Collective chemotaxis: how cells work together to migrate more efficiently

Collective movement is a widespread phenomenon in biology. Examples range from flocking birds and school of fish on a larger scale to swarming bees and ant colonies on a smaller scale. The most crucial collective behaviours for human health, however, occur on a much smaller scale:
Collective cell movement is essential for numerous cellular mechanisms, e.g. in wound healing, cancer migration and embryonic development. In the latter, so-called neural crest cells (NCC) migrate in clusters from the neural tube (prestage of the spine) throughout the whole embryo. This behaviour is necessary for the formation of neurons, glia, bone, tissue, just to name a few. A failure of this migration might lead to birth defects, such as a cleft lip. Once, this phenomenon is understood, the results could potentially help to understand cancer migration.
One of the main drives for this phenomenon is chemotaxis - the guided movement of cells towards the gradient of a chemical substance. The other two mechanisms that enable the formation of clusters and the dispersion of cells throughout the embryo are the co-attraction of cells and the contact inhibition of locomotion, respectively. Previously, this behaviour has been studied in agent-based models, however, these models are difficult to analyse and computationally expensive to simulate.
The aim of this project is to derive a macroscopic, continuous representation of this behaviour, starting from a microscopic model for one cell, a (position jump) random walk that incorporates the three mechanisms mentioned. Incorporating these three mechanisms in a biologically relevant way requires a comprehensive understanding of the underlying biological mechanisms. The macroscopic model obtained will have the form of a system of diffusion-advection-(reaction) partial differential equations (PDEs) and is comparably easy to analyse and implement.
Furthermore, we will analyse the PDE model and compare simulation results from both the macroscopic and the microscopic model.
After having done this, we will consider another modelling approach for the microscopic scale, again derive a macroscopic representation, and compare that to the previously obtained result. The exact approach we will use here is yet to be determined.

MAC-MIGS develops computational modelling and its application to a range of economic sectors, including high-value manufacturing, energy, finance and healthcare. These fields contribute over £500 billion to the UK economy. The CDT involves collaborations with more than a dozen companies and organisations, including large corporations (AkzoNobel, IBM, Dassault, P&G, Aberdeen Standard Investments, Intel), mid-size firms, particularly in the engineering and power sectors (NM Group, which provides monitoring services to power grid operators in 30 countries, Artemis Intelligent Power, the world leader in digital displacement hydraulics, Leonardo, a provider of defense, security and aerospace services, and Oliver Wymans, a management consultancy firm) and startups such as Brainnwave, which develops data-modelling solutions, and Opengosim which designs state-of-the-art and massively parallel software for subsurface reservoir simulation. Government and other agencies involved will include the British Geological Survey, Forestry Commission, James Hutton Institute, and Scottish National Heritage. Engagement will be via internships, short projects and PhD projects. BIS has stated that "Organisations using computer generated modelling and simulations and Big Data analytics create better products, get greater insights, and gain competitive advantage over traditional development processes". Our partners share this vision and are keen to develop deeper collaborations with us over the duration of the CDT.

Our CDT will achieve the following:

- Produce 76 highly skilled mathematical scientists and professionals, ready to take up positions in academia or in companies such as our partners. The students will have exposure to projects, modelling camps and high-level international collaborations.

- Deliver economic and societal benefits through student research projects developed in close collaboration with our partners in industry, business and government and other agencies.

- Create pathways for impact on computer science, chemistry, physics and engineering by involving interdisciplinary partners from Heriot-Watt and Edinburgh Universities in the supervision and training of our students.

- Organise a large number of lectures and seminars which will be open to staff and students of the two universities. Such lectures will inform the wide university communities about the state-of-the-art in computational and mathematical modelling.

- Work with other CDTs both in Edinburgh and beyond to organise a series of workshops for undergraduates, intended to foster an increased uptake of PhD studentship places in technical areas by female students and those from ethnic minorities, with potential impact on the broader UK CDT landscape.

- Organise industrial sandpits and modelling camps which offer the possibility for our partners to present a challenge arising in their work, and to explore innovative ways to tackle that challenge, fully involving the CDT students. This will kick-start a change in the corporate mindset by exposing the relevant staff to new approaches.

- Develop a new course, "Entrepreneurship for Doctoral Students in the Mathematical Sciences" in conjunction with Converge Challenge (Scotland's largest entrepreneurial training programme) and UoE's School of Business. This and other support measures will develop an innovation culture and facilitate the translation of our students' ideas into commercial activities.