BB1: Mathematical modelling of plant/crop growth in stressed environments

Project completed January 31, 2012

Background

With recent reports of global food shortages, it is more important than ever to have a clear understanding of the processes that control crop growth. One of the most influential factors is the availability of nutrients in the soil. Phosphorus is one of the most limited nutrients as it is usually so strongly bound to soil particles that it becomes almost immobile.

Phosphorous is essential for plant growth, and plant roots are adapted for adequate uptake. Some roots release chemicals, such as citrate, to help mobilise nutrients. Specific parts of plant roots (cluster roots and root hair cells) provide a large surface area for nutrient and water uptake. Despite these adaptations, problems arise in nutrient-poor, over-worked soils, where farmers must turn to environmentally damaging phosphorous-based fertilisers to grow crops reliably.

To further understanding of crop growth, researchers at the Oxford Centre for Collaborative Applied Mathematics (OCCAM) have derived new mathematical models for nutrient uptake by root hairs and cluster roots, and a model for how citrate interacts with soil.

Techniques and Challenges

Root hairs: Root hairs are thin, hair-like projections found along the roots of plants, as shown in Figure 1. The importance of root hairs in the uptake of sparingly-soluble nutrients is understood qualitatively, but not quantitatively, and this limits efforts to breed plants tolerant of nutrient-deficient soils. Existing single porosity models cannot account for diffusion between soil particles. Researchers at OCCAM have developed a new dual porosity model of nutrient uptake by root hairs to account for diffusion between soil particles that incorporates root hair geometry and the details of nutrient transport to root hairs through soil.

Cluster roots: The researchers also modelled cluster (proteoid) roots, which are dense, lateral root formations that cover the entire main root surface on some plants in nutrient-poor environments. This proliferation of rootlets in a cluster provides a massive increase in root surface area. Proteoid root clusters also chemically modify the surrounding soil by exuding compounds that facilitate the mobilisation of nutrients.

In modelling cluster roots, the researchers used the theory of homogenisation. They focused mainly on citrate exudation (the release of citrate by the roots) and its effect on phosphate mobilisation.

Citrate sorption: In addition to modelling roots the researchers, in close collaboration with experimentalists, modelled the role of organic acids in soil. Citrate is a key organic acid. It has been intensively investigated in, for example, nutrient uptake. However, little is known about the interaction dynamics of organic acids with the soil.

The researchers developed a new kinetic sorption model for citrate using nonlinear ordinary differential equations. The model incorporates two Freundlich sorption curves. These curves relate the concentration of solid citrate to the concentration of dissolved citrate in the soil.

Results

Root hairs: The new model for the role of root hairs in nutrient uptake predicted greater root uptake of nutrients when compared with existing models. Also, the effect of soil moisture was shown to be less important in the dual porosity model. It proved consistent with experimental observations on the effects of root hair length and root hair density on nutrient uptake in soils of different moistures.

Cluster roots: The model captured the cumulative effect of citrate exudation on phosphate uptake by cluster roots, while retaining all the necessary information about the microscale geometry.

An interesting finding that emerged from this study of cluster roots is that after two days of exudation, the cluster root efficiency dropped dramatically. In fact, after this period, the rate of phosphate uptake became lower than in the absence of exudation, which suggests that it is expected for exudation to stop after two days.

Citrate sorption: The model satisfactorily explained experimental data and was able to predict dynamic adsorption and desorption behaviour.

The Future

Work has already begun on using these results to understand which factors are important for phosphate uptake in different soil environments. This work could lead to a reduction in the use of phosphate-based fertilizers which are both expensive and environmentally damaging. Another direction for future work is in determining how plants allocate resources to achieve maximum growth and how such mechanisms are used by the plant to respond to environmental changes.

Related Publications:

[10/63] Zygalakis K. C., Kirk G. J. D., Jones D. L., Wissuwa M., Roose T.:  A dual porosity model of nutrient uptake by root hairs, New Phytologist