The movement and organization of epithelial tissues plays a central role during development, growth, disease and wound healing.

These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes

acting at the cellular and molecular level. Alongside experimental approaches, mathematical and computational modelling can help us

understand what factors are involved in regulating cell- and tissue-level behaviour, and how this can go wrong. We are developing

and applying a variety of modelling approaches to understand aspects of epithelial dynamics.

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Multiscale modelling of epithelial tissue homeostasis and repair

Jochen Kursawe1, Fergus Cooper1, Jeremy J. Zartman2, Ruth E. Baker1, Alexander G. Fletcher1,* 1 Mathematical Institute, University of Oxford, UK 2 Department of Chemical and Biomolecular Engineering, University of Notre Dame, USA * alexander.fletcher@maths.ox.ac.uk

1. Kursawe et al. bioRxiv doi:10.1101/023184

2. Fletcher et al. Biophys. J. 106:2291 (2014)

3. Fletcher et al. Prog. Biophys. Mol. Biol. 113:299 (2013)

4. Narciso et al. Phys. Biol. 12:056005 (2015)

5. Mirams et al. PLOS Comput. Biol. 9:e1002970 (2013)

6. Osborne et al. PLOS Comput. Biol. 10:e1003506 (2014) Re

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Case study 1: The capabilities and limitations of tissue

size control through passive mechanical forces1

• Differential growth and mechanical regulation generate distinct distributions of cell

shapes

• Spatial regulation of mechanical cell properties can induce asymmetry of cell

death occurrence inside P compartments

• Vertex model2,3 of P compartment dynamics during the last division cycle in the

Drosophila embryonic epidermis

• The Drosophila embryo as a model system for tissue size control

Embryos have a remarkable ability to control tissue size and repair patterning

defects in the face of perturbations. What is the role of cellular mechanics in

this process?

Case study 2: Patterning of wound-induced intercellular

Ca2+ flashes in a developing epithelium4

Differential mechanical force distributions provide important feedback into the

control of an organ’s final size. How do the dynamics of Ca2+ transients reflect

tissue mechanical status?

• The Drosophila wing imaginal disc as a system for the study of wound-induced

Ca2+ flashes

• Intercellular Ca2+ transients show spatially non-uniform characteristics across the

proximal-distal axis, which exhibits a gradient in cell size and anisotropy

• A reaction-diffusion model of intercellular Ca2+ dynamics suggests that local cell

shape anisotropy governs relative flash anisotropy and cell size and elongation

exert opposing effects on flash velocities

Future directions

Placing such models on a more quantitative footing requires advances in:

• Segmentation, data extraction and model inference/validation

• Efficient, flexible and robust computational tools for model simulation5,6

• Techniques for model reduction, coarse graining and analysis

We are working on each of these research strands, for example

through developing the open source software Chaste

(www.cs.ox.ac.uk/chaste)

• This work suggests that trophic signalling pathways could cause cell growth, or

else modulate cell shape through the cytoskeleton – either would explain the

experimentally observed shrinkage or growth when the pathways are perturbed