The unsteady continuous culture of phosphate-limited Monochrysis lutheri droop: Experimental and theoretical analysis

A three-state variable model for phosphate-limited phytoplankton growth in a continuously lit continuous culture is proposed. In the model, the phosphate uptake rate per cell is a Michaelis-Mententype hyperbolic function of ambient nutrient concentration and the growth rate is a Droop-type hyperbolic function of cell quota. Steady-state and short-term uptake experiments with unialgal cultures of Monochrysis lutheri Droop, a marine chrysophyte, were used to calibrate the proposed model. For the long-term unsteady experiments, the model predicts well the culture's dynamic response in terms of cell density to steps down and up in influent concentration of limiting nutrient. For step changes in dilution rate, the model predicts well the culture's response to a step down but predicts poorly the culture's response to a step up. The long-term responses of the cultures to impulses in influent concentration show that the model fails to predict, even qualitatively, the behavior of the phytoplankton. Not unexpectedly, the model fails most dramatically in those experiments involving a rapid increase in cell quota, thereby demonstrating both the inherent flaws in the concept of the instantaneous growth rate as a function of instantaneous cell quota and the need for further dynamic characterization of phytoplankton behavior.