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A comparison of strain and fluid shear stress in stimulating bone cell responses—a computational and experimental study

Centre for Bioengineering, Department of Mechanical Engineering, Trinity College, Dublin, Ireland; and
^* Department of Oral Cell Biology, ACTA-Universiteit van Amsterdam and Vrije Universiteit, Amsterdam, The Netherlands

¹Correspondence: Centre for Bioengineering, Department of Mechanical Engineering, Trinity College, Dublin 2, Ireland. E-mail: pprender{at}tcd.ie

SPECIFIC AIMS

Bone undergoes continuous remodeling in response to mechanical loading, although the mechanism by which bone cells respond to their changing mechanical environment are not well understood. That bone cells respond differently to fluid shear stress and strain stimulation applied to in vitro cultures has not been explained, which presents a significant challenge to our understanding of bone cell mechanotransduction and bone remodeling. In this study, we determined the bone cell nitric oxide (NO) and prostaglandin E₂ (PGE₂) response to 0.6 Pa fluid shear stress and 1000 µ substrate strain, and tested the hypothesis that the differences in response are related to the amount of cellular deformation caused. We developed a computational model of an adherent cell and used it to compute cellular deformation due to both mechanical stimuli.

PRINCIPAL FINDINGS

1. Development of a computational cell model comprising nucleus, cytoplasm, membrane, and cytoskeletal components with which we can determine cellular deformation under imposed stimuli
We developed a computational model of an adherent cell using finite element analysis, a mathematical tool that can be used to calculate the deformation of 3-dimensional shapes divided into a finite number of elements. Our model fuses two approaches to cellular biomechanics—the stress-supported tensegrity approach and the continuum approach—by combining structural cellular components in a simplified morphology, each with specified experimentally derived material properties (Fig. 1 , Table 1 ). Our idealized biomechanical approach may be used to model the complex physical environment of subconfluent adherent cells and is particularly useful for analyzing experiments where mechanical stimulation is the only variable parameter.

View larger version (51K): [in this window] [in a new window]   Figure 1. 3-Dimensional computational biomechanical model of an adherent cell. The model comprises nucleus, cytoplasm (transparent elements), membrane, and interconnected microfilament (gray lines) and microtubule (dark gray lines) components. Half of the cytoplasm and membrane components are omitted for clarity. The cell model dimensions (contact radius, 19.2 µm; height, 7.6 µm; volume, 3000 µm3) are based on experimental observations.

2. Our computational cell modeling approach shows there are qualitative and quantitative differences in cellular deformation caused by fluid shear stress and substrate strain at magnitudes commonly applied in vitro
The displacements of the cell model caused by fluid shear stress of magnitude 0.6 Pa and by substrate strain of magnitude 1000 µ indicate fundamental differences in the cellular deformation caused by both methods of mechanical stimulation; fluid shear stress has a larger overturning effect on bone cells, whereas the effect of strain is greater in the region of the cell-substrate interface (Fig. 2 ). Maximum displacement due to substrate strain was computed as 19 nm at the cell-substrate interface whereas fluid shear stress caused a larger displacement of 106 nm along the apical surface, where resistance to deformation is minimal. The maximum deformation of the membrane caused by fluid shear stress occurs at receptor sites due to the more rigid underlying cytoskeleton and is 7.5-fold higher than the deformation caused by substrate strain (Fig. 2) . Although deformation is smaller in the nucleus and the cytoplasm-nucleus (cyt-nuc) region, the differences caused by both mechanical stimuli are greater in this region (Fig. 2) . This suggests that fluid shear stress transmits deformation more effectively to internal cellular regions compared with strain.

View larger version (33K): [in this window] [in a new window]   Figure 2. Schematic diagram illustrating how our computational cell modeling approach explains differences in cellular responses to fluid shear stress and strain in terms of cellular deformation.

3. Differences in cell deformation caused by fluid shear stress and strain are likely related to bone cell NO and PGE₂ signaling molecule release and to bone matrix production
Qualitative and quantitative differences in cellular deformation predicted by the computational model as a result of fluid shear stress and strain treatments allow us to suggest a physical basis for differences in cellular responses to these two kinds of mechanical stimulus. For example, we (see full text) and others (using similar magnitudes of fluid shear stress and strain) report increased NO and PGE₂ signaling molecule release due to fluid shear stress treatment at shear stress values of 0.6 Pa whereas a strain of 1000 µ had no effect (Fig. 2 and full text). We used NO and PGE₂ as parameters of bone cell mechano-sensitivity because inhibition of either pathway prevents mechanically induced osteogenic response in vivo. By correlating predicted cellular deformations to the corresponding experimentally determined responses (Fig. 2) , our results suggest that higher deformation of all cellular components (i.e., cytoplasm, cytoskeletal, nucleus, and membrane) occurring in fluid shear stress leads to increased NO and PGE₂ release, most likely through enhanced stimulation of the signaling pathways involved. It has been found that 1) flow-induced PGE₂ release by bone cells is dependent on the actin cytoskeleton and 2) fluid shear-induced increases in cyclooxygenase-2 (COX-2) expression involve reorganization of the actin cytoskeleton (COX-2 is a key enzyme for PGE₂ production). The reason 0.6 Pa fluid shear stress but not 1000 µ induces increased bone cell PGE₂ release may therefore be related to higher displacement of the cytoskeleton caused by the fluid shear stress.

The higher NO responses in fluid shear stress stimulation could be due to higher membrane stressing. It has been suggested that mechanically induced formation of NO results from activation of endothelial cell nitric oxide synthase (ecNOS) in bone cells. ecNOS is an enzyme bound to the plasma membrane that may be rendered susceptible to activation by increased stressing of the cell membrane.

Finally, we and others have found that substrate strain of magnitude 1000 µ (and not fluid shear stress) stimulates collagen type I production only, with no effect on NO or PGE₂ release (see full text). We can also propose a mechanism for this because our model indicates that activity related to matrix production may be stimulated by the higher stressing of the cell-substrate regions of the cell that occurs in strain only.

We maintain that when subjecting cells to 1000 µ substrate strain, it is quite likely the cells must deform with the strained substrate to which they adhere because the frequency of applied strains (1 Hz) exceeds the rate at which new adhesion bonds can be formed. That fluid shear stress deformation also has a biological basis is therefore supported by our prediction that 0.6 Pa fluid shear stress causes even greater cellular deformation than 1000 µ substrate strain.

4. If, as the model suggests, release of NO and PGE₂ is deformation dependent, then increasing the magnitude of strain to cause equivalent cellular deformation to that caused by 0.6 Pa fluid shear stress would result in equivalent cellular responses; this hypothesis has been confirmed in several experimental studies
As the material properties assigned to cell model components are linear elastic and since geometric nonlinearities can be neglected (the displacements computed are relatively small), we can infer the deformations that would occur at various magnitudes of fluid shear stress or strain used in other published studies. We found that increasing the magnitude of strain to 5531 µ yielded maximum membrane displacement equivalent to that caused by fluid shear stress (0.6 Pa); strain values required to induce equal stress in the nucleus were even higher (8200 µ), since deformation is not distributed uniformly throughout the cell model. However, if signaling molecule production is related to the amount of cellular deformation occurring, it is possible that higher magnitudes of strain could elicit equivalent NO or PGE₂ responses to those caused by 0.6 Pa fluid shear stress (as described above). In support of this, significant NO release by bone cells has been reported at 3400 and 3800 µ, and significant increases in PGE₂ release by primary human osteoblasts at 4000 µ, further strengthening our contention that mechanically induced NO and PGE₂ release are deformation dependent.

That our (and others’) bone cell cultures distinguish between fluid flow and strain stimuli with responses associated with cells of osteoblastic (e.g., collagen production) or osteocytic (e.g., NO and PGE₂ signaling) phenotype may be related to the fact that the stimuli applied in vitro correspond to the hypothesized in vivo mechanical environment of either osteoblasts (<2000 µ strain and low fluid shear stress) or osteocytes (fluid shear stress from 0.8 to 3 Pa, and up to <27,000 µ around lacunae).

CONCLUSIONS AND SIGNIFICANCE

Our approach to modeling an adherent cell is a significant advance in the development of computational models that can yield useful insights into the effects of mechanical stimuli on cells. We suggest our results have several implications. The differences in cellular deformation caused by both mechanical stimuli are important for interpretation of cellular responses to mechanical stimuli in vitro, regardless of cell phenotype, and in determining magnitudes of stimuli such that cellular responses could be directly comparable. While we can conclude that deformations due to 0.6 Pa fluid shear stress and 1000 µ substrate strain are not equivalent, relating experimentally determined cell responses to fluid shear stress and substrate strain treatment to the corresponding predicted deformation patterns suggests a physical basis for bone cell responses to fluid flow and strain stimuli in several studies. Our results highlight the importance of deformation on a cellular level and provide a qualitative and quantitative basis for independent roles for fluid flow and strain in bone physiology.

FOOTNOTES

To read the full text of this article, go to http://www.fasebj.org/cgi/doi/10.1096/fj.04-2210fje;

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