Scaling Laws in Phytoplankton Nutrient Uptake Affinity

Abstract

Nutrient uptake affinity affects the competitive ability of microbial organisms at low nutrient concentrations. From the theory of diffusion limitation it follows that uptake affinity scales linearly with the cell radius. This is in conflict with some observations suggesting that uptake affinity scales to a quantity that is closer to the square of the radius, i.e., to cell surface area. We show that this apparent conflict can be resolved by nutrient uptake theory. Pure diffusion limitation assumes that the cell is a perfect sink which means that it is able to absorb all encountered nutrients instantaneously. Here, we provide empirical evidence that the perfect sink strategy is not common in phytoplankton. Although, small cells are indeed favored by a large surface to volume ratio, we show that they are punished by higher relative investment cost in order to fully benefit from the larger surface to volume ratio. We show that there are two reasons for this. First, because the small cells need a higher transporter density (p) in order to maximize their affinity, and second because the relative cost of a transporter is higher for a small than for a large cell. We suggest, that this might explain why observed uptake affinities do not scale linearly with the cell radius.

Small pigmented eukaryotes play a major role in carbon cycling in the P‐depleted western subtropical North Atlantic, which may be supported by mixotrophy

“…Therefore, our results support previous findings based on data from laboratory cultures, that marine phytoplankton ability to compete for limiting PO 4 tends to increase with decreasing cell size (Edwards et al ). However, a recent study suggests that although small cells are indeed favored by a large surface‐to‐volume ratio, they suffer from needing a higher transporter density to maximize their affinity and from a higher relative cost of a transporter (Lindemann et al ).…”

The global explosion of eukaryotic algae: the potential role of phosphorus?

“…Many physiological traits such as growth rate, metabolism, light utilisation, access to resources and susceptibility to grazing are significantly correlated to cell size [39]. Therefore, as cell size can affect ecological niches, shape community structure and diversity [24,61,62], it is often termed a ‘master trait’ [43].…”

“…As phytoplankton growth is often limited by nutrient supply, the competitive ability of phytoplankton is affected by their nutrient uptake affinity. Thus, we can think of nutrient uptake affinity as an estimate of their competitive abilities at low nutrient concentrations [39]. Therefore, in order to directly link growth with nutrient uptake, we must first quantify phytoplankton biomass in terms of the amount of limiting nutrient [40].…”

A Phytoplankton Model for the Allocation of Gross Photosynthetic Energy Including the Trade‐Offs of Diazotrophy

“…Nutrient uptake in PCAM is based on a conceptual model of uptake sites ( n ), each with a fixed transporter site area ( A ) and a finite ion handling time ( h ) during which a site is unable to process additional nutrient ions (Aksnes & Egge, ; Fiksen et al, ; Lindemann et al, ) such that where k is transfer velocity and equal to diffusivity divided by cell radius and S is ambient nutrient concentration.…”

“…Nutrient uptake in PCAM is based on a conceptual model of uptake sites (n), each with a fixed transporter site area (A) and a finite ion handling time (h) during which a site is unable to process additional nutrient ions (Aksnes & Egge, 1991;Fiksen et al, 2013;Lindemann et al, 2016) such that…”