One of the major challenges facing mankind is to provide enough food for the expanding world population. This problem is compounded by extreme wet-dry weather cycles induced by rapid climate change, which alters both soil structure and nutrient availability leading to yield reduction in staple and cash crops. These factors combine to present a significant problem for agriculture in both developed and developing countries. Hence, there is an immediate need to develop a new range of crops that can maintain or indeed increase yields in the face of worsening conditions and reduction in the availability and use of fertilisers and pesticides. In order to manipulate and improve plant responses to environmental changes and external mechanical forces we need to evaluate the most important physical and biochemical factors responsible for plant cell biomechanics and for the growth limitation of plant tissues.

The mechanical properties and growth of plant tissues are strongly determined by the structure of the cell wall (the main structural feature of plant cells) and the adhesion between the cells. The high complexity of the microstructure and biochemical processes in the cell wall requires mathematical modelling at the scale of its structural elements to help to close some gaps in the experimentally obtained understanding of the plant mechanics and biochemistry. New mathematical microscopic models for biomechanics of the plant cell wall and tissue will be developed in this project. A microscopic model on the scale of cell wall microfibrils will allow us to consider non-homogeneous distributions of cell wall structural elements and the biochemical interactions between them, as well as changes in the microstructure in response to internal and external stimuli.

As there are thousands of microfibrils in a cell wall and of cells in a plant tissue, effective numerical simulations of the complex microscopic models on the time and length scales of practical interest are not possible and asymptotic analysis techniques need to be applied. The techniques of periodic and locally-periodic homogenisation will be generalised to address non-periodic microstructures of plant cell walls and tissues. By applying asymptotical analysis, the macroscopic properties of plant tissues will be defined from the microscopic description of biochemical and mechanical processes. This multiscale approach and analysis of the macroscopic model will enable us to predict the influence of microscopic interactions on the macroscopic mechanical behaviour.

The new modelling and analytical approaches to be developed in this project will help us to better understand the biomechanics of plant cells and the influence of external mechanical forces on bioche- mical processes inside plant cells. The analytical and numerical results of the mathematical models combined with data from biological experiments will help us to identify new approaches to select, breed and genetically engineer improved cultivars. A better understanding of plant cell biomechanics will enable experimentalists to manipulate plant cell wall properties which in turn will lead to an improvement in the efficiency of wood, paper and biofuel production.

Potential Impact:
The proposed fundamental mathematical research, devoted to the development of new modelling approaches and multiscale analysis techniques, will find its path toward impact on society and economy through collaboration with experimentalists in biology and engineering. The biologically-focussed modelling and analysis will impact the agricultural sector, whilst development of new multiscale analysis techniques will lead to improvement in engineering material performance with beneficial consequences for environment and commercial profitability.

Direct collaboration with experimental groups at The James Hutton Institute working with plant breeders, and interactions with research groups in the College of Life Sciences, Universities of Dundee, studying lignin biosynthesis in the context of biofuel production, will facilitate and ensure the pathway to impact of the proposed research on the society and economy. Both collaborating institutions have direct connections with the industrial and commercial sectors. Discussions with experimentalists in concrete research in the Civil Engineering Department, University of Dundee, and establishing new collaborations with research groups and companies in biomimetics will link the multiscale analysis techniques with the design of new engineering materials. Presentation of the results obtained from the multiscale modelling and analysis to experimental and industrial communities at both national and international conferences and workshops will support the transfer of knowledge and expertise.

There are several ways in which this research will directly contribute to industry-relevant problems:

1. Mathematical modelling of the mechanical properties of plant cells and tissues will give new insights into the control mechanisms of the root growth process and will help experimental biologists to specify the beneficial root traits to select crops ideal for problematic soils and to enhance agricultural efficiency in regions with degraded, hard and unproductive soil.

2. A better understanding of pectin biochemistry will help to manipulate the quality of pectin in plants and will contribute to more efficient production of pectin as a food ingredient.

3. The new knowledge obtained from the mathematical modelling of plant cell walls and changes in the microscopic properties in response to external and internal stimuli will provide new ideas for the possible manipulation of cell wall structural and mechanical properties and impact the efficiency and quality of pulps, paper, wood, and biofuel production.

4. Studies of the influence of the hierarchical microstructure of plant tissues on their mechanical performance will help to improve the development and production of innovative composite materials.

5. The multiscale analysis techniques that will be developed here, when applied to models describing sound and temperature propagation through concrete walls could provide a quantitative relationship between the microscopic structure and propagation impedance and allow the thermal and acoustic isolation of building materials to be optimised. This will have positive consequences for environment and quality of life.

In the context of food production for the growing world population the impact of the proposed work has also an essential international aspect and is especially important for developing countries.

The topic of the proposed research is of wide interest and its dissemination to the public will raise awareness of the innovation and impact of applied mathematical research.