1
|
Sorrell EL, Lubkin SR. Bubble packing, eccentricity, and notochord development. Cells Dev 2021; 169:203753. [PMID: 34728430 DOI: 10.1016/j.cdev.2021.203753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Revised: 08/30/2021] [Accepted: 10/10/2021] [Indexed: 10/19/2022]
Abstract
This paper develops a theoretical basis for the observed relationship between cell arrangements in notochords and analog physical models, and the eccentricity of their cross sections. Three models are developed and analyzed, of the mechanics of cell packing in sheaths. The key ratios governing the packing patterns and eccentricity are cells per unit length λ, tension ratio Γ, and eccentricity e. For flexible and semi-flexible sheaths, the optimal packing pattern shifts from "bamboo", with a symmetric cross section, to "staircase", with an eccentric cross section, at a critical value λ = 1.13. In rigid tubes, this threshold is lowered as imposed eccentricity is increased. Patterns can be observed which are not optimal; pattern transitions may occur below or above the critical λ values. The eccentricity of staircase patterns in flexible and semi-flexible tubes is found to be dependent on the tension ratio Γ, increasing as sheath tension decreases relative to interior cell tension. A novel "serpentine" packing pattern appears for low Γ near the critical λ. The developmental utility of enforcing notochord eccentricity is discussed, as well as potential mechanisms for such control.
Collapse
|
2
|
Norman J, Sorrell EL, Hu Y, Siripurapu V, Garcia J, Bagwell J, Charbonneau P, Lubkin SR, Bagnat M. Tissue self-organization underlies morphogenesis of the notochord. Philos Trans R Soc Lond B Biol Sci 2018; 373:rstb.2017.0320. [PMID: 30249771 DOI: 10.1098/rstb.2017.0320] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/03/2018] [Indexed: 12/13/2022] Open
Abstract
The notochord is a conserved axial structure that in vertebrates serves as a hydrostatic scaffold for embryonic axis elongation and, later on, for proper spine assembly. It consists of a core of large fluid-filled vacuolated cells surrounded by an epithelial sheath that is encased in extracellular matrix. During morphogenesis, the vacuolated cells inflate their vacuole and arrange in a stereotypical staircase pattern. We investigated the origin of this pattern and found that it can be achieved purely by simple physical principles. We are able to model the arrangement of vacuolated cells within the zebrafish notochord using a physical model composed of silicone tubes and water-absorbing polymer beads. The biological structure and the physical model can be accurately described by the theory developed for the packing of spheres and foams in cylinders. Our experiments with physical models and numerical simulations generated several predictions on key features of notochord organization that we documented and tested experimentally in zebrafish. Altogether, our data reveal that the organization of the vertebrate notochord is governed by the density of the osmotically swelling vacuolated cells and the aspect ratio of the notochord rod. We therefore conclude that self-organization underlies morphogenesis of the vertebrate notochord.This article is part of the Theo Murphy meeting issue on 'Mechanics of development'.
Collapse
Affiliation(s)
- James Norman
- Department of Cell Biology, Duke University, Durham, NC 27710, USA
| | - Emma L Sorrell
- Department of Cell Biology, Duke University, Durham, NC 27710, USA.,Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA
| | - Yi Hu
- Department of Chemistry, Duke University, Durham, NC 27710, USA
| | - Vaishnavi Siripurapu
- Department of Cell Biology, Duke University, Durham, NC 27710, USA.,North Carolina School of Science and Mathematics, Durham, NC 27705, USA
| | - Jamie Garcia
- Department of Cell Biology, Duke University, Durham, NC 27710, USA
| | - Jennifer Bagwell
- Department of Cell Biology, Duke University, Durham, NC 27710, USA
| | | | - Sharon R Lubkin
- Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA
| | - Michel Bagnat
- Department of Cell Biology, Duke University, Durham, NC 27710, USA
| |
Collapse
|