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  EASTBIO: Mathematical theories for pattern formation in developing embryos

   School of Medicine, Medical Sciences & Nutrition

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  Dr T Hiscock, Dr Linus Schumacher  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

This fully funded, 4-year PhD project is part of a competition funded by the BBSRC EASTBIO Doctoral Training Partnership.

We are seeking a talented, creative, and friendly individual to join our interdisciplinary team. We build physics-style mathematical models to understand the remarkable processes that allow single-cell embryos to develop into complex animal forms.


 There is a long history in using mathematical theories to understand pattern formation in non-equilibrium systems [1]. Patterns occur throughout the physical and natural world: from undulations of sand at the beach, to the formation of galaxies; from ripples on the surface of a lake, to the microscopic organization of crystalline materials. The shapes and patterns of animal bodies and body-parts are a particularly striking example of pattern formation. These complex structures are self-assembled by the animal itself during its development, a remarkable process that transforms a single-cell embryo into a functioning adult form.

Currently, we have a good linear theory to explain how repeated, periodic patterns (e.g., teeth, hair, fingers) self-organize in developing organisms. This classic approach relies on linear instability analysis of Turing-type reaction-diffusion models [2]. However, many developmental mechanisms include significant nonlinear dynamics and generate non-periodic patterns (e.g., the circularly symmetric arrangement of pupil and iris in the eye). In this project, you will explore how non-linear reaction-diffusion systems allow embryos to self-organize non-periodic yet reproducible patterns.


In this project, we will take two complementary approaches:

(1) We will adapt tools from nonlinear dynamical systems theory (e.g., Green’s functions, energy functionals, Whitham averaging [4,5]) to analyse reaction-diffusion models of pattern formation. We will construct the problem rather generally, but will also build models of specific biological systems where we have access to data (e.g., the vertebrate spinal cord). 

(2) At the same time, we will conduct large-scale numerical simulations to search for unexpected mechanisms of pattern formation. We will build a machine learning pipeline to train partial differential equations that generate specific non-periodic patterns inspired by developmental structures [6].


 Given the mathematics involved in this project, candidates should have strong quantitative skills and, ideally, proficiency in coding. Undergraduates from quantitative disciplines (physics, maths, engineering) will be particularly well-suited; no formal training in developmental biology is required, although curiosity is essential.


 The project will be based in Aberdeen and will benefit from complementary expertise and frequent interactions with our collaborator in Edinburgh. Interested candidates should get in touch with Tom before applying: [Email Address Removed].



  • Applicants should hold a minimum of a 2:1 UK Honours degree (or international equivalent) in a relevant subject. Those with a 2:2 UK Honours degree (or international equivalent) may be considered, provided they have (or are expected to achieve) a Distinction or Commendation at master’s level.
  • All students must meet the eligibility criteria as outlined in the UKRI guidance on UK, EU and international candidates. This guidance should be read in conjunction with the UKRI Training Grant Terms and Conditions, esp. TGC 5.2 & Annex B.
  • It may be possible to undertake this project part-time, in discussion with the lead supervisor, however, please note that part-time study is unavailable to students who require a Student Visa to study within the UK.



  • Please visit this page for full application information: How to apply | eastbio (
  • Please send your completed EASTBIO application form, along with academic transcripts to Alison Innes at: [Email Address Removed]
  • Two references should be provided by the deadline using the EASTBIO reference form. References should be sent to [Email Address Removed]
  • Unfortunately, due to workload constraints, we cannot consider incomplete applications.
  • CV's submitted directly through a FindAPhD enquiry WILL NOT be considered.
Biological Sciences (4) Mathematics (25) Physics (29)

Funding Notes

This fully funded, 4-year PhD project is part of a competition funded by the EASTBIO BBSRC Doctoral Training Partnership.
This opportunity is open to UK and International students (The proportion of international students appointed through the EASTBIO DTP is capped at 30% by UKRI BBSRC).
EASTBIO studentships includes a UKRI doctoral stipend (estimated at £17,668 for the 2023/2024 academic year), plus a training grant of £5,000 per annum (year 1-3; £1,500 year 4) and a travel/conference grant of £230 per annum.
EASTBIO does not provide funding to cover visa and associated healthcare surcharges for international students.



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