Relationship between phosphate affinities and cell size and shape in various bacteria and phytoplankton

Substrate affinity expresses the ability of an osmotroph organism to compete for a substrate at permanently low external concentrations and is thus a central parameter in conceptual and mathematical models of aquatic food webs. Assuming diffusion transport in the surrounding medium to be the limiting process at low external substrate concentrations, the theoretical maximum affinity (alpha(max)) and its dependence on cell size and shape for a given osmotroph organism can be calculated from Fick's law of diffusion in combination with knowledge of the amount of substrate required to form a new cell. For a non-respired substrate, the actual affinity ((x) can also be expressed as the biomass-specific turnover rate of the substrate, alpha = (TB)(-1). Combining a measure of biomass (B), with determination of substrate turnover time (T), the affinity can thus be determined experimentally, We used this approach to compare measured with theoretical maximum affinities for phosphate in laboratory cultures of osmotrophic microorganisms. For bacteria and autotrophic flagellates, we found relatively good agreement between experimental and theoretical maximum values, suggesting that diffusion limitation is actually approached in P-limited cultures. Assuming P-free vacuoles, the theory predicts diatom affinities to exceed that of similarly sized flagellates. This prediction is consistent with our experimental observations. Previous reports of diatoms being unsuccessful under P-limited conditions may therefore need a more complex explanation than lack of competitive ability in diatoms.