glu333OE2 and D1-Asp181OD2 (Fig. 4b).

Figure 5: Possible substrate and product channels to the lumen and Xe positions in PSII.
Figure 5

(a) Detailed view of two of the putative water and oxygen channels (see text for details) connecting the Mn4Ca cluster with the lumen. The walls of the channels are shown in blue (channel A1) and light blue (channel A2), respectively. Residues forming the walls of the channels are shown in stick presentation, along with D1 (yellow), CP43 (magenta), PsbO (green), lipids DGDG1 and DGDG2 (gray). Also shown as spheres are the Mn4Ca cluster (red and orange, Mn2 and Mn3 are not seen), Cl (green labeled Cl) and the closest Xe (Xe5) (purple), with distances given in angstroms. (b) View from the lumenal side onto the membrane plane showing the Mn4Ca cluster and possible water and oxygen channels in blue (A1), light blue (A2) and pink (B), and possible proton channels (C to G) in yellow (exits of merging channels labeled as CD and EF). Position of Cl indicated by a green sphere. Protein omitted for clarity. (c) Stereo view of channels and Xe positions in PSII. One monomer is shown with the cytoplasm above and the lumen below. All 20 protein subunits are shown as gray cylinders, except PsbM, which is colored cyan. Xe positions are shown as purple spheres (labeled 1 to 10). Openings of the channels are labeled A1, A2, B, CD, EF, G.

When T. elongatus is grown in medium containing Br instead of Cl (ref. 17), Br supports the oxygen-evolving activity of PSII18. We used crystals of Br-PSII (see Methods) to confirm the Cl site. Difference electron density at 3.9-Å resolution showed one prominent peak at the 7.2 σ level that corresponds to the Cl site; this was assigned to Br with an occupancy of 0.7.

Moreover, positive difference electron density (σ level 4.6) was observed at the same position in the Xe-PSII data set (see below) measured at X-ray wavelength 2.1 Å, where a weak anomalous contribution from Cl is expected19. This position is unlikely to be occupied by a Xe atom as it would have an unfavorable environment.

Ca2+ binding sites

In addition to the Ca2+ in the Mn4Ca cluster7,9,18 and Ca2+-PsbK, a putative Ca2+ ion was identified on the external surface of the membrane-extrinsic and β-barrel type subunit PsbO, which is ligated by PsbO-Glu81OE1/OE2, PsbO-Glu140OE1/OE2 and PsbO-His257NE2, similarly to the Ca2+ site proposed earlier20 and supported by other X-ray data5,7. Additional electron density close to Ca2+-PsbO might belong to water molecules that could not be located at the present resolution, but it supports the idea21 of an auxiliary role for hydrated Ca2+-PsbO to facilitate H+ ejection from the proton channel leading from the Mn4Ca cluster to the lumen (see below).

Channels to and from the Mn4Ca cluster and Xe-derivatization

Because the optimized transport of substrate (water) and products (protons, dioxygen) to and from the Mn4Ca cluster is essential for efficient catalysis, we analyzed connections from this cluster to the lumen using the program Caver22 (see Methods). This revealed eight potential channels that lead away from the Mn4Ca cluster in a sponge-like arrangement and merge into six exits toward the lumen (Fig. 5 and Supplementary Table 2 online). Channels A1, A2, C and D are formed exclusively by conserved residues from subunits D1 and CP43, with few conserved residues contributed by PsbO and D2.

Water or dioxygen could pass through channels A1, A2 and B, which have a minimum van der Waals diameter of 2.6–2.8 Å (Supplementary Table 2); these channels start at the triangle formed by Mn1, Mn2 and Ca and point away from Mn3 and Mn4. On the other side of the Mn4Ca cluster at Mn3, Mn4 and Ca, five narrower channels initiate that are mostly enclosed by hydrophilic groups. As their minimum van der Waals diameter is 1.3 Å (Supplementary Table 2), they are neither suitable for water nor for oxygen transport but might be important for proton transfer, instead.

To identify possible hydrophobic pathways for dioxygen transfer away from the Mn4Ca cluster, we determined the structure of a PSII crystal derivatized with Xe under pressure (see Methods). Difference electron density maps (Xe-derivative data minus the native data) of the PSII homodimer showed 19 peaks that were attributed to Xe. One Xe (Xe7) rides on the C2 axis, Xe8 and Xe9 of each monomer are located near PsbM and PsbM* at the monomer-monomer interface and seven (Xe1–6 and Xe10) are found within each monomer (Fig. 5c and Supplementary Table 3 online). Of these sites, none is located in the channels described above, and it is notable that all Xe sites are located in a hydrophobic environment formed by fatty acids from lipids, phytol chains from Chls, carotenoids or hydrophobic amino acids. Xe3 is located in the hydrophobic interior of the β-barrel of PsbO, but there is no connection between this site and the Mn4Ca cluster. The remaining Xe sites are found in the membrane-spanning part of PSII at approximately half the height of the membrane and at the interface between D1 and CP43 or D2 and CP47, or close to the binding site of QC (Xe6), but ≥17 Å apart from the cofactors of the ETC.


The PSII model at 2.9-Å resolution includes all 20 known protein subunits characterized by MS and provides a definite assignment of subunits ycf12, PsbY and PsbX (Fig. 1a,b) in accordance with studies on a PsbY-deletion mutant23 and the identification of subunit ycf12 in cyanobacterial PSII10,24.

The total of 25 lipids per monomer yields 0.7 lipids per TMH. This number is high compared to other lipid-containing membrane protein complexes (PSI25, cyt b6f26,27, purple bacterial reaction center28,29 and cytochrome c oxidase30 with 0.1, 0.23, 0.27, 0.46 lipids per TMH, respectively). This suggests a special role for these lipids in PSII function, as discussed below.

Because only few direct protein-protein contacts (PsbM-PsbM*) are formed between the two monomers in the PSII dimer (Fig. 1a,c), lipids, chlorophylls and carotenoids are essential mediators of contacts between the monomers, and this emphasizes the function of lipids in dimer formation and dissociation31. It is possible that they are essential for conveying flexibility32 within PSII required for assembly and disassembly of monomers during the exchange of photodamaged D1 by new D1 (refs. 31,33,34).

Although PGs are believed to be important for the dimerization of PSII35 and trimerization of PSI25 and LHCII36,37, no PG could be identified within the monomer-monomer interface of PSII; however, the presence of four SQDG at the interface might promote dimerization of PSII, at least in T. elongatus. It was suggested that PG is important for the interaction between D1 and CP43 (ref. 38), in good agreement with the location of PG3 and PG22 between these subunits in the present model. These lipids, together with SQDG4 and DGDG2, 5 and 6, could serve as additional lubrication for removal and insertion of CP43, which is believed to take place when photodamaged subunit D1 is replaced by intact D1 (refs. 31,33,34).

Synechocystis variants suggested indirect tuning and stabilization of the PSII electron acceptor QB site by PG39. This is supported by the newly located PG22 close to PG3 that is at the side of the PQ-PQH2 exchange cavity and covered by a loop of D2 (Fig. 2d). The head groups of PG22 and QB are only 8 Å apart, and PG22 makes a hydrogen bond with the conserved D1-Asn266 residue and forms a 'cork' with MGDG18 and SQDG4. The cork nearly seals the PQ-PQH2 exchange cavity9 toward the cytoplasm and possibly provides an area for the attachment of phycobilisome antennae in cyanobacteria40,41. In addition, lipids provide hydrophobic patches that might be essential for diffusion of dioxygen through the body of PSII (see below).

As plastoquinone QB is the terminal electron acceptor in PSII, the fast exchange of reduced PQH2 with fresh PQ from the PQ pool in the thylakoid membrane is essential for the enzymatic function of PSII. The third plastoquinone QC found in our structural model and the arrangement of PQ in the QB and QC sites relative to the entry and exit portals suggests three possible mechanisms for PQ-PQH2 exchange between the QB site and the PQ pool (Fig. 3c).

First, in the 'alternating' mechanism, entry and exit of PQ and PQH2 both proceed through channels I and II in an alternating way. After reduction and protonation of QB, PQH2 leaves PSII through channel II, and QC in channel I moves and binds to the QB site with its isoprenoid tail still located in channel I. Simultaneously, another PQ from the PQ pool enters the transiently empty channel II. After reduction and protonation, PQH2 leaves the QB site now through channel I, and PQ from the PQ pool moves along channel II and binds to the QB site for another cycle.

Second, in the 'wriggling' mechanism, entry of PQ occurs exclusively through channel I, and PQH2 exits through channel II. After reduction and protonation, PQH2 leaves the QB site through channel II, and QC enters the QB site from channel I. After or simultaneously with binding to the QB site, the isoprenoid tail wriggles around the hydrophobic tails of ChlD2, MGDG7 and MGDG18, which are located between the two channels (Fig. 3c, yellow patches). The isoprenoid tail finally points into the empty channel II, and another PQ from the PQ pool enters the QC site through channel I.

Third, in the 'single channel' mechanism, entry and exit proceed only through channel II, and channel I is not involved in PQ-PQH2 exchange. After reduction and protonation, PQH2 leaves the QB site through channel II, and PQ from the pool enters the empty channel II and binds to the QB site for a new cycle. PQ in the QC site remains at this position and does not participate in PQ-PQH2 exchange.

The alternating and wriggling mechanisms provide a second mobile PQ (QC) for rapid electron transfer. By the single-channel mechanism, QC could have other as yet unknown functions in secondary electron transfer or, in cooperation with cyt b-559 (refs. 16,42), in the regulation of PSII function. All three mechanisms could minimize deleterious back reactions, even under low PQ concentrations in the PQ pool, and they might be used under different ambient conditions.

The arrangement of PQ-PQH2 exchange channels in PSII is unique compared with other quinone-quinol–exchanging membrane proteins such as cyt b6f (refs. 26,27), cyt bc1 (refs. 29,43) and the bacterial reaction center28,29. Because their quinone binding pockets are wide and close to the protein-membrane boundary, dedicated channels are not required for exchange of quinone and quinol.

Water, the electron donor to PSII, is oxidized at the Mn4Ca cluster, which is part of the oxygen evolving complex (OEC)3,4 located at the lumenal side of PSII. It is still not possible to derive an atomic model of the Mn4Ca cluster because the 2.9-Å resolution is not sufficient for a distinction between short and long Mn-Mn distances (in the range of 2.7–3.3 Å44), and μ-oxo and di-μ-oxo bridges cannot be seen. In addition, all X-ray diffraction data suffer from inherent radiation damage, leading to reduction of Mn3+ and Mn4+ to Mn2+ associated with possible movement of ions and ligands in the cluster45,46. However, a recent polarized extended X-ray absorption fine structure (EXAFS) study of PSII crystals provided high-resolution models for the Mn4Ca cluster47.

As Cl is known to be essential for the fast turnover of water oxidation in PSII17, the location of Cl bound by water(s) to the Mn4Ca cluster is an important addition to the structural picture of the OEC (Fig. 4), although the effect of radiation damage possibly changing the native arrangement of ligands and ions in the OEC has to be kept in mind. The presence of only one Cl per Mn4Ca, as found in our structural model, is consistent with studies on spinach PSII, where only one functional Cl could be exchanged per monomer48, and the determination of the PSII:Cl stoichiometry for spinach grown on 36Cl yielded about one 36Cl per OEC49. In addition, EXAFS data on Br-exchanged PSII from spinach suggested a Cl···water···Mn4Ca model with a distance of around 5 Å between Cl and Mn-Ca50. It is unlikely that Cl interacts directly with the substrate water being oxidized at the Mn4Ca cluster, because the Mn-cation closest to Cl is Mn4, which was suggested to be redox-inactive during the S-state turnover51,52. Instead, the position of Cl close to the entrance of the possible proton channels C and G and ligated by D2-Lys317NZ agrees with the proposal that Cl together with lysine and other charged amino acids forms a proton-relay network for fast proton removal from the Mn4Ca cluster48.

The locations of two Br ions close to the Mn4Ca cluster in crystals of Br-substituted PSII from T. elongatus were published53 during preparation of our manuscript. Although one of the sites is similar to the Cl position described here, the other does not occur in our native, Br-substituted or Xe data and might be due to poor data quality and artifacts arising from insufficient (4.20-Å53) resolution.

The arrangement of possible substrate and product channels predicted from our structural model suggests a strict spatial separation of water and oxygen fluxes and proton fluxes to and from the Mn4Ca cluster. We could identify eight distinct channels connecting the Mn4Ca cluster with the lumen, the three wider ones and the five narrower ones being possible water and oxygen or proton channels, respectively. Compared to previous studies21,54, we could locate more substrate and product channels, but the inclusion of all cofactors in the calculations revealed several differences. The proposed 'channel i'21 or 'back channel'54 is partially blocked by the head group of DGDG2 and branches into channels A1 and A2, with the new channel A2 being wider compared to A1 (Fig. 5a and Supplementary Table 2). Channels B and C are almost identical to those reported earlier21,54, whereas channels D to G have not been previously reported.

Channel C might be important for proton transfer because it harbors conserved D1-Glu65 at the narrowest (1.3-Å) passage (11 Å away from the Mn4Ca cluster), and exchanges of D1-Glu65 for other amino acids modulate the oxygen evolution of PSII55. Several titratable residues mostly located along channel C were the subject of electrostatic calculations showing a monotonic increase of their pKa values from the Mn4Ca cluster to the lumenal side56, supporting the role of channel C as a possible proton-exit pathway.

An analysis of the Xe sites showed several possible channels connecting Xe sites with the membrane phase and the cytoplasm (data not shown). All of the Xe sites are located ≥17 Å away from the ETC cofactors, which are active in charge separation and electron transport and lie halfway between the Mn4Ca cluster and the cytoplasm. Since Xe is considered as a dioxygen analog and is used for mapping of oxygen channels in crystallography57, our results suggest that the hydrophobic patches in the interior of PSII, constituted partly by lipids, could allow diffusion of the dioxygen through PSII to the cytoplasmic side, thereby channeling dioxygen away from the reaction center region and preventing oxidative damage to P680 as well as accumulation of dioxygen in the lumen of the thylakoid membrane.


X-ray diffraction data processing and refinement.

We purified and crystallized dimeric PSII from T. elongatus as described14. X-ray diffraction data sets were collected at the European Synchrotron Radiation Facility (ESRF; beamline ID 14-2), leading to a refined model at 3.0-Å resolution (PDB 2AXT)9. In parallel to ongoing attempts to grow better crystals from which to collect higher-resolution X-ray diffraction data, we have reprocessed the raw data with the new version of the XDS package (, which is optimized with a new scaling algorithm for mosaic detectors. This led to substantial improvement in data quality, and the resolution limit could be extended to 2.9 Å (Table 1). The amount of unique reflection data increased to 193,457 (compared to 155,340 for the previous 3.0-Å model9), and the unique reflections used in the refinement increased from 129,965 (ref. 9) to 186,169, with II ≥ 2.0, allowing a more reliable refinement. After several iterations of model building in Coot58 and refinement with the CNS package59, the hitherto most complete and realistic model of PSII has been obtained (R/Rfree factors of 0.249/0.292, with r.m.s. deviations from ideal geometry of 0.010 Å for bond lengths and 1.453° for bond angles; Table 1). Figures were generated using PyMol (

Table 1: Data collection and refinement statistics

Supplementary Table 4 online describes the nomenclature of the cofactors in the text and in the new coordinate file in relation to the nomenclature used for the corresponding cofactors in the previous 3.0-Å resolution structure (PDB 2AXT)9.

Analysis of subunit composition.

The subunit composition of homodimeric PSII was studied by MALDI-TOF MS in linear and reflector mode and by N-terminal sequencing. For N-terminal sequencing, proteins were separated using gradient gels60, blotted onto a PVDF membrane and stained with Coomassie R250. The bands were excised from the membrane and directly applied to a gas phase sequencer (Applied Biosystems 473 A Protein sequencer). MALDI-TOF MS was performed in linear and reflector modes using a pulsed UV laser (N2 laser, λ = 337 nm, 3-ns pulse width, type RETOF-MS, Bruker-Franzen) with sinapinic acid as matrix.

Br-substituted crystals.

To obtain PSII with Cl substituted by Br, cell growth, protein preparation and crystallization were as described14 with some modifications. Thermosynechococcus elongatus cells were grown in Cl-free medium containing Br instead, as described17, and in all steps for protein preparation and purification Cl was replaced by Br, and all buffers used were supplemented with 0.5 M betaine. Br-PSII showed similar oxygen-evolving activity (40–52 Chl per four light flashes and evolved molecule of O2) and subunit composition in SDS-PAGE and MALDI-TOF MS (data not shown) as PSII prepared from Cl-grown cells. Crystals of homodimeric Br-PSII were grown with 3.6% (w/v) PEG 2000 as a precipitant, using the micro-batch method. Data were collected at beamline ID 29 (ESRF, Grenoble), wavelength 0.8 Å and beamline ID 23-1 (ESRF, Grenoble), wavelength 0.88 Å. The resolution was 4.0 Å and 3.9 Å, respectively (Table 1).

Xe derivatization.

To elucidate possible hydrophobic oxygen channels, crystals were incubated with Xe at 10 bar for 5 min and immediately flash frozen in liquid nitrogen. Data were collected at 100 K at beamline 14.2 of Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung (BESSY), wavelength 2.1 Å. The resolution obtained was 4.2 Å (Table 1). In a difference electron density map between a native and the Xe-derivative data set, 19 peaks were located in each PSII dimer at or above the 10 σ level (Fig. 5c and Supplementary Table 3).

Calculation of pathways.

To explore possible pathways for mobile molecules (water, oxygen, protons, plastoquinones and plastoquinols) to travel to or from the Mn4Ca cluster or the QB site, we used the program Caver22. The user defines a starting point (ligand binding site, cofactor and so on) as the beginning of a channel that leads to bulk solvent. The program determines a channel profile and assigns grid points located in open space with a low penalty and those that are close to real atoms with a higher penalty. The program output was visualized with PyMol as the surface of a channel with calculated van der Waals diameter.

Accession codes.

Protein Data Bank: Atomic coordinates and structural factors for PSII monomer I and monomer II have been deposited under accession codes 3BZ1 and 3BZ2, respectively.

Note: Supplementary information is available on the Nature Structural & Molecular Biology website.


Primary accessions

Referenced accessions

Protein Data Bank


  1. 1.

    & (eds.) Photosystem II: The Light-Driven Water:Plastoquinone Oxidoreductase (Springer, Dordrecht, 2005).

  2. 2.

    & Photosystem II. Structure and mechanism of the water:plastoquinone oxidoreductase. Photosynth. Res. 94, 183–202 (2007).

  3. 3.

    Oxidative photosynthetic water splitting: energetics, kinetics and mechanism. Photosynth. Res. 92, 407–425 (2007).

  4. 4.

    Water oxidation chemistry of photosystem II. Phil. Trans. R. Soc. Lond. B 363, 1211–1218 (2008).

  5. 5.

    et al. Crystal structure of photosystem II from Synechococcus elongatus at 3.8 Å resolution. Nature 409, 739–743 (2001).

  6. 6.

    & Crystal structure of oxygen-evolving photosystem II from Thermosynechococcus vulcanus at 3.7 Å resolution. Proc. Natl. Acad. Sci. USA 100, 98–103 (2003).

  7. 7.

    , , , & Architecture of the photosynthetic oxygen-evolving center. Science 303, 1831–1838 (2004).

  8. 8.

    , , , & Crystal structure of cyanobacterial photosystem II at 3.2 Å resolution: a closer look at the Mn-cluster. Phys. Chem. Chem. Phys. 6, 4733–4736 (2004).

  9. 9.

    , , , & Towards complete cofactor arrangement in the 3.0 Å resolution structure of photosystem II. Nature 438, 1040–1044 (2005).

  10. 10.

    et al. Ycf12 is a core subunit in the photosystem II complex. Biochim. Biophys. Acta 1767, 1269–1275 (2007).

  11. 11.

    , , , & Lipids in photosystem II: interactions with protein and cofactors. Biochim. Biophys. Acta 1767, 509–519 (2007).

  12. 12.

    et al. Lipids in oxygen-evolving photosystem II complexes of cyanobacteria and higher plants. J. Biochem. 140, 201–209 (2006).

  13. 13.

    , , & A heptad motif of leucine residues found in membrane proteins can drive self-assembly of artificial transmembrane segments. J. Biol. Chem. 274, 9265–9270 (1999).

  14. 14.

    et al. Purification, characterisation and crystallisation of photosystem II from Thermosynechococcus elongatus cultivated in a new type of photobioreactor. Biochim. Biophys. Acta 1706, 147–157 (2005).

  15. 15.

    , , , & Spare quinones in the QB cavity of crystallized photosystem II from Thermosynechococcus elongates. Biochim. Biophys. Acta 1767, 520–527 (2007).

  16. 16.

    , & Evidence for a novel quinone-binding site in the photosystem II (PS II) complex that regulates the redox potential of cytochrome b559. Biochemistry 46, 1091–1105 (2007).

  17. 17.

    et al. Biosynthetic exchange of bromide for chloride and strontium for calcium in the photosystem II oxygen-evolving enzymes. J. Biol. Chem. 283, 13330–13340 (2008).

  18. 18.

    The calcium and chloride requirements of the O2 evolving complex. Coord. Chem. Rev. 252, 296–305 (2008).

  19. 19.

    et al. On the routine use of soft X-rays in macromolecular crystallography. Part IV. Efficient determination of anomalous substructures in biomacromolecules using longer X-ray wavelengths. Acta Crystallogr. D Biol. Crystallogr. 63, 366–380 (2007).

  20. 20.

    & Identification of a calcium-binding site in the PsbO protein of photosystem II. Biochemistry 45, 4128–4130 (2006).

  21. 21.

    & Structural characteristics of channels and pathways in photosystem II including the identification of an oxygen channel. J. Struct. Biol. 159, 228–237 (2007).

  22. 22.

    et al. CAVER: a new tool to explore routes from protein clefts, pockets and cavities. BMC Bioinformatics 7, 316 (2006).

  23. 23.

    , , , & Location of PsbY in oxygen-evolving photosystem II revealed by mutagenesis and X-ray crystallography. FEBS Lett. 581, 4983–4987 (2007).

  24. 24.

    , , , & Absence of the PsbZ subunit prevents association of PsbK and Ycf12 with the PSII complex in the thermophilic cyanobacterium Thermosynechococcus elongatus BP-1. Plant Cell Physiol. 48, 1758–1763 (2007).

  25. 25.

    et al. Three-dimensional structure of cyanobacterial photosystem I at 2.5 Å resolution. Nature 411, 909–917 (2001).

  26. 26.

    , & Structure of the cytochrome b6f complex: quinone analogue inhibitors as ligands of heme cn. J. Mol. Biol. 370, 39–52 (2007).

  27. 27.

    , , & An atypical haem in the cytochrome b6f complex. Nature 426, 413–418 (2003).

  28. 28.

    Lipids in photosynthetic reaction centres: structural roles and functional holes. Prog. Lipid Res. 46, 56–87 (2007).

  29. 29.

    , , , & A comparison of stigmatellin conformations, free and bound to the photosynthetic reaction center and the cytochrome bc1 complex. J. Mol. Biol. 368, 197–208 (2007).

  30. 30.

    et al. Structures and physiological roles of 13 integral lipids of bovine heart cytochrome c oxidase. EMBO J. 26, 1713–1725 (2007).

  31. 31.

    & Photoinhibition of photosynthetic electron transport. in Primary Processes of Photosynthesis: Basic Principles and Apparatus Vol.1 (ed. Renger, G.) 393–425 (Royal Society of Chemistry, Cambridge, 2008).

  32. 32.

    & Lipids in membrane protein structures. Biochim. Biophys. Acta 1666, 2–18 (2004).

  33. 33.

    , , , & Synthesis and assembly of thylakoid protein complexes. Multiple assembly steps of photosystem II. Biochem. J. 388, 159–168 (2005).

  34. 34.

    , & A new paradigm for the action of reactive oxygen species in the photoinhibition of photosystem II. Biochim. Biophys. Acta 1757, 742–749 (2006).

  35. 35.

    et al. Phosphatidylglycerol is involved in the dimerization of photosystem II. J. Biol. Chem. 275, 6509–6514 (2000).

  36. 36.

    et al. Crystal structure of spinach major light-harvesting complex at 2.72 Å resolution. Nature 428, 287–292 (2004).

  37. 37.

    , , & Mechanisms of photoprotection and nonphotochemical quenching in pea light-harvesting complex at 2.5 Å resolution. EMBO J. 24, 919–928 (2005).

  38. 38.

    et al. Role of phosphatidylglycerol in the function and assembly of photosystem II reaction center, studied in a cdsA-inactivated PAL mutant strain of Synechocystis sp. PCC6803 that lacks phycobilisomes. Biochim. Biophys. Acta 1777, 1184–1194 (2008).

  39. 39.

    et al. Phosphatidylglycerol requirement for the function of electron acceptor plastoquinone QB in the photosystem II reaction center. Biochemistry 41, 3796–3802 (2002).

  40. 40.

    , & Interaction of the allophycocyanin core complex with photosystem II. Photochem. Photobiol. Sci. 2, 536–541 (2003).

  41. 41.

    , & The structure of allophycocyanin from Thermosynechococcus elongatus at 3.5 Å resolution. Acta Crystallogr. F63, 998–1002 (2007).

  42. 42.

    et al. Evidence that cytochrome b559 mediates the oxidation of reduced plastoquinone in the dark. J. Biol. Chem. 278, 13554–13560 (2003).

  43. 43.

    et al. Structural basis for the quinone reduction in the bc1 complex: a comparative analysis of crystal structures of mitochondrial cytochrome bc1 with bound substrate and inhibitors at the Qi site. Biochemistry 42, 9067–9080 (2003).

  44. 44.

    & Where water is oxidized to dioxygen: structure of the photosynthetic Mn4Ca cluster from X-ray spectroscopy. Inorg. Chem. 47, 1711–1726 (2008).

  45. 45.

    et al. X-ray damage to the Mn4Ca complex in single crystals of photosystem II: a case study for metalloprotein crystallography. Proc. Natl. Acad. Sci. USA 102, 12047–12052 (2005).

  46. 46.

    , , , & Rapid loss of structural motifs in the manganese complex of oxygenic photosynthesis by X-ray irradiation at 10–300 K. J. Biol. Chem. 281, 4580–4588 (2006).

  47. 47.

    et al. Where water is oxidized to dioxygen: structure of the photosynthetic Mn4Ca cluster. Science 314, 821–825 (2006).

  48. 48.

    & The function of the chloride ion in photosynthetic oxygen evolution. Biochemistry 42, 2025–2035 (2003).

  49. 49.

    & A one-site, two-state model for the binding of anions in photosystem II. Biochemistry 35, 14259–14267 (1996).

  50. 50.

    et al. Bromide does not bind to the Mn4Ca complex in its S1 state in Cl-depleted and Br-reconstituted oxygen-evolving photosystem II: evidence from X-ray absorption spectroscopy at the Br K-edge. Biochemistry 45, 13101–13107 (2006).

  51. 51.

    , , & No evidence from FTIR difference spectroscopy that aspartate-170 of the D1 polypeptide ligates a manganese ion that undergoes oxidation during the S0 to S1, S1 to S2, or S2 to S3 transitions in photosystem II. Biochemistry 44, 1367–1374 (2005).

  52. 52.

    Protein ligation of the photosynthetic oxygen-evolving center. Coord. Chem. Rev. 252, 244–258 (2008).

  53. 53.

    et al. X-Ray crystallography identifies two chloride binding sites in the oxygen evolving centre of photosystem II. Energy. Environ. Sci. 1, 161–166 (2008).

  54. 54.

    & Access channels and methanol binding site to the CaMn4 cluster in photosystem II based on solvent accessibility simulations, with implications for substrate water access. Biochim. Biophys. Acta 1777, 140–153 (2008).

  55. 55.

    , & Amino acid residues that influence the binding of manganese or calcium to photosystem II. 1. The lumenal interhelical domains of the D1 polypeptide. Biochemistry 34, 5839–5858 (1995).

  56. 56.

    , , , & Energetics of a possible proton exit pathway for water oxidation in photosystem II. Biochemistry 45, 2063–2071 (2006).

  57. 57.

    et al. The X-ray crystal structures of wild-type and EQ(I-286) mutant cytochrome c oxidases from Rhodobacter sphaeroides. J. Mol. Biol. 321, 329–339 (2002).

  58. 58.

    & Coot: model-building tools for molecular graphics. Acta Crystallogr. D Biol. Crystallogr. 60, 2126–2132 (2004).

  59. 59.

    et al. Crystallography & NMR system: a new software suite for macromolecular structure determination. Acta Crystallogr. D Biol. Crystallogr. 54, 905–921 (1998).

  60. 60.

    , & An improved sodium dodecyl sulfate-polyacrylamide gel electrophoresis system for the analysis of membrane protein complexes. Electrophoresis 22, 1004–1007 (2001).

Download references


The authors are grateful to the Deutsche Forschungsgemeinschaft for support within the framework of Sfb 498 (projects A4, C7). We also acknowledge W. Kabsch for help with XDS, W. Schröder for help with protein sequencing, P. Franke and C. Weise for MS data collection and J. Biesiadka for cooperation. We thank F. Müh, G. Renger, R. Clarke, V. Yachandra and K. Sauer for discussion and careful reading of the manuscript. Beam time and support at ESRF (Grenoble), SLS (Villigen) and BESSY (Berlin) is gratefully acknowledged.

Author information

Author notes

    • Jan Kern

    Present address: Physical Biosciences Division, Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, 94720 California, USA.

    • Albert Guskov
    •  & Jan Kern

    These authors contributed equally to this work.


  1. Institut für Chemie und Biochemie/Kristallographie, Freie Universität Berlin, Takustrasse 6, D-14195 Berlin, Germany.

    • Albert Guskov
    • , Azat Gabdulkhakov
    •  & Wolfram Saenger
  2. Institut für Chemie/Max Volmer Laboratorium für Biophysikalische Chemie, Technische Universität Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany.

    • Jan Kern
    • , Matthias Broser
    •  & Athina Zouni


  1. Search for Albert Guskov in:

  2. Search for Jan Kern in:

  3. Search for Azat Gabdulkhakov in:

  4. Search for Matthias Broser in:

  5. Search for Athina Zouni in:

  6. Search for Wolfram Saenger in:


M.B., J.K. and A.Z. purified and crystallized the protein; A. Guskov, M.B., J.K. and A. Gabdulkhakov collected diffraction data; A. Guskov and A. Gabdulkhakov did structure determination and model building; A. Gabdulkhakov calculated channels; A. Guskov, J.K., M.B., A. Gabdulkhakov, A.Z. and W.S. designed experiments, analyzed data and prepared the manuscript.

Corresponding authors

Correspondence to Athina Zouni or Wolfram Saenger.

Supplementary information

PDF files

  1. 1.

    Supplementary Text and Figures

    Supplementary Figures 1–3, Supplementary Tables 1‐4 and Supplementary Discussion

About this article

Publication history





Further reading