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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Regulation of Actin Dynamics in the C. elegans Somatic Gonad
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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- Award ID(s):
- 1816640
- NSF-PAR ID:
- 10094737
- Date Published:
- Journal Name:
- Journal of Developmental Biology
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2221-3759
- Page Range / eLocation ID:
- 6
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The migration of cells through constricting spaces or along fibrous tracks in tissues is important for many biological processes and depends on the mechanical properties of a cytoskeleton made up of three different filaments: F‐actin, microtubules, and intermediate filaments. The signaling pathways and cytoskeletal structures that control cell motility on 2D are often very different from those that control motility in 3D. Previous studies have shown that intermediate filaments can promote actin‐driven protrusions at the cell edge, but have little effect on overall motility of cells on flat surfaces. They are however important for cells to maintain resistance to repeated compressive stresses that are expected to occur in vivo. Using mouse embryonic fibroblasts derived from wild‐type and vimentin‐null mice, it is found that loss of vimentin increases motility in 3D microchannels even though on flat surfaces it has the opposite effect. Atomic force microscopy and traction force microscopy experiments reveal that vimentin enhances perinuclear cell stiffness while maintaining the same level of acto‐myosin contractility in cells. A minimal model in which a perinuclear vimentin cage constricts along with the nucleus during motility through confining spaces, providing mechanical resistance against large strains that could damage the structural integrity of cells, is proposed.
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null (Ed.)Cardiac myosin binding protein-C (cMyBP-C) is a thick filament protein that influences sarcomere stiffness and modulates cardiac contraction-relaxation through its phosphorylation. Phosphorylation of cMyBP-C and ablation of cMyBP-C have been shown to increase the rate of MgADP release in the acto-myosin cross-bridge cycle in the intact sarcomere. The influence of cMyBP-C on Pi-dependent myosin kinetics has not yet been examined. We investigated the effect of cMyBP-C, and its phosphorylation, on myosin kinetics in demembranated papillary muscle strips bearing the β-cardiac myosin isoform from nontransgenic and homozygous transgenic mice lacking cMyBP-C. We used quick stretch and stochastic length-perturbation analysis to characterize rates of myosin detachment and force development over 0–12 mM Pi and at maximal (pCa 4.8) and near-half maximal (pCa 5.75) Ca 2+ activation. Protein kinase A (PKA) treatment was applied to half the strips to probe the effect of cMyBP-C phosphorylation on Pi sensitivity of myosin kinetics. Increasing Pi increased myosin cross-bridge detachment rate similarly for muscles with and without cMyBP-C, although these rates were higher in muscle without cMyBP-C. Treating myocardial strips with PKA accelerated detachment rate when cMyBP-C was present over all Pi, but not when cMyBP-C was absent. The rate of force development increased with Pi in all muscles. However, Pi sensitivity of the rate force development was reduced when cMyBP-C was present versus absent, suggesting that cMyBP-C inhibits Pi-dependent reversal of the power stroke or stabilizes cross-bridge attachment to enhance the probability of completing the power stroke. These results support a functional role for cMyBP-C in slowing myosin detachment rate, possibly through a direct interaction with myosin or by altering strain-dependent myosin detachment via cMyBP-C-dependent stiffness of the thick filament and myofilament lattice. PKA treatment reduces the role for cMyBP-C to slow myosin detachment and thus effectively accelerates β-myosin detachment in the intact myofilament lattice. NEW & NOTEWORTHY Length perturbation analysis was used to demonstrate that β-cardiac myosin characteristic rates of detachment and recruitment in the intact myofilament lattice are accelerated by Pi, phosphorylation of cMyBP-C, and the absence of cMyBP-C. The results suggest that cMyBP-C normally slows myosin detachment, including Pi-dependent detachment, and that this inhibition is released with phosphorylation or absence of cMyBP-C.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/jdb7010006
