Three-dimensional chiral morphodynamics of chemomechanical active shells

Abstract

Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.

Chiral Cell Nanomechanics Originated in Clockwise/Counterclockwise Biofunctional Microarrays to Govern the Nuclear Mechanotransduction of Mesenchymal Stem Cells

“…Cell chirality has been extensively interrogated in asymmetrical biomechanics to acknowledge the biological handedness in left−right biased cells. 31,32 The chiral interaction between the biomechanical signal and cell behavior has been a common concern in many research fields of cell nanomechanics, functional biomaterials, and biological chemistry. 33−35 Chiral cells can perceive the tendentious biomechanical signals in an external microenvironment and transfer these stimulations into nuclei for biochemical response.…”

“…Cell chirality has been extensively interrogated in asymmetrical biomechanics to acknowledge the biological handedness in left–right biased cells. , The chiral interaction between the biomechanical signal and cell behavior has been a common concern in many research fields of cell nanomechanics, functional biomaterials, and biological chemistry. − Chiral cells can perceive the tendentious biomechanical signals in an external microenvironment and transfer these stimulations into nuclei for biochemical response. , It is also reported that curved nanoscale fibers can improve cell bridge establishment to affect the mechanotransduction of stem cells by curved sophisticated extracellular matrices (ECMs) . The receptors of specific biomechanics predominantly contain ion channels, G protein-coupled receptors, and integrins. − Therefore, chiral biomechanical signaling transduction may play a very essential role in regulating physiological and pathological processes, such as cell function maintenance, normal physiological metabolism, and disease occurrence. , In this study, surface engineered chiral microarrays were prepared by synthetic photosensitive PVA and a designed photomask (Figure ) to control the chiral geometric morphology of hMSCs (Figure ) and manipulate left-/right-handed FA formation (Figure ).…”

A double Fourier sphere method for $d$-dimensional manifolds

“…Thus, one can take advantage of the efficiency of the FFT to approximate spherical functions. The classical DFS method was originated in 1972 by Merilees [29] and found various applications since, e.g., [4,8,13,16,34,36,39,46,48,49]. Recently, we have shown analytic approximation properties of the classical DFS method [31].…”

Mechanochemical dynamics of collective cells and hierarchical topological defects in multicellular lumens

“…Recent experimental evidences (18,20,31) and theories (32)(33)(34) suggest that mechanochemical feedback is essential for chemical patterning coupled with shape deformation. Although some theoretical works on the interplay between biochemical and mechanical components based on continuous descriptions (35)(36)(37)(38)(39)(40)(41) or discrete models (34,(42)(43)(44)(45)(46) have been developed in two-dimensional (2D) monolayers or single-cell systems, how mechanical forces and chemical signaling at the cellular level are integrated and transmitted to collective cell dynamics that enables the establishment of 3D morphogenetic patterns of tissues remain to be explored.…”