The phycobilisome terminal emitter transfers its energy with a rate of (20 ps)–1 to photosystem II

Ultrafast time resolved emission spectra were measured in whole cells of a PSI-deficient mutant of Synechocystis sp. PCC 6803 at room temperature and at 77K to study excitation energy transfer and trapping. By means of a target analysis it was estimated that the terminal emitter of the phycobilisome, termed allophycocyanin 680, transfers its energy with a rate of (20 ps)–1 to PSII. This is faster than the intraphycobilisome energy transfer rates between a rod and a core cylinder, or between the core cylinders.


Introduction
Photosynthesis is key to the conversion of solar energy to biomass. Light-harvesting antennae absorb sunlight and transfer the excitation energy ultimately to the reaction centers (RCs) (Mirkovic et al. 2017). The phycobilisome (PB) is the light-harvesting antenna of many cyanobacteria, red algae, and glaucophytes (Glazer 1984, Adir 2005, Watanabe and Ikeuchi 2013. Light is absorbed by phycocyanobilin pigments that are covalently bound to phycobiliproteins (Glazer 1984). The rods and core contain phycocyanin (PC) and allophycocyanin (APC), respectively. Together these pigments absorb light between 400 and 650 nm, and excitations of the antenna pigments are efficiently transferred to the chlorophyllcontaining PSI and PSII (Gillbro et al. 1985, Sandström et al. 1988, Tian et al. 2011, 2013bScott et al. 2006, Liu et al. 2013. These photosystems convert the excitations to chemical energy via initial charge separation (van Grondelle et al. 1994), and the combined action of PBs and photosystems (the light reactions of photosyn-thesis) provides the energy input to the cell (Govindjee et al. 2017). Until now, the rate at which the phycobilisome transfers its energy to PSII is not known. Here we measure ultrafast time resolved emission spectra in whole cells of a PSI-deficient mutant of the cyanobacterium Synechocystis sp. PCC 6803 (Shen et al. 1993). With the help of target analysis (Holzwarth 1996, van Stokkum et al. 2004) we estimated the unknown rate of energy transfer from PB to PSII. Fig. 1 schematically depicts the fluorescent species that we expect to be present, and the excitation energy transfer (EET) pathways from the PB rods via the core cylinders to the PSII dimer. Next to the PB-PSII complex with both PSII RCs open (Fig. 1A), part of the complexes may have both PSII RCs closed (Fig. 1B). Additionally, over the time course of an experiment (typically 50-90 min) the sample may change, and part of the PB may no longer be coupled to any PSII (Fig. 1C). Finally, a small fraction of uncoupled PSII dimers with open ( Fig. 1D) or closed , a PB that is not coupled to any PSII (C) as well as an uncoupled PSII dimer with open (D) and closed (E) RCs. Key: blue, rods consisting of three hexamers; top and basal core cylinders respectively in magenta, red and orange; green, PSII dimer. Dark arrows represent intra-PB EET; yellow arrows represent EET from the PB core to PSII. An "X" stands for a closed PSII RC.
( Fig. 1E) RCs may be present. Fig. 2 depicts the different pigments present in a PB-PSII complex. Recently, a functional compartmental model of the PB has been developed ( van Stokkum et al. 2017). A compartment contains pigments with the same light-harvesting function that are considered equivalent. The four colors that are used in Fig. 2 for the core; magenta, red, orange, and black indicate the four groups of pigments that will be lumped into four compartments. Below, the rods will be described by two compartments (PC640 and PC650). The PSII RC contains 6 Chl a and 2 Pheo, the core antennae CP43 and CP47 contain 14 and 17 Chl a, respectively. At room temperature (RT), the 37 Chl a and the 2 Pheo will be lumped in one Chl a compartment. In Fig. 2, a green barrel symbolizes the PSII core containing 39 chlorins. The biexponential decay of the PSII dimer emission (Tian et al. 2013a) will be described by an equilibrium of the Chl a compartment with a radical pair (RP) compartment. Thus we will arrive at a minimal model of twelve compartments (cf. Fig. 4E). Microscopic rate constants describe the rates of EET/ET between the compartments. The spectral properties of the different compartments will be described by species associated spectra (SAS). The parameters of this target model will be estimated from the time resolved emission spectra. Below we will first globally analyze the RT emission data and based thereupon develop a functional compartmental model for the PB-PSII complex. Then, we will verify whether this model also holds at 77K. Fig. 2. The structure of PB-PSII is shown schematically, and the most important pigments are indicated. Each rod contains three hexamers. PC rods in blue (total number of PC640 and PC650 pigments indicated). APC that fluoresces at 660 nm (APC660) in magenta, red and orange (66 pigments in total), and the low-energy part of APC indicated by black dots (six APC680 pigments in total). The letters D,E,F indicate the three different APC680 pigments. The approximate length for each subunit is based on (Arteni et al. 2009).

Materials and methods
Growth conditions and sample preparation: The PSIdeficient mutant of Synechocystis (Shen et al. 1993) was a gift from prof. C. Funk (Umeå University, Sweden) and was stored at -80°C in 15% glycerol. Prior to preparing a liquid culture, cells were streaked on agar plates containing BG-11 (Sigma) supplemented with 0.3% sodium thiosulfate, 35 µg(chloramphenicol) mL -1 , and 10 mM glucose. The strain appeared incompatible with our usual agar, requiring the plates to be solidified using Difco granulated agar (BD). The plates were incubated in an incubator (Versatile Environmental Test Chamber MLR-350H, Sanyo, Japan) with a humidified atmosphere of elevated CO2 (2%) kept at 30°C. Incident light intensity was reduced to below 5 µmol(photon) m -2 s -1 by covering the plates with layers of paper.
Liquid cultures were prepared by inoculating 25 mL of modified BG-11 van Alphen et al. manuscript in preparation) supplemented with 10 mM glucose, 25 mM 1,4-piperazinedipropanesulfonic acid (PIPPS)-KOH buffered at pH 8.0 and 5 µg(chloramphenicol) mL -1 in a 100-mL flask (FB33131, Fisherbrand). The flasks were covered in multiple layers of paper to reduce the incident light intensity to below 5 µmol(photon) m -2 s -1 and were placed in a shaking incubator (Innova 43,New Brunswick Scientific), equipped with a custom built LED panel containing LEDs of 632 nm (orange-red) and 451 nm (blue, both 8 nm full width at half maximum) at 120 rpm and 30°C.
Steady-state absorption of whole cells was measured using a Varian Cary 4000 UV-Vis spectrophotometer additionally equipped with a Varian 900 external diffuse reflectance accessory.

Time-resolved fluorescence:
A series of streak camera measurements (van Stokkum et al. 2008, Wlodarczyk et al. 2016, comprising several image sequences using different parameters, was carried out less than one hour after taking the cells out of the reactor to ensure excellent sample quality. While there is no evidence for significant cell degradation during single sequences, the cells may have changed from one sequence to the next. The different conditions from one sequence to another include two different excitation wavelengths (400 nm for predominant Chl excitation; 590 nm for predominant PB excitation), or different time ranges (TR): from 0 to 400 ps (TR2) and from 0 to 1500 ps (TR4). For measurements performed using TR2 (TR4), the image sequence consists of 300 (150) images, each of which results from a scan of 8 s. In order to achieve a high SNR, each image sequence is used to produce an average image that is, in its turn, corrected for background and lamp shading before analysis. In order to judge whether the sample changed over time, we kept track of the chronological order in sequence acquisition. We indicate the conditions as 'time range/λexc (in nm)'. Measurements were done at room temperature (RT) and at 77K. The acquisition order at RT was: TR2/590 → TR4/590 → TR4/400 → TR2/400. The acquisition order at 77K was: TR2/400 → TR4/400 → TR4/590 → TR2/590.
The samples frozen to 77K in a Pasteur pipette were placed in a cold finger. The diameter of the excitation beam and the optical path length within the sample were both ≈1 mm. The fluorescence at the angle of 90° to the direction of the excitation beam was collimated and focused onto the input slit of spectrograph Chromex 250IS (Chromex, Albuquerque, New Mexico). In one case (77K, 590 nm exc) a cut off filter OC14 was used to block the scattered excitation light. The spectrally resolved emission was detected using a Hamamatsu C5680 synchroscan camera with a cooled Hamamatsu digital camera C10600-10B (ORCA-R2) (Hamamatsu Photonics, Hamamatsu, Japan). In all cases, the laser light was vertically polarized, the laser power was 15 μW, the spot size was of 60 μm, the laser repetition rate was set to 250 kHz, the input slit of the spectrograph was 140 μm and that of the photo-cathode of the streak camera was 220 μm and the detection was parallel (VV) to the incident polarization. At RT, the full width at half maximum (FWHM) of the instrument αresponse function (IRF) was ≈7 ps with TR2 and ≈18 ps with TR4. At 77K, The FWHM of the IRF was ≈13 ps with TR2 and ≈25 ps with TR4.
Global and target analysis of time resolved emission spectra: In target analysis of time resolved emission spectra, the inverse problem is to determine the number of electronically excited states (Nstates) present in the system, and to estimate their spectral properties SASl(λ) (and their populations c l S (t) (superscript S stands for species). The time resolved emission spectra TRES(t,λ) are described by a parameterized superposition model: where the populations are determined by an unknown compartmental model, that depends upon the unknown kinetic parameters θ. In the target analysis constraints on the SAS are needed to estimate all parameters θ and SASl(λ) (van Stokkum et al. 2004, Snellenburg et al. 2013. The population of the l-th compartment is c l S (t). The concentrations of all compartments are collated in a vector: where the transfer matrix K contains off-diagonal elements kpq, representing the microscopic rate constant for energy transfer from compartment q to compartment p. The diagonal elements contain the total decay rates of each compartment. The input to the compartments is The impulse response of the system, which is a sum of exponential decays, has to be convolved with the IRF. Typically, a Gaussian shaped IRF is adequate, with parameters µ for the location of the IRF maximum and Δ for the FWHM of the IRF: where Δ � = Δ/�2�2log (2)�. The convolution (indicated by an *) of this IRF with an exponential decay (with decay rate k) yields an analytical expression which facilitates the estimation of the decay rate k and the IRF parameters µ and Δ: Typically, with streak camera measurements the IRF can be well approximated by a sum of up to three Gaussians.
The solution of the general compartmental model described by the K matrix consists of exponential decays with decay rates equal to the eigenvalues of the K matrix. When the compartmental model consists of independently decaying species their spectra are termed DASl(λ) (decay associated spectra), and when it consists of a sequential scheme with increasing lifetimes the spectra are termed EASl(λ) (evolution associated spectra).
The interrelation between the DAS and SAS is expressed in the following matrix equation: Here the matrix C D (θ, µ, Δ) contains in its l-th column the decay c l D (t, k, µ, Δ) and the matrix C S (θ,μ,Δ) contains in its columns the populations c l S (t) of the general compartmental model.

Simultaneous target analysis:
To resolve the different species and to improve the precision of the estimated parameters, the set of Nexp experiments that describe the same sample (measured with different excitation wavelengths or on different time ranges) can be analyzed simultaneously. For each additional data set TRSe one scaling parameter αe and one time shift parameter µe must be added: The different excitation wavelengths are taken into account via the absorptions of the species that result in C e S (θ, µ e , Δ). Since the two different excitation wavelengths (400 nm for predominant Chl excitation; 590 nm for predominant PB excitation) result in different initial concentrations of the compartments, the different species can be better resolved through simultaneous target analysis.
Residual analysis: Following a successfully converged fit, the matrix of residuals is analyzed with the help of a singular value decomposition (SVD). Formally the residual matrix can be decomposed as where ul and wl are the left and right singular vectors, sl the sorted singular values, and m is the minimum of the number of rows and columns of the matrix. The singular vectors are orthogonal, and provide an optimal least squares approximation of the matrix. The SVD of the matrix of residuals is useful to diagnose shortcomings of the model used, or systematic errors in the data.

Results and discussion
Measurements at room temperature: The ΔPSI absorption spectrum (orange) depicted in Fig. 1SA (supplement available online) clearly displays a decreased Chl a Qy absorption band at ≈680 nm that is largely attributed to PSI in WT cells (green in Fig. 1SA). Still a shoulder is visible in the ΔPSI absorption spectrum at ≈680 nm, attributable to PSII Chl a. Likewise the Soret bands decreased in ΔPSI. Fig. 3 depicts the estimated DAS. The black DAS represents equilibration between the rod phycocyanins PC640 and PC650 in 6-8 ps. The red DAS represents equilibration between the rods and the APC660 pigments of the core cylinders. The blue DAS differs for the 400 and 590 nm excitation. In the latter it is conservative and can be interpreted as equilibration between the PB and PSII. The green DAS is positive everywhere and can be interpreted as trapping by the open PSII RC (the 680 nm peak). The magenta DAS is also positive everywhere and can be interpreted as trapping in the closed PSII RC. These observations can further be tested with the help of a target analysis. Assuming that PB is the same in vivo and in vitro (Tian et al. 2011(Tian et al. , 2012, we adopt the functional compartmental model for the PB from van Stokkum et al. (2017).  It is based upon the schematic structure depicted in Fig. 2. The kinetic scheme contains six different types of functional compartments. Because the PB architecture possesses a C2 rotational symmetry axis, perpendicular to the membrane, the core can be described by three APC660 and one APC680 compartment (black). Three APC660 compartments are needed: the top cylinder (magenta), the APC660 pigments in the D and EF disks (orange), which are in the closest contact to the APC680 pigments,     Acuña et al. (2016a). and the remaining APC660 pigments of the basal cylinders (red). The red rectangle indicates the two basal cylinders. The intercylinder EET is described by an effective rate of 4/ns between the magenta and red APC660 compartments (van Stokkum et al. 2017). The microscopic rate constants connecting the compartments must obey detailed balance. In particular, the rate constants towards the orange APC660 compartment which contains 18 pigments, are 18/24 times as large as the analogous rate constants towards the red APC660 compartment which contains 24 pigments. The simplest description of a rod contains two types of functional compartments: PC640 (cyan) and PC650 (blue). It is assumed that two rods are connected to the top cylinder, whereas four rods radiate from the two basal cylinders. Again, the EET rates to the APC660 compartments from the rods obey detailed balance. Note that this is also an effective rate, which also takes into account the fast EET between the hexamers (van Stokkum et al. 2017). All PB rate constants were fixed to the values estimated in van Stokkum et al. (2017) (Table 1). The differences in the fractions between the two excitation wavelengths explain the differences between their fourth and fifth DAS (cf. Fig. 3). The amount of loose PSII is assumed to be negligible, and in the modelling it cannot easily be distinguished from PSII that is attached to PB. The kinetic schemes for the PB-PSII complex with RCs open or closed are depicted in Fig. 4E and Fig. 2S (supplement available online), respectively. In van Stokkum et al. (2017), the estimated relative precision of each rate constant was 20%. Here, we estimated that the rate of EET from the APC680 compartment to the PSII open compartment is (50 ± 10)/ns, whereas the backward rate was (2.5 ± 0.5)/ns. This ratio of the forward and backward rate constants is consistent with a small energy difference (677.5 vs. 681.7 nm) on top of a large entropy difference. A PSII dimer contains 2 × 39 = 78 chlorins. The energy difference between the APC680 and PSII maxima of 677.5 and 681.7 nm is 91/cm or 11 meV. The entropy difference between compartments with 78 and 6 pigments is which is 65 meV at room temperature. Thus the free energy of the green PSII compartment is assumed to be 76 meV lower than that of the grey APC680 compartment, which corresponds to a ratio of the backward to forward rate constants of 0.05. An effective EET rate to PSII of 10.4/ns has been reported in Maksimov et al. (2011). This rate can be interpreted as an overall effective EET rate from the PB to PSII. The estimates EET rates of Fig. 4E are consistent with calculations of Förster energy transfer rates in rods (Xie et al. 2002). The estimated SAS depicted in Fig. 4A,C are consistent with the properties of the five types of pigments. The maxima of the emission are at 644, 656, 663, 677.5, and 681.7 nm for, respectively, PC640 (cyan), PC650 (blue), APC660 (red), APC680 (black), and PSII Chl a (green). The fit quality of the target analysis is good, cf. Figs. 3S, S, and 5S (supplements available online). Next to the kinetic scheme and its parameters also the relative absorption4s of the different pigments with the different excitation wavelengths have to be estimated. The timezero spectrum is the weighted sum of the SAS of all the excited pigments. Thus, the shape of the SAS of the fastest decaying species, PC640, is the most sensitive to the relative absorption parameters. The parameters of Table 2, which led to the acceptable SAS of Fig. 4, were thus determined iteratively. Based upon this relative absorption the percentage excitation of each pigment type can be calculated. Both numbers are collated in Table 2 and are consistent with the properties of the five types of pigments. In panels B and D of Fig. 4, the total concentration is plotted. For each species, the total concentration is the sum of all excited state populations in the compartments with the spectrum of that species. Thus, the populations of the three APC660 compartments are summed, etc. Note that the initial population of PSII Chl a greatly increases with 400 nm excitation (Fig. 4D), which is absorbed well due to the Soret band of Chl a.
The amplitude matrix of the PB-PSII complex with open RC with 590 nm excitation is shown in After this successful target analysis we can now reconstruct the steady-state emission spectra (SS) of the three different complexes, cf. Fig. 5A. In the PB-PSII complex with RCs open the SS (black) has of course a much smaller area than the complex with RCs closed (red). Both SS have their maximum at 682 nm, whereas the maximum of the non-transferring PB SS is at 663 nm. In Fig. 5B we reproduced the steady state emission spectrum of the PB-PSII complex with open (black) or closed (red) RC from a decomposition of spectrally resolved fluorescence traces that were recorded over several minutes with 100 ms time resolution and were reported in Acuña et al. (2016a). We note that the relative areas of the complexes with RCs open or closed are consistent. The absence of a maximum at 682 nm in the black SS of Fig. 5B suggests that the decomposition reported in Acuña et al. (2016a) was suboptimal. Fig. 6 depicts the estimated DAS at 77K. The black DAS represents equilibration between the rod phycocyanins PC640 and PC650 in 19 ps and also the beginning of the equilibration between the rods and the APC660 pigments of the core cylinders. The red DAS represents the final equilibration between the rods and the core, and most probably also a rise of PSII Chl a near ≈685 nm. The blue DAS is nonconservative, representing a loss of emission with ≈140 ps, in combination with a small rise of PSII Chl a near ≈690 nm. The green DAS is positive everywhere and can be interpreted as quenching (that probably involves formation of a radical pair) in the closed PSII RC (the 680 nm peak) (Snellenburg et al. 2017), with an additional loss below 675 nm that can be attributed to non-transferring PB. The magenta DAS is also positive everywhere and can be interpreted as decay of the red shifted emission of the equilibrated closed PSII RC. Our target model consists of two different complexes: a PB-PSII complex with RCs closed (estimated to be 80% with 590 nm excitation and TR2) and non-transferring PB (20%) ( Table 1S, supplement available online)).

Measurements at 77K:
Since no functional model of the PB at 77K is available, we start out from the PB model of Fig. 4E.
Recently, a functional model of the PSII core at 77K has been established (Snellenburg et al. 2017). Three compartments were needed, one for the bulk Chl a, including the RC, from which excitations are quenched with a rate of ≈3/ns. Two more compartments describe the equilibration with red shifted Chl a in the core antennae CP43 and CP47. Since we have only limited data available, we assume equality of these two red shifted Chl a SAS. The functional model of the PB at 77K is depicted in Fig. 7E. Note that all uphill rate constants (from PC650 to PC640, from APC660 to PC650, from APC680 to APC660, and from PSII to APC680) had to be free parameters, since at 77K the thermal energy is four times smaller than at RT. In addition, we released three more rate constants, from PC640 to PC650, from PC650 to APC660, and the slow intercylinder equilibration rate. These were estimated to be different from the values estimated at RT (cf. Fig. 7E). The largest difference found was the rate from PC650 to APC660, which increased from 12 to 23/ns. This suggests that the structure at 77K more favors the rod to core energy transfer. Most importantly, also the 77K data are consistent with an energy transfer rate of 50/ns [= (20 ps) -1 ] from APC680 to PSII. The fit quality of the target analysis is good, cf. Fig. 6S and Fig. 7S (supplements available  online). The estimated SAS depicted in Fig. 7A,C are consistent with the properties of the six types of pigments. The maxima of the SAS are at 642, 656, 663, 684, 688, and 690 nm for, respectively, PC640 (cyan), PC650 (blue), APC660 (red), APC680 (black), bulk and red PSII Chl a (green, purple). The SAS estimated with 590 nm exc (Fig. 7A) are attenuated on the blue side because a cut off filter had to be used to suppress the scattered excitation light. The PC650 and APC660 SAS (blue and red), estimated with 400 nm exc (Fig. 7C) show small humps in the 680 nm region. Thus more measurements at 77K are needed, in particular to resolve the differences between the APC680 pigments that were observed in mutants (Jallet et al. 2012, Acuña et al. 2016b.
Analogous to Table 2, the percentage excitation of each pigment type can be calculated, as well as the relative absorption per pigment. Both numbers are collated in Table S2 and are consistent with the properties of the five types of pigments. With 590 nm excitation light, two main differences between RT and 77K are: first, light is more selectively absorbed by PC640, which is to be expected because the line hapes are narrower at 77K, thus favoring the PC640 pigment that absorbs nearer to 590 nm. Second, less PSII Chl a absorption appears to be present at 77K.

Conclusion:
From this study we can conclude that the APC680 pigments of the PB transfer their energy with a rate of 50/ns [= (20 ps) -1 ] to PSII (Fig. 4E). More research will be needed to figure out the roles of the different types of APC680 pigments (Fig. 2). The next challenge will be to establish the rate of energy transfer to PSI in the PB-PSII-PSI megacomplex that is present in WT Synechocystis (Liu et al. 2013, Acuña et al. 2016a. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.