Multiscale modelling and analysis of mechanical properties of plant cells and tissues

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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.