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 μm glycocalyx was predicted to increase intracellular stresses by ~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.

Membrane-Stretch-Induced Cell Death in Deep Tissue Injury: Computer Model Studies

“…Specifically, shear moduli of cells were measured by means of pipette aspiration, cytoindentation, atomic force microscopy, magnetic and optical tweezers, shear flow methods, and cell stretching devices. 1,6, 14,19,23,42,46,53 Taken together, these studies indicate that the shear modulus of the cytosol is between 0.5 and 11.5 kPa, and we therefore assumed in our modeling that G of cytosol is 1 kPa. Shear moduli of cell membranes are generally reported in the literature as bending moduli (in the range of 2-10 lN/m 7,22,36 ), but these are structural properties rather than mechanical properties, and they are therefore not suitable for FE modeling.…”

Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics

“…Some of these models, either 2D or 3D, also incorporated nucleus and/or cytoskeletal fibers (McGarry and Prendergast, 2004;Jean et al, 2005;De Santis et al, 2009;Ofek et al, 2009). Just two attempts were made to develop 3D cell models whose geometry is based on imaging individual cells rather than on assuming idealized cell shapes, and these include the study by Ferko et al (2007) who built an endothelial cell model from multimodal fluorescence images, and the study of Dailey et al (2009) who developed alveolar epithelial cell models from confocal microscopy scans. However, both the Ferko and the Dailey studies utilized the small deformation theory.…”

A model of localised Rac1 activation in endothelial cells due to fluid flow

“…Previously, Ferko et al (2007) showed that heterogeneity in intra-cellular could play an important role in the sub-cellular localization of mechano-transduction. However, here we make the simplifying assumptions that the cytosol/cytoskeletal medium is uniform and that force is transmitted to the basal surface locally.…”

“…Only tensile forces are considered and, to simplify the model, a smooth concentration of integrins is assumed; that is, clustering is ignored. Interestingly, Ferko et al (2007) illustrated that focal adhesions focus and amplify shear forces on the apical surfaces of ECs. Hence, the coarse grained approach applied here provides a 5 conservative estimate for the force applied at the basal surface.…”