Finite-Element Stress Analysis of a Multicomponent Model of Sheared and Focally-Adhered Endothelial Cells

Abstract

Hemodynamic forces applied at the apical surface of vascular endothelial cells may be redistributed to and amplified at remote intracellular organelles and protein complexes where they are transduced to biochemical signals. In this study we sought to quantify the effects of cellular material inhomogeneities and discrete attachment points on intracellular stresses resulting from physiological fluid flow. Steady-state shear- and magnetic bead-induced stress, strain, and displacement distributions were determined from finite-element stress analysis of a cell-specific, multicomponent elastic continuum model developed from multimodal fluorescence images of confluent endothelial cell (EC) monolayers and their nuclei. Focal adhesion locations and areas were determined from quantitative total internal reflection fluorescence microscopy and verified using green fluorescence protein-focal adhesion kinase (GFP-FAK). The model predicts that shear stress induces small heterogeneous deformations of the endothelial cell cytoplasm on the order of <100 nm. However, strain and stress were amplified 10-100-fold over apical values in and around the high-modulus nucleus and near focal adhesions (FAs) and stress distributions depended on flow direction. The presence of a 0.4 microm glycocalyx was predicted to increase intracellular stresses by approximately 2-fold. The model of magnetic bead twisting rheometry also predicted heterogeneous stress, strain, and displacement fields resulting from material heterogeneities and FAs. Thus, large differences in moduli between the nucleus and cytoplasm and the juxtaposition of constrained regions (e.g. FAs) and unattached regions provide two mechanisms of stress amplification in sheared endothelial cells. Such phenomena may play a role in subcellular localization of early mechanotransduction events.

Effects of Frequency and Acceleration Amplitude on Osteoblast Mechanical Vibration Responses: A Finite Element Study

“…Poisson's ratio of membrane, cytoplasm, and nucleus was set at 0.33 [27]. Normally, the elastic modulus of the cytoplasm is only one-quarter that of the nucleus [28].…”

“…The initial cellular density was assumed as 1000 kg/m 3 [31], and 1250 kg/m 3 was used as the density of cytoplasm, nucleus, and membrane in the endothelial cell [27]. Previously, the density of an osteoblast was assumed as 125 kg/m 3 [19], and, for osteocyte-like MLO-Y4 cell, 1500 kg/m 3 , 1800 kg/m 3 , and 600 kg/m 3 were set as the densities of cytoplasm, nucleus, and membrane, respectively [26].…”

Shear-induced force transmission in a multicomponent, multicell model of the endothelium

“…They observed maximum displacement of approximately 400 nm at the apical side of the cell, under a uniform shear stress of 2 Pa. We applied a uniform shear stress with magnitude of 2 Pa over the surface of the EC monolayer and observed a maximum displacement of 400 nm over the surface of ECs (figure 2b). Furthermore, Ferko et al [23] developed a model of single EC with nucleus, cytosol and FAs, but not including the apical layer and cytoskeleton. They observed a maximum displacement of 30 nm at the apical side of the single EC when a uniform shear stress of 1 Pa was applied on the cell surface.…”

“…On the other hand, excluding the SFs from the EC model induces a dramatic decrease in stresses around the nucleus. Ferko et al [23] reported the stress amplification of three-to four-fold around the nucleus in their single cell model where a uniform shear stress of 1 Pa was applied on the surface of the EC. The stresses over the nucleus in our one EC model (results not shown), exposed to a uniform shear stress of 1 Pa, are in the same range of stresses observed by Ferko et al [23].…”

“…Ferko et al [23] reported the stress amplification of three-to four-fold around the nucleus in their single cell model where a uniform shear stress of 1 Pa was applied on the surface of the EC. The stresses over the nucleus in our one EC model (results not shown), exposed to a uniform shear stress of 1 Pa, are in the same range of stresses observed by Ferko et al [23]. Figure 9a,b displays the von Mises stress distribution at the surface of the glycocalyx and the surface of the cortical apical layer, respectively.…”