Applicability of cellular equilibrium and monod theory to phytoplankton growth kinetics

Abstract

The two classes of kinetics which are currently applied to phytoplankton growth are compared: Monod theory for which growth rate depends on the external nutrient concentrations; and the formulations in which growth rate depends on the internal cellular nutrient concentration. For the latter kinetics in which nutrient uptake is a function only of external concentrations, it is shown that unrealistically high variations in cellular nutrient concentrations are predicted. The more realistic case, for which both internal and external concentrations control the uptake, is compared to the Monod-theory expression for growth and, at steady state with an appropriate definition of the half-saturation constant, the results are essentially equivalent. That is, the relationships of growth rate to external nutrient concentration are essentially indistinguishable. However, the variation in cellular composition is still substantial in contrast with the assumption of constant stoichiometry inherent in Monod theory and this is the important difference between the formulations. The dynamic equations are investigated using a perturbation analysis which suggests that the cells rapidly achieve equilibrium with respect to their internal and the external nutrient concentrations. This result suggests that it would not be unreasonable to assume that the cells are in internal-external nutrient equilibrium even during non-steady state transitions. The cellular equilibrium equations are numerically compared to the fully-dynamic equations. The conclusion is that the approximation used is quite reasonable and generally simplifies the computational framework for any practical application of phytoplankton kinetics that depend on internal nutrient concentrations, by eliminating a computationally unpleasant fast reaction but still retaining the important feature of varying cellular stoichiometry in response to external nutrient fluctuations.