Mechanical Effects of Cell Anisotropy on Epithelia

Abstract

Theoretical, numerical and experimental methods are used to develop a comprehensive understanding of how cell shape affects the mechanical characteristics of two-dimensional aggregates such as epithelia. This is an important step in relating the mechanical properties of tissues to those of the cells of which they are composed. Statistical mechanics is used to derive formulas for the in-plane stresses generated by tensions gamma along cell-cell interfaces in sheets with anisotropic cellular fabric characterized by average cell aspect ratio kappa. These formulas are then used to investigate self-deformation (strain relaxation) of an anisotropic sheet composed of cells of thickness h and having effective viscosity mu. Finite element simulations of epithelia and of isolated cells and novel relaxation studies of specimens of embryonic epithelia reported herein are consistent with the predictions of the theory. In all cases, geometric factors cause the relaxation responses to be more complex than a single decaying exponential.

Cellular interfacial and surface tensions determined from aggregate compression tests using a finite element model

“…In the 3D case, this material forms a cylindrical volume of radius R 3 and height H. Continuum mechanics can be used to derive formulas for the force that such a volume, if filled with material of viscosity µ, would produce if compressed at a rate Ḣ . This approach assumes that partitioning of the cytoplasm in the aggregate by cell membranes does not affect the bulk force produced by the cytoplasm, an approach employed successfully elsewhere (Brodland et al, 2006;Brodland and Wiebe, 2004). It does not imply that the membranes and their associated proteins are insignificant, but only that separating the cytoplasmic masses associated with each cell from each other by a membrane does not affect the forces they generate.…”

Do lamellipodia have the mechanical capacity to drive convergent extension?

“…They have also provided significant insights into how forces generated by sub-cellular structures give rise to mechanical effects at the cell and tissue levels Brodland and Chen, 2000;Brodland, 2002;Brodland and Veldhuis, 2002;Brodland, 2003;Brodland, 2004;Brodland and Wiebe, 2004). Here, we present a γ-µ finite element model which has been modified so that it can model lamellipodia.…”

“…Unlike man-made (i.e., "engineered") systems, which are typically built up by successively refining a basic system, often by increasing its complexity, biological systems generally present in a complex form and computational models are essential for deconstructing them (Endy and Brent, 2001;Kitano, 2002). Another important feature of a computational model is that, unlike an experiment, it allows one to consider a system that contains only components specified by the user, making possible definitive statements regarding the capacity of specific structures to drive particular actions (Clausi and Brodland, 1993;Taber et al, 1995;Davidson et al, 1999;Chen and Brodland, 2000;Brodland and Chen, 2000;Palsson, 2001;Brodland, 2002;Brodland and Veldhuis, 2002;Brodland, 2003;Brodland, 2004;Brodland and Wiebe, 2004).…”

“…If the edges of the model tissue are restrained so that they cannot move, the cells stretch in the direction in which they are carrying tension (along the convergence axis) and their average aspect ratio is κ =1.59. Computer simulations and experiments show that when a tissue is stretched by external forces (Brodland and Wiebe, 2004) its cells stretch in the direction of tissue elongation. These and other simulations, experiments and analyses Brodland and Wiebe, 2004) show that cell elongation always correlates with the direction of the tension carried by the cells.…”

“…Computer simulations and experiments show that when a tissue is stretched by external forces (Brodland and Wiebe, 2004) its cells stretch in the direction of tissue elongation. These and other simulations, experiments and analyses Brodland and Wiebe, 2004) show that cell elongation always correlates with the direction of the tension carried by the cells. Thus, curiously, when external forces dominate, cells elongate in the direction of tissue elongation while when lamellipodia dominate, they elongate normal to it.…”