Thermodynamic limits on oxygenic photosynthesis around M-dwarf stars: Generalized models and strategies for optimization

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$_{\odot}$). As stellar temperature, $T_{s}$, decreases, the irradiance maximum red-shifts out of the $400 \textrm{nm} \leq \lambda < 750$ nm range of wavelengths that can be utilized by \emph{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 \emph{light-harvesting antennae} that facilitate photosynthesis in very low light. Here we construct general models of photosynthetic light-harvesting 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 \emph{reaction centre}, must overcome a fundamental \emph{entropic barrier}. We show that a plant-like antenna cannot be adapted to the light from stars of $T_{s}<3400$ K, as increasing antenna size offers diminishing returns on light-harvesting. This can be overcome if one introduces a slight \emph{enthalpic gradient}, to the antenna. Interestingly, this strategy appears to have been adopted by Earth's oxygenic cyanobacteria, and we conclude that \emph{bacterial} oxygenic photosynthesis is feasible around even the lowest mass M-dwarf stars.