Open Access

ARTICLE

Tensorial Description of the Geometrical Arrangement of the Fibrous Molecules in Vascular Endothelial Cells

Wei Huang^*

* Department of Bioengineering, University of California San Diego, La Jolla, CA 92093-0412

Molecular & Cellular Biomechanics 2007, 4(3), 119-132. https://doi.org/10.3970/mcb.2007.004.119

Abstract

This work presents a tensorial description of the geometrical arrangement of the cellular molecules in the vascular endothelial cells. The geometrical arrangement of the molecules is the foundation of the mechanical properties of the molecular aggregates, which are the foundation of the physical behavior of the cells and tissues. For better studying the physical behavior of the cells and tissues, the geometrical arrangement of the cellular molecules has to be described quantitatively. In this paper, a second order molecular configuration tensor P_ij^g for fibrous protein in the cells is defined for quantitative measurement. Here, the subscripts i, j refer to the coordinate axes x₁, x₂, x₃, and the superscript g refers to the kind of fibrous protein. Every molecular configuration tensor P_ij^g has 9 components. To give an example, the F-actin fibers in the vascular endothelial cells were studied. These molecules were stained with phalloidin and observed in a confocal microscope. Digitized images of the F-actin fibers were analyzed to determine the F-actin's molecular configuration tensor P_ij^g. The tensor P_ij^g is a simple and definitive description of a complex system of molecules which are important in the research on tissue remodeling of blood vessels. In this article, the P₃₁ and P₃₂ values in the P_ij^g tensor of F-actin fiber in the endothelial cells in rat's abdominal aorta were obtained, and the distributions of these two components in the endothelial cells were presented. The molecular configuration tensor P_ij^g can be applied to other fibrous proteins in the cells and to cells other than vascular endothelial cells.

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Keywords

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