Archaean green-light environments drove the evolution of cyanobacteria’s light-harvesting system

Main

Carl Sagan described the Earth, as imaged by Voyager 1 at a distance of 6 billion kilometres, as a ‘pale blue dot’¹. This description is a consequence of the Rayleigh scattering of sunlight in the atmosphere, in conjunction with the reflection and scattering across the expanse of the ocean. The pale blue colour, serving as a metaphor, symbolizes the cradle of life. Nevertheless, one might enquire: does only a blue hue of a planet serve as an indicator of its potential to nurture life?

The planetary surface has not only been chemically and physically changed by geological events over 4.5 billion years but has also been moulded by life since its emergence. Cyanobacteria, as pioneering oxygenic photosynthetic organisms, spread across the globe by photolysis of water to generate molecular oxygen using solar radiation. This biological evolution caused a pivotal oxygenation event called the great oxidation event (GOE) around 2.4 billion years ago². The GOE probably played an important role in the promotion of aerobic biodiversity³. However, it is worth noting that recent research suggests an emergence of aerobic metabolism and thus an oxygenated biosphere before the GOE⁴.

Cyanobacteria use a giant and complex light-harvesting system called phycobilisomes as a light-harvesting system and transfer the absorbed energy to photosystem I (PSI) and photosystem II (PSII) for photosynthesis⁵. Phycobilisomes consist mainly of three phycobiliproteins: allophycocyanin (APC), phycocyanin (PC) and phycoerythrin (PE)⁶. The two major phycobilin pigments—phycocyanobilin (PCB) and phycoerythrobilin (PEB)—attach to the phycobiliproteins⁷ and can absorb light in the wavelength range 500–650 nm, which is not efficiently absorbed by chlorophyll a (Chl a). Whereas PC and APC constitute integral components of phycobilisomes, the inclusion of PE occurs sporadically in cyanobacteria^8,9 and is closely related to the various light environments of host habitats¹⁰. The absorbed light energy is transferred to PSII via PE, PC and APC. Although the energy transfer efficiency is >95% (ref. ¹¹), phycobilisomes are much larger and more complex than other light-harvesting systems such as the light-harvesting complex (LHC) for higher plants⁶. Hence, the rationale behind the exclusive use of phycobilisomes as the light-harvesting system by cyanobacteria remains unclear. Considering that antenna pigments of cyanobacteria are attuned to the light environment of their habitats¹⁰, the light incident to the habitats of ancestral cyanobacteria, referred to as the ‘light window’, could have played an important role in driving natural selection towards the evolution of phycobilisomes. This co-evolutionary relationship between the light environment and the corresponding photosystem was indeed considered in previous studies^12,13. Hence, the Archaean underwater light window could have been distinct from the modern continuous light windows over the visible wavelength range (that is, white-light window) and favoured the selection of phycobilisomes. Because cyanobacteria, which probably evolved before the GOE^14,15,16, traversed a transition from fully reduced to oxidized environments, their habitats and associated light windows conceivably changed along with the gradual oxidation process of the surface of the Earth (Supplementary Discussions 7 and 8).

Transformation of light window for photosynthetic organisms

We explored the transformation of the light window alongside surface oxidation during the Archaean era, particularly with the rise of photosynthetic organisms. Initially, reduced iron Fe(II) dissolved completely in the reduced aquatic environment¹⁷ (Supplementary Discussions 1, 7 and 8). However, the emergence of cyanobacteria^14,15,16 and phototrophic Fe(II)-oxidizing bacteria^17,18 in the Archaean era led to the oxidation of Fe(II) (Fig. 1a), forming iron hydroxide precipitates (Fe(OH)₃) and contributing to the formation of banded iron formations (BIFs)^18,19,20,21. Given the vertical structure of open oceans^22,23, iron hydroxide probably spread across cyanobacterial habitats as a result of high eddy diffusivity above the pycnocline.

**Fig. 1: Underwater green-light environment after the emergence of cyanobacteria and photoferrotrophs in the Archaean era.**

We performed numerical simulations based on diffusion equations to predict the distributions of oxygen, reduced iron and iron hydroxide in Archaean aquatic environments. On the basis of the concentrations of reduced iron and oxygen defined by the previous studies^17,24,25, we found an average iron hydroxide concentration of ~10 µM in the oxidized zone (Fig. 1b). On the basis of the previous studies^17,26, we assumed that the oxic and anoxic zones were divided by the pycnocline. Since the concentration of oxygen remained constant as a result of the high eddy diffusivity above the pycnocline, iron hydroxide was probably formed at the boundary between the oxic and anoxic zones and may have continuously spread across the cyanobacterial habitats. Importantly, the distributions of oxygen and reduced iron, crucial for maintaining the underwater light environment, were in equilibrium. The equilibrium concentration mainly depends on the influx of reduced iron to the pycnocline, rather than the conditions in the mixed layer, which served as the cyanobacterial habitat. In fact, oxygen concentration above the pycnocline did not influence iron hydroxide level (Extended Data Fig. 1e,f).

Our experiments on the iron hydroxide formation suggest that iron hydroxide particles were probably small (<100 nm) at the time of formation, allowing them to remain buoyant (Extended Data Fig. 2). As a result, iron hydroxide would have consistently influenced the underwater light environment of the cyanobacterial habitat, while reduced iron was continuously oxidized through photoferrotrophic and cyanobacterial activities, although uncertainty in reduced iron influx could lead to iron hydroxide concentrations varying from 1 to 100 µM (Supplementary Discussion 2).

We also measured the molar absorption coefficient of iron hydroxide, aligning with the previous study²⁷ and found that its visible-light coefficient remains unaffected by synthesis methods and particle size (Extended Data Fig. 2 and Supplementary Discussion 3). While different types of iron hydroxide might have existed during the Archaean era²⁸, only the earliest phase of small-sized iron particles probably had the most prolonged impact on the underwater light environment (Supplementary Discussion 5).

Considering that underwater environments could protect cyanobacteria from harmful ultraviolet (UV) radiation in the Archaean era²⁹, we determined the spectrum of the light window available to photosynthetic organisms. In the absence of iron hydroxide, the cyanobacteria habitat could have extended to depths >20 m. The UV light absorption of iron hydroxide suggests the expansion of cyanobacterial habitats into shallow waters (~5 m), in accordance with the geological records (Extended Data Fig. 2)^30,31. At both 5 and 20 m depth, the light window predominantly ranges between 500 and 600 nm under 10 µM iron hydroxide concentration (Fig. 1c). The underwater light window mostly remains consistent even with tenfold changes in iron hydroxide concentration (Extended Data Fig. 3). Our analyses show a striking correlation between the spectra of the light window and the green-absorbing phycobilin pigment, PEB, under a broad range of conditions (Fig. 1d,e, Extended Data Fig. 4 and Supplementary Table 1). This implies that the phycobilin pigment could be helpful for harvesting the light in the Archaean era, compared to Chl a (Supplementary Discussion 4). It is important to note that this implication applies to various cyanobacterial habitats, such as open oceans, coastal areas and freshwater environments. Additionally, because the green-light window spreads only a few metres below the surface, both planktonic and benthic cyanobacterial communities would have grown under similar light conditions, assuming that planktonic cyanobacteria were primarily transported by oceanic diffusions, currents and tides. Thus, regardless of the cyanobacterial species and habitats, the co-evolutionary relationship between the light window and aquatic cyanobacteria can be envisioned (Supplementary Discussion 6).

Our findings further include the contemporary light environment around Iwo Island in the Satsuma archipelago³², where the oxidative conversion of reduced Fe(II) ions emanating from thermal vents created a similar green-light window at a depth of 5.5 m (Extended Data Fig. 5). Intriguingly, at this depth, PEB within cyanobacterial community is more abundant than at the surface (Supplementary Discussion 11), indicating a strong correlation between the light environment and the pigment composition in their natural habitat (Extended Data Fig. 6). This green-light environment was also previously confirmed even in a modern lake with a minor dispersion of iron hydroxide³³.

In conclusion, an underwater green-light environment during the Archaean era was highly plausible, as reduced iron supplied from hydrothermal vents was continuously oxidized at the boundary between oxidized and reduced environments, leading to the formation of BIFs. This specific light condition crucially influenced the evolutionary trajectory of early photosynthetic life.

Natural selection of phycobilin in green-light environments

Our observations bring to light the synchrony between the green-light window and the absorption spectrum exhibited by PEB-containing phycobiliproteins—PE (Fig. 1c). The light energy absorbed by PE transfers to Chl a via the two other phycobiliproteins, PC and APC⁵, progressively diminishing as the wavelengths traverse from green (~565 nm) to red (~670 nm) (Fig. 2b). Here, we examine whether PE was a critical component for photosynthesis under the green-light window. We cultivated two cyanobacterial species (see Supplementary Discussion 6 for the selection of species): Gloeobacter violaceus PCC 7421, characterized by the co-presence of APC, PC and PE, alongside Synechococcus elongatus PCC 7942, endowed only with APC and PC, under two distinct light environments which emulate the green- and white-light windows (Extended Data Fig. 7a). Cell growth patterns reveal an almost indistinguishable proliferation rate for G. violaceus under both the green- and white-light conditions (Fig. 2b), contrasting a slower growth rate for S. elongatus PCC 7942 under the green-light condition relative to the white-light condition (Fig. 2c)³⁴. This observation is consistent with the excitation spectra in cells showing that G. violaceus uses green light for photosynthesis more efficiently than S. elongatus (Extended Data Fig. 7b).

**Fig. 2: Adaptation of cyanobacteria to the green-light window by PEB.**

We further investigated the necessity of the phycobilin pigment PEB that specifically attaches to PE in modern cyanobacteria, by creating genetically engineered S. elongatus PCC 7942, capable of producing PEB, but lacking PE. PEB is biosynthesized through two sequential enzymatic steps from biliverdin IXα by pebA (15,16-dihydrobiliverdin:ferredoxin oxidoreductase) and pebB (phycoerythrobilin:ferredoxin oxidoreductase)⁶. Two transformants mild-expressing and overexpressing the pebA and pebB genes, denoted as PebAB-MX and PebAB-OX, were green–brown and brown, respectively (Extended Data Fig. 8a,b). For both PebAB-MX and PebAB-OX cells, the excitation spectra (Fig. 2d) revealed an effective channelling of energy absorbed by PEB towards the photosystems via PC and APC, without PE, showing the possibility that PEB attaches to PC as previously suggested³⁵. Notably, the peak intensities that originated from PEB and PC were almost equal in the absorption and excitation spectra of PebAB-MX cells, suggesting well-balanced energy transfer from PEB towards the photosystems (Fig. 2d and Extended Data Fig. 8a). Our observation implies that the use of green light itself does not necessarily require PE, but rather it is sufficient for PEB to simply attach to PC. Yet, the evolution of PEB would have promoted a functional or structural specialization of PC, probably resulting in the evolution of PE and ultimately modern phycobilisomes (Supplementary Discussion 9).

When PebAB-MX cells were cocultured alongside wild-type cells in competition, PebAB-MX cells outcompeted wild-type cells under green light, although the growth under white light was slower in PebAB-MX cells than in wild-type cells because of PCB depletion (Fig. 2e and Extended Data Fig. 8c–e). We also found that some PebAB-OX cells tended to lack brown pigmentation³⁵ because of spontaneous mutations mainly in the pebA gene (Extended Data Fig. 8f). Interestingly, the population of PebAB-OX cells producing PEB was enhanced under green-light conditions, whereas the population of PebAB-OX cells without PEB, because of pebA mutations, increased under white-light conditions (Fig. 2f and Extended Data Fig. 8g). These findings substantiate the proposition that, unlike their non-PEB-producing counterparts, cells capable of producing PEB thrived under the selective pressure imposed by the green-light window, reminiscent of natural selection and niche differentiation of photosynthetic organisms caused by differences in pigment composition¹⁰. While the two species analysed in our study are not representatives of marine cyanobacteria, our arguments are not influenced by the species selection and habitats (Supplementary Discussion 6).

Phycobiliproteins in ancestral cyanobacteria

Energy transfer from PE towards Chl a via PC and APC is key for the efficient photosynthesis under the green-light window. Hence, we hypothesize that PE and PEB were critical for early cyanobacteria to survive under green-light environments before the GOE. Our phylogenetic analyses support the presence of the PE–PC–APC triad already in the common ancestor of crown-group cyanobacteria (Fig. 3a,b and Extended Data Fig. 9; Supplementary Discussion 9). These phycobiliproteins seem to have evolved successively through ancient duplication events of a primordial protein, in the order of APC, PC and PE^36,37. Unlike the universal distribution of APC and PC in cyanobacteria, PE is sporadically distributed^8,9, due to PE gene loss in many late-diverging species. However, PE exhibits a broader prevalence in early-diverging species (Fig. 3c), suggesting its higher importance during the earlier stages of cyanobacterial evolution. Given the inferred coexistence of all three phycobiliproteins in the common ancestor of modern cyanobacteria, the energy transfer mechanism from PE to the photosystems via PC and APC was probably established within the stem lineage (that is, extinct ancestor lineage) of cyanobacteria under green-light environments before the GOE.

**Fig. 3: Evolutionary relationship of PC- and PE-associated proteins and change in the relative abundance of PE-bearing species in cyanobacteria.**

The stepwise evolution of phycobilisomes potentially mirrors a gradual shift in the light window of the Earth from blue to green (see section ‘Transition of light window through the history of Earth’ below). Ancestral chlorophyll-based photosynthesis probably used the Soret band absorption of Chl a spanning the range 350–450 nm (Fig. 1c), but the band cannot be used for green light because of the uphill-type energy transfer. However, green-light energy can still be transferred to Chl a via another absorption peak in the red region. APC and PC have large absorption peaks in the red and orange regions, but they also weakly absorb green light (Fig. 1c). Hence, APC and PC possibly had a selective advantage for host cyanobacteria to use green light, even without PE. The progressive transition to the green-light window would have led to the further adaptation of phycobiliproteins towards PE, which have stronger absorption peaks in the green region than APC and PC, yet their absorption spectra overlap with one another and thus enable the consecutive energy transfer from PE to PC, APC and Chl a.

Depending on the evolutionary timing of iron oxidizing bacteria³⁸, photoferrotrophy perhaps induced the green-light window before cyanobacterial evolution and thus primitive cyanobacteria were possibly under selective pressure towards green light from early on. Considering that photoferrotrophs can thrive in very low-light environments, it is possible that photoferrotrophs continued to exist in anoxic regions below the pycnocline even after the green-light environment had fully formed (Fig. 1a). At a depth of 50 m under a 10 µM concentration of iron hydroxide, a very faint light environment (~0.1 µmol m⁻² s⁻¹ nm⁻¹) might exist, with light levels comparable to those in current green-light environments (~0.01% photosynthetically active radiation (PAR))³³. Additionally, the weak absorption spectra of bacteriochlorophyll (BChl) a and b, ranging from 550 to 600 nm, fully overlap with the green-light environment.

Utility of phycobiliproteins for photosynthesis

We further delve into the rationale behind the use of PE and the associated pigment PEB through comparative analyses of PEB with β-carotene, a carotenoid pigment universally distributed in cyanobacteria, in terms of their applicability to photosynthetic antenna systems under green-light conditions. Given that the absorption wavelength peak of β-carotene lies below 500 nm (Fig. 5b, left), PEB is apparently better aligned to absorb green light. The molar extinction coefficient of PEB alone³⁹ is approximately one-second to one-third that of other pigments such as β-carotene and Chl a (refs. ^40,41). However, the covalent attachment of PEB to PE leads to about twofold augmentation of the molar extinction coefficient upon light absorption³⁹. Hence, the efficacy of PEB as a light-harvesting antenna is comparable to that of β-carotene, in terms of the absorption coefficients, and PEB is better suited for green-light absorption than β-carotene.

The green-light energy absorbed by PEB in PE is eventually transferred to Chl a in photosystems via another phycobilin pigment, PCB, attached to ApcE or ApcD in APC⁴² (Fig. 2a). In this sense, the Förster distance R₀, which is the molecular distance that maintains 50% energy transfer efficiency, between PCB and Chl a is another critical factor to determine the overall energy transfer efficiency of phycobilisomes. In our analyses, the Förster distance between PCB in APC and Chl a is found to be approximately seven times longer than that between β-carotene and Chl a (Supplementary Table 2). This is attributed to the high fluorescence quantum yield of PCB and the substantial spectral overlap between APC and Chl a (Fig. 4a and Supplementary Table 2). In general, a larger Förster distance enables energy transfer between more distant molecules. Thus, thanks to the water-soluble phycobiliproteins⁵, large light-harvesting antennas such as phycobilisomes can be formed outside host membranes.

**Fig. 4: Comparison of excitation energy transfer from carotenoids to chlorophylls in photosystems, as evaluated using quantum chemical analysis.**

Moreover, based on the known core antenna structure of a cyanobacterium Synechocystis sp. PCC 6803, the efficiency of energy transfer from carotenoids, including β-carotene, to Chl a in PSII is found to be much lower than that in PSI (Fig. 4b,c and Supplementary Tables 3–5). These observations suggest that β-carotene is not as effective as phycobilin pigments under the green-light window. Hence, the evolution of phycobilisomes was a reasonable and necessary result of the green-light adaptation of cyanobacterial photosystems.

Transition of light window through the history of Earth

Our study presents a comprehensive picture elucidating the co-evolutionary trajectory between cyanobacteria and the light environment. Because of the nearly anoxic atmosphere before the GOE⁴³, the surface of the Earth was potentially exposed to harmful UV-C light >200 nm (ref. ⁴⁴). Primitive cyanobacteria and photoferrotrophs probably thrived in deeper regions of the photic zone (~20–30 m)²⁸ because of the lack of protective shields against UV-C radiation⁴⁵. The light window, predominantly influenced by water, favoured a spectrum leaning towards blue, hence termed the ‘blue-light window’ (left panel of Fig. 5). This could explain the alignment of Chl a– and BChl-based photosynthesis with the blue-light window, suggested by the absorption spectrum of Chl a and BChl, matching the spectral range of this window^46,47.

**Fig. 5: Three light windows for the habitats of photosynthetic organisms.**

Phycobilisomes probably evolved according to the light environment of cyanobacterial habitats. The stepwise development of phycobilisomes seems to mirror the gradual change in the light window due to the oxidation of the aquatic environment by cyanobacteria or the direct oxidation of reduced iron by photoferrotrophs, which may have initiated before the birth of cyanobacteria³⁸. A green-light environment may have additionally been created through the photochemical oxidation of reduced iron (Fe(II)) by UV radiation^48,49. Resulting Fe(III)-rich minerals might have also protected cyanobacterial habitat from harmful UV radiation (Extended Data Fig. 2). This pivotal transition facilitated the evolution of modern-type cyanobacteria that developed phycobilisomes to transfer the green-light energy to Chl a, via three essential phycobiliproteins—PE, PC and APC. Phycobilin pigment biosynthesis may have branched off from chlorophyll biosynthesis, sharing the intermediate protoporphyrin IX, particularly in response to the rise of oxygen, since the intermediate biliverdin IXα is synthesized from protoporphyrin IX via oxygen-dependent haem oxygenase⁵⁰ (Supplementary Discussion 9). Capitalizing on the energy endowed by green light, modern-type cyanobacteria may have ascended as primary producers, triggering the GOE.

Following the two oxidation events of Earth, the GOE and the neoproterozoic oxygenation event, the fully oxidized aquatic environment expanded its light window to white light (Fig. 5, right). This transformation resulted from the depletion of oxidized iron species within the aquatic environment and the formation of the ozone layer, thus opening diverse colour niches for phototrophic organisms¹⁰. Terrestrial cyanobacteria then successfully spread over the entire Earth by adapting to various land conditions⁹. Compared to marine cyanobacteria that thrive under various light environments, including dominant green-light environment, terrestrial cyanobacteria tend to possess only APC and PC⁹ because of PE loss as an adaptation to white-light environments on land. Whereas PE becomes dispensable in brighter white-light conditions on land, it retains a more crucial role in dimmer underwater conditions. From the perspective of energy transfer from the light-harvesting antenna to the photosystem, this adaptation suggests that cyanobacteria may have favoured using pigments absorbing light at wavelengths close to those absorbed by the special pair of Chl a in photosystems.

In conclusion, our study traverses through three distinct light windows—blue, green and white—marking different eras in the history of the Earth. This narrative envisions a pre-GOE Earth as a ‘pale green dot’, symbolizing a potential indicator of aquatic life on distant worlds and contributing to our understanding of the evolutionary journey of photosynthetic organisms.

Methods

Calculation of concentration for iron hydroxide

We quantitatively evaluated the concentration of iron hydroxides in cyanobacterial habitats using numerical simulations. The redox state of the ocean has transitioned through the co-evolution of Earth and life, categorized into four epochs⁵¹ (Supplementary Discussion 1). Our study focuses on the second epoch, spanning from the emergence of cyanobacteria to the GOE. During this period, oxygen produced by cyanobacteria oxidized the mixed layer above the pycnocline, aligning with previous findings that oxygen was present in regional areas with higher concentrations, forming ‘oxygen oases’^25,52. Conversely, the layer below the pycnocline remained largely anoxic, as material exchange across this boundary was markedly limited^26,53. Environments resembling the redox conditions of the Archaean era still exist on present-day Earth, such as Lake La Cruz⁵⁴, Lake Paul⁵⁵, Lake Matano¹⁷, Lake Pavin⁵⁶ and the Red Sea⁵⁷. The distinct boundary layer promotes the production of iron hydroxides in the pycnocline (chemocline), which is largely consistent with the observations in these modern, similar environments³⁴. However, some differences exist between the Archaean era and these modern analogues (Supplementary Discussion 12).

Reduced iron from hydrothermal vents was supplied to the pycnocline, where it was oxidized by dissolved oxygen in water^19,58 and by photoferrotrophs^18,20,21. Iron hydroxide particles, produced through the oxidation of reduced iron, were transported by lateral ocean currents and vertical eddy diffusion before precipitation occurred due to the decoupling of larger particles from the oceanic advection and diffusion processes. While lateral oceanic advection influences the horizontal distribution of iron hydroxide from coastal areas to open oceans, vertical eddies primarily determine the vertical distribution^59,60. There may have been horizontal gradient in the distribution of iron hydroxide on a global scale. However, the local underwater transmission spectrum is mainly determined by the vertical distribution of iron hydroxide. Therefore, we performed numerical simulations to estimate the vertical distribution of iron hydroxide by considering its formation via chemical reaction, eddy diffusion and precipitation. As reduced iron, primarily sourced from the ocean floor, reaches the boundary between oxic and anoxic zones, iron hydroxide is formed via chemical reactions between oxygen and reduced iron. While reduced iron, oxygen and iron hydroxide are transported solely by vertical diffusion, iron hydroxide also undergoes precipitation. As an initial condition, the calculation box contains oxygen only above the pycnocline. We assumed that the concentrations of oxygen in the oxic region (above the pycnocline) and reduced iron at the bottom of the box are constant over the calculation time. Reduced iron supplied from the bottom of the box spreads throughout the box as a result of vertical diffusion over time. All the parameters used for this calculation were compiled in Supplementary Table 6.

On the basis of the above considerations, we modelled a one-dimensional region with a height of 150 m such that lateral advection is negligible. The following equations were established:

$$frac{partial left[{rm{Fe}}^{3+}right]}{partial t}=kappa frac{{partial }^{2}left[{rm{Fe}}^{3+}right]}{partial {z}^{2}}+{k}_{rm{ox}}{left[{rm{{O}}}^{2}right]}^{0.58}{left[{rm{OH}}^{-}right]}^{2}left[{rm{Fe}}^{2+}right]-frac{2}{3}{10}^{-6}left[{rm{Fe}}^{3+}right],$$

(1)

$$frac{partial left[{rm{{O}}}^{2}right]}{partial t}=kappa frac{{partial }^{2}left[{rm{{O}}}^{2}right]}{partial {z}^{2}}-{k}_{rm{ox}}{left[{rm{{O}}}^{2}right]}^{0.58}{left[{rm{OH}}^{-}right]}^{2}left[{rm{Fe}}^{2+}right],$$

(2)

$$frac{partial left[{rm{Fe}}^{2+}right]}{partial t}=kappa frac{{partial }^{2}left[{rm{Fe}}^{2+}right]}{partial {z}^{2}}-{k}_{rm{ox}}{left[{rm{{O}}}^{2}right]}^{0.58}{left[{rm{OH}}^{-}right]}^{2}left[{rm{Fe}}^{2+}right],$$

(3)

where [i] and (frac{partial left[iright]}{partial t}) are the concentration and production rate of the ith species, respectively, κ is the eddy diffusivity and k_ox is the coefficient of the reaction rate between oxygen and reduced iron. The eddy diffusivity is assigned two different values: a higher value above the pycnocline and a lower value below it (Supplementary Table 7). It is necessary to note that [Fe³⁺] and [Fe²⁺] represent the concentrations of iron hydroxide and reduced iron, respectively. The second term of each equation represents iron hydroxide formation under a low oxygen concentration (<10 µM)⁶¹. The first term of each equation describes the vertical transport of each species through diffusion. The third term of equation (1) represents the removal of iron hydroxide from the calculation area through precipitation based on the particle sedimentation velocity as measured in a previous study⁵⁵.

We obtained equilibrium distributions for all three species. Although we assumed that reduced iron is oxidized by the dissolved oxygen in water, the concentration of iron hydroxide remains unchanged regardless of the oxidation process. This is because all the reduced iron can be consumed by photoferrotrophs thanks to its faster oxidation rate than the chemical reaction rate between oxygen and reduced iron (Supplementary Discussion 2).

It is also important to note that silica might have been largely dissolved in the Archaean ocean²¹, leading to a much higher concentration of reduced iron even in the oxidized zone. This is because the dissolved silica is transformed into silica–Fe(II) minerals through reaction with reduced iron⁶². As a result, the concentration of iron hydroxide may have been affected by silica. However, because it is difficult to quantitively evaluate the reaction rate between dissolved silica and reduced iron, we did not consider the impact of the dissolved silica on the underwater transmission spectrum, which should be treated by a future study (Supplementary Discussion 5).

Measurement of iron hydroxide absorption coefficient

Colloidal iron hydroxide was prepared by adding FeCl₃ solution to boiling ultrapure water or by adding NaOH solution to FeSO₄ solution^27,63. The final concentration of FeCl₃ was 100 µM and FeSO₄ solutions were prepared at concentrations of 100 µM or 1 mM, respectively. The solution pH was measured using an Horiba pH meter F-52 (Horiba). The pH values of colloidal suspensions of iron hydroxide prepared from 100 µM FeCl₃, 100 µM FeSO₄ and 1 mM FeSO₄ solution were pH 4, 9 and 7, respectively. At each time after the preparation of iron hydroxide, the transmittance spectra were measured using a V-650 spectrophotometer (Jasco) equipped with an integrating sphere (ISV-722, Jasco), with ultrapure water serving as the reference. It was assumed that all iron formed Fe(OH)₃, and the molar absorption coefficient of colloidal suspension of iron hydroxide was calculated from the transmittance as Fe(OH)₃.

The particle-size distribution of the aqueous colloidal iron hydroxide solution was evaluated from the autocorrelation function determined using dynamic light scattering (DLS) techniques (FeCl₃ and 100 mM FeSO₄) or laser diffraction techniques (1 mM FeSO₄), respectively. DLS measurements were carried out using an Otsuka ELSZ-2 analyser (Otsuka Electronics). Colloidal suspension of iron hydroxide prepared from FeCl₃ at a final concentration of 1 mM was used for DLS measurements, because that of 100 μM was below the detection limit. Laser diffraction measurements were carried out using an Horiba LA-920 (Horiba). Relative refractive index values of 2.39 (iron hydroxide) and 1.33 (H₂O as solvent) were applied for particle-size analysis, according to the instrument manual.

Calculation of light window

The spectral range of light that permeates the habitat of photosynthetic organisms, referred to as the light window, emerges as a consequence of the interplay between solar irradiance and the transmittance properties of both the atmospheric and aquatic environments. Within the visible spectrum, this light window is primarily governed by the product of the water and atmospheric transmittances. In modern water environments, the absorptions of water, dissolved ion, phytoplankton, non-algal particles and coloured dissolved organic matters primarily govern the underwater transmission spectrum⁶⁴. However, given that biomass might have been much lower in the Archaean ocean than in modern water environments as a result of very limited availability of phosphorus⁶⁵, the absorptions of phytoplankton and coloured dissolved organic matters were ignored. It is also important to note that, although reduced iron was abundant in the Archaean water environments, its absorption coefficient is very low, except for the UV wavelength range⁴⁶. As a result, the effects of only water and iron hydroxide as non-algal particles on the underwater transmission spectrum were considered. On the other hand, there may also exist some other factors affecting the light window. The uncertainties related to the light window analysis are covered in Supplementary Discussion 5.

Regarding the incident solar spectrum at the top of the atmosphere, although there was a 30% increase in the brightness of the Sun over the course of the history of the Earth, the solar spectrum is presumed to have remained largely unchanged⁶⁶. Therefore, using the contemporary solar spectrum in our analysis is unlikely to affect the conclusion of this study. The stable nature of atmospheric transmission across the visible spectrum (400–700 nm) both before and subsequent to the GOE⁶⁷ validates the adoption of the air mass 1.5 spectra, as defined by American Society for Testing and Materials.

For the calculation of underwater transmittance, the proportion between the incident irradiance upon the water surface, denoted as I₀ (λ) and that prevailing at a depth d, labelled as I_d (λ), is derived through the expression:

$${I}_{d}left(lambda right)/{I}_{0}(lambda )={mathrm{e}}^{-{K}_mathrm{d}(lambda )d},$$

(4)

where λ is the wavelength of the light and K_d denotes diffuse attenuation coefficient. The measurement value of clear ocean water⁶⁸ was adopted as the diffuse attenuation coefficient for this calculation. During the era spanning the emergence of cyanobacteria to the GOE, as discussed in the second epoch in Supplementary Discussion 1, the absorption coefficient is predominantly influenced by iron hydroxide in the form of mineral particles and by water itself. The molar absorption coefficient of iron hydroxide, detailed in Supplementary Discussion 3, was thus integrated into our analysis. We incorporated the measured molar absorption coefficient of iron hydroxide into this analysis. On the basis of our numerical simulations, documented in Supplementary Discussion 2, the concentration of iron hydroxide in cyanobacterial habitat varied from 1 to 10 µM for the standard model and possibly increases up to 100 µM. It is important to note that only the absorption coefficient was considered, as the scattering coefficient is deemed constant across the visible spectrum⁶⁹.

As discussed in Supplementary Discussion 4, considering that a layer rich in Chl a, formed through the balance between light and nutrients, is typically located at the pycnocline and nitracline in open oceans, we set cyanobacterial habitat depths at 50 and 20 m and calculated the incident light spectrum at these same depths (Extended Data Fig. 3a,b). Provided the high molar absorption coefficient of hydroxide in harmful UV light, the habitat could be expanded to the shallow waters (~5 m), consistent with the geological records^30,31 (Extended Data Fig. 3c).

Sampling site

Water sampling was conducted during cruise of the ship in the sea around Iwo Jima (90 m from shore, 130.320° E, 30.784° N) on 1 November 2023. Water depth, temperature and salinity data were obtained using CTD (smart-ACT, JFE) attached to a Van Dorn water sampler or the spectrometer. Seawater samples were collected for phycoerythrin and Chl a determination, flow cytometry, determination of iron and the measurement of dissolved oxygen (Supplementary Table 8). Transmitted light spectrum was measured with an optical fibre-based compact CCD spectrometer Thorlabs CCS 200 (Thorlabs). On board, dissolved oxygen and pH was measured using Lutron DO-5509 dissolved oxygen meter hydrometer (Mother Tool) and an Horiba LAQUAtwin B-712 pH meter, respectively.

Determination of iron

Quantification of iron in seawater was performed by conventional phenanthroline colorimetric method. The seawater samples (100 ml) were immediately acidified with hydrochloric acid on board and stored in 100 ml polyethylene bottles. An aliquot of 645 μl of sample or reference solution was mixed with 32 μl of 0.3 M hydroxylamine hydrochloride solution. After the reduction of Fe(III) to Fe(II), 162 μl of sodium acetate solution and 162 μl of 0.25% 1,10-phenanthroline were added. After incubation for 15 min at room temperature, absorbance at 510 nm was measured.

Flow cytometry

For flow cytometric analyses of cyanobacteria and pigmented nanoflagellates (PNF), water samples were initially fixed with a 2% glutaraldehyde solution, followed by preservation through freezing in liquid nitrogen and subsequent storage at −80 °C for future analysis via flow cytometry⁷⁰. Upon thawing, the frozen samples were subjected to analysis using a Quantum P flow cytometer (Quantum Analysis) equipped with a laser emitting at 488 nm. Samples were processed at a rate of ~5 μl min⁻¹ until reaching a volume of 600 μl per sample. The presence of cyanobacteria and PNF was initially verified through fluorescence microscopy. Detection of cyanobacteria and PNF was accomplished by plotting yellow/green fluorescence against orange fluorescence⁷¹. The positioning of cyanobacteria with distinct pigments on the cytogram was corroborated using wild-type (PC-only) and PEB-MX (PE) S. elongatus PCC 7942 cells, while the placement of PNF on the cytogram was referenced from the previous study⁷². Furthermore, each group was divided into subgroups with high and low fluorescence values based on orange fluorescence.

Phycoerythrin and Chl a determination

One litre of seawater passed through a hand net (150 μm mesh) was filtered onto 47 mm Whatman GF/F filters and kept frozen until analysis. The extraction method of phycourobilin (PUB) and PEB chromophores was modified from the previous study⁷³. The filters were cut and extracted in 5 ml of 0.1 mol l⁻¹ of NaH₂PO₄ (pH 6.5) and maintained for 3 h at 4 °C in the dark. Filters were resuspended by vigorous vortex mixing and centrifuged for 10 min at 2,500 rpm. The fluorescence of about 3.5 ml of the supernatant was measured using a Shimadzu RF-5300PC fluorescence spectrophotometer at room temperature (Shimazu). The excitation of phycoerythrin was recorded at 1 nm intervals between 450 and 580 nm (emission fixed at 605 nm). Slit widths were set at 5 nm and 5 nm at excitation and emission, respectively. Excitation spectra of PUB appeared around 495–500 nm while excitation spectra of PEB appeared around 540–560 nm. Chl a was extracted in 8 ml of N,N-dimethylformamide (DMF) by immersing the filter fully into a DMF solution in the dark at −30 °C for 24 h. The samples were measured using a Turner Designs Trilogy fluorometer (Turner Designs) with a CHL-A NA Module (SN: 7200-046-W; excitation at 436 nm, emission at 685 nm).

Cyanobacterial strains and culture conditions

We used G. violaceus PCC 7421 and S. elongatus PCC 7942 as model species for natural selection experiments. Gloeobacter represents the earliest-branching clade (Gloeobacterales) within cyanobacteria^14,15,74 and possesses both PE and PC, in addition to APC. It is important to note that Gloeobacter only represents Gloeobacteraceae, while Anthocerotibacteraceae is also classified into the order Gloeobacterales⁷⁵. These two clades diverged 1.4 billion years ago and have distinct features: Anthocerotibacter lack PE and have paddle-shaped phycobilisomes⁷⁶. By contrast, most cyanobacteria, including the well-studied S. elongatus PCC 7942, possess only APC and PC. The difference in growth conditions between these two taxa are of interest to infer the physiological importance of PE and green light for cyanobacteria. G. violaceus and S. elongatus are extant species and so it remains uncertain whether they accurately represent ancestral species that might have dominated in the Archaean era. However, because our window analyses apply to any photosynthetic species, regardless of their taxonomic classification and habitats, the model species selection does not affect the main conclusions of our study (Supplementary Discussion 6).

The cultures of G. violaceus PCC 7421 were purchased from the Pasteur culture collection (PCC), while the cultures of S. elongatus PCC 7942 was prepared from our own collection in the laboratory of Nagoya University. G. violaceus PCC 7421 and S. elongatus PCC 7942 were grown in 100 ml conical flasks containing liquid BG-11 medium at 30 °C (ref. ⁷⁷). For G. violaceus and S. elongatus, cell cultures were grown under static culture conditions and bubbled with air, respectively. For S. elongatus, liquid cultures grown for 3 d after inoculation were used. Cells were illuminated from the bottom of the conical flask with a 5,000 K light-emitting diode (LED) daylight light or green LED light (peak at 520 nm). For G. violaceus and S. elongatus, the light intensity was adjusted to 10 or 40 μmol m⁻² s⁻¹, respectively. It is important to note that the cell cultures stirred by bubbling with air during the experiments had no impact on the transmission spectrum. This observation aligns with the assumption that cyanobacterial abundance might have been low in the Archaean era because of the limited availability of phosphorus⁶⁵.

Optical density (OD) was measured as the absorbance of the cell suspension at 750 nm (G. violaceus) or 730 nm (S. elongatus) using a Genequant100 (GE Healthcare). Both wavelengths measure light scattering by cells without being affected by Chl a absorption, so the OD values do not change largely. For the measurement of the OD of G. violaceus, the cell suspension was diluted by half with 40% glycerol to prevent cell sedimentation.

Spectral analysis

Absorption spectra were acquired using a V-650 spectrophotometer (Jasco) equipped with an integrating sphere (ISV-722). The excitation fluorescence spectra were recorded at 77 K using a FP-6500 fluorescence spectrophotometer (Jasco). For the measurement of G. violaceus, the cell suspension was diluted by half with 40% glycerol to prevent cell sedimentation.

Construction of PEB biosynthesis mutants

To introduce pebAB genes into S. elongatus, pebAB genes from a chromatically acclimating cyanobacterium, Synechococcus sp. RCC307, were placed under the control of the strong promoter for S. elongatus PC subunit gene clusters, cpcB1A1 (ref. ⁷⁸) and introduced into a neutral site II of S. elongatus. For this experiment, the pebAB genes were synthesized by Eurofins Genomics according to the sequence reported in the National Center for Biotechnology Information (NCBI) database (locus tag: SynRCC307_2061 for pebA and SynRCC307_2062 for pebB) and were amplified by polymerase chain reaction (PCR) with primers pebAcpc-f (5′-TTGAAGAATGATGGGATGTTTGATTCCTTCCTCG-3′) and pebB-rv (5′-ACTCTAGAGGATCCGTTACATCCACTTCTTATCAA-3′). The cpcBA promoter was amplified by PCR from the genome of S. elongatus, with primers cpcPro-f2 (5′- CTGGCTGGATGATGGGTCGACCATCAACTTAAAG-3′) and cpcPro-rv (5′- CCCATCATTCTTCAAGAAAACTCTCGATTG-3′). The pebAB genes and the cpcBA promoter were cloned into pNS2KmT∆HincII-Ptrc vector⁷⁹. The DNA fragment including neutral site II and kanamycin-resistance gene were amplified by PCR from the pNS2KmT∆HincII-Ptrc with primers NS2Ptrc-f (5′-CGGATCCTCTAGAGTCGACCTGCAG-3′) and NS2Km-rv (5′- CCATCATCCAGCCAGAAAGTGAGGG-3′). PCR-amplified products of pebAB and the cpcBA promoter were cloned into PCR-amplified products of pNS2KmT∆HincII-Ptrc vector by the In-Fusion HD cloning method (Clontech, Takara Bio). S. elongatus was transformed with the resultant plasmid, named pNS2KmPcpc–pebAB. PebAB-MX was obtained from PebAB-OX cells with spontaneous mutation showing green–brown colour. The cpcBA promoter in PebAB-MX cells had 4 base pair (bp) (GAAG) insertion 14 bp before the translation start site of pebA and had no mutation in pebAB genes.

Competition experiments between PebAB-MX and wild type

Liquid cultures grown for 3 days under white light after inoculation were used. PebAB-MX and wild-type cells were diluted and mixed to an OD₇₃₀ of 0.01. The mixed cultures were grown while being bubbled with air and illuminated from the bottom of the conical flask with an LED daylight light or a green LED light (peak at 520 nm) (40 μmol m⁻² s⁻¹). The cultures were diluted to an OD₇₃₀ of 0.02 every 3–4 or 7 days for white or green light, respectively. To analyse the percentage of PebAB-MX and wild-type cells, small amounts of the PebAB-OX cultures were incubated on solid BG-11 plates with or without kanamycin (10 mg l⁻¹) and the numbers of colonies were counted. Only PebAB-MX cells were selected on BG-11 plates with kanamycin, whereas PebAB-MX and wild-type cells appeared on BG-11 plates without kanamycin. The number of generations was estimated from the OD₇₃₀.

Analysis of spontaneous mutations in PebAB-OX cells

To analyse the spontaneous mutations in PebAB-OX cells, small amounts of PebAB-OX cultures were incubated on solid BG-11 plates and the numbers of green or brown colonies were counted. On 74 randomly chosen colonies, cpcBA promoter and pebA and pebB genes of green colonies of PebAB-OX were sequenced by colony PCR with primers NS2SacIseq-f (5′- CGATAAACGAGCTCGTAAGCGG-3′) and NS2BamHIseq-rv (5′- GCCCTTGCTTTGGGCGATTGAT-3′) using Quick Taq HS DyeMix (Toyobo).

Phylogenetic analyses

Representative sequences for phycobilisome-associated proteins were identified from UniProt (https://www.uniprot.org/). PE-associated proteins include PebA (Q7NL66), PebB (Q7NL65), CpeA (Q7NLD7), CpeB (Q7NLD6), CpeC (Q7NL63), CpeD (Q7NL62), CpeE (Q7NL61), CpeS (Q7NLD4), CpeT (Q7NLD3) and CpeY (Q7NLD8). PC-associated proteins include PcyA (Q7NHE8), CpcA (Q7M7F7), CpcB (Q7M7C7), CpcC (Q7NM19), CpcS1 (Q7NLD5), CpcS2 (Q7NKE7), CpcT (Q7NLE2) and CpcE (Q7NL58). It is noted that the CpcC homologue in Anthocerotibacter is now annotated as CpcJ⁸⁰. These protein sequences were used as enquiries to identify homologous sequences in other cyanobacteria. Sequences were retrieved from GenBank (http://www.ncbi.nlm.nih.gov/) using BLASTp and PSI-BLAST^81,82, with a cutoff threshold of <1 × 10⁻⁵. Sequences were aligned using Muscle v.3.8.31 (ref. ⁸³). The amino acid sites that are conserved in <5% of the analysed species were removed, except the carboxy and amino termini, where amino acid sites with <50% conservation were removed. Phylogenetic trees were constructed by maximum likelihood inference using IQ-TREE v.2.1.06 (ref. ⁸⁴). Substitution models were selected using ModelFinder in IQ-TREE-LG matrix with empirical frequencies estimated from the data (F) and the FreeRate model for rate heterogeneity across sites (R). Branch support was obtained by Ultrafast bootstrap and SH-aLRT in IQ-TREE.

Species selection was based on a recent phylogenomic study of cyanobacteria^8,9 and taxonomically redundant sequences were excluded. Many species were found to possess multiple homologues for enquiry sequences. Therefore, preliminary phylogenetic analyses were performed and the clustering pattern of those homologues was measured. If individual homologues from a species were separately distributed in different clades, all homologues were retained. By contrast, if those homologues were distributed in the same clades that contain only one species, only the homologue that had the shortest branch length was retained as the representative for the clade. Distantly related proteins that did not constitute phycobilisomes were used as the outgroup in the case of phycobilin synthase (PcyA and PebAB) and lyase (CpcS and CpeS). In the case of CpcS, it was not clear which homologues were involved in phycobilisome formation and hence all clades were taken into account (Fig. 3b).

A few cyanobacteria were found to possess CpeC and CpcC homologues that have a multidomain architecture (about three PBP linker domains) even though CpeC and CpcC generally consist of a single domain. The multidomain architecture was found in, for example, the genera Leptolyngbya (CpeC-like; U9W1D6, U9W8A0) and Gloeobacter (CpcC-like; Q7NGT2, Q7NL64). Whether these proteins have the same function as CpeC and CpcC is unclear. These multidomain proteins are homologous to each other and are further homologous to ApcE, which generally has a similar multidomain architecture. Hence, the multidomain architecture might represent an ancestral trait of the entire PBP linker protein family (CpeC, CpcC, ApcE and so on). However, the presence of multidomain proteins is punctate within cyanobacteria for both CpeC and CpcC. Also, in all cases, single-domain and multidomain proteins coexist in host organisms. Hence, single-domain CpeC and CpcC appear to be the dominant form, whereas multidomain homologues are probably later acquisitions in a few specific lineages. For phylogenetic analyses, individual domains were separately treated as single-domain proteins. Phylogenetic analyses suggested that CpeC- and CpcC-like multidomain proteins cluster together with single-domain CpeC and CpcC proteins, respectively, rather than with ApcE. Hence, multidomain proteins are inferred to have evolved from gene duplications and subsequent fusions of the CpeC and CpcC genes within individual host organisms. Also, CpeY consists of two HEAT repeat domains. Only the domain at the N terminus is homologous to CpcE and other PBS-related proteins. Hence, the domain at the C terminus was removed.

Fraction of cyanobacteria possessing the PE gene (cpeA)

The fraction of cyanobacteria having PE that branched before and during the GOE was estimated by comparing the distribution of the PE gene (cpeA; encoding the PE α subunit)^8,9 in the phylum, using a previously published species tree and Bayesian relaxed molecular clock analysis of cyanobacteria^14,15. First, we grouped the species listed in two distinct trees^8,9 in terms of the similarity of 16S ribosomal RNA⁸⁵. The 16S rRNA gene sequences of cyanobacterial strains were obtained using the BLAST-N search programme in the NCBI database (http://www.ncbi.nlm.nih.gov). If the 16S rRNA gene sequence information was unavailable, the respective species were excluded from our samples. The 16S rRNA gene identity for two adjacent strains in Fig. 3 in ref. ⁸ and Fig. 5 in ref. ⁹ was calculated with the BLAST-N search programme or with ClustalW using the web platform https://npsa-prabi.ibcp.fr/cgi-bin/npsa_automat.pl?page=/NPSA/npsa_clustalwan.html. Species having >95.0% similarity to each other were grouped in the same species cluster. By doing so, our calculation remains unaffected by the sampling number of species. If a cluster contained both species that have and lack cpeA, the ratio of the species having cpeA was calculated as the fraction of the number of the species with cpeA to the total number in the cluster. Second, we selected the taxonomic clades that are inferred to have branched before the GOE, based on the two independent molecular clock analyses^14,15. However, the taxonomic groups of Acaryochloris marina MBIC11017, Synechococcus sp. PCC 6312 and Thermostichus lividus PCC 6715 were found to have branched nearly simultaneously with the GOE and the date uncertainty prevented us from securely classifying them as early branching. Therefore, we prepared two sets of the early-branching clades: one included these groups (extended early branching; brown bar in Fig. 3c), while the other excluded them (early branching; green bar). Finally, we calculated the fraction of cyanobacteria having cpeA relative to the total number of species for both early-branching clades and all extant clades.

Calculation of electronic coupling, orientation factor and spectral overlap

The energy transfer efficiency is proportional to the spectral overlap between the fluorescence spectrum of the donor and the absorption spectrum of the acceptor. Spectral overlap calculations were performed using the PhotochemCAD 3 programme⁸⁶, where β-carotene and APC-B fluorescence spectra⁸⁷ and the Chl a absorption spectrum⁸⁸ were adopted.

The Förster distance R₀ is given by the following equation:

$${R}_{0}={left(frac{9left(mathrm{ln}10right){kappa }^{2}{varphi }_{rm{D}}}{128{pi }^{5}{N}_{rm{A}}{n}^{4}}Jright)}^{frac{1}{6}},$$

(5)

where N_A is the Avogadro constant, κ is the orientation factor between the transition dipoles of the donor and acceptor molecules, φ_D is the fluorescence quantum yield of the donor molecule, n is the refractive index and J is the overlap between the fluorescence spectrum of the donor molecule and the absorption spectrum of the acceptor molecule. As summarized in Supplementary Table 6, we used 6.00 × 10⁻¹ and 6.00 × 10⁻⁵ for the fluorescence quantum yields of phycobilin⁴² and β-carotene⁸⁹, respectively; used 1.60 × 10⁻¹² and 1.35 × 10⁻¹³ M⁻¹ cm³ for the spectral overlap of phycobilin–Chl a and β-carotene–Chl a, respectively; and assumed that the other parameters in the Förster distance have the same values between phycobilin and β-carotene. The ratio of the Förster distance of phycobilin–Chl a to β-carotene–Chl a, R₀^P/R₀^C, was then calculated to be 7.01.

The energy transfer efficiency is also proportional to the square of the electronic coupling between the donor and the acceptor molecules. The electronic coupling V, an intermediate physical quantity representing intermolecular interactions between different electronic states, was calculated using the transition charge from electrostatic potential (TrESP) method⁹⁰ (equation (5)), a typical Coulomb interaction:

$$V=mathop{sum }limits_{iin {rm{A}}}mathop{sum }limits_{jin {rm{B}}}frac{{q}_{i}{q}_{j}}{4pi {varepsilon }_{0}{r}_{{ij}}},$$

(6)

where q_i (q_j) is the transition charge of atom i (j) in molecule A (B); ε₀ is the vacuum permittivity; and r_ij is the interatomic distance. The atomic coordinates of PSI and PSII for Synechocystis PCC 6803 were obtained from experimentally determined structures (PDB entries 5oy0 and 7n8o). The atomic transition charge q_i of each chromophore was determined using time-dependent density functional theory at the ωB97X/6-311 + G(2d,p) (ref. ⁹¹) level in the Gaussian16 programme package⁹². The electronic couplings for all carotenoid–chlorophyll pairs in the PSI or PSII were calculated using equation (6).

The orientation factor κ was calculated using the following equation⁹³:

$$kappa =frac{4pi {{varepsilon }_{0}}{{R}_{rm{AB}}^{3}}}{left|{{mathbf{{upmu} }}}_{{{rm{A}}}}right||{{mathbf{{upmu} }}}_{{{rm{B}}}}|}V,$$

(7)

where V is the electronic coupling determined by equation (6); R_AB is the distance between molecules A and B; and μ_A and μ_B are the transition dipole moments of molecules A and B, respectively. The transition moment of molecule A, μ_A, was calculated by equation (8) using the transition charge q_i and position r_i of atom i in molecule A.

$${mathbf{upmu}}_{rm{A}}={sum} _{iin {rm{A}}}{{q}_{i}}{{bf{r}}_{i}}$$

(8)

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.