Functional roles of the hexamer structure of C‐phycocyanin revealed by calculation of absorption wavelength

The phycocyanin trimer structure is the basic building block of the rod of phycobilisome (PBS). However, PBS is composed of one higher hierarchical structure, a unit of hexamer structure that combines two trimers. In this study, we clarify the functional role of the hexamer structure from the viewpoint of light absorption properties and energy transfer of chromophore β155.

(Received 10 August 2020, revised 27 October 2020, accepted 11 November 2020) doi: 10.1002/2211- 5463.13038 Cyanophyta-phycocyanin (C-PC) is the main constituent of the rod of phycobilisome (PBS), which is a highly ordered and large peripheral light-harvesting protein complex present on the cytoplasmic side of the thylakoid membrane in cyanobacteria and red algae. The C-PC monomer comprises two chains, aand b-subunits, and aggregates to form ring-shaped trimers (ab) 3 with rotational symmetry. The ring-shaped trimer (ab) 3 is a structural block unit (SBU) that forms the rod of PBS. Two (ab) 3 SBUs are arranged in a face-to-face manner to form an (ab) 6 -hexamer. In this study, the electronic states of three phycocyanobilins, a84, b84, and b155 in C-phycocyanin, constituting the rod of the PBS, were calculated for both the trimer and hexamer models by considering the effect of the electrostatic field of protein moieties and water molecules. For the hexamer, the absorption wavelengths of a84, b84, and b155 were similar to those obtained experimentally; however, for the trimer, only the absorption wavelength of b155 shifted toward a shorter-wavelength. The nature of the hexamer structure as a hierarchical structure is revealed by considering the calculated absorption wavelength and energy transfer.
C-phycocyanin (C-PC) is the main constituent of the rod of phycobilisome (PBS), which is a highly ordered and large peripheral light-harvesting protein complex occurring on the cytoplasmic side of the thylakoid membrane in cyanobacteria and red algae [1][2][3].
Herein, 'C' indicates the type of source organism (Cyanophyta). A schematic representation of PBS is shown in Fig. 1A. The C-PC monomer comprises two chains, aand b-subunits, and aggregates to form ring-shaped trimers (ab) 3 with rotational symmetry (Fig. 1B). In both the aand b-subunits, phycocyanobilin (PCB), that is, a chromophore, is bound to cysteine-84 by a cysteinyl thioether linkage through the vinyl substituent on the pyrrole ring. The b-subunit contains an additional PCB bound to cysteine-155 in a manner similar to cysteine-84. These PCBs are called a84, b84, and b155, respectively [4,5].
The ring-shaped trimer (ab) 3 is a structural block unit (SBU) that forms the rod of PBS. Two (ab) 3 SBUs are arranged in a face-to-face manner to form an (ab) 6 -hexamer. Two (ab) 6 -hexamers are associated in a back-to-back fashion via a linker protein [6]. Shirmer et al. [5] analyzed the crystal structure of hexameric C-PC obtained from cyanobacterium Agmenellum quadruplicatum and showed that the (ab) 6 -hexamer is the functional unit of the native PBS. On the other hand, almost the same time, Mimuro et al. pointed out from experimental absorption spectra, CD, fluorescence, and fluorescence polarization spectroscopy that first of all the absorption energy of b155 transfers to b84 in the (ab) 3 -trimer, and thus, an (ab) 3 -trimer is not only a SBU but also the functional unit of the energy transfer [7].
Although the term 'functional unit' was used while focusing on the direction of energy flow, the pathway of energy flow is not the only function of PBS. For example, light adaptation or chromatic acclimation (CA) processes in PBS function in hexamer units [8][9][10]. If the hexamer is not a hierarchical structure with functional meaning, then light adaptation or CA processes in PBS might have functioned in trimeric units. To discuss the implications of the hexamer structure being one of the hierarchical structures of PBS from the functional view is inevitable in understanding the relationship between function and structure in PBS. Additionally, to consider the relationship between the hierarchical structure of PBS and its function could lead to understanding the diversity that makes PBS an amazing light-harvesting system or the evolutionary issues of PBS [11,12].
In this study, the electronic states of three chromophores were determined on the basis of the crystal structure [13], including the effects of peptide moieties and water molecules, of both the trimer and hexamer. The functional role of the hexamer structure is also investigated based on the results obtained.

Materials and methods
C-PC was isolated from the cyanobacterium Fremyellia diplosiphone [13]. The resolution of the crystal data was 1.66 A in Protein Data Bank (PDB; PDB ID: 1CPC).

Net charges and hydrogen coordinates of the aand b-subunits
Before calculating light absorption, the coordinates of the hydrogen atoms were determined. First, three successive amino acid residues in the a-subunit or the b-subunit of 1CPC were treated as a trimer, to which hydrogen atoms were added. Then, the coordinates of the hydrogen atoms were optimized with respect to the total energy of the  [13]; PDB ID, 1CPC), and a part of the hexamer in which two trimers are associated with each other. In (A), the trimer form that corresponds to (B) is depicted by the rectangle (dark blue), and the linker protein connecting the hexamers is depicted by the red circle. There are other linker proteins between allophycocyanins constituting the PBS core, between the rod and the core, and between the core and the thylakoid membrane; however, they are omitted in (A). The reaction center complexes are located within the membrane underneath the cores. In (B) and (C), the a-subunit (red) and the b-subunit (green) are drawn using the ribbon model. The chromophores, a84 (blue), b84 (purple), and b155 (black), are drawn by the stick model. In (C), it is shown how the aand b-subunits belonging to one trimer contact the aand b-subunits belonging to the other trimer.
trimer by using the Modified Neglect of Diatomic Overlap -Parametric Method 3 molecular orbital (MO) method [14,15]. For the trimer, the N terminus was set to -NH 2 , but the C terminus, except for the C terminus of C-PC, was replaced with -COCH 3 because the oxygen atom in -OH strongly attracts electrons. At the C terminus of C-PC, -COOH was used. The coordinates and net charges of the central amino acid residue in the trimer were calculated and used. These procedures were performed until the coordinates, and net charges of all the amino acid residues in C-PC were obtained. These values were then utilized for determining the wavelength of light absorption.

Coordinates and net charges in water molecules
Molecular dynamics simulations were performed using Amber 12 to determine the coordinates of water molecules around the trimer or hexamer of C-PC [16]. The Amber ff03 force field [17,18] was used for the proteins. A part of the hexamer comprising A(a-subunit), B(b-subunit), K(asubunit), and L(b subunit) in 1CPC (see Fig. 1C) or the trimer by itself was immersed in water molecules. Hereinafter, the former is called the hexamer model and the latter is called the trimer model. Both models were electrostatically neutralized by counter ions, and an explicit water box (TIP3P) was used. The systems were minimized for 300 steepest-descent steps and equilibrated for 1 ns by gradually increasing the temperature. Finally, 100-ns production runs were performed. The positions of the atoms, except for water molecules, were fixed during the calculation. The temperature and pressure were kept constant by using Berendsen rescaling methods [19], and long-range electrostatic forces were computed using the particle-mesh Ewald method [20]. The net charges of the oxygen and hydrogen atoms of water molecules were À0.3307 and 0.1653, respectively. These values were obtained by using the ab initio MO method for a water molecule with the GAUSSIAN09 software [21] (Gaussian, Inc., Wallingford, CT, USA) at the HF/ STO-3G level.

Calculation of the wavelength of light absorption and the oscillator strength
The wavelength of light absorption and the oscillator strength were calculated using the unique intermediate neglect of differential overlap-configuration interaction (INDO-CI) method [22]. All molecular integrals in the calculation were estimated as functions of electron densities of individual atoms according to Sakuranaga et al. [22]; this INDO-CI method is slightly different from that used by Pople et al. [23]. The resonance integrals were expressed using parameter k b in equation (2.2) in ref. 22, as described by Wolfsberg-Helmholtz [24]. In the present study, all the values except for that of k b are the same as those reported by Sakuranaga et al. [22]. The values of k b were k b (C- 1.20 to reproduce the observed light absorption and oscillator strength of the individual bands of the a84 chromophore in C-PC [25]. Each chromophore was treated as a protonated form [25][26][27][28][29]. A total of 338 lowest singly excited configurations, w (j, m), and doubly excited configurations, w (jj, mm), were considered for calculating the CI. Herein, w (j, m) was constructed by exciting an electron from an occupied MO / j to an unoccupied MO / m , and w (jj, mm) was constructed by exciting a pair of electrons from / j to / m . For CI calculations, the interaction between the chromophore and its surrounding protein moieties or water molecules was considered as the electrostatic interaction between the electronic states of the chromophore and the net charges of its surrounding atoms.
Additionally, for comparison, the calculations using only 169 lowest singly excited configurations, w (j, m), for the CI were carried out for a84 and b84. Figure 2 shows the dependence of k 1 for the S 0 ?S 1 transition on distance R from a given atom of the a84 or b84 chromophore to any atom of the protein moiety and water molecule when the number of only the lowest singly excited configurations, w (j, m), and the lowest singly and doubly excited ones, w (j, m) and w (jj, mm), were 169 and 338, respectively. The wavelength k 1 obtained for the S 0 ?S 1 transition with only the single-CI was about 5% longer than that obtained using the single-CI and double-CI with excitations of two electrons from the same orbital. However, the tendency of the distance dependence was the same for both a84 and b84 (Fig. 2). Dependence of k 1 for the S 0 ?S 1 transition on distance R from the a84 or b84 chromophore, calculated by including the electrostatic interaction of the a84 or b84 chromophore with protein moieties and water molecules within R A. R from the chromophore means the longest distance from a given atom of the chromophore to any atom of the protein or water.
Even if the larger set of excitations between two different orbitals, w (kj, mn), for the CI calculations were considered, the tendency of the distance dependence would show the same tendency including the slight difference in the absorption wavelength. And this difference can be regulated by the values of parameters k b . Indeed, it is important for more accurate results to consider the larger set of excitations between two different orbitals, w (kj, mn), for the CI calculations. However, to validate the purpose of the present study, it is sufficient to consider the single-CI and double-CI containing only excitations of two electrons from the same orbital. Thus, in this study, the values of parameter k b were set based on this level of CI calculations.

Results
Mimuro et al. reported [7] that the maximum light absorption of a84, b84, and b155 is obtained for the transition from the ground state to the first excited state (S 0 ?S 1 ), and the wavelength for each transition is 618, 625, and 594 nm, respectively. Almost the same value has been reported elsewhere too. When the chromophore is electrically neutral, the calculated oscillator strength f 1 for the transition (S 0 ?S 1 ) is small and does not agree with the experimental result. However, when the chromophore is protonated, namely when each nitrogen atom of the central pyrrole rings B and C combines with a hydrogen atom, the calculated oscillator strength f 1 for S 0 ?S 1 increases and agrees with the experimental result. In this study, the protonated form was used and k 1 (k max ), which is the absorption wavelength for S 0 ? S 1 , was utilized as an index.
The chemical geometry of a chromophore is the chief factor that determines its electronic state, followed by its protonation, and the subsequent effect is the electrical interaction from the environment, which consists of the atoms of amino acid in the protein moiety and water molecules. Since the electrical effect of the environment was considered to be distance-dependent, the effect on the electronic state of the chromophore from the environment was estimated by using constancy of the k 1 of the S 0 ?S 1 transition as a measure. When the atoms of amino acids and water molecules within 7 or 8 A from a84 or b84 for the trimer model were taken into account, the fluctuations of k 1 suppressed (Fig. 2). Figure 3A,B show the calculated absorption wavelength of a84 and b84 with the protein moieties and water molecules within 8 A from the a84 and the b84, respectively. For a84, k 1 is 624 nm and f 1 is 1.18, whereas for b84, k 1 is 630 nm and f 1 is 1. 18.
The position and orientation of the water molecule in case of a84 are different from those used through the previous calculation [25], but almost the same wavelength as the previous calculation result was obtained. This implies that a84 is present inside the protein and is largely unaffected by the water outside the PBS. In this study, the calculation result of b84 was also obtained, and the k 1 of b84 was slightly longer than that of a84. This result almost reproduces the experimental observations [7,30]. Although the interaction with the linker protein was not taken into account, this effect would be more helpful for understanding the energy transition mechanism in PBS.
The surrounding environment for a84 or b84 of the hexamer model is the same as that of the trimer model when they are considered within 8 A from the chromophore. However, for b155, a difference in the surrounding environment between the trimer and hexamer models was observed. Figure 3C,D show the calculated results of the trimer and hexamer models, including the condition when the protein moieties and water molecules are within 8 A from b155. For the hexamer model (Fig. 3C), the calculation result (k 1 = 595 nm and f 1 = 1.23) was the same as the experimental result for native PBS; however, for the trimer model (Fig. 3D), k 1 shifted to the shorter-wavelength side (k 1 = 547 nm and f 1 = 1.46) than the experimental value (594 nm [7]). In other words, the calculated absorption wavelengths of a84, b84, and b155 reproduced the experimental results [7,30,31] in the case of the hexamer. In contrast, for the trimer, the wavelength of b155 shifted to the shorter-wavelength side. Figure 4A,B show the atoms within 8 A from b155 considered in the hexamer model. The chromophore is depicted in a licorice representation, and the atoms belonging to the trimer model and the other atoms that belong to the a-subunit of the adjacent trimer (K chain in 1CPC) are represented by green and orange, respectively. As shown in these figures, b155 interacts with the K chain, which is included in the hexamer model, but not in the trimer model. This can also be seen in Fig. 1C. Figure 4C shows the atoms within 8 A from b155 considered in the trimer model, and Fig. 4D shows the model by removing the K chain from the hexamer model. For the trimer model, most of the periphery of b155 is covered with water molecules, which is a different situation from that of the native PBS environment. Figure 5 shows the dependence of k 1 on distance R from b155 for the trimer and hexamer models; the surrounding atoms within R from b155 were incorporated in the calculation. When R is up to 3 A, both the trimer and hexamer models are the same. However, when R ≥ 4 A, the hexamer model shows the effect of the K chain. The k 1 value for b155 alone was 600 nm. Hence, it is clear that the short-wavelength shift of the absorption wavelength is due to the effect of the protein moieties of the trimer and the water molecules surrounding b155. Conversely, the effect of the K chain, that is, the role of the hexamer, results into the long-wavelength shift, which counteracts the effect of the protein moieties of the trimer and the water molecules surrounding b155. Additionally, when the K chain part is removed from the hexamer model (Fig. 4D), the k 1 and f 1 of R = 7 A and R = 8 A are 547 nm and 1.36, or 546 nm and 1.47, respectively. These results show that the hexamer leads to the longwavelength shift.

Discussion
The electronic state and light absorption properties of a84, b84, and b155 in C-PC were calculated for both the trimer and hexamer models using the INDO-CI method based on the crystal structure 1CPC. When the chromophore is electrically neutral, the oscillator strength f 1 for the transition (S 0 ?S 1 ) from the ground state to the first excited state is small and does not agree with the experimental result [25,26]. However, when the chromophore is protonated, f 1 for the S 0 ?S 1 transition becomes large and agrees with the experimental results. Thus, the protonated form was used for the calculations, and k 1 (k max ), which is the absorption wavelength for the S 0 ?S 1 transition, was utilized as an index for the effect of the environment in this study. The protein moieties and water molecules  In the hexamer model, the calculated absorption wavelengths of a84, b84, and b155 agreed with the experimental results for native PBS. In the case of the trimer model, in contrast, only the result of b155, which shifted to the shorter-wavelength side, did not agree with the experiment. The absorption wavelength of b155 was~550 nm for the trimer model, while it was~595 nm for the hexamer model.
More light energy can be harvested using a larger number of chromophores. The chromophore added to the PBS, except for a84 and b84, must be located outside the rod because of the molecular structure of PBS; b155 located outside the rod plays a role in absorbing more light energy. If b155 is surrounded by water, as in the trimer model, its optical absorption wavelength will become shorter than that of the hexamer model, which reflects native PBS. If the energy transfer in PBS can be considered in terms of F€ orster's mechanism, then the efficiency of the energy transfer can be determined using the overlap integral of the emission spectra of b155 and the absorption spectra of a84 or b84 [32][33][34].
Thus, if the absorption wavelength of b155 is not close to that of a84 or b84, the efficiency of energy transfer from b155 to a84 or b84 will be small, and the light energy absorbed by b155 will be in vain. Thus, the light energy absorbed by b155 cannot be used effectively if the trimer is structurally independent and exists in the rod as a basic unit for function. However, if two (ab) 3 -trimers are associated face-to-face with each other and form a hierarchical structure as a (ab) 6 -hexamer, the light energy absorbed by b155 can be effectively transferred to a84 or b84 and utilized. Hence, one of the roles of the hierarchical structure of (ab) 6 -hexamer can be revealed by calculating the absorption wavelength.
Mimuro et al. determined the maximum light absorption of each chromophore in C-PC obtained from Mastigocladus laminosus (a84: 618 nm, b84: 625 nm, b155: 594 nm) [7]; this assignment was verified by Siebzehnr€ ubl et al. (a84: 617 nm, b84: 622 nm, b155: 598 nm) [30,31]. However, Niedzwiedzki et al. [35] recently pointed out that, experimentally, there is no consensus specifically on the absorption wavelength of b155. Eisenberg et al. [36] showed the maximum b155 absorption at~550 nm, and Gryliuk et al. [37] showed that the 4 K absorption spectrum of PBS from Acaryochloris marina partially resolves two bands at 574 and 599 nm. This study might support these experimental results and may have implications for optical absorption experiments on the monomer, trimer, and hexamer in the PBS rod.
One might argue that the semi-empirical MO method is insufficient. Indeed, it is impossible to obtain very high precision values using semi-empirical MO methods; however, it is useful to use the obtained value as an index and for discussion. Herein, the parameters of the INDO-CI method were set to reproduce the experimental values for the optical absorption wavelengths of a84, and these parameters were also applied to determine the optical absorption wavelengths of b84 and b155. Only b155 in the trimer model showed a shorter-wavelength shift of~40 nm. High precision values are not needed for this discussion. Namely, it is not too much to say that only the case of b155 in the trimer model is qualitatively different from the other cases, showing such a large blue shift, in which the value of the overlap integral in F€ orster's formula [32][33][34] becomes smaller than that of the hexamer model. Accordingly, this discussion based on the results of the calculations using the INDO-CI method is effective and valuable.
If we consider one protein chain as the smallest unit of structure, PBS can interestingly be considered to be composed of several hierarchical structures with different functions. First, the a-subunit or b-subunit consists of a globinfold part and X-Y helices [4,5,13]. The Asp87 of globinfolds promotes the protonation of the chromophore, which enables the light harvesting of 620 nm [25,26]. The monomer forms the second hierarchical structure. The X-Y helix portion of the subunit associates the a-subunit with the b-subunit and also simultaneously prevents the Asp87 fluctuations from increasing so as to stabilize the protonation of the chromophore [38,39]. The trimer forms the third hierarchical structure, which is a structural unit assembling PBS. The hexamer, the fourth hierarchical structure, modulates the optical absorption wavelength of b155 and effectively transfers the light energy to a84 or b84. The molecules that play a central role in the fifth hierarchical structure are thought to be linker proteins, which are closely related to the energy transfer in the PBS rod. Recently, the complete structure of PBS, including the linker proteins, has been clarified [40], which will lead to the discovery of new relationships between the PBS structure and function in the near future. Fig. 5. Dependence of k 1 for the S 0 ?S 1 transition on distance R from the b155 chromophore of the trimer and hexamer models, calculated by including the electrostatic interaction of b155 with protein moieties and water molecules within R A.