Effects of growth rate, cell size, motion, and elemental stoichiometry on nutrient transport kinetics

Nutrient acquisition is a critical determinant for the competitive advantage for auto- and osmohetero- trophs alike. Nutrient limited growth is commonly described on a whole cell basis through reference to a maximum growth rate (G(max)) and a half-saturation constant (K(G)). This empirical application of a Michaelis-Menten like description ignores the multiple underlying feedbacks between physiology contributing to growth, cell size, elemental stoichiometry and cell motion. Here we explore these relationships with reference to the kinetics of the nutrient transporter protein, the transporter rate density at the cell surface (TRD; potential transport rate per unit plasma-membrane area), and diffusion gradients. While the half saturation value for the limiting nutrient increases rapidly with cell size, significant mitigation is afforded by cell motion (swimming or sedimentation), and by decreasing the cellular carbon density. There is thus potential for high vacuolation and high sedimentation rates in diatoms to significantly decrease K(G) and increase species competitive advantage. Our results also suggest that G(max) for larger non-diatom protists may be constrained by rates of nutrient transport. For a given carbon density, cell size and TRD, the value of G(max)/K(G) remains constant. This implies that species or strains with a lower G(max) might coincidentally have a competitive advantage under nutrient limited conditions as they also express lower values of K(G). The ability of cells to modulate the TRD according to their nutritional status, and hence change the instantaneous maximum transport rate, has a very marked effect upon transport and growth kinetics. Analyses and dynamic models that do not consider such modulation will inevitably fail to properly reflect competitive advantage in nutrient acquisition. This has important implications for the accurate representation and predictive capabilities of model applications, in particular in a changing environment.