Tensorial description of the geometrical arrangement of the fibrous molecules in vascular endothelial cells.

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(g)ij 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(g)ij 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(g)ij. The tensor P(g)ij 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(g)ij 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(g)ij can be applied to other fibrous proteins in the cells and to cells other than vascular endothelial cells.