PhD Studentship: PDE problems in cell biology

• Monday, August 31, 2020
• Funded PhD Project (European/UK Students Only)

Project Description

Along with experimental studies, mathematical modelling has become an indispensable tool in

understanding phenomena in cell biology. Partial differential equation (PDE) models are

particularly informative in this regard due to their inherent ability to describe spatial and temporal

features. The need to couple physics and biochemistry over different regions, e.g., the cell

membrane and the intra- and extracellular spaces leads to the consideration of coupled systems

of bulk and surface PDEs posed on domains that are potentially time-dependent. Moreover due to

the complexity of the physics and biochemistry the equations are typically nonlinear and hence

numerical approximations are needed. The derivation, analysis and simulation of such models

necessitates the development of new mathematical and computational tools which are of

independent mathematical interest. A PhD project in this area would suit a candidate with an

interest in mathematical biology, the analysis of PDEs, numerical analysis and scientific

computing. Some previous experience with mathematical modelling and the implementation of

numerical methods for the approximation of PDEs would be useful.

Below are some examples of directions for the PhD, but these can be discussed with the

supervisor depending on the student’s own interests and expertise.

1) Multiscale modelling of cell-signalling processes. The goal is to derive, analyse and simulate

multiscale models of receptor-ligand interactions. Such interactions are the mechanism by

which cells sense and respond to all stimuli and therefore, they are crucial to all cell biological

processes. This project would involve homogenisation of nonlinear PDE and the development,

analysis and implementation of multiscale finite element methods. An example of the

approach in which some of the necessary mathematical and computational framework is

developed is given in [1]. An example of the type of modelling and analysis problems that arise

in mathematical approaches to receptor-ligand modelling is given in [2].

2) Mathematical cell motility. The directed migration of cells is crucial to phenomena such as the

immune response, development and tissue growth. Recent modelling studies involving

geometric PDEs coupled to bulk and surface PDEs have proved useful in helping to unravel

the complex processes involved. The goal of this project would be to build on and refine

existing models for cell motility incorporating features such as substrate adhesion, polarisation

and collective migration. The solution to the models would then be approximated using

surface finite element methods. An example of the mathematical and computational

techniques involved is given in [3]. For a candidate more focussed on applications, the use of

the methodology in collaboration with biologists to study applied problems is also an area that

could be explored, see [4] for an example of such a study.

Apply through the postgraduate application system and select the full time PhD in Mathematics with a September 2020 start date

Applications will be considered until a suitable candidate is found.

When you apply, you should include:
•the supervisor’s name (Dr Chandrasekhar Venkataraman) in the ‘Suggested supervisor’ section
•’PDE problems in cell biology’ in the Award Detail Section
•a research proposal/personal statement which describes your suitability for the project
•your transcripts from any previously obtained degrees. If you have not yet completed your undergraduate degree, you can provide an interim transcript or record of any marks obtained so far.

The position will be filled as soon as a suitable candidate is found so you are encouraged to apply as soon as you are able to.

Due to the high volume of applications received, you may only hear from us if your application is successful.

Funding Notes

To be eligible, you must:
•be a UK/European Union (EU) student.
•have (or expect to achieve) a First or Upper Second Class Masters degree in Mathematics, or a related subject.
•Meet the English langugage requirement as detailed here: View Website

•We also welcome applications from self-funded non-EU students interested in our programme.

References

[1] M. Ptashnyk and C. Venkataraman. Multiscale analysis and simulation of a signalling process

with surface diffusion. arXiv, (2018). (https://arxiv.org/abs/1805.02150)

[3] C.M. Elliott, T. Ranner, and C. Venkataraman. Coupled bulk-surface free boundary problems

arising from a mathematical model of receptor-ligand dynamics. SIAM Journal on Mathematical Analysis, (2017).

[3] C.M. Elliott, B. Stinner, and C. Venkataraman. Modelling cell motility and chemotaxis with

evolving surface finite elements., Journal of The Royal Society Interface, 9, 3027–3044. (2012).

[4] A sensor kinase controls turgor-driven plant infection by the rice blast fungus. Lauren S Ryder,

Yasin F Dagdas, Michael J Kershaw, Chandrasekhar Venkataraman, Anotida Madzvamuse, Xia

Yan, Neftaly Cruz-Mireles, Darren M Soanes, Miriam Oses-Ruiz, Vanessa Styles, Jan Sklenar,

Frank LH Menke, Nicholas J Talbot. Nature, (2020).

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