Limits...
Monolayer stress microscopy: limitations, artifacts, and accuracy of recovered intercellular stresses.

Tambe DT, Croutelle U, Trepat X, Park CY, Kim JH, Millet E, Butler JP, Fredberg JJ - PLoS ONE (2013)

Bottom Line: To assess the validity of these assumptions and to quantify associated errors, here we report new analytical, numerical, and experimental investigations.For several commonly used experimental monolayer systems, the simplifying assumptions used previously lead to errors that are shown to be quite small.Out-of-plane components of displacement and traction fields can be safely neglected, and characteristic features of intercellular stresses that underlie plithotaxis remain largely unaffected.

View Article: PubMed Central - PubMed

Affiliation: Department of Environmental Health, Harvard School of Public Health, Boston, Massachusetts, USA. dhananjay@alumni.brown.edu

ABSTRACT
In wound healing, tissue growth, and certain cancers, the epithelial or the endothelial monolayer sheet expands. Within the expanding monolayer sheet, migration of the individual cell is strongly guided by physical forces imposed by adjacent cells. This process is called plithotaxis and was discovered using Monolayer Stress Microscopy (MSM). MSM rests upon certain simplifying assumptions, however, concerning boundary conditions, cell material properties and system dimensionality. To assess the validity of these assumptions and to quantify associated errors, here we report new analytical, numerical, and experimental investigations. For several commonly used experimental monolayer systems, the simplifying assumptions used previously lead to errors that are shown to be quite small. Out-of-plane components of displacement and traction fields can be safely neglected, and characteristic features of intercellular stresses that underlie plithotaxis remain largely unaffected. Taken together, these findings validate Monolayer Stress Microscopy within broad but well-defined limits of applicability.

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Propagation of boundary artifacts away from the optical edge.(a) A thin sheet subjected to sinusoidal perturbations in normal displacements  at one edge, and  at two other edges. (b) Map of average normal stress, and (c) map of maximum shear stress when . (d–e) The stress maps when . (f) Decay of dominant Fourier mode in the stresses induced by the boundary conditions shown in the inset. Blue curves correspond to , and red curves correspond to . The curves marked with circle represent the induced average normal stress, and the curves marked with cross represent the induced maximum shear stress. (g–i) Decay curves of the stresses induced by boundary conditions shown in the inset. At all the boundaries along appropriate axis the natural boundary conditions, i.e. boundary stress = 0 are not mentioned but they are implied. The stresses in (b–f) are normalized with the amplitude of induced normal stress  at the perturbed edge, the stresses in (g,i) are normalized with amplitude of imposed shear stress , and the stresses in (h) are normalized with the amplitude of induced normal stress  at the perturbed edge.
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pone-0055172-g006: Propagation of boundary artifacts away from the optical edge.(a) A thin sheet subjected to sinusoidal perturbations in normal displacements at one edge, and at two other edges. (b) Map of average normal stress, and (c) map of maximum shear stress when . (d–e) The stress maps when . (f) Decay of dominant Fourier mode in the stresses induced by the boundary conditions shown in the inset. Blue curves correspond to , and red curves correspond to . The curves marked with circle represent the induced average normal stress, and the curves marked with cross represent the induced maximum shear stress. (g–i) Decay curves of the stresses induced by boundary conditions shown in the inset. At all the boundaries along appropriate axis the natural boundary conditions, i.e. boundary stress = 0 are not mentioned but they are implied. The stresses in (b–f) are normalized with the amplitude of induced normal stress at the perturbed edge, the stresses in (g,i) are normalized with amplitude of imposed shear stress , and the stresses in (h) are normalized with the amplitude of induced normal stress at the perturbed edge.

Mentions: First, we considered an optical edge adjacent to the free edge, and imposed boundary perturbation comprising sinusoidal normal displacements , where (Fig. 6a). These normal displacements induced average normal stress which decayed monotonically with distance from the boundary (Fig. 6b, and Fig. 6f, blue lines marked with circle); when the wavelength of the perturbation was smaller the decay was faster (Fig. 6d, and Fig. 6f, red lines marked with circle). Indeed, the decay length in each case was comparable to the wavelength of perturbation. While the decay of average normal stress was monotonic, the decay of maximum shear stress was not monotonic (Figs. 6c,e; and Fig. 6f lines marked with cross). Finally, when the perturbed edge was the optical edge away from the free edge, the stresses were similar (Fig. 6h).


Monolayer stress microscopy: limitations, artifacts, and accuracy of recovered intercellular stresses.

Tambe DT, Croutelle U, Trepat X, Park CY, Kim JH, Millet E, Butler JP, Fredberg JJ - PLoS ONE (2013)

Propagation of boundary artifacts away from the optical edge.(a) A thin sheet subjected to sinusoidal perturbations in normal displacements  at one edge, and  at two other edges. (b) Map of average normal stress, and (c) map of maximum shear stress when . (d–e) The stress maps when . (f) Decay of dominant Fourier mode in the stresses induced by the boundary conditions shown in the inset. Blue curves correspond to , and red curves correspond to . The curves marked with circle represent the induced average normal stress, and the curves marked with cross represent the induced maximum shear stress. (g–i) Decay curves of the stresses induced by boundary conditions shown in the inset. At all the boundaries along appropriate axis the natural boundary conditions, i.e. boundary stress = 0 are not mentioned but they are implied. The stresses in (b–f) are normalized with the amplitude of induced normal stress  at the perturbed edge, the stresses in (g,i) are normalized with amplitude of imposed shear stress , and the stresses in (h) are normalized with the amplitude of induced normal stress  at the perturbed edge.
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Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3585344&req=5

pone-0055172-g006: Propagation of boundary artifacts away from the optical edge.(a) A thin sheet subjected to sinusoidal perturbations in normal displacements at one edge, and at two other edges. (b) Map of average normal stress, and (c) map of maximum shear stress when . (d–e) The stress maps when . (f) Decay of dominant Fourier mode in the stresses induced by the boundary conditions shown in the inset. Blue curves correspond to , and red curves correspond to . The curves marked with circle represent the induced average normal stress, and the curves marked with cross represent the induced maximum shear stress. (g–i) Decay curves of the stresses induced by boundary conditions shown in the inset. At all the boundaries along appropriate axis the natural boundary conditions, i.e. boundary stress = 0 are not mentioned but they are implied. The stresses in (b–f) are normalized with the amplitude of induced normal stress at the perturbed edge, the stresses in (g,i) are normalized with amplitude of imposed shear stress , and the stresses in (h) are normalized with the amplitude of induced normal stress at the perturbed edge.
Mentions: First, we considered an optical edge adjacent to the free edge, and imposed boundary perturbation comprising sinusoidal normal displacements , where (Fig. 6a). These normal displacements induced average normal stress which decayed monotonically with distance from the boundary (Fig. 6b, and Fig. 6f, blue lines marked with circle); when the wavelength of the perturbation was smaller the decay was faster (Fig. 6d, and Fig. 6f, red lines marked with circle). Indeed, the decay length in each case was comparable to the wavelength of perturbation. While the decay of average normal stress was monotonic, the decay of maximum shear stress was not monotonic (Figs. 6c,e; and Fig. 6f lines marked with cross). Finally, when the perturbed edge was the optical edge away from the free edge, the stresses were similar (Fig. 6h).

Bottom Line: To assess the validity of these assumptions and to quantify associated errors, here we report new analytical, numerical, and experimental investigations.For several commonly used experimental monolayer systems, the simplifying assumptions used previously lead to errors that are shown to be quite small.Out-of-plane components of displacement and traction fields can be safely neglected, and characteristic features of intercellular stresses that underlie plithotaxis remain largely unaffected.

View Article: PubMed Central - PubMed

Affiliation: Department of Environmental Health, Harvard School of Public Health, Boston, Massachusetts, USA. dhananjay@alumni.brown.edu

ABSTRACT
In wound healing, tissue growth, and certain cancers, the epithelial or the endothelial monolayer sheet expands. Within the expanding monolayer sheet, migration of the individual cell is strongly guided by physical forces imposed by adjacent cells. This process is called plithotaxis and was discovered using Monolayer Stress Microscopy (MSM). MSM rests upon certain simplifying assumptions, however, concerning boundary conditions, cell material properties and system dimensionality. To assess the validity of these assumptions and to quantify associated errors, here we report new analytical, numerical, and experimental investigations. For several commonly used experimental monolayer systems, the simplifying assumptions used previously lead to errors that are shown to be quite small. Out-of-plane components of displacement and traction fields can be safely neglected, and characteristic features of intercellular stresses that underlie plithotaxis remain largely unaffected. Taken together, these findings validate Monolayer Stress Microscopy within broad but well-defined limits of applicability.

Show MeSH
Related in: MedlinePlus