The role of mechanics in the growth and homeostasis of the intestinal crypt

Abstract

We present a mechanical model of tissue homeostasis that is specialised to the intestinal crypt. Growth and deformation of the crypt, idealised as a line of cells on a substrate, are modelled using morphoelastic rod theory. Alternating between Lagrangian and Eulerian mechanical descriptions enables us to precisely characterise the dynamic nature of tissue homeostasis, whereby the proliferative structure and morphology are static in the Eulerian frame, but there is active migration of Lagrangian material points out of the crypt. Assuming mechanochemical growth, we identify the necessary conditions for homeostasis, reducing the full, time-dependent system to a static boundary value problem characterising a spatially heterogeneous “treadmilling” state. We extract essential features of crypt homeostasis, such as the morphology, the proliferative structure, the migration velocity, and the sloughing rate. We also derive closed-form solutions for growth and sloughing dynamics in homeostasis, and show that mechanochemical growth is sufficient to generate the observed proliferative structure of the crypt. Key to this is the concept of threshold-dependent mechanical feedback, that regulates an established Wnt signal for biochemical growth. Numerical solutions demonstrate the importance of crypt morphology on homeostatic growth, migration, and sloughing, and highlight the value of this framework as a foundation for studying the role of mechanics in homeostasis.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

“…to reshape itself to reduce the difference between its actual stress and the a priori known or genetically encoded homeostatic stress [31,35]. Growth laws of the type (2.3) which employ a homeostasis mechanism have been applied to morphogenesis problems, like sea urchin gastrulation [36], the formation of ribs in ammonite seashells [37], and the intestinal crypt [38], as well as other applications such as wound healing [36,39] and discrete networks such as plant cell networks [21].…”

Quantized wrinkles and fracture of stiff membranes on soft films

“…When stiff meets soft, stiff/soft bilayers always lose their stability 1 and form a variety of morphological instability modes 2-4 , such as wrinkles 1,5-8 , localized folds 2,9-11 , and ridges 12,13 , during compression. Such an evolving bilayer system plays a key role in working rationale of bio-systems ranging from ageing skins, lung surfactants to complex and incomprehensible structures of cerebral cortexes [14][15][16][17] , and heralds a wealth of opportunities for applications in advanced materials and devices [18][19][20] .…”

“…When stiff meets soft, stiff/soft bilayers always lose their stability 1 and form a variety of morphological instability modes 2-4 , such as wrinkles 1,5-8 , localized folds 2,9-11 , and ridges 12,13 , during compression. Such an evolving bilayer system plays a key role in working rationale of bio-systems ranging from ageing skins, lung surfactants to complex and incomprehensible structures of cerebral cortexes [14][15][16][17] , and heralds a wealth of opportunities for applications in advanced materials and devices [18][19][20] .Regular wrinkles are the primary instability mode, especially at high stiff/soft modulus ratio and large thickness contrast 3 . Secondary instability occurs in the period-wrinkling membranes upon further compression 2 , manifested mainly as winkle-to-fold transitions driven by stress localization.…”

Modelling realistic 3D deformations of simple epithelia in dynamic homeostasis

“…While valuable and insightful, these approaches provide limited information toward the geometric structure of the epithelium. Another approach is to model the epithelium as a continuum string (2D) [2] or sheet (3D) [17] of cells. However, the insights gained into the geometric structure from deformable continuum models comes with a loss of information into cell topology.…”