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

Abstract

Evaluation of the Michaelis–Menten parameters V m and K t for phosphate (PO 4 3− ) 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 V m and K t ; however, the actual velocity of PO 4 3− uptake by lake plankton cannot be measured because the ambient concentration of PO 4 3− (P n ) is unknown. For natural plankton, a better fit is demonstrated using another nonlinear model which fits the uptake rate constant for 32 PO 4 3− directly to the PO 4 3− added in the kinetic experiment, and the mixed community effect is minimized by isolating different plankton size fractions. Another consequence of not knowing P n is that the estimate of K t cannot be distinguished from P n′ 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 P n . Error in the uptake rate constants influences the estimate of the Rigler P n′ and the Rigler maximum P n is equal to the estimated (K t + P n ) of the 0.2–1 μm size fraction.