Plants Responses to Nutrients Follow the Saturation Kinetic Typical of Enzyme Systems: Biological, Economical and Environmental Implications

Agricultural efficiency has been associated with high plant productivity. However, it is dependent on fertilizers, which are nonrenewable resources. Crop production response to fertilizers is hyperbolic, following the Michaelis-Menten model and the law of diminishing return. Data of crop production (barley, bean, corn, cotton, soybean and wheat) as a function of nitrogen, phosphorus, and potassium fertilization were analyzed by Lineweaver-Burk data transformation (L-B), that allows to calculate the amount of a specific nutrient needed to reach half (k_s) or other percentages of the theoretical maximum response (k_max) and the efficiency of fertilizer use (kg of grain/kg of fertilizer). The efficiency of fertilizer use presented exponential decay by increasing fertilization: 55 to 3; 63 to 5; and 47 to 1 kg of corn/kg of fertilizer, by increasing nitrogen, P₂O₅ and potassium from 40 to 200; 40 to 200; and 60 to 300 kg ha^−1, respectively. The L-B can be an alternative to the linearplateau and polynomial regression methods of recommendation of plant fertilization, in which the fertilizers recommendation should be based on their efficiency of use, avoiding losses of nutrients, environmental pollution, waste of nonrenewable natural resources, and reducing productive costs.