Modelling shape generation by the basement membrane.

Morphogenesis is a biophysical process where cellular forces guide complex cellular deformations that shape animal tissues and organs1. Understanding the relevant forces and how they act on and deform biological tissues is challenging due to the complex, anisotropic material properties of cells and the extracellular matrix (ECM) surrounding them. The basement membrane (BM), a sheet-like ECM, is essential for guiding epithelial morphology2,3.

We recently demonstrated that insufficient BM growth results in geometric frustration, accumulation of elastic pre-stresses and tissue deformation4 (Fig. A). While pre-stress resides in many biological tissues5-8, the conditions under which pre-stress arises and how they feed back on tissue morphology remain unclear.

This interdisciplinary PhD, spanning physics, mathematics, computing and biology, investigates pre-stress, arising from the mechanical interplay between tissue and BM growth, as a universal mechanism of biological shape generation. In close experimental collaboration, the project will yield a 'data-informed' universal modelling framework paving the road for understanding the biomechanics of shape generation in animal development, disease and synthetic systems.

Main objectives

1. Create a novel modelling framework to simulate the growth of tissues (via continuum and vertex-modelling) along with their surrounding BM (via continuum and lattice modelling).

2. Incorporate growth and mechanical anisotropies to give a sophisticated description of the complex material properties of BMs (see Fig. B).

3. Identify how geometric frustrations arise during growth, leading to elastic pre-stress that guides complex tissue shapes.

4. Challenge modelling frameworks in different epithelial systems (Drosophila, zebrafish and organoids) yielding a universal framework to predict tissue morphology based on growth dynamics and material parameters. Approach

Starting from a simplified continuum description of tissue and BM growth, we will design a mathematical model of the growth of tissues. This will involve a vertex model of the cells along with a system of partial differential equations (PDEs) for the BM. These will be solved numerically, based on existing code within the Richards group, using a combination of MATLAB and C++.

Material anisotropies and different elastic models (considering strain-stiffening of the BM) will be included to adequately represent the structurally and mechanically anisotropic fibrous BM layer.

Experimental parameter determination (image segmentation, biophysical essays) and model verification (using the Drosophila wing disc) will be performed together with SH. Subsequently, the model will be expanded to other growing epithelial tissues including the zebrafish optic cup (with Steffen Scholpp, LSI) and epithelial organoids (with Ge Guo, LSI).

Broader impact

Shape and function are inherently linked entities as alterations in morphology can lead to malfunction and disease9,10. This project will yield unprecedented insight into biological shape generation and the mathematical model will provide a powerful tool to understand animal development and for tissue engineering approaches designing custom tissue shapes.