Post-Turing tissue pattern formation: Advent of mechanochemistry

Abstract

Chemical and mechanical pattern formation is fundamental during embryogenesis and tissue development. Yet, the underlying molecular and cellular mechanisms are still elusive in many cases. Most current theories assume that tissue development is driven by chemical processes: either as a sequence of chemical patterns each depending on the previous one, or by patterns spontaneously arising from specific chemical interactions (such as "Turing-patterns"). Within both theories, mechanical patterns are usually regarded as passive by-products of chemical pre-patters. However, several experiments question these theories, and an increasing number of studies shows that tissue mechanics can actively influence chemical patterns during development. In this study, we thus focus on the interplay between chemical and mechanical processes during tissue development. On one hand, based on recent experimental data, we develop new mechanochemical simulation models of evolving tissues, in which the full 3D representation of the tissue appears to be critical for obtaining a realistic mechanochemical behaviour. The presented modelling approach is flexible and numerically studied using state of the art finite element methods. Thus, it may serve as a basis to combine simulations with new experimental methods in tissue development. On the other hand, we apply the developed approach and demonstrate that even simple interactions between tissue mechanics and chemistry spontaneously lead to robust and complex mechanochemical patterns. Especially, we demonstrate that the main contradictions arising in the framework of purely chemical theories are naturally and automatically resolved using the mechanochemical patterning theory.

Fig 1. Schematic view of one of the exemplarily investigated feedback-loops between tissue mechanics and morphogen production.

Local morphogen levels lead to apical constriction in biological cells, which leads (due to the elastic response of the tissue maintaining continuity) to local stretch, which induces again local morphogen production.

Fig 2

(A)-(B) Simulation snapshots showing spontaneous pattern formation based on a simple mechanochemical feedback loop including basal constriction. In (B), the 3D tissue body has been sliced just for the purpose of a better visualisation. An experimental example showing co-localisation of tissue curvature and morphogen concentration during Hydra development can be e.g. found in Ref. [104].

Fig 3

(A)-(B) Simulation snapshots showing spontaneous pattern formation based on a simple mechanochemical feedback loop including apical constriction. In (B), the 3D tissue body has been sliced just for the purpose of a better visualisation. (C) Microscopic pictures showing similar morphogen and curvature patterns in Nematostella during gastrulation (with permission from Ref. [76]).

Fig 4

Simulation snapshots investigating the robustness of mechanochemical patterns with respect to (A) a thicker tissue layer (doubled thickness); (B) a thinner tissue layer (halved thickness); (C) a smaller system (384 biological cells); (D) lower tangential diffusion (quartered); (E) without any tangential diffusion; and (F) basal constriction only in the outer half of biological cells.

Fig 5

(A) Schematic view of the multiplicative decomposition of the deformation gradient tensor. (B) Numerical versus biological cells in the reference configuration (left-hand side) and an example of the deformed simulated tissue body with chemical (morphogen) patterns (right-hand side). Purple color represents high, white color low local morphogen levels. The 3D tissue body has been sliced just for the purpose of a better visualisation.