Mechanochemical induction of wrinkling morphogenesis on elastic shells

Abstract

Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on...

Modeling mechanochemical pattern formation in elastic sheets of biological matter

“…The scaling of spot separation with thickness as well as with the expansion factor, ε = Λ max /Λ min − 1, was verified in detail for this model on a spherical shell in Ref. [31].…”

“…In the expansion-curvature model, a sequence of buckling instabilities leads to regularly spaced lattice-like or scar like arrangements of spots reminiscent of patterns obtained from purely buckling [61] or purely chemical instabilities [62]. We have recently reported similar patterns on spherical shells thereby demonstrating that these phenomena are potentially robust to changes in shell geometry [31]. Further study is required for a better understanding of these patterns in the context of wrinkling theory.…”

“…Physically speaking, chemical or motor fraction rearrangements evolve on longer time scales, whereas fast modes of mechanical conformations follow them quasi-statically. For an epithelial monolayer, we estimate a characteristic timescale of ∼ 10 1 -10 2 s for relaxation of elastic deformation energy [21,31], while morphogen degradation occurs over tens of minutes to hours [50,51]. A similar comparison of timescales can be made for the cell cytoskeleton or actin-myosin gels in vitro that are simulated in Model II.…”

“…Motivated by tissue patterning via spatial gradients of morphogens, diffusible biomolecules that induce gene expression during morphogenesis [26], we consider the interplay of a diffusing chemical signal with mechanical deformations [27][28][29][30][31][32]. In analogy with but to distinguish from morphogens that trigger slow genetic changes, we term these chemical signals "mechanogens" since they are expected to cause faster mechanical changes by affecting motor activity or cytoskeletal remodeling [12,31,33]. In this model, the in-plane stretching stress arises due to chemical-induced local contractility change in the shell (Fig.…”

Computer modeling reveals modalities to actuate mutable, active matter

“…Multi-physics simulations have only recently been developed for SofAM 4 – 7 . While these models capture salient features of mobile, elastic surfaces, they, however, neglect either the host fluid 7 , 8 ; reactions occurring in the solution 4 , or the specific chemistry involved in the reactions 6 . Building on the latter studies, our group 3 developed a computational approach to solve the coupled equations for (1) flow in a fluid-filled chamber; (2) advection and diffusion of chemicals in the solution and their reactions with deformable materials; (3) dynamic behavior of the nodes that make up the elastic material; and (4) fluid–structure interactions between these nodes and the solution (see Fig.…”