READ ME FOR TRACTION FORCE MICROSCOPY AND MONOLAYER STRESS MICROSCOPY

Repository for traction force microscopy and monolayer stress microscopy.

Written by Notbohm Research Group, University of Wisconsin-Madison. https://notbohm.ep.wisc.edu

This document explains the Notbohm Research Group's procedures for analyzing cell tractions and monolayer stresses.

There exist numerous other packages to compute tractions on Github and other online sources. Advantages of this software are that the scripts are minimal and relatively modular--they can be combined with other analyses or easily improved. As a result of the minimalist format, users will benefit from having some experience with Matlab or another coding language.

Relevant publications to read:

Dembo, M. and Wang, Y. L. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys J, 76(4):2307–2316, 1999.
Butler, J. P., Tolic-Norrelykke, I. M., Fabry, B., and Fredberg, J. J. Traction fields, moments, and strain energy that cells exert on their surroundings. Am J Physiol Cell Ph, 282(3):C595–C605, 2002.
del Alamo, J. C., Meili, R., Alonso-Latorre, B., Rodriguez-Rodriguez, J., Aliseda, A., Firtel, R. A., and Lasheras, J. C. Spatio-temporal analysis of eukaryotic cell motility by improved force cytometry. P Natl Acad Sci USA, 104(33):13343–13348, 2007.
Trepat, X., Wasserman, M. R., Angelini, T. E., Millet, E., Weitz, D. A., Butler, J. P., and Fredberg, J. J. Physical forces during collective cell migration. Nat Phys, 5(6):426–430, 2009.
Tambe, D. T., Hardin, C. C., Angelini, T. E., Rajendran, K., Park, C. Y., Serra-Picamal, X., Zhou, E. H., Zaman, M. H., Butler, J. P., Weitz, D. A., et al. Collective cell guidance by cooperative intercellular forces. Nat Mater, 10(6):469–475, 2011.
Tambe, D. T., Croutelle, U., Trepat, X., Park, C. Y., Kim, J. H., Millet, E., Butler, J. P., and Fredberg, J. J. Monolayer stress microscopy: limitations, artifacts, and accuracy of recovered intercellular stresses. Plos One, 8(2):e55172, 2013.
Huang, Y., Schell, C., Huber, T.B. et al. Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells. Sci Rep 9:539, 2019.
Huang, Y., Gompper, G., Sabass, B. A Bayesian traction force microscopy method with automated denoising in a user-friendly software package. Comput Phys Commun, 2020.

CITATION

If used, cite the following:

Huang, Y., Gompper, G., Sabass, B. A Bayesian traction force microscopy method with automated denoising in a user-friendly software package. Comput Phys Commun, 2020. doi:10.1016/j.cpc.2020.107313 (for reg_fourier_TFM.m)

SOFTWARE REQUIREMENTS

All scripts are written in Matlab. They have been tested on Matlab 2019b on a Windows 10 machine, but earlier versions of Matlab and other operating systems are likely to work.

It is recommended to have several GB of RAM available, as some steps, especially digital image correlation, use a lot of RAM. We use machines having at least 16 GB of RAM, though 8 GB of RAM is typically sufficient.

SUMMARY OF DATA REQUIRED

Images of two types:

Images of cells. Phase contrast. These images are required for the script find_boundary.m. They are used to make a domain, an 8-bit image giving 0s at locations without cells and values of 255 at locations with cells.
Images of fluorescent particles in compliant substrate beneath cells. A reference image is needed in the undeformed, stress-free state. The reference image is typically acquired at the end of the experiment: after imaging the cells for a period of time, the cells can be removed from the substrate using trypsin or some other means, allowing for a stress- free image to be acquired.

The two sets of images are used to compute displacements using digital image correlation (also referred to as particle image velocimetry).

A file called ExperimentalSettings.txt. This file contains the following lines:

X --- pixel size (m)

X --- substrate Young's modulus (Pa)

X --- substrate Poisson's ratio (-)

X --- substrate thickness (um)

X --- monolayer Poisson's ratio (matters only slightly; Young's modulus is irrelevant)

X --- monolayer thickness (m)

1 or 2 --- 1-strip; 2-hole/island

An example is included, titled ExperimentalSettings_example.txt. Copy this file into the directory containing your data, rename it to ExperimentalSettings.txt and update the parameters in the file. This will allow you to analyze data with different parameters (pixel size, substrate stiffness, etc.).

SUMMARY OF SCRIPTS TO RUN

Compute cell-induced substrate displacements using Digital Image Correlation on the
images of fluorescent particles in the substrate. We often use FIDIC, written by members of Christian Franck's research group. Citation: Bar-Kochba E, Toyjanova J, Andrews E, Kim K-S, Franck C. A Fast Iterative Digital Volume Correlation Algorithm for Large Deformations. Experimental Mechanics 55:261–274, 2015. Available from https://github.com/FranckLab/ or https://github.com/jknotbohm/FIDIC.
Identify regions in images containing cells using find_boundary.m (Calls function smooth2a.m)
Compute cell-substrate tracitions using run_reg_fourier_TFM.m. (Calls functions Kabsch.m, inpaint_nans.m, smooth2a.m, reg_fourier_TFM.m)
Compute monolayer stresses using run_stress_calculation.m (Calls functions force_moment_equilibrium.m, compute_stress.m)

Each script has detailed comments.

Sources

The following scripts are from the Matlab file exchange:

smooth2a.m: https://www.mathworks.com/matlabcentral/fileexchange/23287-smooth2a
Kabsch.m: https://www.mathworks.com/matlabcentral/fileexchange/25746-kabsch-algorithm. Note that the outputs of this script have been modified slightly by Jacob Notbohm.
inpaint_nans.m: https://www.mathworks.com/matlabcentral/fileexchange/4551-inpaint_nans

The following script is from the Easy-to-use_TFM_package written by the Sabass lab:

reg_fourier_TFM.m: https://github.com/CellMicroMechanics/Easy-to-use_TFM_package

SUMMARY OF OUTPUTS

Digital Image Correlation outputs displacement data and corresponding grid points. In addition to these, the subset size (w0) and spacing (d0) are required. These data are stored in a Matlab mat file that is used in other scripts.
find_boundary.m outputs an image called domain.tif that is used in other scripts. If you only want to compute cell-substrate tractions and not monolayer stresses, you may skip running this file.
run_reg_fourier_TFM.m outputs a mat file containing displacement data that has been modified slightly (eg, by cropping and correcting for drift) and computed tractions
run_stress_calculation.m outputs a mat file containing stresses in the x-y coordinate system (Sxx, Syy, Sxy) and principal stresses and orientation (S1, S2, pangle).

POSTPROCESSING

Sample scripts are included in the directory Cell-Traction-Stress-Velocity-Plots ( https://github.com/jknotbohm/Cell-Traction-Stress-Velocity-Plots ):

plot_displ_tractions.m generates color plot of substrate displacements and and cell-substrate tractions
plot_stress.m generates color plots of monolayer stresses

Further analysis beyond color plots will likely be required. Such analysis has to be custom written by the user.

FORMATTING REQUIREMENTS

Digital Image Correlation

Different versions of Digital Image Correlation software have different image formatting requirements. The DIC software we use reads multipage tif files, where the different pages correspond to different time points.

Traction Calculation

Computing tractions with run_reg_fourier_TFM.m requires the following:

A mat file containing the following variables: w0: scalar, subset/window size. Units: pix. d0: scalar, subset spacing. Units: pix. x, y: 2D arrays containing the gridpoints on which the DIC was computed. This can be made using Matlab's meshgrid command. Units: pix. u, v: 2D or 3D arrays of size (M, N, P) where M and N are the number of rows and columns, which must match the size of x and y. Variable P corresponds to different time points. If there is only one time point, then the array is 2D (i.e., if P=1). Our version of digital image correlation (run_FIDIC.m) outputs a mat file having these variables.
(Optional) A domain file. The file must be a multipage tif with the number of pages equal to the number of time points. As stated above each image is 8-bit with 0s at locations without cells and values of 255 at locations with cells.

Stress Calculation

Computing stresses with run_stress_calculation.m requires the following:

A mat file containing the following variables: x, y: 2D arrays of size (M, N) containing the gridpoints on which the DIC was computed. This can be made using Matlab's meshgrid command. Units: pix. tx, ty: Tractions in horizontal and vertical directions. 2D or 3D arrays of size (M, N, P) where P is the number of time points. d0: Scalar grid point (subset) spacing used in image correlation.
The domain file described above. This file is required for computing stresses.

EXAMPLE WORKFLOWS

Example: Computing stresses for a cell island

A workflow to compute stress may be as follows:

Make ExperimentalSettings.txt file.
Organize your data. Save your images in tif format. Use a multipage tif file for a time lapse data set. Use a separate single-page tif file for the reference image, acquired after removing the cells from the substrate. Put the images and ExperimentalSettings.txt into a single directory.
Run DIC using a cumulative comparison that compares all images to the reference one. Store outputs in a mat file containing w0, d0, x, y, u, v as described above.
Run find_boundary.m. (Required for computing stresses.)
Compute tractions with run_reg_fourier_TFM.m. Output of traction computation is formatted as follows: w0: scalar, subset/window size. Units: pix. d0: scalar, subset spacing. Units: pix. x, y: 2D arrays containing the gridpoints on which the DIC was computed. This can be made using Matlab's meshgrid command. Units: pix. u, v: Displacements computed by image correlation in horizontal and vertical directions. These are 2D or 3D arrays of size (M, N, P) where M and N are the number of rows and columns, which must match the size of x and y. Variable P corresponds to different time points. If there is only one time point, then the array is 2D (i.e., if P=1). tx, ty: Tractions in horizontal and vertical directions. 2D or 3D arrays of size (M, N, P) that matches the size of u and v.
Run plot_displ_tractions.m to bring up a color map of the computed displacements and tractions. Verify that the displacements and tractions are reasonable before going to the next step.
Run run_stress_calculation.m.
Run plot_stress.m to bring up color maps of the computed monolayer stresses.

Example: Computing cell velocities

To compute cell velocities, you can apply DIC to phase contrast images of the cells as follows.

Organize your data. Save all images as a multipage tif. There is no separate reference image.
Run the DIC using an incremental comparison that compares each image to the one preceeding it in the multipage tif file.
Divide displacement by the time between imaging to get the velocity.

Important note: Digital image correlation only works to compute cell velocities for positions in the image that are confluent, i.e., fully covered by cells. If you have images with individual cells, you will have to use a different method, such as fluorescently labeling cell nuclei and tracking them.

TIPS

Organize different data sets by putting them in different directories. Do not change the file names of the outputs of the different scripts (DIC, find_boundary.m, run_traction_finite.m, run_stress_calculation.m). If you keep your file names consistent, you will be able to run batch analyses.
Most of the scripts in this repository have additional commands that were used in development or are useful for debugging. These commands are commented out and typically have notes indicating what they do. If you are having trouble or get unexpected results, read through the script and identify the different commended lines to see if they help you to address your problem.

jknotbohm / Cell-Traction-Stress