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Model-based traction force microscopy reveals differential tension in cellular actin bundles.

Soiné JR, Brand CA, Stricker J, Oakes PW, Gardel ML, Schwarz US - PLoS Comput. Biol. (2015)

Bottom Line: Adherent cells use forces at the cell-substrate interface to sense and respond to the physical properties of their environment.We introduce a new type of traction force microscopy that in contrast to traditional methods uses additional image data for cytoskeleton and adhesion structures and a biophysical model to improve the robustness of the inverse procedure and abolishes the need for regularization.We use this method to demonstrate that ventral stress fibers of U2OS-cells are typically under higher mechanical tension than dorsal stress fibers or transverse arcs.

View Article: PubMed Central - PubMed

Affiliation: Institute for Theoretical Physics and BioQuant, Heidelberg University, Heidelberg, Germany.

ABSTRACT
Adherent cells use forces at the cell-substrate interface to sense and respond to the physical properties of their environment. These cell forces can be measured with traction force microscopy which inverts the equations of elasticity theory to calculate them from the deformations of soft polymer substrates. We introduce a new type of traction force microscopy that in contrast to traditional methods uses additional image data for cytoskeleton and adhesion structures and a biophysical model to improve the robustness of the inverse procedure and abolishes the need for regularization. We use this method to demonstrate that ventral stress fibers of U2OS-cells are typically under higher mechanical tension than dorsal stress fibers or transverse arcs.

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Robustness of MBTFM and comparison with FTTC.(A) Realistic traction patterns are generated by calculating the direct problem for a known test tension distribution. Gaussian noise is added to the resulting displacement vectors. The noise level is defined with respect to the largest displacement in the whole field. With increasing noise level the L2 error estimate increases continuously as expected. (B) Total forces and network forces reconstructed with MBTFM are not affected by the noise level in the simulations, in marked contrast to standard reconstruction methods like FTTC. (C) The precision of tension predictions for individual stress fibers decreases for higher noise level (MRD: mean relative deviation). By evaluating experimental displacement data for noise in traction-free regions, we find a typical experimental noise level between 5–10%. In this region (gray), the MRD does not exceed 10%, which we thus identify with the accuracy of our tension reconstruction for stress fibers. (D) Direct comparison of the total force obtained with FTTC and MBTFM reveals a linear relationship (red). The slope of the linear fit line here depends on the regularization parameter alone. By fitting the regularization parameter to a one-to-one relationship (blue), FTTC can be calibrated based on the biophysical model input instead of traditional noise optimization (red). (E) Comparison of the standard TFM method FTTC and MBTFM. Based on the additional experimental data, the model can achieve a more detailed traction map. Further it allows us to directly map tensions in single stress fibers (black lines in inset) to experimental displacements.
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pcbi.1004076.g004: Robustness of MBTFM and comparison with FTTC.(A) Realistic traction patterns are generated by calculating the direct problem for a known test tension distribution. Gaussian noise is added to the resulting displacement vectors. The noise level is defined with respect to the largest displacement in the whole field. With increasing noise level the L2 error estimate increases continuously as expected. (B) Total forces and network forces reconstructed with MBTFM are not affected by the noise level in the simulations, in marked contrast to standard reconstruction methods like FTTC. (C) The precision of tension predictions for individual stress fibers decreases for higher noise level (MRD: mean relative deviation). By evaluating experimental displacement data for noise in traction-free regions, we find a typical experimental noise level between 5–10%. In this region (gray), the MRD does not exceed 10%, which we thus identify with the accuracy of our tension reconstruction for stress fibers. (D) Direct comparison of the total force obtained with FTTC and MBTFM reveals a linear relationship (red). The slope of the linear fit line here depends on the regularization parameter alone. By fitting the regularization parameter to a one-to-one relationship (blue), FTTC can be calibrated based on the biophysical model input instead of traditional noise optimization (red). (E) Comparison of the standard TFM method FTTC and MBTFM. Based on the additional experimental data, the model can achieve a more detailed traction map. Further it allows us to directly map tensions in single stress fibers (black lines in inset) to experimental displacements.

Mentions: Because MBTFM does not include a regularization scheme, we investigated how it performs in the presence of noise. The spatial resolution of TFM is mainly constrained by experimental uncertainties in measuring bead displacements, which originate from limited optical resolution of the microscopy setup, uncertainties in the image processing procedures and heterogeneities in the substrate material with its embedded marker beads. The uncertainty in a given data set can be determined by analyzing the distribution of absolute displacement magnitudes at cell-free regions of the substrate image. Such evaluations led to Gaussian-shaped distributions in our data set, as reported earlier [33]. We therefore summarize the possible uncertainties under the term displacement noise, for which we find a typical value of 5–10%. In order to test the performance of MBTFM in an experimental context, we first simulated its ability to reconstruct a given traction pattern in the presence of such displacement noise (Fig 4A-C). The deviation between the theoretical prediction and experimental measurement is represented by the relative L2-norm that ranges between 0 for perfect agreement and 1 for a vanishing force field. We sampled 10 different displacement fields for each noise level and averaged over the reconstruction results. While the L2-norm naturally approaches 1 for higher noise levels (Fig 4A), we find that MBTFM still performs very well in the experimentally relevant range of displacement noise from 5–10% (Fig 4B+C). Interestingly, the reconstructed total force remains almost constant over the entire range of simulated noise levels, which confirms the robustness of the method (Fig 4B). In a second evaluation of simulated data, we checked the influence of erroneous segmentation (S3 Fig). We find that segmenting too few SFs leads to a force shifting to neighboring fibers. Because cable networks do not propagate compression, this remains a local effect [45], which is also verified in our test reconstructions. On the other hand, segmenting too many stress fibers barely affects the reconstruction result as these additional degrees of freedom do not have to be used by the optimal solution. We conclude that it is important to avoid undersegmentation rather than oversegmentation of SFs and that MBTFM performs very well in the presence of displacement noise despite the fact that it does not use any regularization scheme. This shows that our biophysical model is a reasonable assumption that leads to well-defined solutions.


Model-based traction force microscopy reveals differential tension in cellular actin bundles.

Soiné JR, Brand CA, Stricker J, Oakes PW, Gardel ML, Schwarz US - PLoS Comput. Biol. (2015)

Robustness of MBTFM and comparison with FTTC.(A) Realistic traction patterns are generated by calculating the direct problem for a known test tension distribution. Gaussian noise is added to the resulting displacement vectors. The noise level is defined with respect to the largest displacement in the whole field. With increasing noise level the L2 error estimate increases continuously as expected. (B) Total forces and network forces reconstructed with MBTFM are not affected by the noise level in the simulations, in marked contrast to standard reconstruction methods like FTTC. (C) The precision of tension predictions for individual stress fibers decreases for higher noise level (MRD: mean relative deviation). By evaluating experimental displacement data for noise in traction-free regions, we find a typical experimental noise level between 5–10%. In this region (gray), the MRD does not exceed 10%, which we thus identify with the accuracy of our tension reconstruction for stress fibers. (D) Direct comparison of the total force obtained with FTTC and MBTFM reveals a linear relationship (red). The slope of the linear fit line here depends on the regularization parameter alone. By fitting the regularization parameter to a one-to-one relationship (blue), FTTC can be calibrated based on the biophysical model input instead of traditional noise optimization (red). (E) Comparison of the standard TFM method FTTC and MBTFM. Based on the additional experimental data, the model can achieve a more detailed traction map. Further it allows us to directly map tensions in single stress fibers (black lines in inset) to experimental displacements.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4352062&req=5

pcbi.1004076.g004: Robustness of MBTFM and comparison with FTTC.(A) Realistic traction patterns are generated by calculating the direct problem for a known test tension distribution. Gaussian noise is added to the resulting displacement vectors. The noise level is defined with respect to the largest displacement in the whole field. With increasing noise level the L2 error estimate increases continuously as expected. (B) Total forces and network forces reconstructed with MBTFM are not affected by the noise level in the simulations, in marked contrast to standard reconstruction methods like FTTC. (C) The precision of tension predictions for individual stress fibers decreases for higher noise level (MRD: mean relative deviation). By evaluating experimental displacement data for noise in traction-free regions, we find a typical experimental noise level between 5–10%. In this region (gray), the MRD does not exceed 10%, which we thus identify with the accuracy of our tension reconstruction for stress fibers. (D) Direct comparison of the total force obtained with FTTC and MBTFM reveals a linear relationship (red). The slope of the linear fit line here depends on the regularization parameter alone. By fitting the regularization parameter to a one-to-one relationship (blue), FTTC can be calibrated based on the biophysical model input instead of traditional noise optimization (red). (E) Comparison of the standard TFM method FTTC and MBTFM. Based on the additional experimental data, the model can achieve a more detailed traction map. Further it allows us to directly map tensions in single stress fibers (black lines in inset) to experimental displacements.
Mentions: Because MBTFM does not include a regularization scheme, we investigated how it performs in the presence of noise. The spatial resolution of TFM is mainly constrained by experimental uncertainties in measuring bead displacements, which originate from limited optical resolution of the microscopy setup, uncertainties in the image processing procedures and heterogeneities in the substrate material with its embedded marker beads. The uncertainty in a given data set can be determined by analyzing the distribution of absolute displacement magnitudes at cell-free regions of the substrate image. Such evaluations led to Gaussian-shaped distributions in our data set, as reported earlier [33]. We therefore summarize the possible uncertainties under the term displacement noise, for which we find a typical value of 5–10%. In order to test the performance of MBTFM in an experimental context, we first simulated its ability to reconstruct a given traction pattern in the presence of such displacement noise (Fig 4A-C). The deviation between the theoretical prediction and experimental measurement is represented by the relative L2-norm that ranges between 0 for perfect agreement and 1 for a vanishing force field. We sampled 10 different displacement fields for each noise level and averaged over the reconstruction results. While the L2-norm naturally approaches 1 for higher noise levels (Fig 4A), we find that MBTFM still performs very well in the experimentally relevant range of displacement noise from 5–10% (Fig 4B+C). Interestingly, the reconstructed total force remains almost constant over the entire range of simulated noise levels, which confirms the robustness of the method (Fig 4B). In a second evaluation of simulated data, we checked the influence of erroneous segmentation (S3 Fig). We find that segmenting too few SFs leads to a force shifting to neighboring fibers. Because cable networks do not propagate compression, this remains a local effect [45], which is also verified in our test reconstructions. On the other hand, segmenting too many stress fibers barely affects the reconstruction result as these additional degrees of freedom do not have to be used by the optimal solution. We conclude that it is important to avoid undersegmentation rather than oversegmentation of SFs and that MBTFM performs very well in the presence of displacement noise despite the fact that it does not use any regularization scheme. This shows that our biophysical model is a reasonable assumption that leads to well-defined solutions.

Bottom Line: Adherent cells use forces at the cell-substrate interface to sense and respond to the physical properties of their environment.We introduce a new type of traction force microscopy that in contrast to traditional methods uses additional image data for cytoskeleton and adhesion structures and a biophysical model to improve the robustness of the inverse procedure and abolishes the need for regularization.We use this method to demonstrate that ventral stress fibers of U2OS-cells are typically under higher mechanical tension than dorsal stress fibers or transverse arcs.

View Article: PubMed Central - PubMed

Affiliation: Institute for Theoretical Physics and BioQuant, Heidelberg University, Heidelberg, Germany.

ABSTRACT
Adherent cells use forces at the cell-substrate interface to sense and respond to the physical properties of their environment. These cell forces can be measured with traction force microscopy which inverts the equations of elasticity theory to calculate them from the deformations of soft polymer substrates. We introduce a new type of traction force microscopy that in contrast to traditional methods uses additional image data for cytoskeleton and adhesion structures and a biophysical model to improve the robustness of the inverse procedure and abolishes the need for regularization. We use this method to demonstrate that ventral stress fibers of U2OS-cells are typically under higher mechanical tension than dorsal stress fibers or transverse arcs.

Show MeSH
Related in: MedlinePlus