Modelling the uptake of nitrate by a growing plant with an adjustable root nitrate uptake capacity

A new model is presented to predict the plant uptake of nitrate supplied by diffusion and mass flow to its roots. Plant growth, root-shoot ratio and the plant's nitrate uptake capacity are all set dependent on the plant's N nutrition state. By thoroughly integrating processes occurring in both plant and soil, the model enables to control the relative importance of both under a wide range of different nutritional scenarios.Soil parameters D₀ diffusion coefficient in water (m² day^-1) - D_e diffusion coefficient in soil (m² day^-1) - C nitrate concentration in soil (mol m^-3) - f tortuosity (-) - volumetric moisture content (-) - R radial distance from root axis (m) Plant parameters b₁, b₂ parameters of biomass partitioning Equation (10) - IR interroot distance (m) - K_mU Michaelis-Menten constant of the uptake system (mol m^-3) - K_mNRA Michaelis-Menten constant of nitrogen reduction system (mol g^-1) - k₁, k₂, k₃ parameters of growth model Equation (9) - L_v Root length density (m m^-3) - NO_{3 set} ^- Set point of the cytoplasmatic nitrate pool (mol g^-1 dw) - NO_{3 c} ^- cytoplasmatic nitrate concentration (mol g^-1 dw) - NO_{3 v} ^- vacuolar nitrate concentration (mol g^-1 dw) - NRA_max maximum nitrate reductase activity (mol g^-1 dw day^-1) - N_re reduced nitrogen content (mol) - N_remax maximum reduced N concentration in the plant (mol g^-1 dw) - P partitioning coefficient of nitrate between cyplasm and vacuole - R(1) root radius (m) - RGR relative growth rate (day^-1) - U uptake rate (mol day^-1 m^-2) - U_max maximum uptake rate (Eq. 6) (day^-1 m^-2) - Vo water flux at root surface (m day^-1) - W_r root dry weight (g) - W_sh shoot dry weight (g) - X model parameter: number of root compartments - Y model parameter: number of nodes