Multiscale Modelling of Soil-Plant Interactions

Interactions of plants with their surrounding soil affect important issues such as cycling of carbon and mineral nutrients, agriculture, phytoremediation and development of rhizotechnologies. Understanding the mechanisms of these processes is required particularly in view of changing environmental conditions and limited resource availability. A serious threat to global food supply is presented by the severe phosphate crisis anticipated for the 21st century if rock phosphate continues to be mined at current rates. Ecological intensification of agroecosystems and decreasing agricultural inputs such as phosphate fertilisers will only be possible if we understand and make use of the mechanisms of nutrient bioavailability. A powerful way forward in gaining insight into those mechanisms is provided by mathematical modelling. Main focus of this project is the development and analysis of a dynamic multiscale model on phosphate uptake by mycorrhizal plants from soil. Mycorrhizas are mutualistic symbiotic associations between plant roots and soil fungi. The external fungal hyphae provide the plant with an additional pathway to access poorly mobile phosphate. In return, the fungus receives photosynthate carbon from the plant for its nutrition. The structure of the external fungal mycelium leads to a mathematically challenging problem because the relevant processes occur over several spatial and temporal scales. The term "effective" in the title has both a biological and a mathematical meaning: a) mycorrhizas make plants more effective in taking up phosphate and b) mycorrhizas make it necessary to derive an effective equation for nutrient transport and uptake in a soil containing a fungal mycelium. Multi-scale modelling is a current frontier in plant and soil research; however has not yet been extended to plant-mycorrhizal fungi-soil interactions. This is a serious shortcoming in the light of the potential benefits mycorrhizas have for agro-ecosystems. Various mathematical upscaling methods are available for dealing with problems on complicated spatial geometries. They simplify those problems in order to reduce computational expense. Furthermore, they facilitate detailed insight into a problem on different scales of observations. Three distinct spatial scales will be included in the proposed mycorrhiza model: a) a single hypha surrounded by soil particles and water, b) a single root with fungal mycelium and c) a mycorrhizal root system. Two upscaling steps will achieve the transition between those scales. Methods used will include the method of homogenisation and computational upscaling method with simplifying assumptions on the microscopic heterogeneities. In close collaborations between modellers and experimentalists, an accompanying experiment will provide data on phosphate uptake by the model legume Medicago truncatula associated with Glomus intraradices. It will provide invaluable benefits with regard to model validation and will support wider acceptance and use of the research results. Results will contribute to sustainable management of phosphate in agriculture and help to advance crop management schemes that increase soil phosphate availability.

This project was interrupted after 15 months to enable the project leader, Andrea Schnepf, to pursue a career opportunity at Forschungszentrum Jülich, Germany. This lead to the fact that Andrea Schnepf was appointed a W2 professorship for Modelling soil, plant root systems and their interactions, jointly by Forschungszentrum Jülich and the University of Bonn. As the Elise Richter Programme grants personal funds that cannot be transferred to another institution, the project was cancelled early in March 2014. However, one of the main goals, namely the career development of the project leader, has been well accomplished. The scientific results of the Elise Richter project are related to three main topics, two of them are already published. A new image analysis approach was developed that enables to extract root architectural parameters from 2-dimensional images of root systems. It relies on a mathematical model of root architecture development for root tracking. It is the first fully-automated algorithm that enables the analysis of images of soil-grown root systems from different sources. A systematic analysis of root architectural parameters will enhance structural-functional models of root architecture and support the investigation of root-soil interactions as well as support the development of new upscaling methods. Plants can chemically mobilise soil phosphate through root exudation of organic chelators (mining strategy). A new single root model for root exudation and its effect on root P uptake was developed and upscaled to the root system scale based on the root architecture model RootBox. It was shown that the overall effect of root exudation on the root system scale is not the same as on the single root scale but highly depends on root age and the position of root exudation along the root axis. This will help to quantify to which extent such a mining strategy will be able to replace phosphate fertilisation. Another mechanism known to be important for plant phosphate nutrition is the symbiosis with mycorrhizal fungi. It was a special focus of this project to develop a new model of root system mycorrhisation and its effect on plant phosphate uptake and to calibrate it with data from an accompanying experiment. Seedlings of Medicago truncatula were allowed to connect to a previously established mycelium of the arbuscular mycorrhizal fungus Glomus intraradices and plant biomass, root length, infection rate, external mycelium, as well as P contents were observed. A first model of root system mycorrhisation that describes root growth and infection simultaneously qualitatively agrees with root infection rate data. Further model development and analysis of experimental data and model calibration were prolonged when the project was interrupted. However, Andrea Schnepf plans to further pursue this topic in her new position together with her collaborators. The model can be used to test different placements of inoculum and to predict mycorrhizal root system interactions with soil.