Scaling laws in phytoplankton nutrient uptake affinity

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 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.