Mathematical Modelling of Nutrient Dynamics around Root Hairs

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In this study, we developed a spatially explicit model for nutrient uptake by root hairs based on X-ray computed tomography images of the rhizosphere soil structure. This work extends our previous work to larger domains and hence is valid for longer times. Unlike the model used previously, which considered only a small region of soil about the root, we considered an effectively infinite volume of bulk soil about the rhizosphere. We asked the question: At what distance away from root surfaces do the specific structural features of root-hair and soil aggregate morphology not matter because average properties start dominating the nutrient transport? The resulting model was used to capture bulk and rhizosphere soil properties by considering representative volumes of soil far from the root and adjacent to the root, respectively. By increasing the size of the volumes that we considered, the diffusive impedance of the bulk soil and root uptake were seen to converge. We did this for two different values of water content. We found that the size of region for which the nutrient uptake properties converged to a fixed value was dependent on the water saturation. In the fully saturated case, the region of soil we needed to consider was only of radius 1.1mm for poorly soil-mobile species such as phosphate. However, in the case of a partially saturated medium (relative saturation 0.3), we found that a radius of 1.4mm was necessary. This suggests that, in addition to the geometrical properties of the rhizosphere, there is an additional effect of soil moisture properties, which extends further from the root and may relate to other chemical changes in the rhizosphere. The latter were not explicitly included in our model.