A dynamic model of nutrient uptake by root hairs

Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes. We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization. Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture. The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.