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.

Model systems for regeneration: Hydra

“…A theoretical investigation of these oscillations, which are common in other multicellular cysts, pointed to a possible role in size regulation of the regenerating tissue (Ruiz-Herrero et al, 2017). Moreover, a new set of models has extended the existing Gierer-Meinhardt theoretical framework to incorporate mechanical and biochemical communication into the symmetry breaking process (Mercker et al, 2015;Brinkmann et al, 2018). One of the next frontiers for the field will be to understand how cells generate and interpret biophysical signals, and how these signals establish the conditions that allow self-organization to emerge.…”

A “Numerical Evo-Devo” Synthesis for the Identification of Pattern-Forming Factors

“…A more direct approach would be to use purely mechanical models, previously shown to produce periodic designs such as dotted arrays in one or two dimensional spaces [73,74]. Alternatively, mechanical and chemical couplings proved powerful: necessary Turing model's conditions were obtained by coupling biomechanical parameters promoting short-range activation and long-range inhibition to only one morphogen, suggesting a crucial role for tissue mechanics in pattern formation [69,75], and providing a new paradigm relaxing the necessity of an inhibitor diffusing at a long range-an important constraint of Turing's model which is yet to be supported in many in vivo systems [76]. In light of the studies described above, numerical methodologies integrating molecular, cellular and mechanical elements may greatly benefit from taking into account the developmental dynamics of pattern formation, and adding elements of variation in the architecture and bio-physical properties of the developing tissue as observed between species displaying relevant pattern differences.…”

“…More generally, in several other systems, the skin physical forces exerted on/by cells by/on the extra-cellular environment (e.g., shear stress, compression, tension, traction, adhesion) have been linked to changes in extra-cellular matrix architecture, cell cycle, cell motility and signalling [ 61 , 62 , 63 , 64 , 65 , 66 ], likely playing a defining role in patterning processes. With the advent of biophysical tools to measure physical parameters in vivo [ 67 ] and the ever growing amount of theoretical frameworks integrating biomechanics [ 68 , 69 , 70 , 71 ], it now becomes possible to explore the role of tissue mechanics with comprehensive experimental modelling approaches. One may infer previous unified models by adding explicit dependence of some parameters of reaction-diffusion and chemotaxis terms on mechanical parameters (e.g., molecular diffusion could be a function of substrate stiffness [ 72 ]).…”

Mechanochemical modelling of dorsal closure reveals emergent cell behaviour in tissue morphogenesis

“…FEM-based simulations have been used to describe how complex biological structures form during development (Brodland & Clausi, 1995;Davidson et al, 1995). Recently, FEM was also used to simulate reaction diffusion equations coupled to material contractility on simple spherical shapes (Brinkmann et al, 2018). We here similarly combined tissue mechanics with cellular actomyosin biochemistry in AS cells, segmented from a living embryo, to simulate and explore AS tissue dynamics during DC.…”