Photosynthesis under a red Sun: predicting the absorption characteristics of an extraterrestrial light-harvesting antenna

ABSTRACT

Here, we discuss the feasibility of photosynthesis on Earth-like rocky planets in close orbit around ultracool red dwarf stars. Stars of this type have very limited emission in the photosynthetically active region of the spectrum (400–700 nm), suggesting that they may not be able to support oxygenic photosynthesis. However, photoautotrophs on Earth frequently exploit very dim environments with the aid of highly structured and extremely efficient antenna systems. Moreover, the anoxygenic photosynthetic bacteria, which do not need to oxidize water to source electrons, can exploit far-red and near-infrared light. Here, we apply a simple model of a photosynthetic antenna to a range of model stellar spectra, ranging from ultracool (2300 K) to Sun-like (5800 K). We assume that a photosynthetic organism will evolve an antenna that maximizes the rate of energy input while also minimizing fluctuations. The latter is the noise cancelling principle recently reported by Arp et al. Applied to the solar spectrum, this predicts optimal antenna configurations in agreement with the chlorophyll Soret absorption bands. Applied to cooler stars, the optimal antenna peaks become redder with decreasing stellar temperature, crossing to the typical wavelength ranges associated with anoxygenic photoautotrophs at ∼3300 K. Lastly, we compare the relative input power delivered by antennae of equivalent size around different stars and find that the predicted variation is within the same order of magnitude. We conclude that low-mass stars do not automatically present light-limiting conditions for photosynthesis, but they may select for anoxygenic organisms.

1 INTRODUCTION

Over 5000 exoplanets (planets orbiting stars other than the Sun) have now been detected and confirmed (NASA Exoplanet Archive, https://exoplanetarchive.ipac.caltech.edu/). In addition to detecting planets, we are in some cases now also able to characterize their masses/radii and hence bulk composition (e.g. Seager et al. 2007; Adams, Seager & Elkins-Tanton 2008; Weiss & Marcy 2014) and through direct imaging and transmission spectroscopy probe their atmospheric compositions (e.g. Benneke & Seager 2012; Nikolov et al. 2016; Hinkley et al. 2022). With this information, we are getting ever closer to developing a census of possible habitats and it is becoming increasingly plausible that the presence of life on exoplanets might be inferred (Des Marais et al. 2002; Scalo et al. 2007; Kaltenegger 2017; Schwieterman et al. 2018).

Empirically, the distribution of stellar masses is well known to follow the stellar initial mass function (Kroupa 2001; Chabrier 2003), wherein low-mass stars are much more common. This, coupled to evidence (Mulders, Pascucci & Apai 2015; Hsu et al. 2019a; Hsu, Ford & Terrien 2020a) that terrestrial planetary occurrence rates are higher around low-mass stars, implies that the majority of terrestrial planets orbit stars that have lower mass than the Sun (⁠|$T_{\textrm {eff}} \ \lt \ 5780\,$| K; Hsu et al. ; Hsu, Ford & Terrien ; Ment & Charbonneau 2023). However, we note that the occurrence rate of giants is lower around low-mass stars (Bryant, Bayliss & Van Eylen 2023) and the planet occurrence rate is also sensitive to the stellar metallicity (e.g. Narang et al. 2018; Lu, Schlaufman & Cheng 2020).

A number of terrestrial planets have been discovered around low-mass stars on compact orbits, including well-known examples such as Trappist-1 (Gillon et al. 2017), Proxima Centauri (Anglada-Escudé et al. 2016; Faria et al. 2022), and LHS 1140 (Dittmann et al. 2017). This includes ‘habitable-zone’ planets where it is expected that water would be in the liquid phase on the surface of a rocky planet (Kasting, Whitmire & Reynolds 1993a; Dittmann et al. 2017; Grimm et al. 2018). Trappist-1 in particular has multiple planets in the habitable zone, making it a high-priority target with over 200 h of observing time allocated to that planetary system in JWST cycle 1. However, to understand habitability we need to go beyond the simple definition of supporting liquid water.

Currently, Earth’s biosphere is largely supported by photosynthesis, with oxygenic photoautotrophs specifically being responsible for |${\gt} 99{{\ \rm per\ cent}}$| of the global primary production (Overmann & Garcia-Pichel 2013). This does, however, depend on the biome, with anoxygenic photosynthesis contributing |${\sim } 30{{\ \rm per\ cent}}$| in ancient, sulphide-rich lakes (Overmann & Garcia-Pichel 2013), and chemosynthetic microbes becoming the dominant producers in desert ecosystems (Bay et al. 2021). Previously, it was argued that evolution of multicellular life, particularly animals, was only possible in an atmosphere oxygenated by photosynthesis, though this view is currently being challenged (Cole et al. 2020; Bozdag et al. 2021). Regardless, oxygenic photosynthesis currently covers |$50\!-\!80{{\ \rm per\ cent}}$| of the Earth’s surface (Field et al. 1998) in the form of canopy forests, savannah, grasslands, and marine cyanobacteria and algae, and is detectable, at least at interplanetary distances, as a sharp increase in solar reflectance for wavelengths λ > 700–750 nm (Sagan et al. 1993; Arnold et al. 2002). This ‘vegetation red edge’ (VRE) is therefore a promising potential biosignature to look for in exoplanet surveys (Seager et al. 2005), though it may be hidden in the case of life beneath substrates (Cockell, Kaltenegger & Raven 2009). Biochemically, it arises from chlorophyll a, the pigment responsible for water oxidation and quinone reduction in photosystem II (PSII) and Nicotinamide adenine dinucleotide phosphate (NADP, a redox carrier) reduction in photosystem I (PSI), photochemical processes that require quanta of λ = 680 and 700 nm, respectively. While higher energy photons (400–700 nm) are readily utilized, since excess energy is shed non-radiatively in the antenna (van Amerongen & van Grondelle 2001), redder photons are insufficiently energetic to drive charge separation. This would imply that low-mass stars, with limited emission in the ‘photosynthetically active’ region of 400 nm < λ < 700 nm (see Fig. 1a), are unlikely to support the complex biospheres (Covone et al. 2021). However, this definition of ‘photosynthesis’ is perhaps too narrow. Several species of cyanobacteria bind redshifted Chl d and f, with absorption maxima at 790–800 nm, as an adaptation to light that is strongly attenuated in the 400–700 nm region by the environment and other organisms (Tros et al. 2021; Viola et al. 2022).

Moreover, anoxygenic photoautotrophs, such as purple (Hu et al. 2002) and green sulphur bacteria (Gregersen, Bryant & Frigaard 2011), utilize light in the 800–1000 nm region. They can do this because they source electrons from compounds such as hydrogen sulphide, ferrous iron, hydrogen, etc., which requires less energy (and therefore longer wavelengths) than splitting water (Bryant & Frigaard 2006). It was previously assumed that anoxygenic photosynthesis evolved first, with oxygenic photoautotrophs evolving around the Great Oxidation Event (Lyons, Reinhard & Planavsky 2014), although this has been challenged recently, with compelling genetic (Sánchez-Baracaldo & Cardona 2019) and geological (Wang et al. 2018) evidence for a much earlier appearance. Even so, recent modelling implies that Earth’s VRE signal may have risen to its current level as recently as only 500 Mya, which may limit the likelihood of VRE detection to older, warmer Earth-like planets (O’Malley-James & Kaltenegger 2018). There is therefore significant motivation to broaden our search to redder, more exotic forms of photosynthesis.

It is assumed that the evolution of photosynthetic processes and structures was largely dictated by the intensity, spectral quality, and dynamics of the available light. An early adaptation was the antenna–RC architecture, which massively enhances the absorption cross-section of the photosystems and allows for dynamic regulation of energy input in a fluctuating light environment (Wolfe et al. 1994; Fleming et al. 2012). Physically, the antenna is a massive, modular assembly of light-harvesting pigment–protein complexes. Their function is to capture light and transfer the resulting excited electronic state or ‘exciton’ to the RCs (which they do with near-total quantum efficiency). Antenna proteins generally bind several types of pigments in order to provide broad spectral coverage, creating a ‘funnel’ structure in which higher energy pigments donate to lower energy ones. For example, the major light-harvesting complex of PSII in higher plants, LHCII, binds Chl a and b along with several carotenoids (Wei et al. 2016). Nevertheless, antenna complexes are not blackbodies, instead possessing well-defined and often narrow absorption peaks.

Kiang et al. (2007b) published a comprehensive review of the relationship between the absorption profiles of Earth’s photoautotrophs and their respective local light environments. Based on empirical trends, they proposed several rules: (1) The absorption peak of the antenna is located close to the local irradiance maximum, to maximize energy input. (2) The absorption peak of the RCs is close to longest wavelength in the irradiance range, since excitons must be funnelled from a higher energy antenna. (3) Accessory pigments (such as Chl b or carotenoids in plants) will absorb towards the shortest wavelength of the irradiance window, since they must funnel excitons to the primary pigments (e.g. Chl a) in the antenna.

Following on from Björn (1976), Marosvölgyi & van Gorkom (2010) applied a different approach, considering the balance between the need to absorb as much light as possible with the potentially prohibitive metabolic cost of synthesizing and maintaining a vast array of different pigment co-factors. The model depends on a cost parameter, C, which reflects the fraction of captured energy that is used to synthesize, regenerate, and repair the light-harvesting antenna. Choosing C ≈ 0.96 reproduces the red absorption band of both the chloroplast of oxygenic eukaryotes and the chromatophore of purple bacteria in their respective native light environments. The argument is that there is an optimum band in which to harvesting photon. Harvesting bluer photons carries the burden of synthesizing additional pigments, while harvesting redder photons is less efficient due to an increased likelihood of ambient thermal excitation of the antenna pigments (making stimulated emission rather than absorption more likely). This seems to miss the distinct blue absorption band of the chloroplast which is composed of the Chl a and b Soret bands and the S₂ bands of various carotenoids. They argue that Chl a and b were selected for their red Q_y bands, with their Soret bands being a (fortunate) side effect of their electronic structures. Similarly, they argue that carotenoids were primarily selected for their structural, antioxidant, and triplet-quenching properties. One criticism of this model is that the predicted spectrum is extremely sensitive to the choice of C. For C = 0.96, the predicted antenna spectrum is in very good agreement with the chloroplast Q_y band, even down to the stoichiometry between Chl a and b. However, C = 0.75 yields a single absorption band covering the entire 500–750 nm region of the spectrum, making it almost black. At C = 0.5, it absorbs more-or-less uniformly across 400–900 nm. Moreover, C = 0.96 seems to imply that nearly all of the light energy captured and converted by the organism is reinvested in synthesizing antenna pigments, though this parameter should not be overinterpreted and the fact that the same value of C = 0.96 was found for both plants and purple bacteria indicates this model captures some fundamental features of the antenna.

More recently, Arp et al. (2020) took a different approach, arguing that the absorption profile of the antenna was primarily determined by a requirement for noise cancellation. An antenna is subject to noise, both externally as fluctuations in spectral intensity, and internally due to the stochastic nature of the branching exciton transfer pathways. This risks periods where the photosystems are either underpowered, which reduces growth rate, or overpowered, which risks photodamage. Arp et al. (2020) argue (very convincingly) that this noise is minimized by a two-channel antenna, composed of a pair of Gaussian absorbers with similar (but different) absorption maxima, located where the gradient of the spectrum is steepest (see Fig. 1b; Arp et al. 2020). This principle seems to predict the Q_y and Soret profiles of plants, purple bacteria, and green sulphur bacteria, based solely on the spectrum of locally available light, though it should be noted that these solutions are neither unique nor necessarily optimal (see below).

These different approaches are complementary rather than contradictory, and the relationship between antenna structure and the local light environment is likely dependent on multiple factors. Since this relationship is based (largely) on fundamental rules of photo/redox chemistry, it is reasonable to assume that it is universal.

In 2002, Wolstencroft and Raven modelled the rate of oxygenic photosynthesis on the surface of habitable-zone planets, with and without cloud cover, orbiting a range of stars (Wolstencroft & Raven 2002). Assuming a model absorption profile taken from the model species Nerium oliander, they found that oxygenic photosynthesis performed best on cloudless planets orbiting F-type stars (6000–7500 K) and very poorly around cooler stars (K- and M-type). The reason for the latter was a mismatch between the spectral irradiance and the N. oliander absorption profile. They then proposed that oxygenic photosynthesis around these low-mass stars may still be feasible via multiphoton processes, in which two or more λ > 1000 nm photons deliver the required energy as opposed to a single λ < 700 nm photon. Tinetti, Rashby & Yung (2006) explored this idea further and proposed that such processes could produce a redshifted VRE in the near-infrared (NIR; 750 nm < λ < 1500 nm).

In a companion paper to the one discussed earlier, Kiang et al. (2007a) applied their empirical antenna–irradiance relationship to model irradiances for Earth-like planets orbiting in the habitable zones around F-, K-, and M-type stars. They predicted that F2V stars (∼1.5 M_⊙) would favour photosynthetic pigments that absorb in the blue, K2V stars (∼0.8 M_⊙) would favour red-orange (as they do on Earth), and M-type stars (red dwarf stars, 0.08–0.6 M_⊙) would favour absorbers in several NIR bands (930–1100, 1100–1400, 1500–1800, and 1800–2500 nm). The reason for the multiple bands is that irradiance in the NIR is strongly modified by atmospheric transmission, leading to multiple, distinct bands in the local spectral flux (Segura et al. 2003).

More recently, Lehmer et al. (2021) applied the model of Marosvölgyi & van Gorkom (2010) discussed earlier to similar model irradiances. Assuming that the C = 0.96 cost parameter that applies to Earth organisms is universal, they predicted similar antenna absorption profiles to Kiang et al. (2007a). The one difference was that even for very low-mass M5V stars (⁠|${\sim } 0.16 \, \text{M}_{\odot }$|⁠), the model did not predict absorption in NIR bands at 1100–1400, 1500–1800, and 1800–2500 nm, instead predicting a broad absorption peak at 1050 nm with an almost negligible shoulder predicted at 987 nm. By the logic of the Marosvölgyi & van Gorkom (2010) model, background thermal excitation of the antenna pigments would become significant at longer wavelengths, making light harvesting less efficient.

Finally, at time of writing, Hall et al. (2023) have published a model in which they define the photosynthetic habitable zone as the range of orbital radii in which both liquid water can occur and oxygenic photosynthesis is feasible. The model assumes that the maximal rate of photosynthesis, P_max, is dependent on surface irradiance (via a set of empirical parameters derived from phytoplankton; Yang et al. 2020), ambient surface temperature, and the dark respiration rate, R_rate. R_rate is essentially the steady-state energy requirement of the organism merely to continue existing, including the metabolic burdens of protein turnover, repair, maintaining homeostasis, etc. To enable growth, reproduction, etc., photosynthesis must generate a surplus to R_rate. On Earth R_rate ≤ 0.3P_max, meaning that less than a third of the photosynthetic yield needs to be reinvested in base-level survival, reflecting generally favourable conditions for life on Earth (Geider & Osborne 1989). If conditions are similarly favourable on other Earth-like planets then oxygenic photosynthesis may be feasible around stars of |$\gt 0.6 \, \text{M}_{\odot }$|⁠. This range can be extended to even smaller stars in the absence of any atmospheric attenuation of light or any greenhouse effect (though the authors admit this may be extremely optimistic).

As with Arp et al. (2020), it may be instructive to apply a different set of criteria to this problem. Here, we apply a modified form of their noise cancelling antenna principle to model spectral fluxes of a range of stars, from very low-mass/temperature M-dwarfs to something more like the Sun. We hypothesize that the antenna absorption profile will evolve to minimize input noise while maximizing the total input power.

2 METHODOLOGY

2.1 Model stellar/solar spectra

We use stellar spectral models for stars of different masses/temperatures generated by the phoenix radiative transfer code (Husser et al. 2013). These are typically over one and half million lines in length, so we smooth and resample the spectrum down to 4000 points, which still captures the large-scale features and reduces the computation time for calculating the optimal antenna absorption characteristics (see Fig. 1a). Smoothing features over wavelength ranges smaller than the smallest absorption band we consider is justified, given that all radiation across the band is absorbed. In other words, antenna bands cannot resolve spectral variations on scales smaller than their own effective width.

The standard solar spectrum used in Fig. 3 is an AM1.5 spectrum generated by the latest version of the smarts code (Gueymard 2004) and published by NREL (SMARTS: Simple Model of the Atmospheric Radiative Transfer of Sunshine, https://www.nrel.gov/grid/solar-resource/smarts.html).

2.2 Determining optimal antenna absorption characteristics for a given stellar spectral flux

Here, we describe how we construct our basic model as a noise cancelling system that maximizes the total power input, as discussed earlier. In line with the previous work of Arp et al. (2020), we assume that the antenna absorption profile is comprised of a closely spaced Gaussian doublet (see Figs 1b and c),

where,

λ₀ is the central wavelength of the absorber pair, Δλ is the separation between peaks, and σ is the standard deviation of the Gaussian curve, hereafter the ‘width’ (see Fig. 1c). To limit the number of free parameters, we assume that A₊ and A₋ have the same width and amplitude. A₊ and A₋ represent the two input channels of the antenna and we define the input power of each channel as,

where σ₀ is the integrated optical cross-section of the antenna, I_s(λ) is the incident spectral flux (see next subsection), h is the Planck constant, and c is the speed of light. Arp et al. (2020) showed that the requirement for a noise cancelling antenna is satisfied by maximizing the power input difference,

subject to the constraint that Δλ < 6σ. They provide a thorough mathematical justification of this and the interested reader is directed to the original article (Arp et al. 2020). Here, we assume that there will be an additional selection pressure to maximize the total power input of the antenna,

particularly in the dim, red light environment provided by M-dwarf stars. We calculate the matrices Δ^op(λ, Δλ) and P_in(λ, Δλ) for widths σ = 10.0, 15.0, 20.0, 25.0, and 30.0 nm, which is reasonably representative of the range of widths observed for photosynthetic pigments on Earth. For example, the 0–0 peak of the Q_y band of Chl a in solution is approximately Gaussian with width σ ≈ 12 nm (Knox & Spring 2003), while the vibronic peaks of carotenoids such as lutein can have σ ≈ 20–40 nm (Gray et al. 2022). Δ^op and P_in are then rescaled so that their maximal values across the entire parameter space equal unity, allowing us to define a product function,

where the tilde indicate rescaled functions. The definition of Π_in means that an antenna configuration with Π_in 1.0 satisfies both the noise cancellation and power input maximization conditions, while Π_in 0.0 means one (or both) of these conditions is not well satisfied.

We therefore generate a set of matrices or maps (each corresponding to a different width, σ) for |$\tilde{\Delta }^{\mathrm{ op}}$|⁠, |$\tilde{P}_{\mathrm{ in}}$|⁠, and Π_in (see Fig. 2). These are then analysed to identify the most topologically significant peaks via the method of persistence homology (Otter et al. 2017; Taskesen 2020). For this particular problem – identifying local maxima on a 2D surface – this has a rather intuitive interpretation. Taking one of the maps shown in Fig. 2, we can scan the z-axis (in our case Δ^op, P_in, or Π_in) from 1 → 0. As we do so peaks will appear, initially as distinct ‘islands’, before merging together. The persistence score of a peak is then the difference between the z-values at which it appears and when it merges with other peaks. A very tall, very sharp peak, well separated from its neighbours, will have a high persistence score, while short, broad, clustered peaks will merge with each other very soon after they appear.

2.3 Comparing power input for optimal antenna configurations around different stars

Having calculated the optimal antenna configurations for given stellar temperature, we then compare the input powers across different temperatures. We define the ratio,

where T and T′ denote specific stellar temperatures. We will assume T′ = 5800 K, effectively treating the Earth-like antenna as our reference configurations. To constrain the parameters space, we need to explore we will assume that the total cross-sections are equivalent, |$\sigma _{0}^{T}=\sigma _{0}^{T^{\prime }}$| but we will discuss the implications of this assumption below.

Equation (7) depends on the relative spectral irradiance of two antennae evolving around different parent stars. Formally, I_s(lambda; T) are spectral flux densities W m⁻² nm⁻¹ at the stellar surfaces, so we therefore estimate the spectral flux at the planetary surface by assuming approximate habitable distance for each start type. Assuming that both the star and the orbiting planet are spherical blackbodies, then the condition of radiative equilibrium implies the relation,

where T_⋆ and T_p are the equilibrium temperatures of the star and planet, respectively, R_s is the stellar radius, and A_p is the planetary orbital radius. We then estimate A_p(T_p; R_s, T_s) for a habitable (liquid water) temperature range 273 K ≤ T_p ≤ 373 K. We then estimate the planetary surface spectral flux as,

where F_s(λ; R_s, T_s) are the stellar surface spectral fluxes given by the phoenix radiative transfer models. A representative selection of I_s(λ) are shown in Fig. 1(a).

3 RESULTS

3.1 Noise reduction and power maximization for the solar spectrum

To validate the model of Arp et al. (2020), we first apply our model to the T_s = 5800 K spectral flux which is representative of the solar spectrum at the top of Earth’s atmosphere (Fig. 2). Fig. 2(a) (left) shows the noise cancelling parameter Δ^op(λ₀, Δλ) for absorber widths σ = 10 nm. The latter was chosen since it gave the absolute optimal solution but the same data for larger σ are listed in fig. S1 of the supplementary material. We see that Δ^op is more strongly dependent on λ₀ than on Δλ. As expected from Arp et al. (2020), the values of (λ₀, Δλ) that maximize Δ^op are those that span the regions of I_s(λ) with the steepest gradient, with two optimal solutions on the blue edge of I_s(λ), centred on λ₀ = 304 and 396 nm [see Fig. 2a (right)].

Fig. 2(a) (left) shows P_in(λ₀, Δλ) for σ = 10 nm, revealing less of a dependence on λ₀ and Δλ than Δ^op. The requirement to maximize P_in results in a single absorption line (Δλ = 0 nm) located at the spectral maximum. One would expect maximizing P_in would select for large σ (see fig. S2 of the supplementary material), to cover as much of the incident spectral flux as possible, but the normalization condition in equation (2) means that broader absorption lines have smaller peak amplitudes. While this may seem like an artificial model constraint it is essentially an assumption that increasing σ is predominantly via increasing inhomogeneous broadening, i.e. increasing the variance in the absorption peaks of chemically identical pigments (due to an anisotropic solvent protein environment) rather than increasing the line width of the pigment itself (homogenous broadening).

Fig. 2(c) (left) shows Π_in(λ₀, Δλ) for σ = 10 nm, which is qualitatively similar to Δ^op(λ₀, Δλ). The key difference is that simultaneously maximizing both P_in and Δ^op favours the antenna configuration closer to the peak of I_s [see Fig. 2c (right)]. Π_in(λ₀, Δλ) for larger σ are shown in fig. S3 of the supplementary material.

Fig. 2 suggests that the optimal light-harvesting system for the solar spectral flux would be composed of a pair of σ = 10 nm absorbers centred on 385 and 415 nm, respectively. This is qualitatively similar to the Chl a and b blue absorption (or ‘Soret’) bands at approximately 450 and 425 nm, respectively, but are not an exact match. Crucially, this model seems to miss the 680 and 650 nm red (or ‘Q_y’) bands of Chl a and b, respectively, though we note that there are several smaller peaks in Δ^op and Π_in on the red side of I_s (Figs 2a and c). Three such configurations, with Π_in ∼ 0.5, are show alongside the absolute optimal configuration in Fig. 3(a). These less optimal solutions cover the range 490 nm < λ₀ < 625 nm.

For Earth-based photosynthesis, we have the benefit of very accurate atmospheric transmission data. Fig. 3(b) shows how the position and height of the Π_in peaks change for an AM1.5 standard solar spectrum. The absolute optimum peak is largely unaffected but the peak at λ = 489 nm in Fig. 3(a) is blueshifted to λ₀ = 443 nm. The peaks on the red side of the spectrum move a little and their relative Π_in scores decrease due to the overall gradient of the spectrum, and therefore Δ^op, decreasing. The |$\tilde{\Delta }^{\mathrm{ op}}$|⁠, |$\tilde{P}_{\mathrm{ in}}$|⁠, and Π_in matrices for the full range of widths are included in figs S4–S6 of the supplementary material, which show that the number and density of distinct bands in Δ^op and Π_in increases dramatically relative to the 5800 K spectrum. This simply reflects the fact that the AM1.5 spectrum contains a number of sharp features on its red edge (see Fig. 3b).

Finally, Fig. 3(c) shows the absorption spectrum of LHCII, the major light-harvesting protein of vascular plants (spectrum digitized from Kondo et al. 2021, structure shown inset), with two of the antenna configurations identified in Fig. 3(b). The broad peaks in the region 400–500 nm of the LHCII absorption spectrum are composed of the Soret bands of Chl a and b, and broad, vibronically structured absorption bands of several carotenoids (Wei et al. 2016), which approximately align with our predicted absorption pair at λ₀ = 443 nm. The red peaks arise from the Q_y bands of Chl a and b, which are roughly in the same place as one of the weaker solutions in Fig. 3(b). We should note that the agreement is, at best qualitative and even then do not represent unique solutions.

3.2 Optimal antenna configurations for different stellar spectral fluxes

We apply the Π_in maximization procedure to stellar spectral fluxes in the 2300 K ≤ T_s ≤ 5800 K range, with T_s = 2300 K representing the lower limit of the M-class stars. We consider incident wavelengths only in the 200 nm < λ₀ < 1200 nm range as this covers (with a wide margin) all Earth-based photoautotrophs. We do not consider any atmospheric modulation of I_s, focusing instead on general qualitative trends. To reduce the parameter space (and because narrower A(λ) performed better for the 5800 K spectrum), we consider only σ = 10 nm.

Fig. 4(a) shows all antenna configurations for which Π_in(λ₀, Δλ) ≥ 0.9 as a function of T_s. These configurations represent highly optimized antennae that strongly satisfy both the requirements for noise cancellation and maximum power input (Δ^op ∼ Π_in ∼ 0.95). As a reference, Fig. 4(a) shows ranges of λ₀ that approximately correspond to the absorption peaks of known photosynthetic pigments and antenna structures. For T_s = 4800 and 5800 K (K- and G-type stars, respectively), the optimum antenna roughly correspond to the blue Soret band of Chl a and b. The Soret band is composed of transitions from the Chl ground state to several high-lying singlet excited states. In LHCII, the Chl Soret band captures blue photons (see Fig. 4c, blue line) though a large proportion of this energy is lost as the resulting excitations rapidly (<1 ps) and non-radiatively relax to the first singlet excited state which composes the Q_y band. The Chl a Q_y band, at ∼680 nm, is central to oxygenic photosynthesis as it is the precursor to the charge-separated states that initiate the photoredox chemistry in the RCs.

For T_s = 3800 K, the lower end of the K-type stars, there is a narrow-band of optimal antenna configurations at λ₀ ∼ 540 nm, within the region of pigments like phycocyanin (see Fig. 4c, green line), the major light-harvesting pigment of the phycobilisome antenna of cyanobacteria. Cyanobacteria are also oxygenic and excitation of phycocyanins similarly rapidly relaxes to the same Chl a Q_y states in the same RCs. It is only at T_s = 3300 K that our model predicts an antenna configuration similar to the Chl a and b Q_y bands.

For T_s ≤ 2800 K, the lower end of the M-dwarf range, the optimal antenna configurations start to resemble the anoxygenic photoautotrophs. For T_s = 2800 K, the optimum is within range of the Bacteriochlorophyll a (BChl a) Q_y band. For reference, Fig. 4(c) shows the 800 and 850 nm bands from the peripheral LH2 antenna complex from the purple bacterium Rhodobacter sphaeroides (maroon line), both of which originate from BChl a. For T_s ≤ 2600 K, the optimum antenna absorbs at λ₀ ∼ 1000 nm which is comparable to the extremely redshifted BChl b found in the antenna of purple bacterial such as Blastochloris viridis (see Fig. 4c, grey line).

In Fig. 4(b), we consider Π_in ≥ 0.5, corresponding to antenna that are highly optimized to either noise cancelling or power input, or somewhat optimized for both (Δ^op ∼ Π_in ∼ 0.7). We see the general temperature dependence is the same but with a broader variance. For example, for both T_s = 3800 and 3300 K there are a set of less optimal solutions in the Chl a and b Q_y regions. For T_s ≤ 2600 K, there are less optimal solutions in the λ₀ ∼ 900 nm region, though on Earth no organisms harvest light in this region as these photons are strongly absorbed by atmospheric water (Stevens 2013).

3.3 Comparing absolute power input for optimal antenna configurations around different stars

The estimated habitable zones for each T_s are listed in Table 1. We note that 〈A_p〉(T_s = 5800 K) ∼ 0.75 au, reflecting our neglect of any atmospheric greenhouse effect in our calculation of radiative equilibrium. Still the estimates of 〈A_p〉(T_a) are qualitatively reasonable.

Fig. 5(a) plots the relative input power, ϕ, as defined in equation (7) and with the optimum antenna configuration for T_s = 5800 K (see Fig. 2c as the reference configuration). Across the entire range of T_s, ϕ decreases by no more than a factor of ∼0.2. This reflects the fact that the assumption of habitable planetary temperatures means that low stellar luminosity,

is compensated for by small orbital radii, A_p. This implies that, in terms of the pure input power from a photosynthetic antenna, light-limiting conditions are not necessarily a feature of exoplanets orbiting M-dwarf stars.

4 DISCUSSION

Since we are discussing the absorption characteristics of hypothetical photosynthetic organisms, and since we are interested in general trends rather than specific exoplanetary systems, we have adopted a relatively simple model. We balance two considerations, the need to minimize input noise and the need to maximize overall energy input. In terms of the validity of the method tested this first on a T_s = 5800 K model stellar spectral flux and then on a standard sea-level terrestrial solar spectrum. In both cases, our model predicts optimal antenna configurations qualitatively similar to the Chl a and b Soret bands. This is also true if, as Arp et al. (2020), we consider only the requirement for noise cancellation. In neither case do we unambiguously predict anything resembling the Chl a and b bands. As Arp et al. (2020) acknowledged, for a realistic incident spectrum there are many local peaks in Δ^op and their reported fits to the antenna of higher plants are obtained by matching solutions (from a selection of many) to known antenna profiles. It should be noted that we employed a different method for identifying local maxima in Δ^op, P_in, and Π_in, compared to Arp et al. (2020) (persistence homology rather than variations in curvature). Moreover, we explicitly compare the relative amplitude of these peaks rather than treating all local maxima as equivalent solutions. We found that Q_y-like antenna configurations were generally topologically indistinct and suboptimal (Δ^op and Π_in < 0.5).

The Chl Soret band functions as an accessory light-harvesting pathway in photosynthetic antenna, capturing blue photons (λ < 500 nm) and converting them to usable lower energy quanta (λ ∼ 700 nm) via non-radiative decay to the Q_y band. Kiang et al. (2007b) identified the Soret band in their rules of the evolutionary relationship between antennae and spectral irradiance, that antennae have accessory pigments/states that absorb on the blue edge of the irradiance window. The Chl Q_y bands are the primary antenna states representing the λ ∼ 700 nm quanta required by the RCs and the immediate precursor states to the primary charge separation event that initiates the photosynthetic light reaction. Clearly, Q_y bands in the antenna are not (strongly) selected by the evolutionary pressures of noise cancellation and maximizing power input, but by the redox requirements of the RCs. These in turn may have been dictated by the availability of electron sources (such as water) and electron acceptors such as quinones and Fe/S clusters (Kiang et al. 2007b). Alternatively, recent quantum chemical simulations suggest that ‘primitive’ tetrapyrole precursor molecules may have existed on Earth before life evolved. Phot0, which resembles the metal-coordinating inner ring of Chl, has a Soret-Q_y absorption profile similar to Chl and could have formed abiotically in the reducing conditions of early Earth (de la Concepción et al. 2022). Therefore, this absorption pattern could have been evolutionarily ‘locked-in’ long before complex photosynthetic pathways appeared.

In line with Lehmer et al. (2021), applying this model to decreasing T_s reveals optimal antenna configurations at increasing wavelengths, tracking the blue edge of the spectral irradiances as it progressively redshifts. At around T_s = 3300 K, the optimum antenna reaches the energetic lower limit of oxygenic photosynthesis (λ₀ ∼ 700–750 nm). In this region, we find the absorption maxima of BChl c–f pigments in the antenna of various green sulphur bacteria (Bryant & Frigaard 2006; Bryant et al. 2007; Gregersen et al. 2011; Vogl et al. 2012). However, there are also species of oxygenic cyanobacteria that harvest light in 700–800 nm region of the spectrum using Chl d and f (Tros et al. 2021; Mascoli et al. 2022). Although it is still a matter of debate, there is compelling evidence that these far-red adapted cyanobacteria still possess the conventional 680 nm (PSII) and 700 nm (PSI) RCs, meaning that 700–800 nm photons absorbed by the antenna are transferred ‘uphill’ to the RCs against a thermodynamic barrier. These organisms therefore sacrifice antenna efficiency for the ability to collect far-red photons for which there is reduced competition with other oxygenic photoautotrophs (Mascoli, Bersanini & Croce 2020).

At T_s = 2800 K, the optimal antenna overlaps with BChl a and b from purple bacteria (805–890 nm). As an example, in Fig. 4(c), we show the absorption profile of the LH2 antenna complex from Rhodobacter sphaeroides that has two well-separated Gaussian peaks at approximately 800 and 850 nm (Papagiannakis et al. 2002). Both peaks originate from BChl a, with the 850 nm band being redshifted due to a combination of pigment–protein and pigment–pigment interactions, illustrating the inherent tunability of the optical properties of antenna pigments.

For the lowest effective temperatures, T_s ≤ 2600 K, the optimal antenna configurations are in the region λ₀ = 1000–1100 nm. There are examples of NIR-capturing antennae in our biosphere, with extremophiles such as Blastochloris viridis (Namoon et al. 2022) and Ectothiorhodospira halochloris (Steiner & Scheer 1985), which possess antenna enriched in extremely redshifted BChl a and b that capture light down to 1020 nm (see Fig. 4c). However, it should be noted that they also absorb in the 800–870 nm region and still possess the usual purple bacterial 870 nm RC. As with the far-red adapted cyanobacteria, the antenna is transferring energy against a thermodynamic gradient. In this case, the barrier is a seemingly prohibitive ∼8k_BT, which may suggest an extreme trade-off between antenna efficiency and the ability to capture a very underutilized region of the spectrum, or that energy transfer occurs in a regime in which the steady-state approximation does not apply.

Assuming a fixed antenna size/cross-section, we find that the input power delivered by these optimal antenna varies surprisingly little with stellar temperature, T_s (see Fig. 5). This is due, in part, to the fact that our model selects for maximal input power, but mainly because the requirement for ‘habitable’ surface temperatures is high surface irradiance. There is some variation in input power, but this is no more than a factor of 0.2. This is an extremely small difference when compared to the variation in photon fluxes that support photosynthesis on Earth. Canopy plants can be subject to fluxes as high as |$2000 \phantom{x}\mu \textrm {mol~photons}\phantom{x} \mathrm{ m}^{-2} \,\mathrm{ s}^{-1}$| (⁠|${\sim } 1.2\times 10^{21} \phantom{x}\textrm {photons}\phantom{x} \mathrm{ m}^{-2} \,\mathrm{ s}^{-1}$|⁠), while for shade-adapted species it can be |${\ll} 100 \phantom{x}\mu \textrm {mol~photons}\phantom{x}\mathrm{ m}^{-2}\, \mathrm{ s}^{-1}$|⁠. If we include the anoxygenic organisms, then there are species of green sulphur bacteria that thrive in fluxes as low as |$10^{-7} \phantom{x}\mu \textrm {mol~photons}\phantom{x} \mathrm{ m}^{-2} \,\mathrm{ s}^{-1}$| from deep sea hydrothermal vents (Beatty et al. 2005). Therefore, in terms of integrated photon flux, even the coolest M-dwarf stars do not appear to automatically present light-limiting conditions for photosynthesis. However, when one considers spectral composition of the flux, anoxygenic photosynthesis may be favoured by the particular selection pressures we have considered here.

It is important to note that we in no way conclude that planets orbiting ultracool M-dwarf stars must necessarily have anoxic atmospheres. Even if we could confidently exclude the possibility of oxygenic photosynthesis, there are several examples of microbial metabolic processes, such as chlorate respiration (Van Ginkel et al. 1996) and nitrite-mediated methane oxidation (Ettwig et al. 2010), that can produce oxygen independently of photosynthesis and do not require a pre-existing oxygenated atmosphere. However, we simply cannot exclude the possibility of oxygenic photosynthesis, due to a key omission in our model: the inherent adaptability of photosynthetic light-harvesting structures.

Photosynthetic RCs are highly conserved. Plants, mosses, algae, and cyanobacteria all possess the same PSII and PSI RC complexes, which are strongly homologous to, respectively, the type II (purple bacteria, chloroflexus) and type I (green sulphur bacteria, heliobacteria) RCs found in anoxygenic organisms (Blankenship 2021). Light-harvesting structures, however, are more varied and flexible, having evolved within different light environments that are each highly dynamic. For example, plant species differ in average leaf size/orientation, chloroplast density, the ratio of RCs to antenna proteins, etc., depending on their native light environment (Bateman et al. 1998). These parameters are also variable, to a lesser degree, within a single species, with plants such as ivy (Hedera helix) capable of adapting to both high light (⁠|${\sim } 1000 \phantom{x}\mu \textrm {mol~photons}\phantom{x} \mathrm{ m}^{-2}\, \mathrm{ s}^{-1}$|⁠) and low light (⁠|${\lt} 100 \phantom{x}\mu \textrm {mol~photons}\phantom{x} \mathrm{ m}^{-2}\, \mathrm{ s}^{-1}$|⁠), though growth rate is limited at the lower limit and photodamage is a problem at the upper limit (Oberhuber & Bauer 1991). Even a single organism can up- or downregulate light harvesting in response to fluctuations in incident photon flux (Gjindali & Johnson 2023).

Throughout we have assumed that antenna cross-section remains constant, independent of stellar temperature. However, it is reasonable to assume that an oxygenic organism could compensate for limited flux in the 400 nm < λ < 700 nm range by simply synthesizing a larger antenna. Recently, Battistuzzi et al. (2023) demonstrated this exact phenomenon in two species of cyanobacteria (the model organism Synechocystis sp. PCC 6803 and the far-red adaptable Chlorogloeopsis fritschi). Both species were able to acclimate to the spectral fluxes typical of low-mass (T_s ∼ 2800 K) M-dwarf stars by upregulating pigment synthesis, effectively increasing antenna cross-section, allowing them to maintain normal growth rates. While this is acclimation of an organism to low light stress, and not the evolution of an organism specifically to suit these light conditions, it does indicate that our model (and previous) is too pessimistic in predicting the range of light conditions for oxygenic photosynthesis.

Finally, models based purely on average incident spectral flux neglect wider considerations of habitability. We would actually expect a large proportion of the habitable-zone planets orbiting M-dwarf stars to be tidally locked (Kasting, Whitmire & Reynolds ; Barnes 2017). Of these, a significant fraction may therefore lack the tectonic activity needed to maintain a carbon cycle (Cockell et al. 2016), which in turn would preclude the atmospheric stabilization needed to maintain liquid water (McIntyre 2022). While anoxygenic photoautotrophs do not exploit water as an electron source, they do require it as the universal intracellular solvent. Even if liquid water does exist, it is not clear how the lack of a diurnal cycle would impact photosynthesis. On Earth, photosynthetic organisms depend on a diurnal cicadian clock (Dvornyk 2016) and there is some evidence that the evolution of oxygenic photosynthesis was influenced by increasing day length on young Earth (Klatt et al. 2021). Conversely, Tang & Vincent (2000), in experiments on cyanobacteria, showed that net photosynthetic productivity decreases significantly in the absence of a period of darkness. The influence of tidal locking may therefore have as significant an impact on photosynthetic viability as incident light quality.

In conclusion, though the question of photosynthetic viability around low-mass stars is extremely complex and multivariate, we have shown that lack of light is most likely not a reason to exclude it. However, around the lowest mass stars photosynthesis may resemble Earth’s anoxygenic bacteria rather than complex oxygenic organisms. However, an immediate extension of this work will be a more careful consideration of antenna structure that factors in the inherent adaptability of Earth’s photosynthetic light harvesters.

ACKNOWLEDGEMENTS

TJH was funded by a Royal Society Dorothy Hodgkin Fellowship, which also funded a summer studentship of GC. CDPD was funded by BBSRC (BB/T000023/1).

DATA AVAILABILITY

The python scripts used to produce the models presented in this paper are available via https://github.com/QMUL-DuffyLab/Exo-Photosynthesis. Raw data used to generate all figures is available in ASCI format upon request from c.duffy˜qmul.ac.uk

References