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Calcium and mechanics in embryogenesis: continuum and cell-based models

Please note that this project is self-funded.

The aim of this project is to extend models to systems of nonlinear partial differential equations to study the rheology of the embryonic epithelial tissue as a viscoelastic medium.


Calcium (Ca2+) signalling and its interplay with cellular mechanics plays a crucial role in development as well as in most other body processes, but it is poorly understood. Recent technical advances in molecular and live imaging provide an unprecedented opportunity to understand the complex mechanochemical processes of development. However, the large imaging datasets now generated should be carefully interpreted.

In embryogenesis, congenital malformations and cancer can result when the mechanochemical, complex mechanisms go wrong. In the development of the central nervous system, cells undergo a dramatic shape change, called Apical Constriction (AC), which generates a mechanical force and triggers the neural plate to form a tubular structure in Neural Tube Closure (NTC). When NTC fails the second most frequent embryo malformation occurs. Spina bifida, the second most frequent human birth defect, is the direct result of failure of NTC.  Despite its importance, AC is only partially understood.

It has recently been established that contractions play a crucial role in AC, that they are calcium-driven and that disrupting the Ca2+ signals leads to malformations. Very few models of Ca2+ signalling in AC exist and even fewer mechanochemical models. Dr Katerina Kaouri, in collaboration with leading mathematical modellers in Oxford and experimentalists in Cambridge and Cyprus, has recently developed a simple mechanochemical model, consisting of coupled nonlinear ordinary differential equations, in which embryonic tissue is modelled as a continuum viscoelastic medium (see refs). This work provides a framework for understanding the mechanochemical coupling in AC.

Project aims and methods

You will develop cell-based mechanochemical models using Chaste a comprehensive, open-source, cell-based modelling framework.  The cell-based and the continuum viscoelastic models will be compared. The models will be validated with experimental data and then used as predictive tools for exploring scenarios that cannot be explored in the laboratory and thus inform the design of future, feasible, experiments. Your aim is to elucidate the mechanism of Apical Constriction and ultimately inform clinical practice.

Biochemists have recently established that contractions in Apical Constriction are driven by calcium. With new data comes the need for new theoretical frameworks. The recent novel work of Dr Katerina Kaouri and collaborators on creating the first simple, continuum mechanochemical model of AC ensures that this project is both timely and at the cutting edge.

You will develop multiple theoretical skills, such as: analysis of coupled systems of Ordinary and Partial Differential Equations (ODEs; PDEs) using computational methods, perturbation methods, multiscale modelling, cell-based modelling.


Dr Katerina Kaouri

Dr Katerina Kaouri

Lecturer in Applied Mathematics

+44 (0)29 2087 5259
Professor Tim Phillips

Professor Tim Phillips

Head of School, Mathematics

+44 (0)29 2087 4194

Programme information

For programme structure, entry requirements and how to apply, visit the Mathematics programme.

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