Bio-chemo-mechanical theory of active shells

Living thin structures such as cell cortex layers and multicellular sheets often exhibit intricate morphologies and dynamic behaviors, including Turing’s pattern, periodic oscillation, and wave propagation. In this paper, we present a bio-chemo-mechanical theoretical framework to model these morphog...

Full description

Saved in:
Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2021-07, Vol.152, p.104419, Article 104419
Main Authors: Yin, Sifan, Li, Bo, Feng, Xi-Qiao
Format: Article
Language:English
Subjects:
Active shell
Bifurcation
Bifurcations
Bio-chemo-mechanical feedback
Evolution
Feedback
Gametocytes
Morphogenesis
Morphology
Pattern transition
Shell theory
Stability analysis
Traveling waves
Wave propagation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Living thin structures such as cell cortex layers and multicellular sheets often exhibit intricate morphologies and dynamic behaviors, including Turing’s pattern, periodic oscillation, and wave propagation. In this paper, we present a bio-chemo-mechanical theoretical framework to model these morphogenetic processes and to unveil the underlying mechanisms. On the basis of the nonlinear non-Euclidean shell model, we formulate an active solid shell theory which couples the excitation and transmission of biochemical signals with mechanical forces. Through linear stability analysis, it is found that Hopf and Pitchfork bifurcations induced by chemomechanical feedback are two primary mechanisms that may trigger pattern formation. A numerical scheme is developed to solve the coordinated mechanical and biochemical fields in the active shell system and thus, to track the dynamic pattern evolution beyond the stationary state. For illustration, the proposed theory is applied to starfish oocytes and to decipher the synchronous protein dynamics and surface contraction pattern emerging in the anaphase of meiosis, which involves both global oscillation and traveling waves. This study underscores the crucial role of bio-chemo-mechanical feedback in driving morphogenetic pattern evolution. •Active shell theory is proposed to model bio-chemo-mechanical processes of living thin structures.•Hopf and Pitchfork bifurcations are revealed as primary mechanisms that trigger pattern formation.•Numerical simulations track the dynamic pattern evolution far beyond the stationary state.
ISSN:0022-5096
1873-4782
DOI:10.1016/j.jmps.2021.104419