Rémy Rigo-Mariani
email: remy.rigo-mariani@grenoble-inp.fr

Vincent Debusschere
email: vincent.debusschere@grenoble-inp.fr

Marie-Cécile Alvarez-Herault
email: marie-cecile.alvarez-herault@univ-grenoble-alpes.fr

A Modified DistFlow for Distributed Generation Planning Problems in Radial Grids

Keywords: Optimal Power Flow, DistFLow, Linearization, Optimal Planning I

This paper focuses on a simplified expression of the load flow constraints for the optimal planning of distributed generation (DG) in radial grids. The proposed approach lies on the conventional DistFlow equations improved with the consideration of linearized bi-directional losses and their impact on the voltage profiles. The method is validated on various radial test cases and allows to run time coupled power flows in order to consider dynamic constraints (e.g. battery state of chare) in short computational times. With the help of the proposed method, a DG placement problem is solved in less than 2 minutes with an exhaustive search over a 69 buses system and the operation is simulated along a single representative day. A scalability test is finally performed with longer time horizons and greater numbers of connected DG. The developed approach allows to run the operation of a 69 buses system over 2 months and with 20 connected DGs in less than 5 minutes.

The benefits of distributed generation (DG) integrated in conventional power systems have long been identified -with losses and emissions reduction, improved voltage profiles and enhanced system reliability as well as the opportunity to defer significant grid investments [START_REF] Jordehi | Allocation of distributed generation units in electric power systems: a review[END_REF]. Oftentimes, in the framework of DG planning studies, the objective is to find the best type, location and size of the considered resources that may be renewable based or fossil fueled generators and energy storage units [START_REF] Paliwal | Planning of grid integrated distributed generators:a review of technology, objectives and techniques[END_REF]. One of the main technical challenges encountered is to avoid prohibitive computational times. Indeed, when integrated design and management problems are investigated, the operation of the systems has to be simulated for a great number of configurations before finding the optimal DG plan [START_REF] Rigo-Mariani | A clusterized energy management with linearized losses in the presence of multiple types of distributed generation[END_REF]. Especially, when storage devices are considered, the system operation is estimated over a representative period (day, month, year). With energy constraints linked across the successive time steps, the power flow equations have to be simulated over the whole horizon, and typical AC power flow (ACPF) cannot be run successively for every time step, as seen in [START_REF] Ochoa | Distribution network capacity assessment: variable DG and Active networks[END_REF]. One way to leverage that complexity is to consider DC power flow (DCPF) constraints [START_REF] Villasana | Transmission Network Using Linear Programming[END_REF] at the cost of extensive simplifications that are not relevant for distribution networks, to which most of the small distributed resources are expected to be connected. In particular, reactive power and voltage drop are not considered. For radial systems, a simplified DistFlow approach allows to efficiently compute the active/reactive power flows while updating the voltage drop form the slack bus (typically the point of common coupling, PCC) to the termination node of every feeder [START_REF] Baran | Optimal capacitor placement on radial distribution systems[END_REF]. Linearized approaches of the DistFlow are encountered in planning studies or in the presence of distributed resources for faster computation [7] [8]. Similarly to the DCPF equations, those approaches lie on strong assumptions, the line losses being oftentimes neglected when computing the branch flow or bus voltages. This paper proposes a modified version of the linearized DistFlow to overcome those shortcomings. A particular attention is attached to the consideration of bi-directional active/reactive losses in the context of resources allocation that may incur backfeed power. The method is then validated over various test cases before a generic, simple DG planning problem is considered. The main contribution of the work are:

 A DistFlow formulation that considers linearized bidirectional losses and their impact on the voltage.

 The validation of the method for a simple allocation problem solved in less than 2 min in a 69 bus system.  A scalability test for longer planning horizons and greater numbers of distributed resources.

III. MODIFIED DISTFLOW

A. Classical DistFlow Equations

The original DistFlow formulation for radial systems is based on the iterative computation of the branch flows and node voltage from the slack bus down to the termination buses of the considered radial network (Fig. 1) [START_REF] Baran | Optimal capacitor placement on radial distribution systems[END_REF]. The classical equations in per unit are written while introducing the sets of upstream/downstream lines and buses with (1) and ( 2) written from every bus b perspective and (3) considered for every line l. As already mentioned, the power flow implemented in this paper is intended to simulate scheduled operations over a representative period, which explains the introduction of the temporal set T compared to traditional formulation. Also note that, for radial networks, the set of upstream lines attached to each bus only consists of a single branch. Finally, in the absence of distributed generation (i.e. injection at the slack bus only), the bus injections P b,t ,Q b,t are equal to the loads

P b,t 𝐿 ,Q b,t 𝐿 . ( ) ( ) ( ) ( ) ( ) () 2 2 , , , , , 2 () ,
.

u b u b d b u b u b db l t l t l t l t b t l l D b bt pq p p P r V         ( ) ( ) ( ) ( ) ( ) () 22 , , , , 2 () ,
.

u b u b d b u b u b db l t l t l t l t b t l l D b bt pq q q Q x V             ( ) ( ) () 2 2 , , 2 2 2 2 , , , , 2 , 2. . .
. d l u l ul l t l t b t b t l l t l l t l l bt pq V V r p x q r x V        
Typical linearization approaches [START_REF] Turitsyn | Distributed Control of Reactive Power Flow in a Radial Distribution Circuit with High Photovoltaic Penetration[END_REF] consist in neglecting the quadratic term that represent the active and reactive line losses in (1) and ( 2) respectively. At the same time the voltage at each bus is assumed to be close to the reference voltage V0. with (Vb,t ̵ V0) 2 ~ 0, which allows (3) to be rewritten following (4) and while neglecting the losses in the computation of the voltage and branch flows. However, the quadratic formulation of the losses is sometimes still considered as the objective function of the considered optimization problems. Similarly to [START_REF] Turitsyn | Distributed Control of Reactive Power Flow in a Radial Distribution Circuit with High Photovoltaic Penetration[END_REF] and [START_REF] Wang | Decentralized Energy Management System for Networked Microgrids in Grid-Connected and Islanded Modes[END_REF], those losses are then computed somewhat independently, which does not capture their impact on the voltage drops and line flows. The resulting load flow is then a linearly constrained quadratic problem.

 

( ) ( ) , , , , 0 .
. /

d l u l b t b t l l t l l t V V r p x q V     

B. Bi-Directionnal Line Flows and Losses

In the context of a resources allocation problem, the losses should not be entirely neglected as different solutions (resources location and size) are most of the time discriminated with regard to the system oveall efficiency. In addition, with the connection of distributed generation, lines flow are not necessary unidirectional from the slack bus to the termination nodes. Indeed, local injection at a given bus may result in reverse power flow in the absence of significant enough load consumption. In order to represent potential bidirectional line flows and associated losses, additional semi definite positive variables are introduced in this paper (refer to Fig. 2 and(5)), and the standard DistFlow equations are rewritten following ( 6)- [START_REF] Wang | Decentralized Energy Management System for Networked Microgrids in Grid-Connected and Islanded Modes[END_REF]. That formulation specifically allows to estimate the impact of the losses on the bus voltage and line flows, independently for both active and reactive contributions, and for every possible combination of flow directions.

, ,

t l t l t lt lt p p p q q q           and , , , , , , l t l
t l t l t lt lt p p p q q q                    ( ) ( ) ( ) , , , , l t l
d b d b u b u b b t db l t l t l t l t l D b p p p p P             ( ) ( ) ( ) ( ) () , , ( ) , , , , , ()
d b d b u b u b db L l t l t l t l t b t l D b q q q q Q                 ( ) , , , ()
/ d l d l b t b t l l t l t l l t l t V V r p p x q q V          ( ) , , , , , , 0 . .
The power balance at each node is further modified, so that the positive and negative contributions of the line losses are accounted as additional load at the start and end buses. Typically, the positive component of a line loss is considered as a surplus of load at the upstream bus while the negative component is added to the load at the downstream bus (( 9)). Finally, constraint [START_REF] Carrión | A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[END_REF] ensures that the line power and loss flow in the same direction.

, ( ) () () , ( ) () () , , , () , , , ()
l t d b ub db l t d b ub db L b t b t l t l D b L b t b t l t l D b P P p p Q Q q q                            , , , , , , , , ,
,

l t l t l t l t l t l t l t l t p p p p q q q q                       

C. Losses Linearization

This subsection focuses on the computation of the active and reactive losses introduced in the previous equations. Those losses are linearized following the typical piecewise to end bus [START_REF] Paliwal | Planning of grid integrated distributed generators:a review of technology, objectives and techniques[END_REF] to end bus (1)

b 3 l 1 from slack bus l 2 l 3 p l q l p l q l p l q l   2 1 2 2 3 2 1 ( ) 2 ( ) 3 ( )
, ( ) decomposition [START_REF] Carrión | A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem[END_REF]. The active and reactive branch flows are then represented by an additional set of positive variables, defined along the number of piece wise linear (PWL) segments. Following the linearization of the square function of a variable x displayed in Fig. 3, based on [START_REF] Cavalcante | Centralized Self-Healing Scheme for Electrical Distribution Systems[END_REF], the PWL segments have the same length, equal to the expected maximum value of x divided by the number of linear blocks (i.e. K segments here). Constraint [START_REF] Cavalcante | Centralized Self-Healing Scheme for Electrical Distribution Systems[END_REF] then computes the overall line flows from each block contribution and considering the maximum power. Finally, the losses are estimated following ( 12) and ( 13) with the computation of the square function for both active and reactive flows in every possible direction. Note that if [START_REF] Wang | Decentralized Energy Management System for Networked Microgrids in Grid-Connected and Islanded Modes[END_REF] allows to estimate the voltage drop, the loss estimations considers V0=1 p.u., on the other hand, in order to avoid non linarites.

u b u l d l l l D b l l b b b b     b 2 b 1 b 4 P b Q b P b Q b P b Q b P b Q b b 2 to end bus b 1 b 3 l 1 from slack bus l 2 p l p l q l q l p l p l q l q l δp l ,
, , ,

/ l t l k t l t l k t l k t l k t l t l k t l t l k t l k t l k t l k K k K l k K k K p p p p p p p K q q q q q q q K                                        , , , , , , , , , , , , , , , , , , , , , 0 , / , , 0 ,
. . 2. 1 . l k t l k t l k t l k t l t l t l l l kK p p p q q q r p p k K K V                                , , , , , , , , , , 2 0 .
. . 2. 1 . l k t l k t l k t l k t l t l t l l l kK p p p q q q x q q k K K V                          , , , , , , , , 2 0 .
One shortcoming of the considered linearization is that the obtained accuracy is highly impacted by the values chosen for the maximum line flows (both active and reactive), independently from the number of PWL blocks. Especially, the approximation of the square function is more accurate when the maximum expected flows are close to the actual values, which cannot be known a priori. Thus, this paper investigates two ways to set the values for the various 𝑝̅ l , 𝑞 ̅ l . At first, those values are set to a theoretical maximum line capacity that considers the sum of buses active/reactive loads penalized with a 'safety margin' of 50 % (i.e. α = 1.5 in (14)). That approach denoted as S0 then corresponds to a case in which all the feeders have the same rated capacity which is typically encountered in radial distribution networks operated in open loops.

   

, ,

. max and . max An alternative proposed here is to set the branch maximum flows p ̅ l , q ̅ l closer to the expected actual value. That approach denoted as S1, consists in doing a graph search, i.e. considering the active and reactive loads at all the buses located downstream each line while paying attention to potential feeder bifurcation (refer to Algo I with # denoting the cardinal function). As previously, the expected maximum flows are affected by a safety margin sufficient enough to guarantee the convergence of the power flow formulation (i.e. the actual line flows are expected to be within the specified boundaries with the given distribution of the bus load/injection).

L L l b t l b t b B b B p P q Q t T            

D. Validation Runs

The previous equations are entered as constraints of an optimization problem that represents the practical implementation of the considered power flow. To be consistent with typical OPF, the objective to minimize is the total system losses, indiscriminately on the active and reactive components (in per unit in (15)). The corresponding linear problem is written using YALMIP toolkit [START_REF] Lofberg | YALMIP: a toolbox for modelling and optimization in MATLAB[END_REF] and solved with CPLEX 12.10.0 (8 GB RAM, 1.6 GHz processor).

, , : min ( . .) ( . .)

l t l t t T l L obj p p u q p u       
At first, the modified DistFlow is developed and tested on a simple 7 buses system displayed in Fig. 4, before being scaled to 18, 33, 69 and 85 nodes networks, and while considering only a snapshot for the bus load (i.e. single element in the temporal set T). Also, only the import from the upstream grid is considered at first with no distributed resources connected to the considered systems. The results obtained are compared with the outputs of a conventional ACPF run with MATPOWER. Especially, three error criteria are defined to estimate the deviation in the voltages bus, active and reactive losses with regard to the ACPF results (denoted with the upper script . AC ). Those errors are normalized with regard to the mean deviation of the voltage computed over the total number of buses and the mean losses estimated over all the branches (( 16)). , .

, l t p    2 , l t p  ,1, l t p  ,2, l t p  , , l k t p  k=1 k=2 k=K l p   2 / l p K   2 4 / l p K   2 2 / l k p K   2. 1 . / l k p K 
1 1 # # # # AC b b V AC bB b bB AC AC l l l l P Q AC AC l L l L l l l L l L VV B V B p p q q L L p q L L                                         
Table I presents the results obtained for the different validation runs. Tests with the 7 buses systems show an increased model accuracy with greater numbers of PWL segments. Note that the error for the active and reactive line losses are equal for the case study as the xl/rl ratio is constant for all the branches. For the other test cases, the best performances (5 % error on average) are returned with K = 2 and while estimating the branches maximum flows considering the aggregated load at the downstream buses for every line. The great improvements (error divided by ten) observed when using S1 highlight the impact of the 𝑝̅ l , 𝑞 ̅ l in the considered linearization method. That approach should be furtherly investigated while adapting the 'safety margin' α, or considering other intputs for the branch expected maximum flow (e.g. DC power flow results). Fig. 5 displays the performances of the modified DistFlow applied to the 33 bus test case. Especially, different settings are considered in order to highlight the successive improvements (both in terms of losses and voltage errors) while increasing the number of PWL segments, and then computing the maximum line flow according to S1. Another noticeable results of Fig. 5 is that the rank of the buses with the greatest voltage drop and the branches with the greatest losses is the same when considering the reference ACPF and the modified DistFlow introduced in the paper. It suggests that, in the context of an optimal design, the DistFlow appropriately discriminates the best allocations of the distributed resource, even though the estimation of the losses and voltage may not be the most accurate.

IV. TEST CASE FOR RESOURCES ALOCATION

A. DG Alocation Problem Formulation

In this section, a generic, simple DG allocation problem is considered in order to investigate the computational performances of the proposed method. The IEEE 69 buses radial test case is considered (Fig. 6) and the objective of the study is to optimally determine the best site for a DG consisting of 500 kWp of solar panels and a 500 kW/ 500 kWh battery. The implemented DistFlow is then run every time a new site is investigated in order to simulate the system operation over a representative period. A single day is considered here with hourly profiles for the solar radiation as well as for the different types of loads (i.e. industrial, commercial and residential for a total of 48 distinct patterns). With given profiles for the load and generation, the only degree of freedom of the system is the scheduling of the storage over the simulated period. The problem formulation described in the previous section is then appended to integrate the operating constraints for the battery. A typical linear formulation is used while discriminating the charge and discharge powers of the battery to compute the state of charge with a given efficiency [START_REF] Pandžić | Nearoptimal method for siting and sizing of distributed storage in a transmission network[END_REF]. The set of constraints (17) then ensures the fulfilment of the power/energy limitations and From 23.1 % to 2.8 % in the voltage error

From 462.5 % to 5.3 % in the active losses error enforces any storage device to come back at its initial state of charge SOC at the end of the simulated day (typically 50 %).

 

, ,

                            
In addition, the active power balance at each bus is modified following (18) in order to take the solar and battery injections into account. A single solar/storage installation is considered. Thus, the battery variables and parameters for the PV generation are only considered for the connection bus, with the use of appropriate matrixes not described in this paper. The objective of the allocation problem is to reduce the system losses. The objective (15) remains unchanged with the minimization of the system losses, consisting not only of the grid effects but also of the storage loses implicitly captured in (18). Ultimately the optimal scheduling problem is run over a representative day with 25,000 variables and a little more than 50,000 linear constraints for an average computational time of 1 to 2s.

, ( ) () () , , , , , , () l
               

B. Obtained Resuls

The optimization method in charge of determining the best location is not in the scope of the paper. Typically, evolutionary or heuristic approaches or heuristics are considered in order to investigate the best potential sites. With the fast computation allowed by the implemented DistFlow, an exhaustive search investigates the connection of the PV/battery system at every node of the 69 buses system in less than 2 minutes. The operation of the battery is then optimized in every case over the simulated day and the system losses are compared to a base case in which no distributed resources are installed (i.e. daily load supplied by the upstream grid only). Fig. 6 displays the obtained results with three areas defined according to the loss reduction compared to the base case scenario. Greater efficiencies are reached when the resources tend to be installed at the end of the longest feeder (3-6 %) and closer to the most significant point of consumption (i.e. the industrial load here) with more than 8 % loss reduction for the simulated day. It is important to note that the estimated losses reduction are mostly (> 75 %) allowed by the integration of the solar generation. Indeed, the storage does not participate that much to the savings due to its internal losses and the energy conservation constraint (final SOC). The loss reduction allowed by the storage corresponds to the peak shaving of the total injected power. As mentioned, the best configuration is obtained with the installation connected to bus 65, at the end of the feeder hosting the heaviest customer. Especially, the solar generation during the daily hours tends to decreases the voltage drop by more than 0.01 p.u. compared to the base case scenario (Fig. 7a). With the significant amount of locally injected energy, the power flowing through the incident branch (i.e. from bus 64 to bus 65) takes negative values during the sun peak hours (i.e. reverse power) as observed on Fig. 7b. Without any consideration of energy prices or battery degradation, the optimal operation of the storage follows the dynamics of the solar generation respectively to the load profiles. Part of the solar is locally self-consumed to charge the battery during the day while the morning and evening peak load tends to be lowered with appropriate discharge rates of the storage (Fig. 7c).

C. Scaliability and Computational Performances

The implemented solution then allows fast computation and the solution is quickly found with the simple validation study considered above. However, problems encountered in the literature and at the grid planner level may display higher degree of complexity: wider systems in terms of nodes, longer planning horizons, finer time resolutions, greater numbers of distributed resources, uncertain parameters, non linearities, etc… Thus, a last set of runs is performed in order to test the scalability of the proposed approach. As the full spectrum of complexity cannot be investigated, the authors Energy injected upstream focus here on the duration of the simulated period as well as the numbers of installed resources. The number of time steps T is then increase from 24 (i.e. one day here at 1 h resolution) to 2160 (i.e. ~ 3 months), while the number of installed DG varies up to fifty units. A maximum computational time of 5 min arbitrarily chosen. As already mentioned, the solving duration of the system operation should not be too significant as several runs are likely to be executed for optimal DG placement problems. Table II displays the results obtained with "N.A." in case the time limit is exceeded. For the considered 69 buses system the modified DistFlow allows to compute up to 3 months at an hourly resolution and with 10 different DG connected at 10 different buses. It is worth mentioning that the DG assets are assumed to be controlled in a centralized fashion here, which might not be the case in actual deployment due to technical and regulatory limitations. The main objective here is merely to test the mathematical scalability of the proposed approach. Globally, with the computational capabilities considered in the study, the time limit to solve the fully linear problem is reached for around 2 million variables or more. That number of variables depends on the size of the system (B buses), the time horizon (T time steps) as well as the number of DG resources denoted as N. Finally (19) allows to plot an expected feasible region (Fig. 8) that represents the size of the problem with an acceptable solving time. In theory the developed method would allow to simulate a monthly operation of a 100 buses system with a hundred connected DG. This paper successfully implements a linearized DistFlow that intent to be used in grid simulation for DG planning studies. Compared to conventional linearized approaches, the formulation presented here allows to consider the effects of the losses on the voltage drop and discriminates the flow direction of both active and reactive powers. The method is validated and tested on various systems before a generic DG planning problem is solved on a 69 buses network in less than 2 minutes with an exhaustive search. Scalability tests of the implemented linear algorithm show its ability to solve more complex problems on longer time horizons. Future works consist in taking advantage of that fast computation to investigate more advanced planning strategies, multi objectives approaches, different types of DG or more complex control modes.

Fig. 1

 1 Fig. 1 Single line diagram of a radial network for original DistFlow formulation

Fig. 2

 2 Fig. 2 Introduction of variables for the line losses and bidirectional flows

Fig. 3

 3 Fig.3Piewise linearization of quadratic functions applied to the line flow[START_REF] Cavalcante | Centralized Self-Healing Scheme for Electrical Distribution Systems[END_REF]

Fig. 4 7

 4 Fig. 4 7 buses systemsa) 7 bus Ab) 7 bus B 100 . 1 # 1 # 100 100 . , . 1 1 # # # #

Fig. 5

 5 Fig. 5 Validation runs for 33 bus test casea) bus voltageb) active losses

  ranked in decreasing active losses K=1maximum flows with S 0 K=2maximum flows with S 0 K=1maximum flows with S 1

Fig. 6

 6 Fig. 6 Considered 69 bus system and allocation results

Fig. 8

 8 Fig. 8 Feasible region with a solving time lower or equal at 5 min

TABLE I

 I

		.	RESULTS OF VALIDATION RUNS
		Maximum line flow S0	Maximum line flow S1
		K=1	K=2	K=3	K=1	K=2	K=3
	7 bus A
	ΔV (%)	4.5	0.9	0.5	1.8	0.4	0.3
	ΔδP (%)	106.6	22.1	9.38	44.5	9.1	2.8
	ΔδQ (%)	106.6	22.1	9.38	44.5	9.1	2.8
	7 bus B
	ΔV (%)	8.3	2.6	1.1	2.4	0.6	0.3
	ΔδP (%)	130.7	37.3	12.4	42.3	7.4	4.2
	ΔδQ (%)	130.7	37.3	12.4	42.3	7.4	4.2
	ΔV (%)	39.5	6.9	3	3.2	2	3.2
	ΔδP (%)	437.4 161.7	73.3	19.3	9.5	18.7
	ΔδQ (%)	198.7 188.1	18.4	22.6	6.15	15.4
	33 bus
	ΔV (%)	23.15	6.9	2.2	1.75	2.8	3.2
	ΔδP (%)	462.5 161.8	80.4	35.9	5.3	6.9
	ΔδQ (%)	519	188.1	95.4	35.1	4.7	7.7
	69 bus
	ΔV (%)	19.5	5.5	2.2	1.2	2.2	2.7
	ΔδP (%)	414.9 139.6	63.5	35.6	5.2	8.2
	ΔδQ (%)	425.6 145.3	68.8	35.1	6.1	7
	85 bus
	ΔV (%)	26.15	6.2	1.4	2.9	4.6	5.3
	ΔδP (%)	377.3 118.9	66.8	27.3	6.5	11.8
	ΔδQ (%)	316.6	90.2	50.3	28	6.2	11.1


P

hotosystem I (PSI) is an integral component in the lightdependent reactions of oxygenic photosynthesis in cyanobacteria, algae and plants 1 . Upon illumination, PSI accepts an electron from plastocyanin or cytochrome c and transfers this electron to its major acceptor, ferredoxin. Whereas algal and plant PSI have been reported to exist mostly as monomers [START_REF] Gardian | Organisation of photosystem i and photosystem iI in red alga Cyanidium caldarium: encounter of cyanobacterial and higher plant concepts[END_REF][START_REF] Watanabe | Novel supercomplex organization of photosystem I in Anabaena and Cyanophora paradoxa[END_REF][START_REF] Ben-Shem | Crystal structure of plant photosystem I[END_REF][START_REF] Kouril | Photosystem I: a search for green plant trimers[END_REF][START_REF] Veith | The monomeric photosystem I-complex of the diatom Phaeodactylum tricornutum binds specific fucoxanthin chlorophyll proteins (FCPs) as light-harvesting complexes[END_REF] , and recently as dimers in spinach thylakoid membrane [START_REF] Wood | Dynamic thylakoid stacking regulates the balance between linear and cyclic photosynthetic electron transfer[END_REF] , cyanobacterial PSI has been reported to exist as a trimer in most studies. Trimeric PSI structure has been observed in the cyanobacteria Synechococcus [START_REF] Boekema | Evidence for a trimeric organization of the photosystem I complex from the thermophilic cyanobacterium Synechococcus sp[END_REF] and in diverse filamentous and unicellular cyanobacteria [START_REF] Shubin | Isolation from Spirulina membranes of 2 photosystem i-type complexes, one of which contains chlorophyll responsible for the 77-K fluorescence band at 760 Nm[END_REF][START_REF] Shubin | Trimeric forms of the photosystem I reaction center complex pre-exist in the membranes of the cyanobacterium Spirulina platensis[END_REF][START_REF] Tsiotis | Isolation and structural characterization of trimeric cyanobacterial photosystem I complex with the help of recombinant antibody fragments[END_REF][START_REF] Garczarek | Isolation and characterization of photosystem I from two strains of the marine oxychlorobacterium Prochlorococcus[END_REF][START_REF] Bibby | Low-light-adapted Prochlorococcus species possess specific antennae for each photosystem[END_REF][START_REF] Boekema | A giant chlorophyll-protein complex induced by iron defciency in cyanobacteria[END_REF][START_REF] Tucker | Analysis of chlorophyll-protein complexes from the cyanobacterium Cyanothece sp. ATCC 51142 by non-denaturing gel electrophoresis[END_REF][START_REF] Casella | Dissecting the native architecture and dynamics of cyanobacterial photosynthetic machinery[END_REF][START_REF] Macgregor-Chatwin | Lateral segregation of photosystem I in cyanobacterial thylakoids[END_REF] , including the most primitive known cyanobacterium, Gloeobacter violaceus PCC 7421 [START_REF] Mangels | Photosystem I from the unusual cyanobacterium Gloeobacter violaceus[END_REF] . Early protein crystallography structures corroborated these findings of trimeric PSI in cyanobacteria [START_REF] Almog | Monomeric and trimeric forms of photosystem I reaction center of Mastigocladus laminosus: crystallization and preliminary characterization[END_REF][START_REF] Jordan | Three-dimensional structure of cyanobacterial photosystem I at 2.5 A resolution[END_REF] , such as the structure of trimeric PSI from the thermophilic cyanobacteria Thermosynechococcus elongatus BP-1 [START_REF] Jordan | Three-dimensional structure of cyanobacterial photosystem I at 2.5 A resolution[END_REF] . Because of these early reports, it was assumed that PSI in all cyanobacteria was trimeric, in contrast to the monomeric form found in plants and algae. Recently, a tetrameric form of PSI was observed in the cyanobacteria Nostoc sp. PCC 7120 [START_REF] Watanabe | Novel supercomplex organization of photosystem I in Anabaena and Cyanophora paradoxa[END_REF][START_REF] Watanabe | Attachment of phycobilisomes in an antennaphotosystem I supercomplex of cyanobacteria[END_REF] and Chroococcidiopsis sp. TS-821 (TS-821) [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF][START_REF] Semchonok | Cryo-EM structure of a tetrameric cyanobacterial photosystem I complex reveals novel subunit interactions[END_REF] , challenging the notion of PSI existing only as a trimer in cyanobacteria. Nevertheless, the PSI tetramer has not been considered as a major oligomeric state in cyanobacteria. Although tetrameric PSI is known to occur in two species, the mechanism controlling the oligomeric assembly and stability remain unknown. Furthermore, the physiological and evolutionary significance of this structural change has yet to be elucidated. A recent cryo-EM structure of PSI tetramer from TS-821 showed that tetrameric PSI is actually a dimer of dimers with two different interaction interfaces between monomers [START_REF] Semchonok | Cryo-EM structure of a tetrameric cyanobacterial photosystem I complex reveals novel subunit interactions[END_REF] . This structure suggests subtle changes in the placement of the central subunit PsaL, yielding changes in helical bundling that has been implicated as critical in the formation of PSI trimers.

In light of the recent discovery of tetrameric PSI, we investigated a large and diverse set of cyanobacteria to characterize the oligomeric state of PSI structure throughout the cyanobacterial phylum. To investigate an underlying mechanism for tetrameric PSI formation, we probe the correlation between PSI oligomeric states, PsaL sequence and genomic structure using bioinformatics and biochemical techniques. Finally, although the physiological significance of the PSI tetramer is not well understood in cyanobacteria, we have explored several growth conditions that may alter the formation of the tetramer. Our findings indicate that exposure to high light intensity induces a significant increase in PSI tetramer formation, while also increasing carotenoid content. These results shed light on the role and function of higher order oligomers of PSI and provide insight into the possible cyanobacterial lineage associated with the origin of the plastid.

PSI oligomeric states in cyanobacteria

To understand how PSI evolved from its cyanobacterial multimeric forms to the monomeric form in algae and plants, a comprehensive and unbiased understanding of the cyanobacterial PSI oligomeric forms is needed. This requires an investigation of the PSI structures that includes diverse cyanobacteria. Here, we have investigated the oligomeric states of PSI in 61 cyanobacteria including 34 heterocystforming cyanobacteria and 5 close unicellular relatives, as well as a set of 22 widely divergent unicellular and filamentous cyanobacteria for comparison (Supplementary Data). For most heterocyst-forming cyanobacteria and their close unicellular relatives (collectively referred to as HCR), blue native polyacrylamide gel electrophoresis (BN-PAGE)

Physiological and evolutionary implications of tetrameric photosystem I in cyanobacteria

Meng Li 1,2,8 , Alexandra Calteau 3 , Dmitry A. Semchonok 4 , Thomas A. Witt 1 , Jonathan T. Nguyen 1 , Nathalie Sassoon 5 , Egbert J. Boekema [START_REF] Ben-Shem | Crystal structure of plant photosystem I[END_REF] , Julian Whitelegge 6 , Muriel Gugger 5 and Barry D. Bruce 1,2,7 * Photosystem I (PSI) is present as trimeric complexes in most characterized cyanobacteria and as monomers in plants and algae. Recent reports of tetrameric PSI have raised questions regarding its structural basis, physiological role, phylogenetic distribution and evolutionary significance. Here, we examined PSI in 61 cyanobacteria, showing that tetrameric PSI, which correlates with the psaL gene and a distinct genomic structure, is widespread among heterocyst-forming cyanobacteria and their close relatives. Physiological studies revealed that expression of tetrameric PSI is favoured under high light, with an increased content of novel PSI-bound carotenoids (myxoxanthophyll, canthaxanthan and echinenone). In sum, this work suggests that tetrameric PSI is an adaptation to high light intensity, and that change in PsaL leads to monomerization of trimeric PSI, supporting the hypothesis of tetrameric PSI being the evolutionary intermediate in the transition from cyanobacterial trimeric PSI to monomeric PSI in plants and algae.

showed the presence of tetrameric and/or dimeric PSI, as well as the abundant monomeric PSI, as the major PSI oligomers (Fig. 1a and Supplementary Fig. 1). Similarly, BN-PAGE analysis of T. elongatus BP-1 and Synechocystis PCC 6803 consistently indicated the presence of trimeric PSI (Fig. 1a and Supplementary Fig. 1). Specifically, 30 out of 34 heterocyst-forming cyanobacteria, including poorly studied species such as Spirirestis rafaelensis UTEX B 2660 (Fig. 1a and Supplementary Fig. 1n), appeared to contain tetrameric or dimeric PSI (Supplementary Data). To verify that the altered electrophoretic mobility was truly indicative of the PSI tetramer, PSI oligomers of several species were examined using transmission electron microscopy (TEM), confirming their tetrameric structure (Fig. 1b and Supplementary Fig. 1). Surprisingly, a few heterocyst-forming cyanobacteria, such as Anabaena inaequalis UTEX B381, Calothrix membranacea UTEX B379 and Cylindrospermum licheniforme UTEX B2014, possessed only monomeric PSI (Supplementary Fig. 1u). Nostoc sp. PCC 9335 was the only species of cyanobacteria in the study that had significant amounts of both trimeric and dimeric forms of PSI (Supplementary Fig. 2a). Analysis of the unicellular cyanobacteria that are closely related to the heterocyst-forming cyanobacteria, including TS-821, Synechocystis sp. PCC 7509 and Gloeocapsa sp. PCC 7428 (Supplementary Fig. 1a,b), showed that they contain more tetrameric, dimeric and monomeric PSI than trimeric PSI. The other two species of Chroococcidiopsis that we tested, Chroococcidiopsis thermalis PCC 7203 (Fig. 1a and Supplementary Fig. 1c) and Chroococcidiopsis sp. PCC 7434 (Supplementary Fig. 2a), contained primarily monomeric PSI with some dimeric PSI. Collectively, these results revealed that besides monomeric PSI, tetrameric and dimeric PSI rather than trimeric PSI comprise the majority of PSI oligomers in the HCR. Trimeric PSI was either not detectable or only present as a minor species in cyanobacteria placed in this clade (Supplementary Data), suggesting that there is a structural and potentially physiological basis for the tendency to form dimeric or tetrameric PSI in these related cyanobacteria.

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In contrast to HCR, most other cyanobacteria that we studied contained predominantly trimeric PSI (Fig. 1c, Supplementary Figs. 1 and2 and Supplementary Data). This trimeric form of PSI can be confirmed by TEM, as shown for PCC 6712 (Fig. 1d).

Among this group of PSI trimer-containing cyanobacteria were T. elongatus and Synechocystis PCC 6803, in which the presence of trimeric PSI has been confirmed by crystallography [START_REF] Semchonok | Cryo-EM structure of a tetrameric cyanobacterial photosystem I complex reveals novel subunit interactions[END_REF][START_REF] Malavath | Structure and function of wild-type and subunit-depleted photosystem I in Synechocystis[END_REF] . Many of the other cyanobacteria studied were also observed to contain trimeric PSI (Fig. 1c, Supplementary Figs. 1 and2 and Supplementary Data). Occasionally, BN-PAGE indicated more unusual PSI oligomers in these diverse cyanobacteria. For example, a potential PSI hexamer was observed in Chroococcidiopsis sp. PCC 6712, in equilibrium with the primary PSI trimer in vitro (Fig. 1c,d and Supplementary Fig. 1c,d). Although the BN-PAGE reveals some other minor PSI oligomeric forms in these strains, such as the PSI dimer in Microcystis sp. PCC 7806 (Fig. 1c and Supplementary Fig. 2a,b and Supplementary Data), and a potential PSI tetramer in Planktothrix paucivesiculata PCC 8926 (Supplementary Fig. 2c), the predominant PSI oligomer in these diverse cyanobacteria is trimeric. In contrast to other PSI trimer-containing strains, the PSI monomer was clearly dominant in Chamaesiphon minutus PCC 6605 and Leptolyngbya sp. PCC 7124, which harboured substantial amounts of PSI dimers and monomers (Fig. 1c and Supplementary Fig. 2a).

Correlation of PsaL and PSI oligomers

Previous structural studies on cyanobacterial PSI have identified different PsaL-PsaL interactions within the trimeric and tetrameric PSI oligomers [START_REF] Jordan | Three-dimensional structure of cyanobacterial photosystem I at 2.5 A resolution[END_REF][START_REF] Semchonok | Cryo-EM structure of a tetrameric cyanobacterial photosystem I complex reveals novel subunit interactions[END_REF] , shown schematically in Figs. 1b,d. Previous work has identified not only subtle differences in the protein sequence of the PsaL subunits, but also a change in the genomic organization and genomic location of psaL in the TS-821 cyanobacterial genome [START_REF] Almog | Monomeric and trimeric forms of photosystem I reaction center of Mastigocladus laminosus: crystallization and preliminary characterization[END_REF] . In the context of the larger group of cyanobacteria presented here, we investigated whether this correlation holds true across the different PSI oligomeric forms identified. To allow visualization of the distribution of PSI oligomers within cyanobacteria, we localized the distribution of psaL in relation to psaI, psaF and psaJ genes on a species tree (Fig. 2 and Supplementary Fig. 3a). We analysed the psaL distribution of cyanobacteria within a known genomic dataset and 14 additional heterocyst-forming strains. In all HCR, the psaL gene is located downstream of psaF and psaJ (psaF-psaJ-psaL) (Fig. 2 and Supplementary Fig. 3b), in agreement with an earlier report [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] . This PsaL encoded by psaF-psaJ-psaL, along with the prevailing tetrameric and dimeric PSI, clearly delineates the clade of cyanobacteria, namely HCR, represented by the green lines and the inset in Fig. 2.

In cyanobacteria that fall outside of the HCR clade, psaL is frequently flanked by psaI (psaL-psaI) or, in a few cases, it is found as psaF-psaJ-psaL or isolated from other psa genes altogether (Fig. 2 and Supplementary Fig. 3a). Besides the 9 strains with reported PSI trimers, BN-PAGE analyses of the PSI oligomers identified an additional 16 strains with trimeric PSI (shown in blue text, Fig. 2). These PSI trimer-bearing cyanobacteria, spreading out in the cyanobacteria phylum outside HCR, cover each major branching point and clade. This group also includes the well characterized reference strains T. elongatus and Synechocystis PCC 6803. Although the absence of PsaL, encoded by psaF-psaJ-psaL, is clearly correlated to the presence of PSI trimer in cyanobacteria (Fig. 2), the presence of PsaL does not always indicate a tetrameric or dimeric PSI. The phylogenetic analysis of PsaL revealed that PsaL encoded by psaF-psaJ-psaL falls into different lineages, with those in HCR being a distinct clade (dark green in Supplementary Fig. 3b).

Some cyanobacteria with tetrameric PSI, such as Fischerella muscicola PCC 7414, also harbour two copies of the psaL gene, one copy organized as psaF-psaJ-psaL and the second organized as psaL-psaI (Fig. 2 and Supplementary Fig. 3a). The copy in psaF-psaJ-psaL resembles HCR and indicates tetrameric or dimeric PSI (Supplementary Fig. 3b, coloured in dark green), while the second form of PsaL (in the psaL-psaI locus) is closely related to the recently identified far-red-light-responsive PsaL found in monomeric PSI in Leptolyngbya sp. strain JSC-1 [START_REF] Gan | Extensive remodeling of a cyanobacterial photosynthetic apparatus in far-red light[END_REF] (Supplementary Fig. 3b, coloured in red) [START_REF] Gan | Extensive remodeling of a cyanobacterial photosynthetic apparatus in far-red light[END_REF] . This indicates that some of the HCR may express this psaL gene (in psaL-psaI) during far-red-light acclimation.

To verify a direct correlation between a specific PsaL protein and the formation of the PSI tetramer, we performed subunit analyses of the isolated PSI trimer and tetramer from three different cyanobacteria, TS-821, PCC 7428 and PCC 7414, using liquid chromatography with tandem mass spectrometry (LC-MS/MS). Of note, for all three species, the same PsaL protein, encoded by psaL in psaF-psaJ-psaL, was observed in both tetrameric and trimeric PSI (Supplementary Fig. 4). Moreover, genome sequencing of TS-821 revealed only a single form of psaL. Although PCC 7414 encodes two copies of the psaL gene (Fig. 2), only the PsaL encoded by psaL in the psaF-psaJ-psaL structure was found in either PSI form isolated under our experimental conditions. These results reinforced the possibility that the psaL encoded in psaL-psaI in PCC 7414 is an example of a far-red-light-responsive PSI gene [START_REF] Gan | Extensive remodeling of a cyanobacterial photosynthetic apparatus in far-red light[END_REF][START_REF] Gan | Adaptive and acclimative responses of cyanobacteria to far-red light[END_REF] . These farred-light-responsive genes have a distinct genomic organization. Moreover, in a maximum-likelihood tree of PsaL, the group of farred-light-responsive forms of PsaL form a distinct clade (red text, Supplementary Fig. 3b). Phylogenetic analysis revealed that psaL from psaF-psaJ-psaL loci of HCR form a single clade. However, the observation that the same PsaL is observed in both tetrameric and trimeric PSI in TS-821, PCC 7428 and PCC 7414 suggests that the unique PsaL encoded in psaF-psaJ-psaL is necessary, but not sufficient, to direct PSI tetramer formation.

PsaL replacement affects PSI oligomerization

To investigate precisely which structural property of PsaL is key to the determination of the PSI oligomeric state, we performed gene-replacement experiments in the mesophilic cyanobacteria Synechocystis sp. PCC 6803. Replacing wild-type (WT) PsaL in Synechocystis sp. PCC 6803 by homologous recombination with either TS-821 PsaL or Arabidopsis PsaL resulted in monomeric PSI in both mutants (Fig. 3a,b). Western blotting of these monomeric forms of PSI showed that they too contained PsaL bound to PSI (Fig. 3c,d). This observation suggests that the monomerization of PSI in these transgenic lines is not due to the lack of PsaL expression and/or assembly. These findings suggest that small differences in the PsaL structure alone can lead to the monomerization of trimeric PSI in cyanobacteria, as found with the predominantly monomeric PSI in PCC 6605 (Fig. 1c and Supplementary Fig. 2a).

Previous work on TS-821 suggested that the loop in PsaL between the second and third transmembrane helices might have key roles in PSI oligomerization and PsaL evolution [START_REF] Almog | Monomeric and trimeric forms of photosystem I reaction center of Mastigocladus laminosus: crystallization and preliminary characterization[END_REF] . The structure of this loop was not resolved in the trimeric PSI crystal structure from T. elongatus (Protein Data Bank ID 1JB0), but subsequent improved plant PSI monomer structures showed the interaction between this loop sequence and PsaH [START_REF] Qin | Structural basis for energy transfer pathways in the plant PSI-LHCI supercomplex[END_REF][START_REF] Mazor | The structure of plant photosystem I super-complex at 2.8 A resolution[END_REF] . TS-821 PsaL has an unusual multiproline motif in this loop sequence; we therefore examined the conservation of this loop sequence between PsaL second and third transmembrane helices in all HCR in our study in relation to their PSI oligomeric states (Supplementary Fig. 5). Using a logo plot to analyse these regions of all 38 HCR PsaLs, we identified a conserved proline-rich motif, frequently occurring as NPPXP followed by PNPP (Supplementary Fig. 5). Most of the PsaLs from species outside the HCR clade with trimeric PSI lack this motif. However, this motif is shared by both copies of PsaL in PCC 6605 (Supplementary Fig. 5) which has predominantly monomeric PSI (Fig. 1c and Supplementary Fig. 2a). These observations suggest a similar mechanism of trimeric PSI destabilization in PCC 6605, involving a multiproline motif similar to the one in this region of PsaL in the heterocyst-forming cyanobacteria.

Influence of environmental factors

The formation of PSI tetramers is restricted to a specific subset of cyanobacteria; however, although we were able to 'map' this trait to the HCR, there was no clear understanding of the physiological or evolutionary role driving this change in oligomerization. Since most heterocyst-forming cyanobacteria have tetrameric PSI, the we investigated the influence of nitrogen sources and presence of heterocysts on PSI tetramer formation. We grew three heterocyst-forming strains (PCCC 7414, PCC 7120 and PCC 7122) in both nitrate depleted BG-11 media (BG-110) and BG-11 supplemented with NH 4 + . On the basis of the similar PSI pattern observed with BN-PAGE (Supplementary Fig. 6a) as observed in the strains cultured in standard BG-11 media (Supplementary Fig. 1j,k), the results indicate that the nitrogen sources did not affect the presence of tetrameric PSI.

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Similar results were obtained for Fischerella sp. UTEX LB 1829 (BG-110 vs BG-11, Supplementary Fig. 1e). These strains did not develop heterocysts with supplemented NH 4 + , indicating the presence of tetrameric PSI in vegetative cells. The presence of tetrameric PSI in unicellular strains such as TS-821, PCC 7509 and PCC 7428 (Fig. 1a and Supplementary Fig. 1a,b) also agrees with a PSI tetramer independent from heterocyst development, even though tetrameric PSI was shown in heterocysts [START_REF] Cardona | Electron transfer protein complexes in the thylakoid membranes of heterocysts from the cyanobacterium Nostoc punctiforme[END_REF] . In the case of Nodularia PCC 73104, the small amount of PSI tetramer was only observed in BG-11 medium (Supplementary Fig. 1j), whereas the addition of NH 4 + or salt in the culture media appeared to diminish the tetrameric PSI (Supplementary Fig. 6c). The special case of Nodularia PCC 73104 needs more studies to elucidate the significance of its response, since Nodularia are usually found in brackish or oceanic environments and some strains do not abolish their heterocysts in the presence of NH 4 + (refs. [START_REF] Vintila | Ammonium ions inhibit nitrogen fixation but do not affect heterocyst frequency in the bloom-forming cyanobacterium Nodularia spumigena strain AV1[END_REF][START_REF] Vintila | Variability in the response of the cyanobacterium Nodularia spumigena to nitrogen supplementation[END_REF] ).

Growth temperature had little, if any, effect on the presence of tetrameric or trimeric PSI (Supplementary Fig. 6b) on the four different cyanobacteria investigated. With respect to salinity, we cultured two strains of Nodularia-heterocyst-forming cyanobacteria isolated from brackish or saline water-in both fresh water and artificial seawater nutrient medium III (ASNIII); we observed little difference in the amount of the tetramer/dimer (Supplementary Fig. 6c). Salinity also had no effect on the presence and amount of trimeric PSI in Pseudanabaena sp. B SP48 (Supplementary Fig. 2e). Together these results suggest that none of the factors presented thus far, i.e. nitrogen source, heterocyst development, temperature stress or salinity, have an effect on the formation of tetrameric and trimeric PSI.

PSI tetramer in response to light intensity

In contrast to the other environmental factors we investigated, altering the light intensity during growth had a clear effect on the ratio of the PSI oligomeric forms. Our study on TS-821 showed that in response to a change from low light (LL) to high light (HL) intensity, there was accumulation of tetrameric PSI and a decrease in trimeric PSI [START_REF] Semchonok | Cryo-EM structure of a tetrameric cyanobacterial photosystem I complex reveals novel subunit interactions[END_REF] . To confirm that light intensity was a common factor determining PSI tetramer/trimer ratio, we investigated the HL response of other cyanobacterial strains. We observed an increase in quantity and stability of the tetrameric PSI for both PCC 7428 and PCC 7414 under HL conditions (Fig. 4). In addition, the amount of trimeric PSI was much higher for PCC 7428 when grown at low light (LL) levels (Fig. 4a,b). The difference observed in PCC 7414 under HL versus LL was slightly smaller than that observed in PCC 7428 (Fig. 4c,d) possibly due to self-shading within the intertwined filaments of PCC 7414 (Supplementary Fig. 7). Nevertheless, these results point towards a common HL response, in which tetrameric PSI accumulates and trimeric PSI is suppressed in strains having both forms of the PSI oligomers. Therefore, it is reasonable to speculate that tetrameric PSI is better adapted to HL than trimeric PSI.

We next performed a more detailed study of PSI oligomer profiles for TS-821 cultured under several different light intensities, which supported the hypothesis that tetrameric PSI is an adaption to HL. As shown in Fig. 5, the stability and relative quantity of the PSI tetramer in TS-821 increased as the intensity of light was increased from 50 to 800 μmol m -2 s -1 (Fig. 5a-g). Plotting the relative amount of PSI tetramer (percentage over all PSI oligomers) against light intensity showed that the apparent maximum increased with light intensity (0.4% n-dodecyl-β-d-maltopyranoside (DDM); Fig. 5g). The stability of PSI tetramer, indicated by the relative quantity at higher detergent concentration (0.8% DDM; Fig. 5g), was also enhanced by higher light intensities. By contrast, the relative amount of trimeric PSI decreased almost linearly as the light intensity increased (Fig. 5h). This ability to alter the oligomeric form of PSI is not found in all species of Chroococcidiopsis, as indicated by the observation that the absence of PSI tetramer in PCC 7203 was not affected by light intensity (Supplementary Fig. 6d).

To investigate whether tetrameric PSI in TS-821 undergoes a shift in pigment composition, or biochemical or biophysical changes under different light intensities, we compared absorption spectra and 77K fluorescence spectra of different PSI oligomers isolated from cells grown under different light conditions (Fig. 6a,b and Supplementary Fig. 8). Whereas the 77K emission spectra of these isolated PSI oligomers did not show significant differences (Supplementary Fig. 8), tetrameric PSI produced under HL exhibited additional absorption in the range around 440-560 nm compared with tetrameric PSI produced under LL (Fig. 6a,b). The difference spectrum between these two samples showed at least three discernable absorption peaks (450, 490 and 520 nm) (Fig. 6b). The absorption spectrum of the LL PSI tetramer also had a similar additional absorption around 400-500 nm when compared with the PSI trimer under LL (Supplementary Fig. 8).

Interestingly, when the PSI tetramer was treated with 5% DDM and dissociated into dimers, a substantial amount of carotenoids stayed in the top layer of the sucrose gradient after separation by centrifugation (Fig. 6c). It is very likely that these carotenoids are associated with the interdimer interface and may even reside in the centre of the tetrameric structure, only being released upon dissociation. Interestingly, the absorption spectrum of released carotenoids (Fig. 6d) resembled the increased absorbance observed in the HL tetramer (Fig. 6b). Moreover, spectral analysis of the tetrameric PSI in both TS-821 and PCC 7414 reveal an increase in absorption in the range of 400-550 nm compared with the PSI dimer and trimer (Supplementary Fig. 9c,d), resembling the absorption spectrum of the interdimer carotenoids (Fig. 6d). These results suggest that tetrameric forms of PSI are generally rich in carotenoids compared to trimeric and dimeric forms of PSI. When these interdimer carotenoids were isolated and analysed by high-performance liquid chromatography, we identified novel PSI cofactors: myxoxanthophyll, canthaxanthin and echinenone, in addition to the known cofactors chlorophyll (Chl) and β-carotene (Fig. 6e). The semi-quantitative comparison of the HL PSI tetramer and LL PSI tetramer also revealed that tetrameric PSI harboured more myxoxanthophyll, canthaxanthin and echinenone, and less β-carotene (per Chl) under HL (Fig. 6f).

Discussion

Our results indicate that tetrameric PSI is a characteristic shared by most, if not all, heterocyst-forming cyanobacteria and their closest unicellular relatives. The distribution of tetrameric PSI in this clade of cyanobacteria indicates a shared physiological characteristic between the two morphologically distinct cyanobacteria. The previous classification of PCC 7428 and TS-821 would place these cyanobacteria in section II on the basis of their reproduction by multiple fission giving rise to baeocytes [START_REF] Rippka | Generic assignments, strain histories and properties of pure cultures of cyanobacteria[END_REF] , but our current work on these PSI dimer and tetramer containing unicellular cyanobacteria support a different placement. Phylogenetic analyses based on the 16S rRNA gene as well as a more universal set of conserved genes suggest that these tetramer-forming cyanobacteria are closely related to heterocyst-forming cyanobacteria [START_REF] Fewer | Chroococcidiopsis and heterocystdifferentiating cyanobacteria are each other's closest living relatives[END_REF][START_REF] Shih | Improving the coverage of the cyanobacterial phylum using diversity-driven genome sequencing[END_REF] . However, no further physiological or biochemical evidence had been reported to support the close evolutionary linkage between the two groups. In this study, we have shown similar physiological and biochemical properties of the PSI oligomers observed in those two groups, providing further support of a phylogenetic placement of the unicellular cyanobacteria with PSI dimer and tetramer near heterocyst-forming strains as one clade, HCR.

Additionally, the phylogenetic analysis provided a clear classification of PsaL correlating to the PSI oligomeric state (Supplementary Fig. 3). The major PSI oligomeric states can be predicted from the cyanobacterial psaL sequences, even though specific strains may deviate from the major correlation between PsaL and PSI oligomer; for example, the PSI monomer found in heterocyst-forming cyanobacteria (Supplementary Fig. 1). The formation of the tetrameric PSI may be a result of changes in the PsaL subunit, as previously proposed [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] , and psaL genomic location in relation to psaF-psaJ, which may contribute to expression regulation and PSI assembly control. However, the differences in PsaL are not sufficient to cause PSI tetramer formation, consistent with the observations of PSI monomers in PCC 6803 expressing TS-821 PsaL. Besides differences in PsaL, other factors such as carotenoids and PSI assembly chaperones may contribute to the formation of tetrameric PSI.

The discovery of a pool of PSI interdimer carotenoids also suggests a possible physiological significance of tetrameric PSI over trimeric PSI, since these additional carotenoids may protect PSI from excessive influx of photons under HL. This inference is further supported by the fact that the carotenoid content, as well as the relative quantity and stability of PSI tetramer increased under HL (Figs. 5 and6). Even under LL, PSI tetramer has a higher content of carotenoids compared with PSI trimer (Supplementary Fig. 9). This is in line with the observations of antennae cooperativity between the three T. elongatus PSI monomers that yield an increased optical cross-section of the trimer [START_REF] Iwuchukwu | Self-organized photosynthetic nanoparticle for cell-free hydrogen production[END_REF][START_REF] Baker | Comparative photoactivity and stability of isolated cyanobacterial monomeric and trimeric photosystem I[END_REF] , whereas tetrameric and dimeric PSI did not show significant cooperativity among monomers [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] . In sum, tetrameric PSI alone, compared with trimeric PSI, is a less efficient form of PSI for light harvesting but a better form of PSI in relation to dissipation of excess photonic energy under HL conditions, thereby avoiding photoinhibition. Thus, these cyanobacteria can alter the oligomeric state of PSI under increasing light conditions while also increasing the content of photoprotective carotenoids. It is not clear whether it is the increase in the carotenoids that facilitates the formation of the tetramer or vice versa, but it is attractive to speculate that the tetrameric structure provides a mechanism to accumulate carotenoids, possibly via an unknown carotenoid-binding mechanism. The light-responsive adaptive behaviour of the PSI oligomeric state and the ability of a PSI tetramer to adjust its carotenoid content represents an early evolutionary and unique photoprotective mechanism in HCR.

Exposure to HL may be the driving force for a change in PSI oligomerization. The shift of PSI oligomeric structure from trimeric to tetrameric under HL intensities supports that the HL condition associated with terrestrial environments may have been the selection pressure for PSI tetramer formation. Synechocystis sp. PCC 6803, although it has mainly trimeric PSI, accumulates more PSI monomer when grown under HL [START_REF] Wang | The high light-inducible polypeptides stabilize trimeric photosystem I complex under high light conditions in Synechocystis PCC 6803[END_REF] , suggesting that monomeric PSI may also be advantageous over trimeric PSI under increased light intensity. Our study on Chroococcidiopsis sp. PCC 7203, which has mostly monomeric PSI and some dimeric PSI, showed no obvious oligomeric shift when transferred from LL to HL (Supplementary Fig. 6). Whether monomeric PSI is a further adaptation to HL remains to be investigated.

Nevertheless, it is reasonable to speculate that early plastid ancestors of green algae and plants, and probably ancestors of HCR, needed to be able to cope with HL irradiance as they moved from relatively light-limiting aquatic settings to the surface of a terrestrial environment. These ancestral plastids and cyanobacteria would have benefited from having a PSI tetramer or monomer that is more adapted to HL intensity. These PSI oligomers are also well suited for the addition of other PSI subunits such as PsaH and light-harvesting complexes that bind to the inter-monomer faces of PSI. The observation of a very similar PSI tetramer in the glaucophyte Cyanophora paradoxa [START_REF] Watanabe | Novel supercomplex organization of photosystem I in Anabaena and Cyanophora paradoxa[END_REF] suggests that the closest cyanobacterial relative to plastid ancestors may also have had tetrameric PSI, reinforcing the evidence of the gene homologies and phylogenomic conclusions that heterocyst-forming cyanobacteria are the most closely related to the plastid ancestor [START_REF] Dagan | Genomes of Stigonematalean cyanobacteria (subsection V) and the evolution of oxygenic photosynthesis from prokaryotes to plastids[END_REF] . Yet, this view of plastid origin is contradictory to recent research pointing towards the deep branching cyanobacterium Gloeomargarita lithophora as the closest relative to the common plastid ancestor of glaucophytes, red algae, green algae and plants [START_REF] Sánchez-Baracaldo | Early photosynthetic eukaryotes inhabited low-salinity habitats[END_REF][START_REF] Ponce-Toledo | An early-branching freshwater cyanobacterium at the origin of plastids[END_REF] . If this theory of deep branching cyanobacteria being the closest relative to ancestor of Archaeplastida holds, then the structural shift of PSI oligomer away from a trimer and the adaptation of photosynthesis to a HL environment in HCR, green algae and plants are examples of convergent evolution in photosynthesis.

Our results support the hypothesis that PSI oligomers evolved from trimeric to tetrameric in cyanobacteria en route to exclusively monomeric in plants and green algae. An earlier hypothesis, by comparing PSI trimeric structure from cyanobacteria and PSI monomeric structure from plants suggested that PSI evolved from a trimer to a monomer due to the presence of PsaH, which prevents the formation of the PSI trimer [START_REF] Amunts | Plant photosystem I design in the light of evolution[END_REF] . However, the presence of exclusively monomeric PSI in cyanobacteria (Supplementary Fig. 1), red algae and heterokonts [START_REF] Alboresi | Conservation of core complex subunits shaped the structure and function of photosystem I in the secondary endosymbiont alga Nannochloropsis gaditana[END_REF] without the involvement of PsaH suggests that PSI monomerization preceded the introduction of the PsaH subunit. Changes in PsaL appear to be sufficient for PSI monomerization, notably with Synechocystis expressing Arabidopsis PsaL exhibiting exclusively monomeric PSI (Fig. 3b). Therefore, plant PsaL appears to be biochemically more closely related to cyanobacterial PsaL in relation to tetrameric and monomeric PSI. The presence of exclusively monomeric PSI in heterocyst-forming cyanobacteria (Supplementary Fig. 1) or mostly monomeric PSI in examples such as Chroococcidiopsis sp. PCC 7203 (Fig. 1a and Supplementary Fig. 1) suggests that the monomerization of PSI in plants and green algae shared the same or a closely related route to that of PSI tetramer formation during evolution.

Methods

Cyanobacterial growth conditions. The routine growth conditions for three control strains, Synechocystis sp. PCC 6803 (WT and mutants), Chroococcidiopsis sp. TS-821 (TS-821) and T. elongatus BP-1 were described in an earlier study [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] . Cyanobacteria from UTEX were maintained as recommended by the Culture Collection Center at University of Texas, Austin and the Pasteur Culture Collection of Cyanobacteria at the Institut Pasteur, Paris (standard culture conditions are presented in the Supplementary Data). To achieve sufficient cell mass for PSI oligomer identification, the cyanobacteria were cultured in feasible media with light intensity in the range of 20-100 μmol photons m -2 s -1 (Supplementary Data). The modified ASNIII medium contains BG-11 medium with addition of ASNIII medium major salts (25 g l -1 NaCl, 3.5 g l -1 MgSO 4 •7H 2 O, 2.0 g l -1 MgCl 2 •6H 2 O and 0.5 g l -1 KCl).

To study the physiological significance of PSI tetramer in cyanobacteria, non-standard culture conditions were tested. To investigate the effect of nitrogen sources, some heterocyst-forming cyanobacteria were cultured separately in BG-11, BG-110 or BG-11 + NH 4 + (BG-11 supplemented with 1 mM NH 4 Cl two days before collecting cells). To test the effect of temperature, some thermophilic cyanobacteria were cultured at 45 °C versus 37 °C. In addition, a culture of Fischerella muscicola PCC 7414 grown at 37 °C was incubated at 24 °C before collection. To investigate the effect of salinity, some marine cyanobacteria were cultured in both BG-11 and modified ASNIII media.

The standard HL and LL comparison experiments for TS-821, PCC 7414, PCC 7428 and PCC 7203 were done as described before [START_REF] Semchonok | Cryo-EM structure of a tetrameric cyanobacterial photosystem I complex reveals novel subunit interactions[END_REF] . To eliminate the potential stress from cell culture density and/or differences from lighting sources, a systematic analysis of how TS-821 respond to different levels of light intensity was done by culturing similar inoculum in a photobioreactor for two days under five light conditions (50, 100, 200, 400 and 800 μmol photons m -2 s -1 ). For each light condition, half of the light intensity was provided by white LEDs and the other half was from red LEDs. The mid-log phase TS-821 cell (optical density at 680 nm (OD 680) 0.6-0.8) cultures under white light fluorescent light were inoculated in the 25 l bioreactor to a starting OD 680 of 0.04 (measured with a fluorometer probe from Photon Systems Instruments) before turning on the bioreactor lights. Cells were collected and stored -20 °C before PSI oligomer analysis.

Thylakoid membrane isolation. For thylakoid membrane preparation, cells were lysed by French press. Cyanobacterial cell pellets were washed in buffer A (50 mM MES-NaOH, pH 6.5, 5 mM CaCl 2 and 10 mM MgCl 2 ) and then pelleted by centrifugation [START_REF] Watanabe | Is the photosystem II complex a monomer or a dimer?[END_REF] . Cell pellets were resuspended in lysis buffer (buffer A containing 0.5 M sorbitol) and homogenized by French press. In the case of Scytonema crispum UTEX LB 1556, cell aggregates were broken into small fragments by grinding in liquid nitrogen before resuspension in lysis buffer and homogenization. Homogenized cell suspensions were processed through the French press three times at 1,500 or 2,000 psi (10 to 14 MPa), then unbroken cells were removed by pelleting at 10,000g for 5 min.

In most cases, thylakoid membranes were pelleted from cell lysate by centrifugation at 40,000 r.p.m. (193,000g in a Type 50.2 Ti rotor, Beckman) for 30 min at 4 °C. Thylakoid membrane pellets were resuspended in buffer A + 12.5% glycerol and homogenized before storing at -20 °C or -80°C. For HL versus LL experiments, thylakoids were washed in buffer A once and pelleted at 193,000g for 15 min before final resuspension. In some special cases where cell mass was low and large membrane fragments could be pelleted at lower g forces, thylakoids were resuspended after spinning at 10,000g for 5 min. Chl concentration was determined as described previously [START_REF] Iwamura | Improved methods for determining contents of chlorophyll, protein, bibonucleic acid, and deoxyribonucleic acid in planktonic populations[END_REF] .

PAGE analyses and western blot.

In most cases, 4-16% BN-PAGE gels (Invitrogen) were used to analyse solubilized thylakoids or isolated photosystems, according to the user manual and references [START_REF] Schägger | Blue native electrophoresis for isolation of membrane protein complexes in enzymatically active form[END_REF]46 . In addition, laboratoryprepared BN-PAGE gels were used to analyse larger amounts of sample. To analyse PSI oligomeric states, thylakoid membranes were solubilized in different concentrations of DDM (Glycon) at 25 °C for 1.5 h. Insoluble material was removed by centrifugation at 180,000g for 5 min or 98,000g for 10 min at 4 °C. Supernatants were taken for BN-PAGE analysis. Gel images were taken before fixation and staining to identify green bands for photosystems. After Coomassie staining, gel images were taken using a UVP transilluminator to visualize proteins with lower abundance and for quantification. To identify the photosystems after BN-PAGE, a second dimension Tris-Tricine SDS-PAGE was used as described previously [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] .

Western blots were used to detect the presence of PsaL in Synechocystis mutants. Protein bands were transferred from polyacrylamide gels to a 0.45 μm PVDF membrane (Millipore) using a blotting cassette (idEA). Membranes were blocked with TBS-T + 3% NFM (non-fat milk powder) at room temperature for 1 h. Primary antisera were diluted from 1:5,000 in TBS-T + 3% NFM, depending on their efficiency before treating the blocked membranes overnight at 4 °C. Secondary antibody (goat anti-rabbit) conjugated to horseradish peroxidase (HRP) was diluted in TBS-T + 3% NFM to 1:50,000 before treating the washed membranes for 1 h at room temperature. The targeted proteins were detected using chemiluminscence HRP substrate (Millipore) and the signal was recorded using a ChemiDoc XDS system (Bio-Rad).

Antigen design and antibody production. PsaL sequences are not sufficiently well conserved for antigen design from a single consensus sequence. To produce one antigen that could be used to antisera against all PsaL of interest in this study, that is, Chroococcidiopsis sp. TS-821, Arabidopsis, T. elongatus BP-1 and Synechocystis sp. PCC 6803, a chimeric protein (CATSPsaL) containing fragments of the

Articles

NatuRe PLaNtS

different PsaLs was designed. The Kolaskar and Tongaonkar antigenicity method [START_REF] Kolaskar | A semi-empirical method for prediction of antigenic determinants on protein antigens[END_REF] via the Immune Epitope Database (http://tools.immuneepitope.org/bcell/) and ABCpred [START_REF] Saha | Prediction of continuous B-cell epitopes in an antigen using recurrent neural network[END_REF] (http://www.imtech.res.in/raghava/abcpred/index.html) were used to predict suitable epitopes. The antigen sequence was aligned against different PsaL fragments and the predicted antigens to ensure a high probability of obtaining an antibody for each PsaL (Supplementary Fig. 10). In addition to the N-terminal fragments, the loop insertion between second and third transmembrane helices of TS-821 PsaL was also used to achieve high antigenicity for TS-821.

A synthetic CATSPsaL coding sequence (Integrated DNA Technologies) was cloned into pTYB2 (NEB) plasmid. The expression plasmid DNA was then transformed into E. coli ER2566 for antigen expression. IMPACT Chitin Resin (NEB) was used as column matrix for antigen purification. Antibody was produced at Pocono Rabbit Farm using the 91 d protocol on 2 rabbits. For PsaL antibody production, purified antigen at 1 mg ml was used as inoculum.

PSI isolation and characterization. Sucrose density gradient centrifugation (SDGC) was used for PSI isolation as described previously [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] . SDGC was also used to study PSI oligomeric states, as a parallel or complementary technique to BN-PAGE profiling. Thylakoid membranes containing 0.4 mg ml -1 Chl were solubilized in 0.6-1% DDM. After removing insoluble fragments, the solubilized membranes containing 1 mg Chl were loaded on a 10-30% sucrose density gradient in buffer A containing 0.01% DDM. This method showed comparable results with BN-PAGE analysis. For larger capacity loading of solubilized membrane (containing 1-3 mg Chl) on a sucrose density gradient, centrifugation was performed twice with the first 20-24 h spin followed by dialysis and another 24 h spin (SW32Ti, 30,000 r.p.m.). Lower ionic strength, such as 0.4× buffer A was tried in sucrose density gradients for PCC 7414 PSI but showed no observable difference for PSI profiles. Inter-dimer carotenoids (Fig. 4e) were isolated after SDGC following treatment of PSI tetramer with 5% DDM for at least 1 h at room temperature. Isolated PSI samples were dialysed before analysis. For the proteomic comparison between PSI trimers and PSI tetramers, isolated PSI oligomers were further purified by BN-PAGE and gel slices were analysed.

Low temperature (77K) fluorescence spectra were acquired with excitation wavelength at 430 nm and the emission spectra at 600-800 nm were recorded. Each emission spectrum was averaged from ten technical repeats to enhance signal-tonoise ratio. Absorption spectra of isolated proteins and pigments were taken using a Cary 300 UV-Vis spectrometer (Agilent). The sample buffers were used as blanks. For PSI oligomer absorption spectra comparisons, A 680 was adjusted close to 0.5 or 1. The PSI absorption differences were calculated after normalizing the data at A 680 . Electron microscopy and single particle analyses were done as described in previous studies [START_REF] Watanabe | Attachment of phycobilisomes in an antennaphotosystem I supercomplex of cyanobacteria[END_REF][START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] . Pigment analyses were done using high-performance liquid chromatography by DHI (Hørsholm, Denmark). psaL gene cloning and TS-821 genome sequencing. Most cyanobacterial DNA extraction for psaL cloning was done as described [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] . TS-821 DNA for genome sequencing and some cyanobacterial DNA for psaL cloning were extracted using the NucleoBond DNA isolation kit (Macherey-Nagel Inc.). For psaL cloning of heterocyst-forming cyanobacteria with unknown genome data, different primer sets (Supplementary Tables 1 and2) from psaF and gmk genes were used to amplify the psaL gene and its flanking region. The cyanobacteria of interests were classified using their known DNA sequences or genus names to facilitate picking primer pairs. PCR products were ligated into pJET vectors using CloneJET PCR cloning kit (Thermo Fisher). Plasmids containing cloned psaL were sequenced by Sanger sequencing at University of Tennessee Genomics Core.

TS-821 culture was purified as described [START_REF] Rippka | Generic assignments, strain histories and properties of pure cultures of cyanobacteria[END_REF] before DNA extraction for genome sequencing. The DNA was submitted to University of Tennessee Genomic Core for sequencing using Illumina MiSeq Kit v.2 with 2 × 250 bp read length. The resulted FASTQ files were analysed using SPAdes (v.3.7.1) [START_REF] Bankevich | SPAdes: a new genome assembly algorithm and its applications to single-cell sequencing[END_REF] . The assembled contigs were submitted to PATRIC [START_REF] Wattam | the bacterial bioinformatics database and analysis resource[END_REF] for annotation, which uses the RAST [START_REF] Overbeek | The SEED and the Rapid Annotation of microbial genomes using Subsystems Technology (RAST)[END_REF] system.

Phylogenetic and psaL analyses. The species tree was generated by a concatenation of 29 conserved proteins selected from the phylogenetic markers previously validated for cyanobacteria using a maximum-likelihood method as described previously [START_REF] Calteau | Phylum-wide comparative genomics unravel the diversity of secondary metabolism in cyanobacteria[END_REF] . Protein sequences were aligned using MAFFT v.7.307 [START_REF] Katoh | MAFFT multiple sequence alignment software version 7: Improvements in performance and usability[END_REF] ; ambiguous and saturated regions were removed with BMGE v.1.12 (with the gap rate parameter set to 0.5) [START_REF] Criscuolo | Block Mapping and Gathering with Entropy): a new software for selection of phylogenetic informative regions from multiple sequence alignments[END_REF] . The best-fitting model of amino acid substitution for this dataset was selected with ProtTest v.3.2 [START_REF] Darriba | ProtTest 3: Fast selection of best-fit models of protein evolution[END_REF] . A maximum-likelihood phylogenetic tree was generated with the alignment using PhyML 3.1.0.2 56 using the LG amino acid substitution model with gamma-distributed rate variation (six categories), estimation of the proportion of invariable sites and exploring tree topologies. One-hundred bootstrap replicates were performed. The phylogenetic trees were displayed and annotated using the interactive tree of life (iTOL) online tool [START_REF] Letunic | Interactive tree of life (iTOL) v3: An online tool for the display and annotation of phylogenetic and other trees[END_REF] .

Genomic context of psaL, psaI, psaF and psaJ genes and PsaL protein sequences were extracted from the MicroScope platform [START_REF] Vallenet | MicroScope in 2017: An expanding and evolving integrated resource for community expertise of microbial genomes[END_REF] , public databases and data generated in a previous study [START_REF] Schirrmeister | Cyanobacteria and the Great Oxidation Event: evidence from genes and fossils[END_REF] or this study Supplementary Data). The logo plot for the PsaL linker was generated using the WebLogo 3 website (http://weblogo. threeplusone.com) [START_REF] Crooks | A sequence logo generator[END_REF] .

Construction of Synechocystis psaL mutants. Some of the psaL mutants were obtained in a previous study [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] with low expression efficiency. To improve the expression level of exogenous PsaL, codon-optimized synthetic psaL DNAs in pBSK vector were obtained from Integrated DNA Technologies. Similar methods were used for cloning and Synechocystis transformation as described [START_REF] Li | Characterization and evolution of tetrameric photosystem I from the thermophilic cyanobacterium Chroococcidiopsis sp. TS-821[END_REF] . The mutants were named as Synechocystis sp. PCC 6803 expressing synthetic Chroococcidiopsis sp. TS-821/A. thaliana psaL (SCHL/SAtL).

Reporting summary. Further information on research design is available in the

Statistics

For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section.

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The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly

The statistical test(s) used AND whether they are one-or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section.

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A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted Give P values as exact values whenever suitable.

For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes Estimates of effect sizes (e.g. Cohen's d, Pearson's r), indicating how they were calculated Our web collection on statistics for biologists contains articles on many of the points above.

Software and code

Policy information about availability of computer code

Data collection

No special software was used for data collection except those installed for instruments, see Methods for instruments used.

Data analysis

The following softwares or web-services are used for data analyses: ABCpred, IEDB Analysis Resource, SPAdes (version 3.7.1), RAST system, MAFFT v7.307, BMGE v1.12, ProtTest v3.2, PhyML 3.1.0.2, interactive tree of life (iTOL), WebLogo, GraphPad Prism Ver. 8. Detailed references or links to resources are provided in the Methods section.

For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors/reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Research guidelines for submitting code & software for further information.

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All manuscripts must include a data availability statement. This statement should provide the following information, where applicable:

-Accession codes, unique identifiers, or web links for publicly available datasets -A list of figures that have associated raw data -A description of any restrictions on data availability

The cloned cyanobacterial psaL sequences can be found in GenBank through the following acces-sion numbers: KY575410, KY575411, KY575412, KY575413, KY575414, KY575415, KY575416, KY575417, KY575418, KY575419, KY575420, KY575421, KY575422, KY575423, KY575424. TS-821 Whole Genome Shotgun project has been deposited at DDBJ/ENA/GenBank under the accession MVDI00000000. The version described in this paper is version MVDI01000000.

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Life sciences study design

All studies must disclose on these points even when the disclosure is negative.

Sample size n = 5 was used to calculate trimeric PSI fraction in native gel (Figure 5). Other experiments with technical/biological repeats were described in each figure legend where applicable.

Data exclusions The 0.4% DDM lane for 800 umol/m2/s condition has little trimeric PSI, so the 0.4% DDM solubilization condition was excluded for comparison.

Replication

Most experiments have technical/biological repeats to confirm the experimental findings. Some experiments were done once with different materials/methods to confirm similar findings/conclusions.

Validation

Pocono Rabbits Farm generated the anti-PsaL serum using purified antigen; validated by data provided in the manuscript.

Fig. 1 |

 1 Fig. 1 | Examples of BN-PAGE and TEM analyses of PSI oligomeric states in different cyanobacteria. a, BN-PAGE analyses of the PSI oligomeric states of various heterocyst-forming cyanobacteria and their close relatives. Arrowheads indicate the position of the trimeric form of PSI (PSI tri), the monomeric form of PSI and/or PSII (PSI/II mon), and the dimeric form of PSI (PSI dim). b, TEM structure of PSI tetramer from PCC 7414 (top) compared with a TS-821 PSI tetramer model (bottom). c, BN-PAGE analyses of the PSI oligomeric states of cyanobacteria that are distantly related to heterocyst-forming cyanobacteria. d, TEM structure of PSI trimer from PCC 6712 compared with a BP-1 PSI trimer model. In a and c, for each strain, the solubilization result of 0.4 mg ml -1 Chl in 1% DDM is shown. TS-821, Synechocystis sp. PCC 6803 (PCC 6803) and T. elongatus (BP-1) are used as controls. The approximate migration distances for photosystem monomer (mon), dimer (dim), trimer (tri), tetramer (tet) and potential hexamer (hex?) are indicated by arrows. All BN-PAGE were performed with at least two technical repeats; BN-PAGE for some strains used for physiology studies was performed more than three times. In b and d, the locations of PsaL (L), PsaI (I), PsaF (F) and PsaJ (J) subunits are coloured and labelled. Scale bars, 10 nm.

Fig. 3 |

 3 Fig. 3 | BN-PAGE and western blot analyses of PSI oligomers in Synechocystis sp. PCC 6803 expressing different PsaL. a, BN-PAGE of solubilized thylakoid membranes from Synechocystis sp. PCC 6803 WT, ΔpsaL and expressing TS-821 PsaL (SCHL). Slices containing PSI samples were taken from the gel for subsequent SDS-PAGE and western blotting to detect PsaL. Each lane was loaded with solubilized membrane containing 16 μg Chl. b, BN-PAGE of solubilized thylakoid membranes from Synechocystis sp. PCC 6803 WT and mutant expressing Arabidopsis thaliana PsaL (SAtL). c, Western blot of the PSI samples from the BN-PAGE analysis in a. PSI trimer (tri) from WT, PSI monomers (mon) from ΔpsaL and SCHL, as well as potential PSI tetramer (tet?) were analysed. d, Western blot of the PSI bands isolated after the BN-PAGE in b. Whole A. thaliana seedling was used as a control. BN-PAGE of transgenic lines, SCHL and SAtL were done with three independent lines and showed similar monomeric PSI phenotypes. Western blots confirming the presence of exogenous PsaL were performed as two technical repeats.

Fig. 4 |

 4 Fig. 4 | BN-PAGE analyses of cyanobacterial PSI oligomeric states under different light intensities. a-d, BN-PAGE of solubilized thylakoid membranes from PCC 7428 (a, unstained gel; b, Coomassie-stained gel) and PCC 7414 (c, unstained gel; d, Coomassie-stained gel). Left lanes, LL (40 μmol m -2 s -1 ); right lanes, HL (800 μmol m 2 s -1 ). Thylakoid membranes with 0.2 mg ml -1 Chl were solubilized in different concentrations of DDM (w/v, %) as indicated for each lane. Approximately 1.6 μg Chl was loaded for each condition. Main bands corresponding to PSI monomer (Mon), dimer (Dim), trimer (Tri) and tetramer (Tet) are labelled. BN-PAGE was performed as two technical repeats, which showed similar PSI oligomeric shifts under different light intensities.

Fig. 5 |

 5 Fig. 5 | Comparison of TS-821 PSI oligomeric profiles under different light intensities. a-f, BN-PAGE of solubilized thylakoid membrane from TS-821 cultured under different light intensities. a,c,e, Unstained gels. b,d,f, Coomassie-stained gels for quantification. Thylakoid membranes with 0.2 mg ml -1 Chl were solubilized in different concentrations of DDM (w/v, %) as indicated for each lane. Approximately 1.6 μg Chl was loaded for each condition. Main bands corresponding to PSI monomer (Mon), dimer (Dim), trimer (Tri), and tetramer (Tet) are labelled. g, Relative quantities of PSI tetramer under different light intensities. Two solubilization conditions, 0.4% and 0.8% DDM, are presented to show the observed maximum quantities and the stabilities of PSI tetramer under different light intensities. h, Relative quantities of PSI trimer under different light intensities. Data are mean ± s.d. (n = 5 solubilization conditions for each light intensity, 0.6 to 4.0% DDM). The experiments with incremental light intensities were performed once; the comparisons between HL and LL were performed more than three times.

Fig. 6 |

 6 Fig. 6 |The impact of light intensities on tetrameric PSI in TS-821. a, Absorption spectra of PSI tetramers isolated from TS-821 grown under LL and HL conditions. b, Difference between HL and LL absorption spectra for PSI tetramers calculated from spectra in a. c, Sucrose density gradient ultracentrifugation of isolated PSI tetramer. The sample treated with 5% DDM is compared with untreated PSI tetramer. Main bands corresponding to interdimer carotenoids, PSI monomer (Mon), dimer (Dim), trimer (Tri) and tetramer (Tet) are labelled. The release of carotenoids on 5% DDM treatment was observed in all three independent experiments tested. d, Absorption spectrum of interdimer carotenoids isolated from treated PSI tetramer after sucrose density gradient ultracentrifugation in c. e, Quantitative analysis of interdimer carotenoids. f, Quantitative comparison of carotenoids in PSI tetramer isolated under HL and LL conditions, presented as the ratio of carotenoids to Chl. The detected carotenoids include myxoxanthophyll (Myx), canthaxanthin (Can), echinenone (Ech) and β-carotene (β-Car). Asterisks denote where detected quantities are below the limit of quantification. Absorption data are the mean of three technical repeats. Pigment analysis data reflect results of one experiment.

  Nature Research Reporting Summary linked to this article. 1 nature research | reporting summary October 2018 Corresponding author(s): Barry D Bruce Last updated by author(s): Oct 8, 2019 Reporting Summary Nature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Research policies, see Authors & Referees and the Editorial Policy Checklist.

| Distribution of PSI oligomers and the location of psaL genes among cyanobacteria with sequenced genomes. The

  relative locations of psaL to psaI, psaF and psaJ genes are colour coded after each strain number, followed by the observed or reported oligomeric states of PSI in that cyanobacterium. The clade including HCR is expanded for clarity, indicated by green arrows. Strains whose PSI oligomeric states are investigated in this study are coloured in cyan or green. Bootstrap values (%) of some major branches are labelled. A fully expanded species tree is shown in Supplementary Fig.3.

	100		G. violaceus PCC 7421 Synechococcus sp. PCC 7336	Legend:
	100		Pseudanabaena sp. PCC 7367			psaL	psaI
	100		Synechococcus sp. PCC 7502 Pseudanabaena sp. PCC 7704	psaL/I
	100				psaI	psaL
			T. elongatus BP-1
			Leptolyngbya sp. PCC 6306	psaL		psaL
	100
			Leptolyngbya sp. PCC 7104 Leptolyngbya sp. PCC 7124	psaF/J/L	psaF	psaJ	psaL
			Leptolyngbya sp. PCC 6406
	100	100	S. elongatus PCC 7942 P. marinus SS120	PSI dimer	PSI trimer	PSI tetramer
			P. marinus MED4
		100	P. marinus MIT 9313 Prochlorococcus spp.
			and
			Synechococcus spp.
	100		Synechococcus sp. WH 7803
			Oscillatoria sp. PCC 10802
	93
		Arthrospira spp.	100	Synechocystis sp. PCC 7509 Gloeocapsa sp. PCC 7428 L. redekei PCC 9416
					Chrooccidiopsis sp. PCC 8201
					C. thermalis PCC 7203
		Planktothrix spp.	100	Rivularia sp. PCC 7116 Calothrix sp. PCC 7103
					Calothrix sp. PCC 6303
					S. hoffmanni PCC 7110
					M. repens PCC 10914
	94			100	Scytonema sp. PCC 10023 Chlorogloeopsis sp. PCC 7702
		100			Chlorogloeopsis sp. PCC 9212
					C. fritschii PCC 6912
					Fischerella sp. PCC 9605
			Heterocyst-forming cyanobacteria	100	Fischerella sp. PCC 9339 F. muscicola PCC 73103 Fischerella sp. PCC 9431
			and close relatives		F. muscicola PCC 7414
					F. thermalis PCC 7521
					Fischerella sp. JSC-11
	100			Tolypothrix sp. PCC 9009
					Nostoc sp. PCC 7107
					Nostoc sp. PCC 7524
					Nostoc sp. PCC 7120
					A. variabilis ATCC 29413
			C. minutus PCC 6605	100	Calothrix sp. PCC 7507 N. punctiforme ATCC 29133 Tolypothrix sp. PCC 7910
	100		96	C. stagnale PCC 7417 Microchaete sp. PCC 7126 N. spumigena CCY 9414
			Chroococcidiopsis sp. PCC 6712 Synechocystis sp. PCC 6308 Synechococcus sp. PCC 7002		R. brookii D9 Anabaena sp. PCC 7108 A. cylindrica PCC 7122 C. raciborskii CS-505
			Synechocystis sp. PCC 6803		A. circinalis ACBU02
					Anabaena sp. 90
		100	Cyanothece sp. ATCC 51142
			Pleurocapsa sp. PCC 7327
		100	Microcystis spp.
			M. aeruginosa PCC7806
	Fig. 2

  Reporting for specific materials, systems and methodsWe require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material, system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response.

	Randomization Not relevant
	Blinding	Not relevant
	Materials & experimental systems	Methods
	n/a Involved in the study	n/a Involved in the study
	Antibodies		ChIP-seq
	Eukaryotic cell lines	Flow cytometry
	Palaeontology	MRI-based neuroimaging
	Animals and other organisms
	Human research participants
	Clinical data
	Antibodies
	Antibodies used

non-commercial, Anti-PsaL Rabbit Serum described in Methods

NATurE PLANTS | VOL 5 | DECEMBER 2019 | 1309-1319 | www.nature.com/natureplants

Acknowledgements

Support to B.D.B., M.L. and J.T.N. was provided by the Gibson Family Foundation, the Bredesen Center for Interdisciplinary Research and Education, the Tennessee Plant Research Center, a UTK Professional Development Award, the Dr. Donald L. Akers Faculty Enrichment Fellowship to B.D.B. and National Science Foundation support to B.D.B. (DGE-0801470 and EPS-1004083). M.L. has been supported as a CIRE Fellow at University of Tennessee, Knoxville. A Professional Development Award from the Graduate School at UTK supported travel of B.D.B. to the Netherlands and to the Institut Pasteur. NWO Chemical Sciences supported work at University of Groningen. J.P.W. has been supported by NIH P30 DK063491. The Institut Pasteur supported Pasteur Culture Collection of cyanobacteria. We thank Y. I. Park for the use of the cyanobacterial genome of PCC 7124, and N.G. Brady and T. Cardona for helpful comments on the manuscript.

Data availability

The cloned cyanobacterial psaL sequences have been deposited in GenBank with the accession numbers KY575410, KY575411, KY575412, KY575413, KY575414, KY575415, KY575416, KY575417, KY575418, KY575419, KY575420, KY575421, KY575422, KY575423 and KY575424. The TS-821 whole-genome shotgun project has been deposited at DNA Data Bank of Japan/European Nucleotide Archive/ GenBank under the accession MVDI00000000. The version described in this paper is version MVDI01000000.

Author contributions

Competing interests

The authors declare no competing interests.