Mathematical theories of symmetry breaking in embryos, organs and organoids

We are seeking a talented, creative, and friendly individual to join our interdisciplinary team. You will build physics-style mathematical models to understand symmetry breaking mechanisms that allow simple embryos to develop into complex animals. This studentship is fully funded for 4 years as part of an ERC Starting Grant award.

PROJECT:

There is a long history in using mathematical models (e.g., PDEs) 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, and result from self-organizing mechanisms in the early embryo. Whilst some of these processes are similar to pattern formation in physical systems (e.g., [2]), there are some patterns that are fundamentally distinct to anything in the physical world and may be unique to embryonic development. We thus suspect that embryos can teach us new mechanisms of pattern formation unexplored by physics or applied mathematics.

In this project, you will focus on one such example – the mysterious ability of embryos to break symmetry in a size-invariant manner. Size-invariance means that the embryo develops normally regardless of its size; for example, if it is chopped in half, the patterning length-scales adjust perfectly to match its smaller size. Whilst we have good models for how embryos break symmetry, none of these models are size-invariant. For example, they predict that smaller embryos would have no head, whereas bigger embryos would have multiple heads; whereas experiments show that embryos develop a single head regardless of their size. We hope to uncover the dynamical mechanisms underpinning this counterintuitive phenomenon.

APPROACH:

We will draw on ideas and techniques from many disciplines, including physics and mathematics, as well as developing our own theories and approaches. We will use and extend tools from nonlinear dynamical systems theory (e.g., bifurcation theory, Green’s functions, asymptotics, variational formulations [3,4]) to analyse PDE-based models of pattern formation, alongside collaborations with experimentalists. We will combine analytical work with large scale numerical simulations in the Julia programming language.

CANDIDATE BACKGROUND:

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.

To be considered for PhD study at the University of Aberdeen, applicants must typically hold a UK Honours Degree with a 2:1 classification (or international equivalent). Applicants with a 2:2 undergraduate degree may also be considered if they hold a commendation or distinction at master’s level, or have significant relevant experience.

FURTHER INFORMATION:

The project will be based in Aberdeen in the beautiful Northeast of Scotland. Please email Tom with a CV for informal enquiries: thomas.hiscock@abdn.ac.uk.

Lab website: https://twhiscock.github.io/

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APPLICATION PROCEDURE:

• Formal applications can be completed online: https://www.abdn.ac.uk/pgap/login.php
• You should apply for Medical Sciences (PhD) to ensure your application is passed to the correct team for processing (the programme applied for may not be representative of the programme which will be offered to a successful candidate, this is for administrative purposes only)
• Please clearly note the project title and lead supervisor in the respective fields on the application form
• Your application must include: A personal statement, an up-to-date copy of your academic CV, and clear copies of your educational certificates and transcripts.
• Pease provide two academic references with your application.
• Please note: you DO NOT need to provide a research proposal with this application
• Applications for this project may be shared with any external funders of this PhD Studentship, and any external members of the supervisory team.
• If you require any additional assistance in submitting your application or have any queries about the application process, please don’t hesitate to contact us at pgrs-admissions@abdn.ac.uk