Mathematical modelling of cell shape and localised cell growth | Courses

Overview

The correct cell shape is essential for proper cell function. For example, in the brain signalling between neurons is received by dendritic spines, Dendritic spines are protrusions on the surface of the neuron, they come in different shapes, the most well-known being mushroom shaped. Dendritic spine shape and number is deregulated in several diseases such as Alzheimer’s, schizophrenia and autism. It is therefore important that we understand how cell shape, and in particular localised cell growth, is controlled.

About this opportunity

In this project we will use mathematical and computational modelling to understand the mechanisms controlling healthy cell shape/growth and how the mechanisms are changed when the cell is in a diseased state.

The mathematical model will utilise partial differential equations (PDEs) to describe protein reactions and movement. The equations will be solved numerically using finite difference and finite element methods. Part of the project is to write our own numerical solvers.

The student will be trained in; how to build a meaningful mathematical model of a biological system; numerical solutions to PDEs; coding; how to interpret model solutions and use them to help design experiments; presentation skills and scientific writing.

Who is this opportunity for?

This project is open to self-funded UK and international applicants. The project is suited to a student with at least a good BSc Upper Second, in Mathematics, Theoretical Physics, Engineering, or any degree with a substantial numerical methods content.

How to apply

1. Contact supervisors
- Dr Natasha Savage.
2. Prepare your application documents

You may need the following documents to complete your online application:
- A research proposal (this should cover the research you’d like to undertake)
- University transcripts and degree certificates to date
- Passport details (international applicants only)
- English language certificates (international applicants only)
- A personal statement
- A curriculum vitae (CV)
- Contact details for two proposed supervisors
- Names and contact details of two referees.
3. Apply

Finally, register and apply online. You'll receive an email acknowledgment once you've submitted your application. We'll be in touch with further details about what happens next.

Fees and funding

Your tuition fees, funding your studies, and other costs to consider.

Tuition fees

UK fees (applies to Channel Islands, Isle of Man and Republic of Ireland)

Full-time place, per year - £5,006

International fees

Full-time place, per year - £31,250

Fees stated are for the 2025-26 academic year.

Additional costs

We understand that budgeting for your time at university is important, and we want to make sure you understand any costs that are not covered by your tuition fee. This could include buying a laptop, books, or stationery.

Find out more about the additional study costs that may apply to this project, as well as general student living costs.

Funding your PhD

The project is open to both UK and international students. It is unfunded and applicants are encouraged to contact the Principal Supervisor directly to discuss their application and the project. Assistance will be given to those who are applying to international funding schemes.

The successful applicant will be expected to provide the funding for tuition fees and living expenses, as well as research costs of £1,000 per year. New self-funded applicants may be eligible for a tuition fees bursary.

If you're a UK national, or have settled status in the UK, you may be eligible to apply for a Postgraduate Doctoral Loan worth up to £30,301 to help with course fees and living costs.

There’s also a variety of alternative sources of funding. These include funded research opportunities and financial support from UK research councils, charities and trusts. Your supervisor may be able to help you secure funding.

We've set the country or region your qualifications are from as United Kingdom.

Scholarships and bursaries

We offer a range of scholarships and bursaries that could help pay your tuition fees and living expenses.

Duncan Norman Research Scholarship

If you’re awarded this prestigious scholarship, you’ll receive significant funding to support your postgraduate research. This includes full payment of your PhD fees and a cash bursary of £17,000 per year while you study. One award is available in each academic year.

John Lennon Memorial Scholarship

If you’re a UK student, either born in or with strong family connections to Merseyside, you could be eligible to apply for financial support worth up to £12,000 per year for up to three years of full-time postgraduate research (or up to five years part-time pro-rata).

Sport Liverpool Performance Programme

Apply to receive tailored training support to enhance your sporting performance. Our athlete support package includes a range of benefits, from bespoke strength and conditioning training to physiotherapy sessions and one-to-one nutritional advice.

Discover our full range of scholarships and bursaries.

Contact us

Have a question about this research opportunity or studying a PhD with us? Please get in touch with us, using the contact details below, and we’ll be happy to assist you.

Dr Natasha Savage

Mathematical Modelling of Cell Shape and Localised Cell growth.