Physics of growing biological tissues: the complex cross-talk between cell activity, growth and resistance

Abstract

For many organisms, shapes emerge from growth, which generates stresses, which in turn can feedback on growth. In this review, theoretical methods to analyse various aspects of morphogenesis are discussed with the aim to determine the most adapted method for tissue mechanics. We discuss the need to work at scales intermediate between cells and tissues and emphasize the use of finite elasticity for this. We detail the application of these ideas to four systems: active cells embedded in tissues, brain cortical convolutions, the cortex of Caenorhabditis elegans during elongation and finally the proliferation of epithelia on extracellular matrix. Numerical models well adapted to inhomogeneities are also presented. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

Mechanochemical control of epidermal stem cell divisions by B-plexins

“…During embryogenesis, tissue growth and shape are intimately connected 1 . Tissue growth intrinsically generates mechanical strains and compressions, and, conversely, mechanical deformations provide a fundamental regulatory feedback for growth control 1 – 3 .…”

“…During embryogenesis, tissue growth and shape are intimately connected 1 . Tissue growth intrinsically generates mechanical strains and compressions, and, conversely, mechanical deformations provide a fundamental regulatory feedback for growth control 1 – 3 . This feedback requires cells to sense mechanical forces, which are then transformed into biochemical signals that in turn control cellular functions including the rate of cell divisions 3 – 6 .…”

Rivlin's legacy in continuum mechanics and applied mathematics

“…Ben Amar et al [28] provide a compelling case for the introduction of finite elasticity models into the description and understanding of many biological processes. In their review article, they cover morphogenesis, tissue mechanics, tissue growth and active cell mechanics.…”

Physical forces driveC. elegansembryonic deformation

“…Previous work has focused on genes and other biomolecules that shape bodies, while mechanical forces have received much less attention (Dance, 2021). Physical forces play a central role in tissue morphogenesis (Ben Amar et al, 2019; Gilmour et al, 2017; Kuhl, 2016; Molnar and Labouesse, 2021; Tallinen et al, 2016) and animal development (Fei et al, 2020; Vuong-Brender et al, 2017; Valet et al, 2022; Zhang et al, 2011), including active forces exerted by molecular motors and muscle activity, and passive mechanical resistance forces due to tissue elasticity (Ackermann et al, 2022). Understanding how physical forces influence morphogenesis and embryonic development remains to be elucidated.…”