Multiscale modelling of three-dimensional plant root growth

Virtually all our food comes ultimately from plants, either directly or when used as feedstock for animals. Thus to ensure a secure food supply for the future, particularly in the light of global climate change and population growth, it is essential that we fully understand how plants, in particular their roots, grow so we may optimise their growth in challenging environmental conditions (for example during a drought or a flood).

A plant root grows via the elongation of some of its cells, pushing the root forward into the surrounding soil. Plant cells cannot move relative to one another, and so tight control of growth across all cells in an organ such as a root is required. As the root grows, it twists and bends in response to its own internal stresses, as well as by actively varying its mechanical properties (via hormonal control) across the root cross section. This leads to improved penetration of the soil and responses to gravity and touch, for example. These internal stresses and mechanical properties are related to the complex and continually evolving microstructure of the plant cell wall, which consists of a highly organised network of components and is the key mechanical regulator of growth. In particular, the structure of the cell wall gives it anisotropic properties, i.e. these are different depending on which direction you consider them in.

This is a highly complex problem, with the structure of the cell wall determining the mechanical properties of a cell wall segment, which determines the growth and behaviour of the entire root, which in turn feeds back to changes in the structure of the cell wall. Information from the microscopic scale therefore governs what happens to the whole root. We thus need to develop detailed mathematical models to extract the key features and mechanisms which control this growth.

Most current mathematical models only describe straight growing roots and do not allow for any curving, so they cannot answer questions in which this curvature is important or as to how it is generated. Similarly, when considering the mechanical properties of the structured cell wall network, current models are overly simplified, neglecting many important features such as the reorientation of components during growth. Finally, whilst progress has recently been made at each individual scale, combining these models to form a fully multiscale model remains challenging. This project has two components: developing the new mathematical methodologies required to describe such systems, and analysing the resulting models to determine the key biological effects driving root growth.

Using techniques from continuum mechanics, we will derive accurate and biologically relevant models to describe these phenomena. Analysing the models using asymptotic and numerical techniques will lead to novel biological hypotheses which can then be tested experimentally. By developing these mathematical models and techniques we will further understand plant growth, and the tools produced are likely to also be useful to understand other systems which have complex microstructures, whether found in biology, medicine or industry.

Plants are critical to life, providing us with food and forming the basis for the biofuel production that will reduce our dependence on fossil fuels. It is therefore vital to maintain a stable supply of healthy plant material to cover all these needs, along with the capacity to increase yield as necessary. In particular, to ensure sufficient nutritious food is available to sustain our growing population, it is predicted that agricultural productivity must increase by 60% by 2050. However, the damage caused by climate change may actively reduce our current productivity by as much as 80% by the end of the century (data from American Society of Plant Biologists). The need to develop agricultural technology is therefore urgent for the future of humankind.

It is thus essential to undertake substantial research in plant sciences to ensure the most efficient plant growth for a desired output, for example maximising biomass for fuel usage or edible material for food. Increased production must be achieved whilst minimising resource input and potentially within challenging environmental conditions. These are complex problems with multiple interacting components, providing an urgent opportunity for mathematical modelling to achieve far-reaching influence.

This research will identify the key mechanical features required to produce certain macroscopic root behaviour, such as a root with given twisting characteristics to improve soil penetration. Linking these desirable macroscale traits to the required changes in the microstructure will enable us to identify the molecular pathways which regulate this behaviour and thus produce plants which display these traits (short to medium term). Whilst we will focus on the model plant Arabidopsis, this knowledge can be transferred to crop plants leading to more effective plant growth in normal and stressed conditions (medium to long term). There are clearly wide ranging economic benefits within the commercial sector, from the design and sale of more effective plants/seeds and chemicals, to higher yields for farmers (long term). In turn higher yields will lead to more readily available food both in the UK and the rest of the world, including those experiencing environmentally stressed conditions such as droughts (long term). In the light of global population growth combined with climate change, increased food security is essential to maintain a healthy population, and so this research has clear advantages to society. Similarly, a greater understanding of root architecture has applications in the bioenergy sector, since the majority of plant biomass is located within the cell wall. Following a similar procedure as detailed above for food production, this research can be used to increase the biomass generated by a single plant, leading to efficiency savings for the bioenergy industry (long term). Effective ways of producing renewable energy in the future are essential to maintain and raise standards of living across the world.

The mathematical models and techniques produced during the grant will be relevant to other areas within the industrial, medical or biological communities, and as such will be useful to mathematical modellers working within or for these communities. Potential areas to consider include the textile industry, composite production and synthetic biology. For the final category, their use for microfibre suspension devices will be facilitated through our recently-funded PhD studentship. These areas may in turn have wide ranging effects on the economy or quality of life.