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Developing stochastic mathematical frameworks for modelling cell migration

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  • Full or part time
    Dr Kit Yates
  • Application Deadline
    No more applications being accepted
  • Funded PhD Project (European/UK Students Only)
    Funded PhD Project (European/UK Students Only)

Project Description

Biological Scenario:
Neural crest cells, are cells of the early embryo that form part of many diverse tissue types. Failure of neural crest cells to travel to their target locations can result in a wide range of human birth defects collectively known as neurocristopathies (e.g. Hirschsprung’s disease, Waardenburg syndrome). Melanocytes are a sub-population of neural crest cells responsible for the pigmentation of hair and skin. They fill the growing embryo from the back to the front. If, for some reason (perhaps a genetic mutation), the cells are unable to complete their journey, areas at the front of the embryo are left unpigmented. In humans this condition is known as piebaldism.

Stochastic modeling:
Randomness at the cellular level can lead to interesting and counterintuitive phenomena. However, it is only recently that the simulation of reaction-diffusion models incorporating randomness has become a popular way to investigate biological processes at the cell scale. Such models provide realism at the cost of significant computational resources. Modelling at the cell scale requires modelling frameworks to run as efficiently as possible which necessitates the development of new mathematical techniques. For example, hybrid (mixed) representations which combine the best features of existing schemes or efficient simulation algorithms which ensure feasible simulation times for complex biological models.

My group (5 PhD students and numerous experimental and theoretical collaborators) is based in the renowned Centre for Mathematical Biology at the University of Bath. Our work focusses on the realistic representation of biological systems in which stochasticity plays an important role. As Mathematical Biologists we are genuinely interested in representing biological systems rather than making convenient assumptions which allow us to use familiar mathematical tools, but leave the models bereft of predictive power. Consequently, when working in close collaboration with our experimental colleagues we often find it necessary to develop novel modelling methodologies in order to accurately capture pertinent biological phenomena. The interdisciplinary nature of our work has led to several high-profile publications in recent years, in application areas from the collective swarming of locusts ( [1] to the migration patterns of cells in early embryonic diseases ( [2] – systems linked only by the importance of randomness to their behaviour.

The project:
Throughout this project the candidate will attempt to answer questions in Developmental Biology by creating novel mathematical modelling methodologies which allow for both detailed realistic representation and efficient simulation. In each case my experimental collaborators will provide the data required to parameterise and validate the models or perform experiments to investigate model-generated predictions. The methodologies will be developed in sufficient generality that they can be applied to a wide range of reaction-diffusion systems across the sciences.

This project will focus on the development of efficient spatially extended modelling frameworks for the representation of cell migration and more general reaction-diffusion processes. The models themselves will incorporate some or all of the flowing experimentally-motivated facets: domain growth, volume exclusion, diffusion, proliferation, chemotaxis, cell-cell signalling. These sophisticated models will be efficient enough to incorporate detailed biological information, provided through a long-standing experimental collaboration, on a range of biological mechanisms which contribute to the overall migration. This will allow investigate a wider range of complex biological of scenarios.

This research will provide significant insight into the behaviour of neural crest cells and the diseases associated with migration failure. A better understanding of the developmental origins of neural crest cell disorders will benefit both our clinical understanding of the diseases and the advancement of diagnostic and therapeutic strategies.

Training Opportunities:
The student would be offered the possibility of “aligned status” with the Department’s SAMBa Centre for Doctoral Training. Effectively this would give the student access to a wide range of both generic and specifically mathematical training courses as well as mentoring and the opportunity to become part of a cohort of students who develop together and share expertise. Alignment also provides the chance for students to attend symposia seminars covering a wide range of topics in applied mathematics, week-long Integrative Think Tanks involving industry, academics and students as well as transferable skills training (in addition to the multitude of skills training course offered by the University at large) and support to attend academic conferences. The support and structure provided by the first year SAMBa cohort experience is highly rated by the current participants. As such, the opportunity adds great deal of value to this PhD placement.

Funding Notes

The successful candidate will be fully funded for 3.5 years. This will cover the Home/EU tuition fees, a training support fee of £1,000/annum and a tax-free maintenance payment of at least £14,057/annum (15/16 rate).

Please note: only Home & EU students are eligible for this studentship.
The mathematical tools that will be used will be diverse and range from on/off lattice individual-based models to partial differential equations and probability theory. An idea candidate will have a strong background in applied mathematics with some experience of probability and an interest in biological problems and direct collaboration with experimentalist providing data.


[1] C.A. Yates, R. Erban, C. Escudero, I.D. Couzin, J. Buhl, I.G. Kevrekidis, P.K. Maini and D.J.T. Sumpter, (2009). PNAS, 106(14), 5464-5469.
[2] R.L. Mort, R.J.H. Ross, K.J. Hainey, O. Harrison, M.A. Keighren, G. Landini, R.E. Baker, K.J. Painter, I.J. Jackson and C.A. Yates (2015). (To appear in Nat. Commun.).

About Dr Christian Yates:
I have a strong, long-lived and productive collaboration with an experimental scientist at the University of Edinburgh with whom I have published several high impact papers.
I also have a well-established network of theoretical collaborators, whose expertise can be drawn upon, several burgeoning experimental collaborations.
I work in an interdisciplinary field at the interface of Mathematics and Biology.
As such there are numerous training opportunities in both fields. This gives the chosen candidate the opportunity to become a well-rounded Mathematical Biologist capable of working with both experimentalists and theoreticians.
I am also the department’s widening participation and outreach coordinator. As such I am a keen deliverer of interactive mathematical displays/demonstrations about my research and mathematics more widely. My research has also been featured on the BBC website, on BBC radio 4’s Today programme, as well as a wide range of other media outlets. The chosen candidate will gain the ability to engage the general public with their research and have the opportunity to see their work covered by a wide range of media outlets.

For more information, please see my website:

Listen to Dr Christian (Kit) Yates talk of his project in this short video:

How good is research at University of Bath in Mathematical Sciences?

FTE Category A staff submitted: 44.40

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