C–N exchange model of legume–Rhizobium symbiosis incorporating ATP budget constraints and energy–mass balance between the species

We present a comparative advantage model of carbon-nitrogen exchange in legume-Rhizobium symbiosis that incorporates ATP budget constraints and the energy-mass balance between the host and symbiont. In this framework, the uptake of carbon and nitrogen is limited by the ATP available to each partner, and any imbalance in trade is compensated by adjustments in symbiont biomass. Using empirical estimates of the ATP costs of carbon and nitrogen uptake, together with data on body C:N ratios, the model generates three key predictions, and we prove that they align with empirical results. (i) The condition for the establishment of symbiosis derived from the model is consistent with measured ATP costs in both host and symbiont. (ii) At equilibrium, the model predicts a relatively low carbon supply from the legume and a relatively high nitrogen supply from Rhizobium, in agreement with reported patterns of exchange. (iii) The model further predicts that the proportion of carbon supplied decreases as the host C:N ratio increases, and that the proportion of nitrogen supplied decreases as the symbiont C:N ratio decreases, which are consistent with the empirically observed decline in nodulation during host aging.