Living Systems Institute

Wedgwood Group


The Wedgwood group uses a combination of mathematical modelling and electrophysiology experiments to understand how collective rhythms, such as synchronised oscillations, are generated in biological tissues.

PhD opportunities

1. Mathematical modelling of cytoneme-based biochemical signalling studentship

Scheme: Department-funded (Home students only)

Closing date: Friday 20th January 2023

Overview: Cytonemes are cellular protrusions that enable long distance communication between cells. They are implicated in establishing the morphogenetic gradients associated with pattern formation during development, in the growth of gastric tumours and have recently been suggested to promote synapse formation in neurons. Despite their pivotal role in such important physiological processes, cytonemes have received relatively little mathematical treatment. In this project, we will use a combination of mathematical modelling and data analysis techniques to determine the signalling properties of cytonemes that are relevant for tissue patterning and tumour growth.

The mathematical models developed in the project will be based on a PDE-formulation and will build on our recent work describing tissue patterning in growing domains. The models will describe the dynamics of two processes. The first will be the growth and retraction of the cytonemes and hence the dynamics of long-range signalling. The second will be the mechanical forces underlying the growth of the biological tissue. These mechanical forces are generated by the movement of cells which, in turn, is dependent on the degree of signalling across the tissue. As such, the tissue growth dynamics are tightly coupled to the cytoneme dynamics. Data to parametrise the models of both processes will be available through our experimental partner Dr Steffen Scholpp.

Objectives: Using our developed model, we will study three related projects. Specifically, we will investigate:

  • 1) How cytoneme signalling contributes to the acquisition of robust boundaries between forebrain, midbrain, and hindbrain regions during gastrulation. We will compare results with our previously developed model, in which transport occurs by linear diffusion, to assess what advantages a cytoneme-signalling system might possess over purely diffusive systems.
  • 2) How gastric tumour growth is regulated by cytoneme signalling. We will derive quantitative links between parameters associated with cytoneme dynamics and those associated with tumour spheroid growth. Using these, we explore different drug-based strategies for limiting or reversing tumour growth by manipulating cytoneme dynamics.
  • 3) How cytonemes underpin synapse formation. We will append our model with additional processes to describe calcium signalling events that are associated with synapse formation. Using this appended model, we will identify cytoneme parameters that lead to successful synapse formation and further explore how neuronal networks develop in response to cytoneme signalling.

Research overview

Our research aims to understand temporal rhythm generation pattern formation in biological tissues such as neuronal and neuroendocrine tissue. To this, we combine techniques from mathematical modelling and dynamical systems, such as bifurcation analysis, PDE theory, machine learning and numerical simulation with experimental techniques including patch clamp electrophysiology and live cell imaging.

Current projects include:

  • Developing technology to control synaptic interactions in neuronal networks
  • Machine-learning based image analysis of human pancreatic islets
  • Understanding the role of heterogeneity in collective oscillations in pancreatic islets
  • Wave propagation in spiking neuronal networks
  • Controlling higher order interactions in coupled oscillator networks
  • Constructing bifurcation diagrams for living neurons
  • Closed-loop interrogation of endocrine systems

Research themes


Neuronal networks perform computations via the collective action of large numbers of neurons acting in concert to produce robust electrical rhythms across the network. Such rhythms include low-dimensional behaviour such as synchronised global oscillations and travelling waves, as well as more temporally complex patterns of activity. In all cases, the rhythms are generated via a combination of the intrinsic excitable nature of neurons and the electrical and chemical communication between distinct cells. Disruption to either intrinsic neuronal or communication properties, as expected in diseases such as dementia and epilepsy, often result in disrupted electrical network rhythms and hence functional deficits, such as impaired cognition.

Left: Patch clamp of single cell. Middle: Voltage time series recorded under whole cell current clamp. Right: The dynamic clamp protocol in which a mathematical model is used to alter intrinsic neuronal properties.

Our group aims to better understand the role of synaptic communication between neurons in the generation of network rhythms. To do this, we collect data from individual neurons and neuronal networks and use these to build and parametrise mathematical models of the network electrical activity. We 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. We then experimentally test these predictions using closed-loop experiments that embed mathematical models with patch clamp electrophysiology experiments.

Pancreatic islets

The islets of Langerhans in the pancreas are one of the primary regulators of blood glucose levels and are their dysfunction is heavily implicated in diseases such as diabetes. Much like neuronal networks, the islets operate through collective electrical oscillations over the networks of ~1000 cells, which are generated via a combination of intrinsic cell excitability and interactions between cells within the islet. Such electrical oscillations underpin the secretion of a variety of hormones such as insulin and glucagon that regulate blood glucose levels by encouraging other organs, such as the liver and muscles, to store and release glucose as necessary.

Left: Fluorescence microscopy (immunocytochemistry) staining of a human pancreatic islet. The different colour stains correspond to different types of islet cell. Middle: Network structure of the islet as extracted via machine learning. Right: Ca2+ dynamics (showing peaks only) of two populations of islet cell types showing globally synchronised oscillations.

Our group aims to understand how collective electrical oscillations are generated in the islets. We work with experimental collaborators at the University of Exeter Medical School (Prof. Noel Morgan, Dr Carol Yang) to build mathematical models of islet structure and dynamics across a range of species, including zebrafish, rodents and humans. We then analyse these models using techniques from dynamical systems to generate hypotheses on the contribution of each of the different types of islet cell and the overall islet structure to the islet dynamics. We then work with our experiment partners to design experiments to collect new data to test our hypotheses.

Tissue patterning

During the early stages of embryogenesis, developing tissue is pre-patterned via chemical signals that influence which parts of the tissue adopt which cell types. As such, this pre-patterning is important for establishing boundaries between different tissues (e.g., which part of the head is brain and which is not). A relatively recent finding showed that the chemical signalling in developing tissue may be transported via long cellular projections known as cytonemes, that facilitate targeted, long-range signal transmission. Whilst the overall role of cytonemes is unclear, they have also been hypothesised to play a role during the development in the development of gastric tumours.

Left: Morphogen (pattern inducing chemical) distribution over the surface of a developing zebrafish embryo. Middle: Bifurcation analysis of a model of cell fate acquisition at a single point along the zebrafish embryo, showing two possible stable steady states (high blue/low orange and low blue/high orange). Solid lines indicate stable steady states, dashed lines represent unstable steady states. Right: Robust pattern formation in a three cell fate model posed over a growing domain.

Our group aims to understand the role of cytoneme-based signalling during development. We work with experimental collaborators in the Living Systems Institute (Dr Steffen Scholpp) to build and analyse PDE and agent-based models that predict how tissue growth and cytoneme-based signalling properties affect the formation of robust tissue boundaries in developing tissue. We then work with Steffen’s group to design experiments to test predictions from our model analysis.

Other possible projects

I am happy to supervise any projects in the fields of:

  • Excitable cell dynamics
  • Travelling waves in non-locally coupled systems
  • Glucose dynamics and homeostasis
  • Pattern formation

Such projects could be funded via the EPSRC Doctoral Training Partnership, which is open for applications until 27th February 2023. Further information on this scheme can be found here:

Group members

Nicolás Verschueren van Rees – Postdoctoral fellow in the EPSRC Hub for Quantitative Modelling in Healthcare. Working on modelling of islet structure and dynamics.

Bonnie Liefting – 4th year PhD student. Working on designing coupling strategies to control higher order interactions.

Henry Kerr – 2nd year EXE-MATH PhD student. Working on analysing travelling wave dynamics in 2D spiking neuronal networks.

Akshita Jindal – 1st year BBSRC SWBio PhD student. Working on investigating synaptic interactions in neuronal networks.

Victor Applebaum – 1st year PhD student in the EPSRC Hub for Quantitative Modelling in Healthcare. Working on uncertainty quantification in healthcare data.


We are grateful for funding from EPSRC.