Estimating Michaelis–Menten Parameters and Lake Water Phosphate by the Rigler Bioassay: Importance of Fitting Technique, Plankton Size, and Substrate Range

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Abstract
Evaluation of the Michaelis–Menten parameters Vmand Ktfor phosphate (PO43−) uptake by plankton is difficult because of differences in nutrient uptake by the various species. Studies using simulated data have shown that fitting the equation by nonlinear regression is preferable to linearized transformations for estimating Vmand Kt; however, the actual velocity of PO43−uptake by lake plankton cannot be measured because the ambient concentration of PO43−(Pn) is unknown. For natural plankton, a better fit is demonstrated using another nonlinear model which fits the uptake rate constant for32PO43−directly to the PO43−added in the kinetic experiment, and the mixed community effect is minimized by isolating different plankton size fractions. Another consequence of not knowing Pnis that the estimate of Ktcannot be distinguished from Pn′and the sum of the two is always obtained. The low substrate region of the Michaelis–Menten curve is used in the Rigler bioassay as a means of estimating the upper bound to Pn. Error in the uptake rate constants influences the estimate of the Rigler Pn′and the Rigler maximum Pnis equal to the estimated (Kt + Pn) of the 0.2–1 μm size fraction.