About the Project
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 . An example of the type of modelling and analysis problems that arise
in mathematical approaches to receptor-ligand modelling is given in .
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 . 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  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
•2 academic references
•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.
•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: https://www.sussex.ac.uk/study/phd/degrees/mathematics-phd
•We also welcome applications from self-funded non-EU students interested in our programme.
with surface diffusion. arXiv, (2018). (https://arxiv.org/abs/1805.02150)
 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).
 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).
 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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