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Research Papers

A Model of Force Generation in a Three-Dimensional Toroidal Cluster of Cells

[+] Author and Article Information
Asha Nurse1

L. B. Freund

Jacquelyn Youssef

School of Engineering,  Brown University, Providence, RI 02912jacquelyn_youssef@brown.edu

1

Corresponding author.

J. Appl. Mech 79(5), 051013 (Jun 29, 2012) (6 pages) doi:10.1115/1.4006257 History: Received October 18, 2010; Revised February 27, 2012; Posted March 03, 2012; Published June 28, 2012; Online June 29, 2012

Observation of the self-assembly of clusters of cells in three dimensions has raised questions about the forces that drive changes in the shape of the cell clusters. Cells that self-assemble into a toroidal cluster about the base of a conical pillar have been observed in the laboratory to spontaneously climb the conical pillar. Assuming that cell cluster reorganization is due solely to surface diffusion, a mathematical model based on the thermodynamics of an isothermal dissipative system is presented. The model shows that the cluster can reduce its surface area by climbing the conical pillar, however, this is at the expense of increasing its gravitational potential energy. As a result, the kinetics of the climb are affected by parameters that influence this energy competition, such as the slope of the conical pillar and a parameter of the model κ that represents the influence of the surface energy of the cluster relative to its gravitational potential energy.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 6

Diagram showing the forces acting on the cluster: the weight W per unit length along the circumference 2πa, the normal force N exerted by the cone per unit circumferential length, and the internal tensile force F acting in the circumferential direction and generated by the cells in the cluster

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Figure 5

Graph showing numerical results of Eq. 9 at varying values of α using the initial data and input parameters from the experiments

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Figure 4

Graph showing the numerical results of Eq. 9 at varying values of κ using the initial data and input parameters from the experiments

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Figure 3

An illustration of the origin of the surface energy in the cell cluster

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Figure 2

Diagram showing the physical parameters of the model

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Figure 1

Side view and top view microscopy images of the experimental chamber with a toroidal cluster

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