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The reproductive system of the hermaphroditic nematode C. elegans consists of a series of contractile cell types—including the gonadal sheath cells, the spermathecal cells and the spermatheca–uterine valve—that contract in a coordinated manner to regulate oocyte entry and exit of the fertilized embryo into the uterus. Contraction is driven by acto-myosin contraction and relies on the development and maintenance of specialized acto-myosin networks in each cell type. Study of this system has revealed insights into the regulation of acto-myosin network assembly and contractility in vivo.
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Emergence of traveling waves and their stability in a free boundary model of cell motility
We consider a 2D free boundary model of cell motility, inspired by the 1D contraction-driven cell motility model due to P. Recho, T. Putelat, and L. Truskinovsky [Phys. Rev. Lett. 111 (2013), p. 108102]. The key ingredients of the model are the Darcy law for overdamped motion of the acto-myosin network, coupled with the advection-diffusion equation for myosin density. These equations are supplemented with the Young-Laplace equation for the pressure and no-flux condition for the myosin density on the boundary, while evolution of the boundary is subject to the acto-myosin flow at the edge. The focus of the work is on stability analysis of stationary solutions and translationally moving traveling wave solutions. We study stability of radially symmetric stationary solutions and show that at some critical radius a pitchfork bifurcation occurs, resulting in emergence of a family of traveling wave solutions. We perform linear stability analysis of these latter solutions with small velocities and reveal the type of bifurcation (sub- or supercritical). The main result of this work is an explicit asymptotic formula for the stability determining eigenvalue in the limit of small traveling wave velocities.
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- Award ID(s):
- 2005262
- PAR ID:
- 10424985
- Date Published:
- Journal Name:
- Transactions of the American Mathematical Society
- Volume:
- 376
- Issue:
- 1066
- ISSN:
- 0002-9947
- Page Range / eLocation ID:
- 1799 to 1844
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1090/tran/8824
