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  Mathematical modelling of multicellular interactions in stem cell regulation and tissue regeneration

   College of Medicine and Veterinary Medicine

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  Dr Linus Schumacher, Prof Ramon Grima  No more applications being accepted  Funded PhD Project (Students Worldwide)

About the Project


Tissue regeneration is an emergent phenomenon at the scale of cell populations, and interactions between stem cells and the tissue they reside in are required to self-regulate this behaviour. Theoretical considerations suggest that such regulation depends on the structure of the intercellular interactions [2,4,5], more so that the precise molecular identity of the mediators of these interactions. While some models of cellular interaction networks have been studied [1-5], an integrative theoretical understanding that is connected to the biology remains elusive.

We are looking for an ambitious and motivated postgraduate candidate to design a mathematical framework for understanding complex multicellular interactions in regeneration. This project will use tools from dynamical systems theory, statistical physics/stochastic processes, and Bayesian inference. A particular focus will lie on finding distinguishing measurable features of particular interaction networks, and from these to generate predictions that could be tested in collaboration with experimental labs.

The student will learn to develop novel mathematical models of cell population self-regulation, critically review the literature in the field, and communicate with experimental groups. They will characterise model behaviours analytically and through computational simulations, and extend existing models, for example to explore role of stochastic fluctuations and/or spatial effects. The student will have some freedom to define their own project in the context of the group’s research interests, and this is expected to increase later in the PhD.

The successful applicant will be based in the group of Dr Linus Schumacher ( at the MRC Centre for Regenerative Medicine and will also be working closely with Dr Ramon Grima ( The Schumacher group develops mathematical models of cell populations in development and regeneration, working closely with experimental collaborators with the long-term aim to formulate principles that apply to multiple biological systems, gain insight into misregulation in disease, and inform improvements to regenerative therapy. The Grima group has extensive expertise in the building and theoretical analysis of stochastic models of intracellular dynamics and cell-cell interactions.

This is an opportunity to conduct research on mathematical and computational biology, embedded in a world-leading centre for stem cell biology and regenerative medicine. The student will also have the opportunity to engage with the mathematical and systems biology research community at other departments in Edinburgh.

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Applicants should have a 1st/2.1 undergraduate degree (or equivalent), or a Master’s degree, in one of the following: mathematics, physics, computer science, engineering, or similar. A relevant postgraduate degree is desirable. Graduates from a biology/biochemistry/biomedical degree will be considered if they have strong skills and interest in quantitative approaches and relevant scientific programming experience.

Applicants should submit the following documents to our e-mail address [Email Address Removed]:
(1) Personal statement about your research interests and reasons for applying
(2) CV
(3) References (letters of recommendation, on letterhead, signed and dated within 6 months of application)
(4) Marks for degree

Funding Notes

Funding includes stipend, fees (UK/EU/overseas), and travel/research expenses.


1. Becker, N. B., Günther, M., Li, C., Jolly, A., & Höfer, T. (2018). Stem cell homeostasis by integral feedback through the niche. Journal of Theoretical Biology, (2019).
2. Komarova, N. L., & van den Driessche, P. (2018). Stability of Control Networks in Autonomous Homeostatic Regulation of Stem Cell Lineages. Bulletin of Mathematical Biology, 80(5), 1345–1365.
3. Kunche, S., Yan, H., Calof, A. L., Lowengrub, J. S., & Lander, A. D. (2016). Feedback, Lineages and Self-Organizing Morphogenesis. PLoS Computational Biology, 12(3), 1–34.
4. MacLean, A. L., Kirk, P. D. W., & Stumpf, M. P. H. (2015). Cellular population dynamics control the robustness of the stem cell niche. Biology Open, 4(11), 1420–1426.
5. Renardy, M., Jilkine, A., Shahriyari, L., & Chou, C. S. (2018). Control of cell fraction and population recovery during tissue regeneration in stem cell lineages. Journal of Theoretical Biology, 445, 33–50.

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