Mathematics and Statistics

Photo of Dr Kyle Wedgwood

Dr Kyle Wedgwood

Lecturer

 K.C.A.Wedgwood@exeter.ac.uk

 (Streatham) 7485 or (Streatham) 7463

 01392 727485 or 01392 727463

Overview

About me

I am a lecturer in the Department of Mathematics and Statistics, housed with the Living Systems Institute. I work primarily in the Faculty of Environment, Science and Economy, but work closely with the Faculty of Health and Life Science. In my research, I apply techniques from mathematical modelling (dynamical systems theory, bifurcation analysis) to understand how networks of cells come together to form biological networks that can perform functional tasks. I am particularly interested in spatio-temporal patterns of neural activity in the brain and their role in memory and spatial navigation, and the synchronisation of electrical activity amongst the insulin-secreting beta cells in the pancreas.

Research Themes - Biology and Healthcare

1) Neuroscience

My current projects aim to better understand the role of synaptic communication between neurons in the generation of network rhythms. To do this, I collect data from individual neurons and neuronal networks and use these to build and parametrise mathematical models of the network electrical activity. I analyse these models using techniques from dynamical systems theory to find quantitative links between parameters of the synaptic interactions the the properties of the network rhythms and make predictions on how the latter change with respect to the former. I then experimentally test these predictions using closed-loop experiments that embed mathematical models with patch clamp electrophysiology experiments. By understanding how synaptic alterations associated with dementias impact upon network rhythms, I aim to uncover specific pharmacological targets to improve treatment for diseaes such as Alzheimers' Disease.

2) Diabetes and pancreatic islets

My research into diabetes addresses how alterations in intercellular communication between beta cells in the islets of Langerhans impact their ability to secrete sufficient insulin to regulate blood glucose levels. This research aims to provide new avenues to explore in treatment for type 2 diabetes by understanding how to compensate for the loss of function in beta cell networks. As a by product of this research, I am investigating how mathematical models of beta cells have evolved over the past 4 decades, in particular, as new modelling components and biological processes have been incorporated.

3) Pattern formation in zebrafish

The zebrafish has emerged as one of the key animal models for understanding development in verterbrate species. In my research, I focus on how the fore-, mid- and hind-brain of the zebrafish form during gastrulation; a process involving the establishment of a morphogenetic gradient across what will become the fish's neural plate. In contrast to the classical Turing mechanism of pattern formation, the morphogen signal in zebrafish appears to be transported by long, finger-like projections that facilitate direct cell-to-cell communication. Using a variety of agent-based and PDE models, I aim to uncover under what conditions this transport mechanisms leads to successful pattern formation, and under what conditions it fails.

Research Themes - Mathematics

4) Coarse-grained bifurcation analysis

Almost every question one could ask in biology addresses how phenomena at one temporal or spatial scale affect those at another. Linking these often disparate scales provides a difficult mathematical challenge. One potential way to overcome this hurdle is to use our knowledge of dynamics at fine scales to form approximations of behaviours at coarser scales. Once these equations are formed, we then analyse the coarse-grained system using traditional mathematical techniques. Through this process, we then learn about how small-scale perturbations give rise to distinct behaviour at the coarse scale.

5) Phase-oscillators

Oscillations are ubiquitous in biology. We can observe them on vastly different scales, from those on the order of milliseconds in neurons to those on the order of months and years in diseases such as diabetes. A crucial part of the genesis of rhythms is biology in the synchronisation of activity within networks involving many cells. One way we can attempt to understand the origins of synchrony in such networks, which often arises in the absence of any coordinating group of cells, is to treat the cells as clocks whose natural frequency can be perturbed by other cells in the network. By understanding how biological networks establish robust rhythms, we can hope to find ways to intervene when these important rhythms are disrupted.

Funding

I am genereously supported by an EPSRC New Horizons Grant (with Dr Joël Tabak) and am a co-investigator on the EPSRC Hub for Quantitative Modelling in Healthcare.

I have previously been supported by the Medical Reseach Council as a Skills Development Fellow and via a Royal Society Newton Mobility Grant to support a collaborative project with Dr. Marco Herrera and Prof. Hiriart (UNAM, Mexico) to study the interaction of stress hormones and metabolism.

I am happy to support applications for summer internships for undergraduate students to the Society for Endocrinology, British Society for Neuroendocrinology and the London Mathematical Society. I have previously supervised three such internships in the past.

Research team

Postdoctoral research fellows:

Nicolás Verschueren van Rees 

PhD students:

Bonnie Liefting
Henry Kerr
Akshita Jindal
Victor Applebaum

Prospective PhD students

Please get in touch if you wish to discuss developing a research proposal for PhD study. I am open to any project that invovles dynamical systems and biology, particularly if it involves diabetes, neuroscience or pattern formation.

Project page

Further details of my research projects can be found here.

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Publications

Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.

| 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2013 | 2012 | 2011 |

2023

2022

  • Galvis D, Hodson DJ, Wedgwood KCA. (2022) The influence of spatial configuration in collective transitions: the importance of being sorted. [PDF]

2021

2020

2019

2018

2017

2016

2015

2013

  • Wedgwood KCA, Lin KK, Thul R, Coombes S. (2013) Phase-amplitude descriptions of neural oscillator models, The Journal of Mathematical Neuroscience 2013, 3:2. [PDF]

2012

2011

  • Lin KK, Wedgwood KCA, Coombes S, Young L-S. (2011) Limitations of perturbative techniques in the analysis of rhythms and oscillations. [PDF]

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