Limits...
Live Cells Exert 3-Dimensional Traction Forces on Their Substrata.

Hur SS, Zhao Y, Li YS, Botvinick E, Chien S - Cell Mol Bioeng (2009)

Bottom Line: The method was evaluated regarding accuracy and precision of displacement measurements, effects of FE mesh size, displacement noises, and simple bootstrapping.This technique can be applied to study live cells to assess their biomechanical dynamics in conjunction with biochemical and functional activities, for investigating cellular functions in health and disease.ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s12195-009-0082-6) contains supplementary material, which is available to authorized users.

View Article: PubMed Central - PubMed

ABSTRACT
The traction forces exerted by an adherent cell on a substrate have been studied only in the two-dimensions (2D) tangential to substrate surface (Txy). We developed a novel technique to measure the three-dimensional (3D) traction forces exerted by live bovine aortic endothelial cells (BAECs) on polyacrylamide deformable substrate. On 3D images acquired by confocal microscopy, displacements were determined with image-processing programs, and traction forces in tangential (XY) and normal (Z) directions were computed by finite element method (FEM). BAECs generated traction force in normal direction (Tz) with an order of magnitude comparable to Txy. Tz is upward at the cell edge and downward under the nucleus, changing continuously with a sign reversal between cell edge and nucleus edge. The method was evaluated regarding accuracy and precision of displacement measurements, effects of FE mesh size, displacement noises, and simple bootstrapping. These results provide new insights into cell-matrix interactions in terms of spatial and temporal variations in traction forces in 3D. This technique can be applied to study live cells to assess their biomechanical dynamics in conjunction with biochemical and functional activities, for investigating cellular functions in health and disease. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s12195-009-0082-6) contains supplementary material, which is available to authorized users.

No MeSH data available.


Simulation of traction force recovery and introduction of displacement noises. (a) Four balanced forces for the generation of displacement fields. (b) Calculated displacement field from the traction fields. (c) Contour plot of traction difference (//T(recovered) − T(input)//). (d) Effects of the introduced Gaussian noises of 0, 0.01, 0.05, 0.1, and 0.2 μm on the RMS of traction force error (ΔT = //T(with noise) − T(without noise)//). The R2 value was 0.999. U = magnitude of displacement, and T = magnitude of traction
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC2749171&req=5

Fig4: Simulation of traction force recovery and introduction of displacement noises. (a) Four balanced forces for the generation of displacement fields. (b) Calculated displacement field from the traction fields. (c) Contour plot of traction difference (//T(recovered) − T(input)//). (d) Effects of the introduced Gaussian noises of 0, 0.01, 0.05, 0.1, and 0.2 μm on the RMS of traction force error (ΔT = //T(with noise) − T(without noise)//). The R2 value was 0.999. U = magnitude of displacement, and T = magnitude of traction

Mentions: To assess how accurately the traction field can be recovered in our FEM method, we have simulated the traction force recovery using the following steps. First, we computed a displacement field from the known traction field prepared from four balanced distributed loads of 2.0 nN on the area of 4 μm2 each (Fig. 4a). Second, this displacement field was used as an input to calculate the traction field (Fig. 4b). Then, the traction fields at step one and step two were compared (Fig. 4c). U is the magnitude of displacement, and T is the magnitude of traction.Figure 4


Live Cells Exert 3-Dimensional Traction Forces on Their Substrata.

Hur SS, Zhao Y, Li YS, Botvinick E, Chien S - Cell Mol Bioeng (2009)

Simulation of traction force recovery and introduction of displacement noises. (a) Four balanced forces for the generation of displacement fields. (b) Calculated displacement field from the traction fields. (c) Contour plot of traction difference (//T(recovered) − T(input)//). (d) Effects of the introduced Gaussian noises of 0, 0.01, 0.05, 0.1, and 0.2 μm on the RMS of traction force error (ΔT = //T(with noise) − T(without noise)//). The R2 value was 0.999. U = magnitude of displacement, and T = magnitude of traction
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2749171&req=5

Fig4: Simulation of traction force recovery and introduction of displacement noises. (a) Four balanced forces for the generation of displacement fields. (b) Calculated displacement field from the traction fields. (c) Contour plot of traction difference (//T(recovered) − T(input)//). (d) Effects of the introduced Gaussian noises of 0, 0.01, 0.05, 0.1, and 0.2 μm on the RMS of traction force error (ΔT = //T(with noise) − T(without noise)//). The R2 value was 0.999. U = magnitude of displacement, and T = magnitude of traction
Mentions: To assess how accurately the traction field can be recovered in our FEM method, we have simulated the traction force recovery using the following steps. First, we computed a displacement field from the known traction field prepared from four balanced distributed loads of 2.0 nN on the area of 4 μm2 each (Fig. 4a). Second, this displacement field was used as an input to calculate the traction field (Fig. 4b). Then, the traction fields at step one and step two were compared (Fig. 4c). U is the magnitude of displacement, and T is the magnitude of traction.Figure 4

Bottom Line: The method was evaluated regarding accuracy and precision of displacement measurements, effects of FE mesh size, displacement noises, and simple bootstrapping.This technique can be applied to study live cells to assess their biomechanical dynamics in conjunction with biochemical and functional activities, for investigating cellular functions in health and disease.ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s12195-009-0082-6) contains supplementary material, which is available to authorized users.

View Article: PubMed Central - PubMed

ABSTRACT
The traction forces exerted by an adherent cell on a substrate have been studied only in the two-dimensions (2D) tangential to substrate surface (Txy). We developed a novel technique to measure the three-dimensional (3D) traction forces exerted by live bovine aortic endothelial cells (BAECs) on polyacrylamide deformable substrate. On 3D images acquired by confocal microscopy, displacements were determined with image-processing programs, and traction forces in tangential (XY) and normal (Z) directions were computed by finite element method (FEM). BAECs generated traction force in normal direction (Tz) with an order of magnitude comparable to Txy. Tz is upward at the cell edge and downward under the nucleus, changing continuously with a sign reversal between cell edge and nucleus edge. The method was evaluated regarding accuracy and precision of displacement measurements, effects of FE mesh size, displacement noises, and simple bootstrapping. These results provide new insights into cell-matrix interactions in terms of spatial and temporal variations in traction forces in 3D. This technique can be applied to study live cells to assess their biomechanical dynamics in conjunction with biochemical and functional activities, for investigating cellular functions in health and disease. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s12195-009-0082-6) contains supplementary material, which is available to authorized users.

No MeSH data available.