EPSRC DTP PhD studentship: Controlling noise effects in models of excitable cells

University of Exeter - College of Life and Environmental Science

This project is one of a number which are funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2017. The studentships will provide funding for a stipend which, is currently £14,296 per annum for 2016-2017, 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.

Main supervisor:  Prof Krasimira Tsaneva-Atanasova (University of Exeter)
Co-supervisor:  Dr Jan Sieber (University of Exeter)
Co-supervisor:  Dr Joël Tabak (University of Exeter)

Project Description: This is a project that combines biological modelling and general mathematical analysis of the influence of noise on multiple-timescale systems. It will give the student the opportunity to work on open mathematical questions and see their results applied in experiments on living cells.

Many types of cells such as neurons, heart and hormone-releasing cells generate impulses of electrical activity, organized as single spikes or bursts of impulses. In cells of the pituitary gland – the master hormonal gland of the body – the features of electrical activity patterns determine how much hormone is released into the circulation. Hence, understanding how the characteristic features of electrical activity arise is crucial to understanding how these cells function, and how they may malfunction in disease. Mathematical modelling and analysis techniques have proven very successful in helping unravel fundamental mechanisms controlling the behaviour of excitable cells.

Electrical activity is driven by the interactions between ion channels of the cell membrane, which produce noisy electrical currents. The mathematical models of electrical activity thus contain random and deterministic parts, which typically appear as separate terms (e.g., the deterministic drift and the Brownian-motion induced diffusion in stochastic differential equations). In experimental practice this distinction is not as clear. For example, ion channels in cells with electrical activity generate noisy signals, driving systematically the electrical and chemical activity in the cell, which operate also on several time scales. It is still unclear how this randomness influences electrical activity in real cells.

This PhD project will investigate how one can use control to identify the systematic (deterministic) component of trajectories in dynamical systems with random inputs (such as ion channel noise) that operate on two or three different time scales (such as spiking or bursting cells). A first goal to separate a systematic, approximately periodic, signal without knowledge of the period using control and geometric methods in a reconstructed phase space. Preliminary investigations with noise on a single time scale interacting with a two-timescale oscillation (spiking) have shown that this is in principle possible. It is an open question how this can be generalized to periodic behaviours with a more complicated geometry (such as bursting), interacting with noise effects that occur on two time scales. Another open question is how the geometric control and noise identification is related to extended time-delayed feedback, which creates a reference signal from a geometric time series of past outputs. 

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South West England