Description
- Abstract:
- Observation of self assembly of clusters of cells in three dimensions has raised questions about the forces that drive the changes in shape of the cell clusters and the stability of the clusters formed. Cells that self-assemble into a toroidal cluster about the base of a conical pillar have been experimentally observed to spontaneously climb the conical pillar. In other cases, toroidal clusters do not climb the pillar but, instead, they may undergo localized thinning at one or more cross-sections around the circumference of the cluster.Assuming that cell cluster reorganization is due solely to surface diffusion, a mathematical model based on thermodynamics of an isothermal dissipative system is presented. The model shows that the cluster can reduce its surface area by climbing the conical pillar but at the expense of increasing its gravitational potential energy. As a result, the kinetics of the climb is affected by parameters that influence this energy competition such as the slope of the conical pillar or the surface mobility of the diffusing cells. The development of localized deformations in clusters that do not climb the conical pillar is examined by means of a linear stability analysis wherein a nominally uniform toroidal cluster has its shape perturbed by a periodic perturbation in its minor radius. Analysis reveals that the cluster is stable if the surface energy density is spatially uniform. However, if the surface energy density is allowed to vary from point to point around the circumference of the toroid, unstable configurations may develop. The stability of the cluster is observed to depend on its initial minor radius, the radius of the conical pillar and the wave number of the applied sinusoidal perturbation. A stability analysis of nominally cylindrical bodies which evolve in shape due to surface diffusion was then carried out to understand the role of nonlinearity in the stability criteria in such bodies. This analysis may serve as a basis for a future study of the stability of toroidal clusters or toroidal shapes beyond the range of linear behavior.
- Notes:
- Thesis (Ph.D. -- Brown University (2011)
Access Conditions
- Rights
- In Copyright
- Restrictions on Use
- Collection is open for research.
Citation
Nurse, Asha K.,
"Driving Forces for Cell Cluster Shape Evolution and Stability"
(2011).
Mechanics of Solids Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0MP51HK
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Mechanics of Solids Theses and Dissertations
Theses and Dissertations for the Mechanics of Solids department....