A theoretical model for nutrient uptake in phytoplankton

A model for nutrient uptake rate (V) in phytoplankton is derived: V = n A v S / ( l + h A v S ) where n is cellular number of uptake sites, A is area of the uptake site, h is time required for handling one nutrient ion, vis the mass transfer coefficient, and S i s substrate concentration. The model is based on 2 time requirements necessary for active uptake of nutrients: (i) time required for realizing encounters with nutrient Ions and (ii) time necessary for handling of ions. The Michaelis-Menten model applied to algal nutrient uptake is a special case of the proposed model, and shortcomings of this model are discussed in view of the more general model. While maximum uptake rate (V,,,,, = nh-l) may b e considered as a parameter reflecting solely biological constraints, the half-saturation (K, = (hAv) l ) and affinity (a = n AV) depend on both biological and physical constraints. Interrelations between maximum uptake rate, half-saturation constant and affinity are demonstrated and discussed with reference to actual observations. On the basis of the model we hypothesize that maximum uptake rate should increase linearly with the square of cell radius, whlle half-saturation constant and affinity should increase linearly with cell radius. Furthermore, maximum uptake rate should increase exponentlally with temperature, while half-saturation should also increase with temperature, but at a slower rate than maximum uptake rate. Affinity should increase with temperature in the same way as molecular diffusion does.

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