Mechanotransduction and strain amplification in osteocyte cell processes

Abstract

A paradox in bone tissue is that tissue-level strains due to animal and human locomotion are too small to initiate intracellular chemical responses directly. A model recently was proposed to resolve this paradox, which predicts that the fluid flow through the pericellular matrix in the lacunar-canalicular porosity due to mechanical loading can induce strains in the actin filament bundles of the cytoskeleton that are more than an order of magnitude larger than tissue level strains. In this study, we greatly refine this model by using the latest ultrastructural data for the cell process cytoskeleton, the tethering elements that attach the process to the canalicular wall and their finite flexural rigidity EI. We construct a much more realistic 3D model for the osteocyte process and then use large-deformation "elastica" theory for finite EI to predict the deformed shape of the tethering elements and the hoop strain on the central actin bundle. Our model predicts a cell process that is 3 times stiffer than in a previous study but hoop strain of >0.5% for tissue-level strains of >1,000 microstrain at 1 Hz and >250 microstrain at frequencies >10 Hz. We propose that this strain-amplification model provides a more likely hypothesis for the excitation of osteocytes than the previously proposed fluid-shear hypothesis.

Fig. 1.

Sketches (not to scale) of the osteocyte process and its attachment to the canalicular wall that show the structure of the central hexagonally packed actin filament bundle and the arrangement of the fimbrin cross-bridges, cross-filaments, and transverse elements. (A) Radial cross section. (B) Longitudinal cross section (cross section A). (C) Organization of fimbrin cross-linkages along an interior actin filament. (D) Spiraling double-helical coil of cross-filaments around the central actin bundle.

Fig. 2.

Model of the deflection of each transverse element due to the hydrodynamic loading w.

Fig. 3.

Static-force analysis on the central actin filament bundle of the cell process. (Left) Axial cross section of the entire bundle. (Right) Enlarged view of the loading on a single interior filament (open circle in A).

Fig. 4.

Loading of outer filament ring. (A) Force balance on the actin filament at the corner of outer filament ring (see Fig. 3) of the bundle. (B) Force analysis on the actin filament at the middle of outer filament ring (see Fig. 3) of the bundle.

Fig. 5.

The hoop strain of the osteocyte process as a function of loading frequency for tissue loading σ of 1 MPa.

Fig. 7.

Strain amplification ratio, the ratio of cellular-level cytoskeletal hoop strain ε_c to whole-tissue strain ε_t as a function of whole-tissue strain at two frequencies, 1 and 20 Hz, for EI = 0 and EI = 700 pN·nm² (20).

Fig. 6.

Hoop strain of the osteocyte process is plotted as a function of loading frequency with tissue loading amplitude as a parameter. Note that EI can approximately be treated as 0 for loads ≥1 MPa.