Saturating growth rate against phosphorus concentration explained by macromolecular allocation.

The saturating relationship between phytoplankton growth rate and environmental nutrient concentration has been widely observed, yet the mechanisms behind the relationship remain elusive. Here, we use a mechanistic model of phytoplankton and show that the saturating relationship between growth rate and phosphorous concentration can be interpreted by intracellular macromolecular allocation. At low nutrient levels, the diffusive nutrient transport linearly increases with the phosphorous concentration, while the internal phosphorous requirement increases with the growth rate, leading to a non-linear increase in the growth rate with phosphorous. This increased phosphorous requirement is due to the increased allocation to biosynthetic and photosynthetic molecules. The allocation to these molecules reaches a maximum at high-phosphorous concentration, and the growth rate no longer increases despite the rise in phosphorous concentration. The produced growth rate and phosphorous relationships are consistent with the data of phytoplankton across taxa. Our study suggests that the key control of phytoplankton growth is internal, and nutrient uptake is only a single step in the overall process. IMPORTANCE The Monod equation has been used to represent the relationship between growth rate and the environmental nutrient concentration under the limitation of this respective nutrient. This model often serves as a means to connect microorganisms to their environment, specifically in ecosystem and global models. Here, we use a simple model of a marine microorganism cell to illustrate the model's ability to capture the same relationship as Monod, while highlighting the additional physiological details our model provides. In this study, we focus on the relationship between growth rate and phosphorus concentration and find that RNA allocation largely contributes to the commonly observed trend. This work emphasizes the potential role our model could play in connecting microorganisms to the surrounding environment while using realistic physiological representations.