Mathematical modelling of embryonic tissue elongation

Abstract

Spatiotemporal changes in tissue mechanics during embryonic development have been shown to be critical for body axis elongation. A minimal in vitro system recapitulating this process are gastruloids: synthetic embryos generated from mouse embryonic stem cells that elongate asymmetrically along a predefined axis. However, the biophysical mechanism underlying this process is still unknown. In this study, we use a hydrodynamic model to explore potential mechanisms for uniaxial tissue elongation, focusing on changes in tissue rheology. To model this process, we use a two-component model that accounts for cell and interstitial fluid interactions, proposed by Ranft et al. (2012). We solve the model in 1D and investigate how different biophysical gradients lead to asymmetric growth. Specifically, we obtain that the growth of the tissue predicted by the model is linear and restricted on its boundaries. We also obtain asymmetric growth of the tissue provided that its size is larger than the hydrodynamic length-scale of the system. Our study identifies viscosity and friction gradients as potential drivers of asymmetric growth.