Multiscale modelling of three-dimensional plant root growth
Lead Research Organisation:
University of Birmingham
Department Name: School of Mathematics
Abstract
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.
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.
Planned Impact
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.
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.
Organisations
People |
ORCID iD |
Rosemary Dyson (Principal Investigator) |
Publications
Chakraborty J
(2021)
Lockhart with a twist: Modelling cellulose microfibril deposition and reorientation reveals twisting plant cell growth mechanisms.
in Journal of theoretical biology
Dietrich D
(2017)
Root hydrotropism is controlled via a cortex-specific growth mechanism.
in Nature plants
HOLLOWAY C
(2018)
Linear Rayleigh-Bénard stability of a transversely isotropic fluid
in European Journal of Applied Mathematics
Holloway CR
(2018)
Influences of transversely isotropic rheology and translational diffusion on the stability of active suspensions.
in Royal Society open science
Smithers E
(2024)
A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure
in The European Physical Journal E
Smithers ET
(2019)
Mathematical principles and models of plant growth mechanics: from cell wall dynamics to tissue morphogenesis.
in Journal of experimental botany
Tyrrell J
(2019)
Regularized Stokeslet rings: An efficient method for axisymmetric Stokes flow with application to the growing pollen tube
in Physical Review Fluids
Ziegler C
(2019)
Model selection and parameter estimation for root architecture models using likelihood-free inference.
in Journal of the Royal Society, Interface
Description | We have developed a framework which allows for dynamic changes in cellulose microfibre deposition angle during single cell growth. Hypotheses about which mechanisms determine the angle of cellulose microfibre deposition during growth can thus be tested. The model also determines how twisting of the cell is induced via mechanical anisotropy and variable material properties. We find that competition between growth and twisting/torque (in the form of relative elongation and twist rates) determines the dynamics of root elongation, twisting and microfibre evolution. We have shown that small changes to the dynamics of how cellulose microfibres are laid down can lead to a dramatic slowing in growth which could be a potential mechanism for halting growth. The model also demonstrates an intrinsic "handedness" to cell twisting. This model is providing an exciting framework to interpret newly published (2019/2020) experimental findings; one paper is under review, with another in preparation. We have also incorporated the effects of cellulose microfibre realignment on the remodelling of the cell wall network at the microscale. This determines the evolution of the macroscale cell wall mechanical properties over time, identifying a potential mechanism which will naturally inhibit plant cell growth after a period of time. We have further developed this model to incorporate recent findings about the cell wall microstructure, in particular the effect of "hot spots" which bind together cellulose fibres. Work to include pectin dynamics is underway. A publication (for an invited special issue) is close to submission. The modelling developed has been used to investigate root bending during a hydrotropic response; this work is published in Nature Plants. We have developed new mathematical methodology to enable the dispersion of fibres to be modelled, of use in this project as well as several other application areas. By linking the transversely isotropic fluid and active fluids literature, we can now express the macroscale anisotropic mechanical parameters which appear within the transversely isotropic stress tensor in term of the solvent fluid and aspect ratio of the fibres. This work is published in Royal Society Open Science. Related work has taken ideas from plant cell wall modelling undertaken here, and used them to model vesicle motion and cytoplasmic streaming in pollen tube growth. This work is published as an "Editor's suggestion" in Physical Review Fluids; a further publication is being prepared for submission. Other research is being finalised following the end of the award. |
Exploitation Route | The underlying methodology developed here can be exploited in the context of design for additive manufacture. By drawing an analogy between additive manufacture and plant root growth, we aim to develop a more intuitive software to design parts for manufacture, with a particular focus on the biomaterials sector. This work has been funded by the EPSRC, and is being further persued by a PhD student from the EPSRC-funded Topological Design CDT. The models of plant growth developed can be extended to incorporate multiple cells or the dispersion of cellulose microfibres. The hypotheses can be tested by experimental researchers. These novel mathematical models focus on developing methodology for fibre-laden flows which can also be used in areas such as tissue engineering, active fluids and fertility treatment. |
Sectors | Agriculture Food and Drink Digital/Communication/Information Technologies (including Software) Manufacturing including Industrial Biotechology Pharmaceuticals and Medical Biotechnology Other |
Description | We have developed a virtual reality "Virtual Plant Laboratory" which has been trialled at University Open days and is being integrated into the university's VR suite. We have also trained a number of undergraduate ambassadors on delivering the sessions, who have thus learned about the material at the same time. This has increased the understanding and interest in mathematical modelling within plant sciences, along with the importance of plant science to a sustainable society. The research developed through this award is currently being used as a foundation for another EPSRC New Investigator award in Mechanical Engineering, developing software for design for additive manufacture. Here we draw an analogy between additive manufacture and plant root growth, aiming to develop more intuitive and robust software which allows the user to more naturally explore design space. The research is therefore underpinning development in the manufacturing sector. I have given several public engagement talks to broad audiences, including 800 year 12 students and as part of the Birmingham Arts and Science Festival, based on the research undertaken for this award. This had broadened the awareness of both plant science research and the wider role of mathematical modelling to society. |
First Year Of Impact | 2015 |
Sector | Education,Manufacturing, including Industrial Biotechology,Other |
Impact Types | Societal |
Description | EPSRC CDT Topological Design studentship |
Amount | £80,997 (GBP) |
Funding ID | EP/S02297X/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 09/2020 |
End | 09/2024 |
Description | MIBTP Research Experience Placement |
Amount | £2,500 (GBP) |
Organisation | Midlands Integrative Biosciences Training Partnership |
Sector | Academic/University |
Country | United Kingdom |
Start | 05/2016 |
End | 09/2016 |
Description | PhD studentship |
Amount | £75,000 (GBP) |
Organisation | University of Birmingham |
Sector | Academic/University |
Country | United Kingdom |
Start | 08/2017 |
End | 09/2020 |
Description | Temporal Design for Additive Manufacture: GrowCAD |
Amount | £237,591 (GBP) |
Funding ID | EP/S036717/1 |
Organisation | Engineering and Physical Sciences Research Council (EPSRC) |
Sector | Public |
Country | United Kingdom |
Start | 02/2020 |
End | 07/2023 |
Description | University of Birmingham Alumni Impact Fund |
Amount | £4,880 (GBP) |
Organisation | University of Birmingham |
Sector | Academic/University |
Country | United Kingdom |
Start | 02/2019 |
End | 09/2019 |
Description | University of Birmingham Funding for an Impact Fellow |
Amount | £360,000 (GBP) |
Organisation | University of Birmingham |
Sector | Academic/University |
Country | United Kingdom |
Start | 04/2018 |
End | 04/2021 |
Description | British Council's Researcher Link workshop entitled "Using systems and synthetic biology to tailor plant cell walls for a better future" |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Other audiences |
Results and Impact | This workshop in Brazil involved young researchers working in the wider Plant Cell wall community, many of whom were previously unaware of my research and significantly outside of my normal community (I was the only mathematician present). My research talk sparked questions and discussion, and the initial stages of collaborations and funding applications are underway. |
Year(s) Of Engagement Activity | 2015 |
Description | IMA East Midlands Branch Talk |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | An interactive talk to around 40 members of the general public, discussing multiscale modelling using plants as an example. It generated increased engagement with mathematical biology, and modelling in plant sciences in particular, with some interest on in Twitter. |
Year(s) Of Engagement Activity | 2016 |
URL | http://ima.org.uk/_db/_documents/Dyson%2022.11.16.pdf |
Description | Maths Taster Day |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Schools |
Results and Impact | Talk to approx. 20 year 12 students to engage them with mathematics. Activity to demonstrate the broadness of mathematics, based on modelling in plant sciences. |
Year(s) Of Engagement Activity | 2018 |
Description | Popular Maths Lecture, Birmingham |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | A talk as part of the Birmingham Arts and Science festival on current research. Following the talk there was lots of discussion and further contact with audience members. |
Year(s) Of Engagement Activity | 2015 |
URL | http://www.birmingham.ac.uk/schools/mathematics/news-and-events/birmingham-popular-maths-lecture.asp... |
Description | The Training Partnership |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | National |
Primary Audience | Schools |
Results and Impact | 800 year 12 students attended a talk on my current research, aiming to inspire them to continue with mathematics post school. |
Year(s) Of Engagement Activity | 2015 |
URL | http://www.thetrainingpartnership.org.uk/study-days/subjects/mathematics/mathematics-asa-level-ib/ |
Description | Virtual Plant Lab VR simulation activity |
Form Of Engagement Activity | Participation in an open day or visit at my research institution |
Part Of Official Scheme? | No |
Geographic Reach | National |
Primary Audience | Schools |
Results and Impact | We have developed a virtual reality environment in which to engage people with research into plant growth. We have run this at several open days, as a training session for undergraduate students and are currently rolling it out within the University's VR suite which will enhance the reach of the work. Current numbers engaged are small, but with a very high level of engagement (one on one discussion for 20-30 minutes during an open day). This is leading to a higher level of understanding on how mathematical modelling can be used in plant science, along with an increased appreciation of the fundamental societal importance of plant science. The exhibit was futher developed by an undergraduate intern during summer 2020, engaging a Liberal Arts and Natural Sciences student with the research. |
Year(s) Of Engagement Activity | 2019,2020 |