Dynamic models for ammonium inhibition of nitrate uptake by phytoplankton

Two systems of differential equations are proposed to describe the dynamic effects of NH4+ on NO3− uptake. The inhibitory function is of the form 1/(1 + [NH4+]/K4), where K4 is the Michaelis constant for NH4+ uptake. In the first system, concentrations of particulate nitrogen, NO3− and NH4+ are modeled, and NH4+ inhibits NO3− uptake directly. In the second, a pool of cellular reductant is added into which both reduced NO3− and NH4+ flow. Nitrate reductase also is included, and its formation is inhibited by NH4+. In each case, solutions agree well with published observations on a deep-tank culture of Ditylum brightwellii.