Cell migration

I work in collaboration with experimentalists in Edinburgh on a gene called Kit! Mutations in Kit can cause slower migration of melanocyte neural crest cells leading to non-pigmented areas of skin. I work on linking two different modelling paradigms (discrete stochastic and deterministic continuum) for cell migration and exploiting their complementary advantages when modelling a biological system.

Spatial hybrid simulation methods for reaction-diffusion systems

Reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique for reaction-diffusion systems that has predominated due to its analytical tractability and ease of simulation has been the use of partial differential equations (PDEs). However individual-based models have become a popular way to investigate the effects of noise in such systems.

In a wide variety of biological situations, computationally-intensive, high-resolution models are relevant only in particular regions of the spatial domain. In other regions, coarser representations may suffice to capture the important dynamics. Such conditions necessitate the development of hybrid models in which some areas of the domain are modelled using a coarse-grained representation and others using a more fine-grained representation. A significant part of the work of my group focussed on developing and testing such methods.

Stochastic simulation methodologies

With a variety of collaborators and PhD students I work on the development of efficient stochastic simulation algorithms. In part I work on developing general methodologies for stochastic simulation (Multi-level for continuous time Markov processes, recycling random numbers in the SSA, avoiding negative populations in tau-leaping). I also work on the development of simulation algorithms specifically designed to speed up the simulation of spatially extended systems (hybrid methods, non-local jumping, adaptive mesh refinement for position-jump processes).

Collective motion

I model the collective migration of locust (and other animal) swarms using self-propelled particle models and more basic stochastic interaction models. In collaboration with scientists in Slovakia I have also started modelling decision making in ants.

The evolution of pleiotropy and redundancy

I model the potential for the evolution of pleiotropy and redundancy as a mechanism by which cheating is regulated in bacterial communities. We use experimental data to inform our stochastic evolution models.

Sleeping sickness

In collaboration with experimentalists from Nottingham and Oxford I work on modelling the methods by which the causative parasites in the disease sleeping sickness are able to effectively evade the immune system.

Nematode dynamics

I model the interaction dynamics between migrating nematode worms and more sedentary bacteria which act as food for the worms. We use cellular automaton/PDE hybrid models informed by experimental data.

Egg patterning

In collaboration with experimental biologists in Harvard and Yale I contrive computer models which are able to investigate the possible mechanisms by which egg patterns form.

Cell Tracking

I can ofer a wide variety of projects across the range of stochastic modelling in biology. Please contact me for further details or to discuss a tailored project proposal.

I have been lecturing at Bath since 2014.

By undertaking the Bath course at the University of Bath I have become a Fellow of the Higher Education academy.

I have also become interested in various aspects of Mathematical pedagogy. You can hear my speak about some of the methods and teaching philosophies I employ here.