Richards Group


The Richards Group uses a combination of mathematical modelling, computer simulation, machine learning, image analysis and wet-lab experiments to study a variety of areas of biology and biomedicine.

Main group webpage:


Our research typically involves using a combination of dynamical systems, reaction-diffusion equations, spatio-temporal modelling, numerical simulation, machine learning and image analysis. Currently we are working on the following projects:

  • Target shape dependence during phagocytosis
  • The multistage nature of phagocytic engulfment
  • Computer simulations of early embryogenesis
  • Machine learning of microglial state
  • Understanding the growth of filamentous fungi
  • The dynamics of peroxisome shape
  • The role of noise in pituitary cells
  • Plant response to phytopathogens

One of the main areas of our research is phagocytosis (the way that our immune cells engulf and destroy relatively large target particles such as bacteria and dead cells). In particular, we study how phagocytosis depends on properties of both the immune cell (such as membrane tension) and the target (such as size and shape). This work uses an integrated modelling-experimental approach that couples computational models of membrane shape with dual-micropipette experiments. This has applications to both the design of microparticle drug delivery systems and various medical conditions such as lupus and Wiskott-Aldrich syndrome.

Human neutrophil, held by a micropipette, engulfing a plastic bead.

Sketch of a phagosome (red) moving within a cell (green).

Some phagocytic target shapes: sphere, spheroid, capped-cylinder and hourglass.

Other work includes computer simulations of early embryogenesis (where embryo development is modelled from the single fertilised egg up to the mature blastocyst), automatic image analysis of muscle ultrasound (with the aim of improving clinical practice and patient treatment in the rehabilitation clinic), machine learning of microglial state (with application to neurodegenerative diseases such as Alzheimer’s and Motor Neuron Disease), and understanding the growth of filamentous fungi (including the role and nature of calcium signalling).

Mature blastocyst with trophectoderm/ epiblast/hypoblast in orange/green/red.

Sketch of a microglial cell. Cell shape depends on cell state.

Fungal calcium traces for three separate cells showing a number of spikes.

Currently available PhD projects

1. Modelling human embryo development: a combined mathematics and lab approach

Scheme: GW4 BioMed2 DTP (MRC-funded)

Closing date: Wednesday 2nd November 2022

Overview: During this PhD, you will use mathematics, computer programming and lab-based experiments to investigate how the human embryo develops, focusing on the very first few days after fertilisation when the embryo grows from a single egg to several hundred cells. The findings will have important implications for improving IVF treatment. Unlike most PhDs, this is an excellent opportunity to be trained in both the experimental and mathematical aspects of modern research.

Objectives. 1. Mathematical simulation of blastocyst formation. Building on our proof-of-principle model, a Cellular Potts model will be developed to simulate cell shape, motion and lineage specification. This will involve a combination of MATLAB and C++. 2. Time-lapse microscopy of developing blastoids. In the lab, you will culture and capture time-lapse images of blastoid development. Our knock-in fluorescent protein reporters for each lineage will allow individual cell types and shapes to be identified. 3. Image analysis. Based on our existing code, you will design image analysis software that automatically extracts and tracks cell shape and position in the developing blastoid. This information will be used to inform and validate the mathematical model. 4: IVF scoring. Using our collaboration with the Aria Fertility IVF clinic, improved ways of automatically scoring human embryos will be investigated. This will involve visiting the clinic and using images of human embryos to fit the model parameters.

Click here for more information and the application form.

2. Spindle orientation in the developing fly embryo: a joint mathematical-experimental approach

Scheme: SWBio DTP (BBSRC-funded)

Closing date: Monday 5th December 2022

Overview: During this PhD, you will investigate how cells formed from the first few divisions of the fertilised egg orientate themselves. You will use a multidisciplinary approach that combines mathematical modelling, computer simulations, light sheet microscopy and image analysis to answer these questions in the fruit fly. This will allow you to learn a wide range of different skills and techniques, ideal for a future career in academia or elsewhere. You are not expected to already know both mathematical modelling and wet-lab techniques; full training will be provided in both areas during the PhD.

Objectives. 1. Design a three-dimensional mathematical model of mitotic spindle orientation. This will be based on the famous Ising model of interacting spins from physics. These models will be simulated and analysed using MATLAB and/or C++. 2. Use our brand new, state-of-the-art light sheet microscope to obtain images of the developing Drosophila embryo. 3. Develop image analysis software to automatically extract the spindle orientation. This will then be able to inform both the mathematical modelling in part 1 and the experiments in part 2. 4. Apply the model to the oriented cell divisions of the Drosophila larval testes niche. This interplay between experiment and modelling is a key part of this project and will make for a truly exciting PhD.

Click here for more information and the application form.

Other possible PhD projects

Some examples of possible PhD project ideas:

  • Simulations of early embryogenesis
  • Mathematical modelling of cell shape across organisms
  • Models of engulfment during phagocytosis
  • Simulations of the dynamics of peroxisome shape
  • Quantitative understanding of the plant response to fungal attack
  • Machine learning to identify microglial state
  • Image analysis of filamentous fungi

Current group members

The group currently includes:

  • Jim Lees – MRC-funded Postdoctoral Research Fellow – working on “The Fundamentals of Phagocytosis: Integrating Theoretical Models and Experiments”
  • Jordan Hembrow – PhD student – working on “Mathematical modelling of phytopathogen-targeted secretion pathways”
  • Peyman Shadmani – PhD student – working on “Models of cell shape during phagocytosis”
  • Alaina Cockerell – PhD student – working on “Simulation of human blastocyst development”
  • Sophie Nye – PhD student – working on understanding and modelling fungal growth
  • Amber Connerton – PhD student – working on “The role of Rho GTPases in plant immunity”
  • Victoria Armer – PhD student – working on “Exploring communication mechanisms between fungal pathogens and plant cells”
  • Ifeoma Nwabufo – Master’s student – working on a machine learning approach to identifying microglial state


We are grateful for funding from the MRC, BBSRC and Wellcome Trust.