Effect of the glycocalyx layer on transmission of interstitial flow shear stress to embedded cells

Abstract

In this paper, a simple theoretical model is developed to describe the transmission of force from interstitial fluid flow to the surface of a cell covered by a proteoglycan / glycoprotein layer (glycocalyx) and embedded in an extracellular matrix. Brinkman equations are used to describe flow through the extracellular matrix and glycocalyx layers and the solid mechanical stress developed in the glycocalyx by the fluid flow loading is determined. Using reasonable values for the Darcy permeability of extracellular matrix and glycocalyx layers and interstitial flow velocity, we are able to estimate the fluid and solid shear stresses imposed on the surface of embedded vascular, cartilage and tumor cells in vivo and in vitro. The principal finding is that the surface solid stress is typically one to two orders of magnitude larger than the surface fluid stress. This indicates that interstitial flow shear stress can be sensed by the cell surface glycocalyx, supporting numerous recent observations that interstitial flow can induce mechanotransduction in embedded cells. This study may contribute to understanding of interstitial flow-related mechanobiology in embryogenesis, tumorigenesis, tissue physiology and diseases and has implications in tissue engineering.

Fig. 1

Simple schematic of a suspended cell in an infinite Darcy media exposed to interstitial flow. Velocity profile near a cell surface embedded in an infinite extracellular matrix (Darcy media). The Brinkman layer is the surface boundary layer where the flow transitions from an external Darcy flow at velocity u_∞ to a no-slip condition at the surface of the cell

Fig. 2

Glycocalyx senses interstitial flow. Summary figure showing the velocity profile in the ECM (extracellular matrix) and the GCX (glycocalyx) surrounding a cell. Interstitial flow shear stress can be sensed by the glycocalyx layer. The ratio of the surface solid stress (τ_wg) to the surface fluid stress (τ_w) is $H∕\sqrt{K_g}$. The solid stress can be 10–100-fold higher than fluid stress at the plasma membrane. Glycocalyx-mediated interstitial flow mechanotransduction may depend on ECM-integrin-cytoskeletal linkage. For simplicity, integrins and the cytoskeleton are not shown in the figure. H-glycocalyx thickness, K_g-Darcy permeability of the glycocalyx, K_m-Darcy permeability of the surrounding media, u-the superficial velocity far from the surface, u_g-the velocity in the glycocalyx layer far from the cell surface (beyond the Brinkman layer)

Fig. 3

Three representative cases of velocity and stress profiles to mimic cells suspended in collagen gels, tumor cells in vivo and SMCs in the arterial wall, respectively. K_m and K_g were chosen as follows: K_m > K_g (a), K_m = K_g (b), and K_m < K_g (c). The detailed parameters for each case are listed in Table 3. The velocity profiles extend into the ECM space (top figures). The profiles for fluid and solid stresses are only shown for the glycocalyx layer that is untethered (middle figures). The fluid stress profiles near the cell membrane (0–50nm) are highlighted (bottom figures)

Fig. 4

Plots of the normalized fluid and solid cell surface stresses ($\overline{{\tau }_w}$ and $\overline{{\tau }_{wg1}}$) as functions of K_g/K_m and $\mathrm{H}\sqrt{K_g}∕K_m$. According to Table 3, physiological K_g/K_m ranges from 0.01 to 100 and $H\sqrt{K_g}∕K_m$ ranges from 1 to 1,000. Fluid (a) and solid (b) surface stresses (dimensionless) are plotted versus $H\sqrt{K_g}∕K_m$ with K_g/K_m varying from 0.001 to 1,000. Plots are for untethered conditions. The physiological dimensionless fluid and solid stresses at the cell surface (membrane) obtained from Table 3 are in the ranges of (0.01–100) and (1–800) for the untethered cases, respectively. The physiological ranges of fluid and solid stresses and $H\sqrt{K_g}∕K_m$ are indicated in the shaded areas on (a) and (b). The close-up plots of fluid and solid stresses as $H\sqrt{K_g}∕K_m\to 0$ are shown in (a') and (b'), respectively