Thermodynamic Limits on Oxygenic Photosynthesis Around M-dwarf Stars: Abstract and Introduction

(1) Samir Chitnavis, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK; (2) Thomas J. Haworth, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (3) Edward Gillen, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (4) Conrad W. Mullineaux, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK; (5) Christopher D. P. Duffy, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK (Email: c.duffy@qmul.ac.uk). Table of Links Abstract and Introduction 2 Methodology 2.1 Local spectral irradiance as a function of stellar temperature 2.2 Thermodynamic model of an oxygenic light-harvesting system 2.3 Lattice model of an oxygenic light-harvesting system 3 Results 3.1 Orbital distances and incident spectral fluxes 3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR 3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR 3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’ 4 Discussion Acknowledgements, Author Contribution Statement, Authors disclosure statement and References Abstract We explore the feasibility and potential characteristics of photosynthetic light-harvesting on exo-planets orbiting in the habitable zone of low mass stars (< 1 M⊙). As stellar temperature, Ts, decreases, the irradiance maximum red-shifts out of the 400nm ≤ λ < 750 nm range of wavelengths that can be utilized by oxygenic photosynthesis on Earth. However, limited irradiance in this region does not preclude oxygenic photosynthesis and Earth’s plants, algae and cyanobacteria all possess very efficient light-harvesting antennae that facilitate photosynthesis in very low light. Here we construct general models of photosynthetic lightharvesting structures to determine how an oxygenic photosystem would perform in different irradiant spectral fluxes. We illustrate that the process of light-harvesting, capturing energy over a large antenna and concentrating it into a small reaction centre, must overcome a fundamental entropic barrier. We show that a plant-like antenna cannot be adapted to the light from stars of Ts < 3400 K, as increasing antenna size offers diminishing returns on light-harvesting. This can be overcome if one introduces a slight enthalpic gradient, to the antenna. Interestingly, this strategy appears to have been adopted by Earth’s oxygenic cyanobacteria, and we conclude that bacterial oxygenic photosynthesis is feasible around even the lowest mass M-dwarf stars. 1 Introduction Of the roughly 5000 exo-planets that have now been identified [NASA Exoplanet Archive], how many of them are capable of supporting life? Since the laws of physics and chemistry are universal, there is presumably some (as yet unknown) general rule-set that determines the feasibility and likely characteristics of exobiospheres. While establishing these rules is, to say the least, a hard problem, the laws of thermodynamics dictate that any biosphere must be founded on autotrophic species. A biosphere cannot be a closed system and the organisms at the base of the food chain cannot, by definition, feed on other forms of life. Earth’s current biosphere, highly-diverse and abundant in specialized multicellular organisms, is (largely) founded upon oxygenic photosynthesis. This is the process of using light to oxidize H2O and ultimately produce two molecules: Adenosine triphosphate (ATP) and the reduced form of Nicotinamide adenine dinucleotide phosphate (NADPH). These are, respectively, the energy source and reducing power needed for a myriad of biochemical reaction, including carbon dioxide fixation via the Calvin-Benson cycle [S´anchez-Baracaldo and Cardona, 2019, Soo et al., 2017, Kiang, 2014]. The earliest photosynthetic organisms, however, were anoxygenic, oxidising compounds such as H2S, H2, F e(II), etc. [Ozaki et al., 2019]. These species were (and remain today) prokaryotes, singlecell organisms lacking a nucleus and any other membrane-enclosed organelles. Today they contribute less than 1% of the global primary production, though this can locally rise to ∼ 30 % in sulphide-rich ancient lakes [Overmann and Garcia-Pichel, 2013] It has been proposed that oxygenation of Earth’s atmosphere by early oxygenic organisms was a necessary prerequisite for the evolution of multi-cellular life (though there is considerable debate [e.g Wood et al., 2020, Mills and Canfield, 2014, Butterfield, 2009, Cole et al., 2020, Bozdag et al., 2021]). If so then oxygenic photosynthesis may be a universal requirement for biospheres that support ‘complex’ life. Regardless, it may present the best chance for detecting an exo-biosphere in the near future [Kiang, 2014]. The presence of ozone (O3), produced by photo-excitation of biotically-maintained O2, would produce distinct bands in atmospheric transmission spectra [Mendillo et al., 2018, Olson et al., 2018a,b, Lyons et al., 2014, Schwieterman et al., 2018]. Moreover, widespread oxygenic communities on Earth are responsible for its ’vegetation red edge’ (VRE), the depletion of the 400 < λ < 750 nm region in Earth’s integrated surface reflectance spectrum due to preferential absorption by said organisms [Sagan et al., 1993, O’Malley-James and Kaltenegger, 2018, Seager et al., 2005, Arnold, L. et al., 2002]. It is worth noting, however, that widespread oxygenic photosynthesis may still be present without giving rise to either bio-signature [Cockell et al., 2009, O’Malley-James and Kaltenegger, 2018]. In addition to all of the basic conditions necessary for life, such as liquid water, bio-available carbon, along with moderate radiation, pressure, etc. [Meadows and Barnes, 2018, McKay, 2014], oxygenic photosynthesis requires so-called photosynthetically active radiation (PAR), photons in the wavelength range 400 < λ < 750 nm (see Fig. 1 a) [McCree, 1966, 1971]. The blue limit reflects the fact that UV-light is photo-damaging to cellular material generally and many photosynthetic organisms produce UV-absorbing compounds such as scytonemin to actively screen against UV over-exposure. The red limit at 700−750 nm, appears to be enforced by the fundamental redox chemistry of water oxidation, with photons of longer wavelengths being insufficiently energetic to drive the necessary charge-separation processes [Mascoli et al., 2020, 2022, Tros et al., 2021, N¨urnberg et al., 2018]. The existence of a hard red limit may then impose strong restrictions on the distribution of oxygenic photosynthesis in our galaxy. For some exo-planets it is possible to characterise their masses/radii and hence bulk compositions [e.g. Seager et al., 2007, Adams et al., 2008, Weiss and Marcy, 2014], and through direct imaging and transmission spectroscopy, probe their atmospheric compositions [e.g. Benneke and Seager, 2012, Nikolov et al., 2016, Hinkley et al., 2022]. Along with the opportunity for detecting bio-signatures, it allows for detailed modelling of the spectral irradiance on the planet surface and therefore the feasibility and possible characteristics of photosynthesis. Stars range in mass from less than 0.1 to greater than 100 Solar masses [Wu et al., 2016], but follow the stellar initial mass function meaning low mass stars are much more common [Kroupa, 2001, Chabrier, 2003]. Moreover, there is evidence that planets occur more frequently around stars of lower mass than the Sun [Mulders et al., 2015, Hsu et al., 2019, 2020], with the planets of Trappist-1 [Gillon et al., 2017], Proxima Centauri [Anglada-Escud´e et al., 2016, Faria et al., 2022] and LHS 1140 [Dittmann et al., 2017] being notable examples. A fraction of these are terrestrial planets orbiting at distances close enough for liquid water to exist on their surfaces [Grimm et al., 2018, Dittmann et al., 2017]. However, particularly at the lower end of the stellar mass/temperature range (Ts < 3000 K), the emission peak wavelength of the parent star is red-shifted well below the PAR range (see Fig. 1 a). It may be that the spectral irradiance on the surface of exoplanets orbiting very low mass stars like Trappist-1 is simply insufficient to “power” oxygenic photosynthesis, a hypothesis supported by the thermodynamic modelling of Covone et al.[Covone et al., 2021]. On Earth, there is considerable diversity in photosynthesis, reflecting huge variability in local light intensity and spectral quality. Vascular plants, mosses and green algae use chlorophyll a and b (Chl a and b) which absorb strongly in the red (650 − 700 nm) and blue (350 − 500 nm) regions of the Solar spectrum (see Fig. 1 b) [Knox and Spring, 2003]. Cyanobacteria and red algae, which are also oxygenic, use Chl a but also bind pigments such as phycocyanobilin (620−650 nm) and phycoerythrobilin (560−580 nm), giving them much broader spectral coverage than plants. Some species of deep-water marine cyanobacteria also bind phycourobilin (∼ 495 nm), an adaptation of the predominantly blue light that penetrates to those depths [Saer and Blankenship, 2017, Kolodny et al., 2022]. Yet, other cyanobacteria bind red-shifted Chl d and f (750 − 800 nm), possibly to take advantage of the scarce red light not prioritized by their cousins [Viola et al., 2022, Tros et al., 2021]. There are also numerous anoxygenic prokaryotes that utilize redder photons in the λ ∼ 800 − 900 nm and even λ ∼ 1000 nm ranges [Bryant and Frigaard, 2006]. They bind various Bacteriochlorophylls (BChls) and include groups like the purple bacteria [Hu et al., 2002] and green sulphur bacteria [Gregersen et al., 2011]. However, despite this considerable diversity, all photosynthetic organisms utilize an evolutionary strategy known as the antenna-reaction centre architecture [Wolfe et al., 1994, Fleming et al., 2012]. This is a division of labour in which a small subset of pigments are incorporated into the reaction centres (RCs), the specialized proteins that carry out the first steps of the photosynthetic light reactions (photo-oxidation of a substrate, reduction of a mobile electron carrier). The remaining pigments (the vast majority) are bound to large modular assemblies of light-harvesting or antenna complexes (LHCs, see Fig. 1 c) which capture light and transfer the resulting excitations to the RCs (Fig. 1 d). LHCs generally bind several types of pigments in order to provide broad spectral coverage and create a ‘funnel’ structure in which higher energy pigments donate to lower energy ones. The antenna evolved to facilitate photosynthesis in very low light, an extreme example being some species of green sulphur bacteria which utilize the faint black-body radiation emitted by deep-sea hydrothermal vents [Beatty et al., 2005]. Nevertheless LHCs are not black bodies but rather absorb over selective (and often quite narrow) bands. Elucidating a general set of rules that quantitatively relates the absorption properties of antennae to the local light environment in which they evolved is an active topic. Kiang et al. derived a set of empirical rules based on general observation [Kiang et al., 2007b]: (1) The absorption peak of the antenna is close to the local irradiance maximum. (2) The absorption peak of the RCs is close to the longest wavelength in the irradiance range. (3) ‘Secondary’ pigments (such as Chl b or carotenoids in plants) will absorb towards the shortest wavelength of the irradiance window. Bj¨orn [1976] and later Marosv¨olgyi and van Gorkom [2010] considered 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. This neatly predicts the very different absorption maxima of both plants and purple bacteria. More recently, Arp et al. [2020] argued that the absorption profiles of LHCs are optimized to be robust against fluctuations in both irradiance (termed “external noise”) and pigment-to-pigment energy transfer (“internal noise”). In effect this requires the that LHCs bind two similar pigments (e.g. Chl a and b) with close absorption maxima centred on the steepest part of the local spectral irradiance (Fig. 1 b). These various rule-sets have been applied to spectral irradiances from lower mass stars. Wolstencroft and Raven simply took the action spectrum of the plant Nerium oleander and applied it to a range of model spectral irradiances, concluding oxygenic photosynthesis performs best around F-type stars (Ts = 6000−7500 K) and very poorly around around K and M-type (Ts < 5200 K)[Wolstencroft and Raven, 2002]. Similarly, Hall et al. [2023] took an action spectrum measured for phytoplankton [Yang et al., 2020]) and concluded that, given otherwise favourable conditions, oxygenic photosynthesis may be possible for larger K-type stars. Kiang et al applied their empirical rule-set to Earth-like planets orbiting F, K and M-type stars and predicted that the latter would favour LHCs that absorb in the NIR (930 − 2500 nm) which have no direct analogue on Earth [Kiang et al., 2007a]. Lehmer et al. [2021] applied Marosv¨olgyi’s and van Gorkom’s model to the same stellar spectra, predicting a progressive red-shift in the optimal antenna with decreasing Ts, arriving at the NIR (∼ 1000 nm) for the lowest mass M-dwarfs. A similar trend was predicted by Duffy et al. [2023] who applied a modified version of the noise cancelling criteria of Arp et al. [2020], suggesting that anoxygenic photosynthesis would be favourable around M-dwarf stars. Lastly, Lingam et al. [2021] correlated Ts to the pi-electron conjugation length that a pigment molecule would need to most effectively absorb light, assuming the pigment has an optical gap tuned to the stellar emission peak. They concluded that these pigments would need roughly twice the number of π-electrons for Ts < 3000 K compared to Ts ∼ 6000 K, again supporting the idea that the emission spectra of low mass stars may select for NIR-absorbing, anoxygenic organisms. All of these models focus on the intrinsic optical properties of pigment cofactors or assume a fixed action spectrum, making no assumptions regarding the antenna superstructure. This neglects two defining characteristics of antenna systems: That they initially evolved to maximize light capture in low light environments and, through their modular structure, they are highly adaptable to changes in light [Lokstein et al., 2021]. Hereafter we will focus exclusively on Photosystem II (PSII) which is the water-oxidizing photosystem in vascular plants, algae, mosses, and cyanobacteria. It is PSII that maintains the O2 content of Earth’s atmosphere and therefore produces an obvious bio-signature. While the PSII is more-or-less conserved across all oxygenic species, the lightharvesting antenna varies considerably. We will, initially atleast, focus on the PSII antenna of vascular plants, since this accounts for roughly half the chlorophyll on Earth [Jansson, 1994] and is the foundations of the Earth’s forests, savannas and arable land. The basic unit of plant PSII antenna is LHCII, a cyclic trimer shown in Fig. 1 a. It binds both Chl a and Chl b, with the latter transferring energy to the former, plus several green-absorbing carotenoids [Liu et al., 2004]. LHCII, plus some monomeric (“minor”) variants, bind to a dimer of PSII RC complexes to form the PSII supercomplex which is shown in Fig. 1 d [Kouˇril et al., 2012, Wei et al., 2016]. Not shown is the pool of additional, loosely-bound LHCII trimers that make up the disordered peripheral PSII antenna. The process of light-harvesting and conversion proceeds (approximately) as follows:- 1. A Chl b or other accessory pigment absorbs a photon and the resulting excitation rapidly (∼ 1 ps) relaxes to Chl a. Direct excitation of Chl a is also likely [Novoderezhkin et al., 2011]. 2. The excitation equilibrates (∼ 1 ps) across the Chl a molecules of the LHCII trimer [Novoderezhkin et al., 2011]. 3. Over ∼ 10 − 100 ps the excitation “hops” stochastically between different antenna complexes, following a (very slight) energetic gradient towards the RC [Valkunas et al., 2009]. 4. The excitation arrives on the PSII Chl a special pair (given the spectroscopic name P680 due to its fluorescence maximum) and is converted into a meta-stable intermolecular charge-separated state. This is known as primary trapping and takes ∼ 5 ps [Broess et al., 2006]. 5. The charge separated state reduces a mobile electron carrier (a quinone) which initiates the photosynthetic electron transport chain. This is the rate limiting step, typically taking ∼ 10 ms [Oja and Laisk, 2000]. This is a highly-efficient process, with roughly 85% of the photons captured by the antenna going on the generate an electron in the RC [Baker and Rosenqvist, 2004]. Moreover, the PSII antenna is extremely adaptable, being able to alter its size, efficiency and connectivity to the RC in response to changing light levels. For sustained periods of limited illumination the organism will “acclimate” by (among a range of physiological responses) expressing more LHCII [Bailey et al., 2001] and modulating protein packing to increase the coupling between PSII and the peripheral antenna [Kouˇril et al., 2013]. This is not unique to plants and while the antennae of, say, cyanobacteria differ strongly in terms of structure, they operate on the same basic principles. With the concept of the antenna introduced it seems reasonable that hypothetical oxygenic organisms could compensate for limited PAR emitted by an ultra low mass star by simply evolving a very large antenna, composed of lots of LHCs. However, a larger antenna comes at a cost, most obviously in increased metabolic burden of synthesizing large amounts of pigments and protein. Setting this aside, there is potentially a more fundamental limit. Light-harvesting essentially involves generating excitations (i.e. capturing photons) over a large area and then concentrating them into a small one, a process which decreases local entropy. In certain cases (see Methods) this will impose a thermodynamic barrier to light-harvesting that will only get steeper for a larger antenna. In this work, using a series of generalized antenna models, we explore how a fundamental thermodynamic barrier may restrict the effectiveness of plant-like oxygenic photosynthesis around low mass stars. We then discuss general evolutionary strategies for over-coming the barrier and how these have already been realized in Earth’s oxygenic cyanobacteria. This paper is available on arxiv under CC 4.0 license. (1) Samir Chitnavis, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK; (2) Thomas J. Haworth, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (3) Edward Gillen, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (4) Conrad W. Mullineaux, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK; (5) Christopher D. P. Duffy, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK (Email: c.duffy@qmul.ac.uk). (1) Samir Chitnavis, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK; (2) Thomas J. Haworth, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (3) Edward Gillen, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (4) Conrad W. Mullineaux, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK; (5) Christopher D. P. Duffy, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK (Email: c.duffy@qmul.ac.uk). Table of Links Abstract and Introduction 2 Methodology 2.1 Local spectral irradiance as a function of stellar temperature 2.2 Thermodynamic model of an oxygenic light-harvesting system 2.3 Lattice model of an oxygenic light-harvesting system 3 Results 3.1 Orbital distances and incident spectral fluxes 3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR 3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR 3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’ 4 Discussion Acknowledgements, Author Contribution Statement, Authors disclosure statement and References Abstract and Introduction Abstract and Introduction 2 Methodology 2.1 Local spectral irradiance as a function of stellar temperature 2.1 Local spectral irradiance as a function of stellar temperature 2.2 Thermodynamic model of an oxygenic light-harvesting system 2.2 Thermodynamic model of an oxygenic light-harvesting system 2.3 Lattice model of an oxygenic light-harvesting system 2.3 Lattice model of an oxygenic light-harvesting system 3 Results 3.1 Orbital distances and incident spectral fluxes 3.1 Orbital distances and incident spectral fluxes 3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR 3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR 3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR 3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR 3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’ 3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’ 4 Discussion 4 Discussion Acknowledgements, Author Contribution Statement, Authors disclosure statement and References Acknowledgements, Author Contribution Statement, Authors disclosure statement and References Abstract We explore the feasibility and potential characteristics of photosynthetic light-harvesting on exo-planets orbiting in the habitable zone of low mass stars (< 1 M⊙). As stellar temperature, Ts, decreases, the irradiance maximum red-shifts out of the 400nm ≤ λ < 750 nm range of wavelengths that can be utilized by oxygenic photosynthesis on Earth. However, limited irradiance in this region does not preclude oxygenic photosynthesis and Earth’s plants, algae and cyanobacteria all possess very efficient light-harvesting antennae that facilitate photosynthesis in very low light. Here we construct general models of photosynthetic lightharvesting structures to determine how an oxygenic photosystem would perform in different irradiant spectral fluxes. We illustrate that the process of light-harvesting, capturing energy over a large antenna and concentrating it into a small reaction centre, must overcome a fundamental entropic barrier. We show that a plant-like antenna cannot be adapted to the light from stars of Ts < 3400 K, as increasing antenna size offers diminishing returns on light-harvesting. This can be overcome if one introduces a slight enthalpic gradient, to the antenna. Interestingly, this strategy appears to have been adopted by Earth’s oxygenic cyanobacteria, and we conclude that bacterial oxygenic photosynthesis is feasible around even the lowest mass M-dwarf stars. 1 Introduction Of the roughly 5000 exo-planets that have now been identified [NASA Exoplanet Archive], how many of them are capable of supporting life? Since the laws of physics and chemistry are universal, there is presumably some (as yet unknown) general rule-set that determines the feasibility and likely characteristics of exobiospheres. While establishing these rules is, to say the least, a hard problem, the laws of thermodynamics dictate that any biosphere must be founded on autotrophic species. A biosphere cannot be a closed system and the organisms at the base of the food chain cannot, by definition, feed on other forms of life. Earth’s current biosphere, highly-diverse and abundant in specialized multicellular organisms, is (largely) founded upon oxygenic photosynthesis. This is the process of using light to oxidize H2O and ultimately produce two molecules: Adenosine triphosphate (ATP) and the reduced form of Nicotinamide adenine dinucleotide phosphate (NADPH). These are, respectively, the energy source and reducing power needed for a myriad of biochemical reaction, including carbon dioxide fixation via the Calvin-Benson cycle [S´anchez-Baracaldo and Cardona, 2019, Soo et al., 2017, Kiang, 2014]. The earliest photosynthetic organisms, however, were anoxygenic, oxidising compounds such as H2S, H2, F e(II), etc. [Ozaki et al., 2019]. These species were (and remain today) prokaryotes, singlecell organisms lacking a nucleus and any other membrane-enclosed organelles. Today they contribute less than 1% of the global primary production, though this can locally rise to ∼ 30 % in sulphide-rich ancient lakes [Overmann and Garcia-Pichel, 2013] It has been proposed that oxygenation of Earth’s atmosphere by early oxygenic organisms was a necessary prerequisite for the evolution of multi-cellular life (though there is considerable debate [e.g Wood et al., 2020, Mills and Canfield, 2014, Butterfield, 2009, Cole et al., 2020, Bozdag et al., 2021]). If so then oxygenic photosynthesis may be a universal requirement for biospheres that support ‘complex’ life. Regardless, it may present the best chance for detecting an exo-biosphere in the near future [Kiang, 2014]. The presence of ozone (O3), produced by photo-excitation of biotically-maintained O2, would produce distinct bands in atmospheric transmission spectra [Mendillo et al., 2018, Olson et al., 2018a,b, Lyons et al., 2014, Schwieterman et al., 2018]. Moreover, widespread oxygenic communities on Earth are responsible for its ’vegetation red edge’ (VRE), the depletion of the 400 < λ < 750 nm region in Earth’s integrated surface reflectance spectrum due to preferential absorption by said organisms [Sagan et al., 1993, O’Malley-James and Kaltenegger, 2018, Seager et al., 2005, Arnold, L. et al., 2002]. It is worth noting, however, that widespread oxygenic photosynthesis may still be present without giving rise to either bio-signature [Cockell et al., 2009, O’Malley-James and Kaltenegger, 2018]. In addition to all of the basic conditions necessary for life, such as liquid water, bio-available carbon, along with moderate radiation, pressure, etc. [Meadows and Barnes, 2018, McKay, 2014], oxygenic photosynthesis requires so-called photosynthetically active radiation (PAR), photons in the wavelength range 400 < λ < 750 nm (see Fig. 1 a) [McCree, 1966, 1971]. The blue limit reflects the fact that UV-light is photo-damaging to cellular material generally and many photosynthetic organisms produce UV-absorbing compounds such as scytonemin to actively screen against UV over-exposure. The red limit at 700−750 nm, appears to be enforced by the fundamental redox chemistry of water oxidation, with photons of longer wavelengths being insufficiently energetic to drive the necessary charge-separation processes [Mascoli et al., 2020, 2022, Tros et al., 2021, N¨urnberg et al., 2018]. The existence of a hard red limit may then impose strong restrictions on the distribution of oxygenic photosynthesis in our galaxy. For some exo-planets it is possible to characterise their masses/radii and hence bulk compositions [e.g. Seager et al., 2007, Adams et al., 2008, Weiss and Marcy, 2014], and through direct imaging and transmission spectroscopy, probe their atmospheric compositions [e.g. Benneke and Seager, 2012, Nikolov et al., 2016, Hinkley et al., 2022]. Along with the opportunity for detecting bio-signatures, it allows for detailed modelling of the spectral irradiance on the planet surface and therefore the feasibility and possible characteristics of photosynthesis. Stars range in mass from less than 0.1 to greater than 100 Solar masses [Wu et al., 2016], but follow the stellar initial mass function meaning low mass stars are much more common [Kroupa, 2001, Chabrier, 2003]. Moreover, there is evidence that planets occur more frequently around stars of lower mass than the Sun [Mulders et al., 2015, Hsu et al., 2019, 2020], with the planets of Trappist-1 [Gillon et al., 2017], Proxima Centauri [Anglada-Escud´e et al., 2016, Faria et al., 2022] and LHS 1140 [Dittmann et al., 2017] being notable examples. A fraction of these are terrestrial planets orbiting at distances close enough for liquid water to exist on their surfaces [Grimm et al., 2018, Dittmann et al., 2017]. However, particularly at the lower end of the stellar mass/temperature range (Ts < 3000 K), the emission peak wavelength of the parent star is red-shifted well below the PAR range (see Fig. 1 a). It may be that the spectral irradiance on the surface of exoplanets orbiting very low mass stars like Trappist-1 is simply insufficient to “power” oxygenic photosynthesis, a hypothesis supported by the thermodynamic modelling of Covone et al.[Covone et al., 2021]. On Earth, there is considerable diversity in photosynthesis, reflecting huge variability in local light intensity and spectral quality. Vascular plants, mosses and green algae use chlorophyll a and b (Chl a and b) which absorb strongly in the red (650 − 700 nm) and blue (350 − 500 nm) regions of the Solar spectrum (see Fig. 1 b) [Knox and Spring, 2003]. Cyanobacteria and red algae, which are also oxygenic, use Chl a but also bind pigments such as phycocyanobilin (620−650 nm) and phycoerythrobilin (560−580 nm), giving them much broader spectral coverage than plants. Some species of deep-water marine cyanobacteria also bind phycourobilin (∼ 495 nm), an adaptation of the predominantly blue light that penetrates to those depths [Saer and Blankenship, 2017, Kolodny et al., 2022]. Yet, other cyanobacteria bind red-shifted Chl d and f (750 − 800 nm), possibly to take advantage of the scarce red light not prioritized by their cousins [Viola et al., 2022, Tros et al., 2021]. There are also numerous anoxygenic prokaryotes that utilize redder photons in the λ ∼ 800 − 900 nm and even λ ∼ 1000 nm ranges [Bryant and Frigaard, 2006]. They bind various Bacteriochlorophylls (BChls) and include groups like the purple bacteria [Hu et al., 2002] and green sulphur bacteria [Gregersen et al., 2011]. However, despite this considerable diversity, all photosynthetic organisms utilize an evolutionary strategy known as the antenna-reaction centre architecture [Wolfe et al., 1994, Fleming et al., 2012]. This is a division of labour in which a small subset of pigments are incorporated into the reaction centres (RCs), the specialized proteins that carry out the first steps of the photosynthetic light reactions (photo-oxidation of a substrate, reduction of a mobile electron carrier). The remaining pigments (the vast majority) are bound to large modular assemblies of light-harvesting or antenna complexes (LHCs, see Fig. 1 c) which capture light and transfer the resulting excitations to the RCs (Fig. 1 d). LHCs generally bind several types of pigments in order to provide broad spectral coverage and create a ‘funnel’ structure in which higher energy pigments donate to lower energy ones. The antenna evolved to facilitate photosynthesis in very low light, an extreme example being some species of green sulphur bacteria which utilize the faint black-body radiation emitted by deep-sea hydrothermal vents [Beatty et al., 2005]. Nevertheless LHCs are not black bodies but rather absorb over selective (and often quite narrow) bands. Elucidating a general set of rules that quantitatively relates the absorption properties of antennae to the local light environment in which they evolved is an active topic. Kiang et al. derived a set of empirical rules based on general observation [Kiang et al., 2007b]: (1) The absorption peak of the antenna is close to the local irradiance maximum. (2) The absorption peak of the RCs is close to the longest wavelength in the irradiance range. (3) ‘Secondary’ pigments (such as Chl b or carotenoids in plants) will absorb towards the shortest wavelength of the irradiance window. Bj¨orn [1976] and later Marosv¨olgyi and van Gorkom [2010] considered 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. This neatly predicts the very different absorption maxima of both plants and purple bacteria. More recently, Arp et al. [2020] argued that the absorption profiles of LHCs are optimized to be robust against fluctuations in both irradiance (termed “external noise”) and pigment-to-pigment energy transfer (“internal noise”). In effect this requires the that LHCs bind two similar pigments (e.g. Chl a and b) with close absorption maxima centred on the steepest part of the local spectral irradiance (Fig. 1 b). These various rule-sets have been applied to spectral irradiances from lower mass stars. Wolstencroft and Raven simply took the action spectrum of the plant Nerium oleander and applied it to a range of model spectral irradiances, concluding oxygenic photosynthesis performs best around F-type stars (Ts = 6000−7500 K) and very poorly around around K and M-type (Ts < 5200 K)[Wolstencroft and Raven, 2002]. Similarly, Hall et al. [2023] took an action spectrum measured for phytoplankton [Yang et al., 2020]) and concluded that, given otherwise favourable conditions, oxygenic photosynthesis may be possible for larger K-type stars. Kiang et al applied their empirical rule-set to Earth-like planets orbiting F, K and M-type stars and predicted that the latter would favour LHCs that absorb in the NIR (930 − 2500 nm) which have no direct analogue on Earth [Kiang et al., 2007a]. Lehmer et al. [2021] applied Marosv¨olgyi’s and van Gorkom’s model to the same stellar spectra, predicting a progressive red-shift in the optimal antenna with decreasing Ts, arriving at the NIR (∼ 1000 nm) for the lowest mass M-dwarfs. A similar trend was predicted by Duffy et al. [2023] who applied a modified version of the noise cancelling criteria of Arp et al. [2020], suggesting that anoxygenic photosynthesis would be favourable around M-dwarf stars. Lastly, Lingam et al. [2021] correlated Ts to the pi-electron conjugation length that a pigment molecule would need to most effectively absorb light, assuming the pigment has an optical gap tuned to the stellar emission peak. They concluded that these pigments would need roughly twice the number of π-electrons for Ts < 3000 K compared to Ts ∼ 6000 K, again supporting the idea that the emission spectra of low mass stars may select for NIR-absorbing, anoxygenic organisms. All of these models focus on the intrinsic optical properties of pigment cofactors or assume a fixed action spectrum, making no assumptions regarding the antenna superstructure. This neglects two defining characteristics of antenna systems: That they initially evolved to maximize light capture in low light environments and, through their modular structure, they are highly adaptable to changes in light [Lokstein et al., 2021]. Hereafter we will focus exclusively on Photosystem II (PSII) which is the water-oxidizing photosystem in vascular plants, algae, mosses, and cyanobacteria. It is PSII that maintains the O2 content of Earth’s atmosphere and therefore produces an obvious bio-signature. While the PSII is more-or-less conserved across all oxygenic species, the lightharvesting antenna varies considerably. We will, initially atleast, focus on the PSII antenna of vascular plants, since this accounts for roughly half the chlorophyll on Earth [Jansson, 1994] and is the foundations of the Earth’s forests, savannas and arable land. The basic unit of plant PSII antenna is LHCII, a cyclic trimer shown in Fig. 1 a. It binds both Chl a and Chl b, with the latter transferring energy to the former, plus several green-absorbing carotenoids [Liu et al., 2004]. LHCII, plus some monomeric (“minor”) variants, bind to a dimer of PSII RC complexes to form the PSII supercomplex which is shown in Fig. 1 d [Kouˇril et al., 2012, Wei et al., 2016]. Not shown is the pool of additional, loosely-bound LHCII trimers that make up the disordered peripheral PSII antenna. The process of light-harvesting and conversion proceeds (approximately) as follows:- 1. A Chl b or other accessory pigment absorbs a photon and the resulting excitation rapidly (∼ 1 ps) relaxes to Chl a. Direct excitation of Chl a is also likely [Novoderezhkin et al., 2011]. 2. The excitation equilibrates (∼ 1 ps) across the Chl a molecules of the LHCII trimer [Novoderezhkin et al., 2011]. 3. Over ∼ 10 − 100 ps the excitation “hops” stochastically between different antenna complexes, following a (very slight) energetic gradient towards the RC [Valkunas et al., 2009]. 4. The excitation arrives on the PSII Chl a special pair (given the spectroscopic name P680 due to its fluorescence maximum) and is converted into a meta-stable intermolecular charge-separated state. This is known as primary trapping and takes ∼ 5 ps [Broess et al., 2006]. 5. The charge separated state reduces a mobile electron carrier (a quinone) which initiates the photosynthetic electron transport chain. This is the rate limiting step, typically taking ∼ 10 ms [Oja and Laisk, 2000]. This is a highly-efficient process, with roughly 85% of the photons captured by the antenna going on the generate an electron in the RC [Baker and Rosenqvist, 2004]. Moreover, the PSII antenna is extremely adaptable, being able to alter its size, efficiency and connectivity to the RC in response to changing light levels. For sustained periods of limited illumination the organism will “acclimate” by (among a range of physiological responses) expressing more LHCII [Bailey et al., 2001] and modulating protein packing to increase the coupling between PSII and the peripheral antenna [Kouˇril et al., 2013]. This is not unique to plants and while the antennae of, say, cyanobacteria differ strongly in terms of structure, they operate on the same basic principles. With the concept of the antenna introduced it seems reasonable that hypothetical oxygenic organisms could compensate for limited PAR emitted by an ultra low mass star by simply evolving a very large antenna, composed of lots of LHCs. However, a larger antenna comes at a cost, most obviously in increased metabolic burden of synthesizing large amounts of pigments and protein. Setting this aside, there is potentially a more fundamental limit. Light-harvesting essentially involves generating excitations (i.e. capturing photons) over a large area and then concentrating them into a small one, a process which decreases local entropy. In certain cases (see Methods) this will impose a thermodynamic barrier to light-harvesting that will only get steeper for a larger antenna. In this work, using a series of generalized antenna models, we explore how a fundamental thermodynamic barrier may restrict the effectiveness of plant-like oxygenic photosynthesis around low mass stars. We then discuss general evolutionary strategies for over-coming the barrier and how these have already been realized in Earth’s oxygenic cyanobacteria. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Thermodynamic Limits on Oxygenic Photosynthesis Around M-dwarf Stars: Abstract and Introduction

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