Living Systems Institute

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
  • Spindle orientation in the developing fly embryo
  • Shape generation by the basement membrane
  • 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. Spindle orientation in the developing fly embryo: a joint mathematical-experimental approach

Scheme: SWBio DTP (BBSRC-funded)

Closing date: Monday 4th December 2023

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.

2. Modelling shape generation by the basement membrane

Scheme: LSI-funded PhD

Closing date: Monday 8th January 2024

Overview: Morphogenesis is the process that generates three-dimensional tissue and organ shape during embryonic growth. The major building blocks of our organs are epithelial cells, which form sheet-like tissues that are deformed in a controlled manner to form the complex 3D morphologies of functional organs. Epithelia are coated by a specialised extracellular matrix, the basement membrane. The BM acts as a structural base for epithelial cells and its mechanical properties (such as stiffness) directly influence cell and tissue shape. Excitingly, we have recently demonstrated that the interplay between epithelial and BM growth is instructive in guiding cell and tissue morphology (Harmansa 2023). However, we still lack conceptual understanding of (1) the complex mechanical interplay between tissue and BM growth, (2) how stresses accumulate in growing tissues and (3) how such stresses integrated with the local mechanical properties of the BM are transformed into morphological shape changes.

Objectives. During this PhD project you will establish a novel mathematical modelling framework to simulate how growth dynamics and mechanical properties of tissues and their BM interact and guide organ morphology. You will combine a 2D/3D cellular vertex model with a lattice coarse-graining of the underlying basement membrane layer. This will involve a combination of modelling (e.g. dynamical systems analysis) along with computational simulation (e.g. in MATLAB or C++). You will also use the fruit fly Drosophila melanogaster as a model system and work in close collaboration with both experimentalists and theoreticians. Given the interdisciplinary and collaborative nature of the project, you will have the excellent opportunity to be trained and mentored in both the theoretical and experimental aspects of modern research, offering excellent future career prospects. Ideally you will have a theoretical background and a strong interest in biology, good communication skills and share our excitement to work in an interdisciplinary environment addressing fundamental scientific questions.

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.