Understanding Emergent Complex Noisy Patterns in Biological Cells - Mathematics - EPSRC DTP funded PhD Studentship

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Location: Streatham Campus, Exeter

Project Description

One of the most fascinating phenomena in nature is that small random disturbances can create systematic large-scale patterns of motion. Mathematically, this is described by the theory of nonlinear dynamics. One essential process governed by this theory is electrical signalling in animal and plant cells. Biological cells communicate with periodic or more complex patterns of electrical signals that underlie thinking, hormone release or muscle movement. These patterns are extremely sensitive to various types of noise present in cells such as rapid fluctuations and slow random drift. A general mathematical question is how precisely the different types of small noise perturbations influence the emergent patterns in nonlinear systems. Applications of the insights gained from mathematical analysis to understanding and controlling living cells would allow us to inform novel therapies for hormonal or neural disorders such as chronic stress response or essential tremor for example.

Traditionally, mathematical modelling of cells has been applied to idealised, noise-free models. This funded PhD studentship will investigate how small noise drives and controls periodic and non-periodic patterns in general, and specifically in excitable cell models and experiments.

The student will design a method to remove noise from emergent electrical patterns, using techniques from dynamical systems theory and feedback control theory. Joel Tabak (one of the project supervisors) has developed a proof of concept methodology for periodic patterns that is similar to what is used in noise-cancelling headphones, but uses concepts from dynamical systems to determine the perturbing noise. Being able to remove noise will allow us to compare the patterns in noisy and noise-free conditions. This will help scientists understanding how noise controls electrical patterns in many types of electrically active cells.

The student will design further new methods for removing noise in mathematical models (ordinary differential equations) of electrically active cells. The PhD studentship will benefit from close collaboration with Joel Tabak’s neuroscience laboratory. This laboratory is able to perform experiments with live cells in real time using electrical signals in dynamic clamp experiments. Thus, the student will have the opportunity to immediately test how their methods perform in a real biological system, and use the experimental results as a guide to refine their methodology. By interacting with experimental researchers, the student will also gain important experience in working within a multidisciplinary scientific team. Depending on the student’s interests and progress during the PhD studentship, there will also be the opportunity to learn electrophysiology in order to record the electrical activity from live cells.

This project would suit a student keen to 1) learn and apply new maths concepts (nonlinear dynamical systems, multi-scale analysis, stochastic processes); 2) interact with people from different scientific fields; and 3) present their results at national and international conferences.

Entry Requirements

You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in mathematics or a natural sciences or engineering programme with a strong quantitative component. Experience in nonlinear dynamics, mathematical biology or probability, and some programming experience are desirable.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes. If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.