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

人类面临的主要挑战之一是为不断增长的世界人口提供足够的食物。快速气候变化引起的极端干湿天气循环使这一问题更加复杂，它改变了土壤结构和养分供应，导致主粮和经济作物减产。这些因素结合在一起，对发达国家和发展中国家的农业都提出了一个重大问题。因此，迫切需要开发一种新的作物，在条件恶化和化肥和农药的供应和使用减少的情况下，能够保持或确实增加产量。为了操纵和改善植物对环境变化和外部机械力的反应，我们需要评估影响植物细胞生物力学和植物组织生长限制的最重要的物理和生化因素。植物组织的力学性能和生长在很大程度上取决于细胞壁的结构（植物细胞的主要结构特征）和细胞间的粘附。细胞壁的微观结构和生化过程的高度复杂性需要在其结构元素的尺度上进行数学建模，以帮助填补在实验中获得的对植物力学和生物化学的理解的一些空白。本项目将开发新的植物细胞壁和组织生物力学的数学微观模型。细胞壁微原纤维的微观模型将允许我们考虑细胞壁结构元素的非均匀分布和它们之间的生化相互作用，以及微观结构在响应内部和外部刺激时的变化。由于细胞壁和植物组织中的细胞中有成千上万的微原纤维，因此不可能在实际感兴趣的时间和长度尺度上对复杂的微观模型进行有效的数值模拟，需要应用渐近分析技术。周期性和局部周期性均质化技术将被推广到解决植物细胞壁和组织的非周期性微观结构。通过应用渐近分析，植物组织的宏观特性将从生物化学和机械过程的微观描述来定义。这种宏观模型的多尺度方法和分析将使我们能够预测微观相互作用对宏观力学行为的影响。本项目开发的新的建模和分析方法将帮助我们更好地理解植物细胞的生物力学以及外部机械力对植物细胞内生化过程的影响。数学模型的分析和数值结果与生物学实验数据相结合，将有助于我们找到选择、培育和基因工程改良品种的新方法。更好地了解植物细胞生物力学将使实验学家能够操纵植物细胞壁特性，从而提高木材、纸张和生物燃料生产的效率。

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.