SignificanceMorphogenesis, the emergence of shape and form in biological systems, is a process that is fundamentally mechanochemical: Shape changes of material are driven by active mechanical forces that are generated by chemical processes, which in turn can be affected by the deformations and flows that occur. We provide a framework that integrates these interactions between the geometry of deforming materials and active processes in them by introducing the shape dynamics of self-organized active surfaces. We show that the tight coupling between surface mechanics and active processes gives rise to the spontaneous formation of nontrivial shapes, shape oscillations, and directed peristaltic motion. Our simple yet general description lays the foundation to explore the regulatory role of shape in morphogenetic processes.
The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities. arXiv:1909.12804v1 [physics.bio-ph] 26 Sep 2019 S3 2.3 Components of the Jacobian for l ≥ 2Following the general procedure outlined in Sec. 2.1, we derive in the following the components of the system's Jacobian. The Jacobian diagonalizes in the space of spherical harmonics and contributes for each mode l with J l = J l RR J l Rc J l cR J l cc
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.