Inaugural Sneddon Lecture on "Modelling collective cell movement" by Professor Philip Maini FRS

Prof Maini

On 18th April 2017, the world-renowned Mathematical Biologist, Professor Philip Maini from the University of Oxford, visited the School of Mathematics & Statistics and gave the inaugural Sneddon Lecture in Applied Mathematics (abstract below). The Lecture is named in honour of Professor Ian Sneddon FRS who was the first holder of the Simson Chair of Mathematics at the University of Glasgow. 

Professor Maini is beginning a collaboration with three members of SofTMech, Robert Insall, Nick Hill, and PhD student Peter Mortensen, developing partial differential equation models for populations of migrating cells that Prof. Insall has shown to self-generate chemotaxis gradients that are a key feature of metastasis in cancer. This work is based on Peter Mortensen's final year undergraduate project in 2016, supervised by Prof. Hill.


Collective cell movement is ubiquitous in biology, occurring both in normal processes (for example, development, wound healing) and in disease (for example, cancer). In most of these examples, how cells coordinate their movement is still not well understood. We will consider two examples: (i) angiogenesis is the process by which new blood vessels are formed in response to, for example, wounding or tumour growth. Typically, this has been modelled phenomenologically using the well-known snail-trail framework, leading to a coupled system of nonlinear partial differential equations for two key endothelial cell populations (tips and sprouts). Here, we revisit this model and show that a more formal derivation of the PDE model, from a discrete master equation framework, leads to a novel coupled system of PDEs to those studied in the literature; (ii) neural crest cell invasion is a very important early developmental process and also shares many common features with melanoma cell invasion. Here, we use a combined experimental and mathematical modelling study to shed light on a number of questions regarding the basic principles of this phenomenon.

First published: 6 July 2017

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