Cellular force generation and force transmission are of fundamental importance for numerous biological processes and can be studied with the methods of Traction Force Microscopy (TFM) and Monolayer Stress Microscopy. Traction Force Microscopy and Monolayer Stress Microscopy solve the inverse problem of reconstructing cell-matrix tractions and inter- and intra-cellular stresses from the measured cell force-induced deformations of an adhesive substrate with known elasticity. Although several laboratories have developed software for Traction Force Microscopy and Monolayer Stress Microscopy computations, there is currently no software package available that allows non-expert users to perform a full evaluation of such experiments. Here we present pyTFM, a tool to perform Traction Force Microscopy and Monolayer Stress Microscopy on cell patches and cell layers grown in a 2-dimensional environment. pyTFM was optimized for ease-of-use; it is open-source and well documented (hosted at https://pytfm.readthedocs.io/) including usage examples and explanations of the theoretical background. pyTFM can be used as a standalone Python package or as an add-on to the image annotation tool ClickPoints. In combination with the ClickPoints environment, pyTFM allows the user to set all necessary analysis parameters, select regions of interest, examine the input data and intermediary results, and calculate a wide range of parameters describing forces, stresses, and their distribution. In this work, we also thoroughly analyze the accuracy and performance of the Traction Force Microscopy and Monolayer Stress Microscopy algorithms of pyTFM using synthetic and experimental data from epithelial cell patches.

Department of Physics Friedrich Alexander University Erlangen Nürnberg Erlangen Germany

Laboratory of Integrative Biology Institute of Molecular Genetics of the Czech Academy of Sciences Prague Czech Republic

See more in PubMed

Pelham RJ, Wang Yl. Cell locomotion and focal adhesions are regulated by substrate flexibility. Proceedings of the National Academy of Sciences. 1997;94(25):13661–13665. doi: 10.1073/pnas.94.25.13661 PubMed DOI PMC

Engler AJ, Sen S, Sweeney HL, Discher DE. Matrix Elasticity Directs Stem Cell Lineage Specification. Cell. 2006;126(4):677–689. doi: 10.1016/j.cell.2006.06.044 PubMed DOI

Steinwachs J, Metzner C, Skodzek K, Lang N, Thievessen I, Mark C, et al.. Three-dimensional force microscopy of cells in biopolymer networks. Nature Methods. 2015;13(2):171–176. doi: 10.1038/nmeth.3685 PubMed DOI

REHFELDT F, ENGLER A, ECKHARDT A, AHMED F, DISCHER D. Cell responses to the mechanochemical microenvironment Implications for regenerative medicine and drug delivery. Advanced Drug Delivery Reviews. 2007;59(13):1329–1339. doi: 10.1016/j.addr.2007.08.007 PubMed DOI PMC

Pascalis CD, Pérez-González C, Seetharaman S, Boëda B, Vianay B, Burute M, et al.. Intermediate filaments control collective migration by restricting traction forces and sustaining cell–cell contacts. Journal of Cell Biology. 2018;217(9):3031–3044. doi: 10.1083/jcb.201801162 PubMed DOI PMC

Mammoto T, Ingber DE. Mechanical control of tissue and organ development. Development. 2010;137(9):1407–1420. doi: 10.1242/dev.024166 PubMed DOI PMC

Mark C, Grundy TJ, Strissel PL, Böhringer D, Grummel N, Gerum R, et al.. Collective forces of tumor spheroids in three-dimensional biopolymer networks. eLife. 2020;9. doi: 10.7554/eLife.51912 PubMed DOI PMC

Peschetola V, Laurent VM, Duperray A, Michel R, Ambrosi D, Preziosi L, et al.. Time-dependent traction force microscopy for cancer cells as a measure of invasiveness. Cytoskeleton. 2013;70(4):201–214. doi: 10.1002/cm.21100 PubMed DOI

Liberzon A, Lasagna D, Aubert M, Bachant P, Jakirkham, Ranleu, et al. OpenPIV/openpiv-python: fixed windows conda-forge failure with encoding; 2019. Available from: https://zenodo.org/record/3566451.

Maskarinec SA, Franck C, Tirrell DA, Ravichandran G. Quantifying cellular traction forces in three dimensions. Proceedings of the National Academy of Sciences. 2009;106(52):22108–22113. doi: 10.1073/pnas.0904565106 PubMed DOI PMC

Dembo M, Wang YL. Stresses at the Cell-to-Substrate Interface during Locomotion of Fibroblasts. Biophysical Journal. 1999;76(4):2307–2316. doi: 10.1016/S0006-3495(99)77386-8 PubMed DOI PMC

Huang Y, Schell C, Huber TB, Şimşek AN, Hersch N, Merkel R, et al.. Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells. Scientific Reports. 2019;9(1). doi: 10.1038/s41598-018-36896-x PubMed DOI PMC

Butler JP, Tolić-Nørrelykke IM, Fabry B, Fredberg JJ. Traction fields, moments, and strain energy that cells exert on their surroundings. American Journal of Physiology-Cell Physiology. 2002;282(3):C595–C605. doi: 10.1152/ajpcell.00270.2001 PubMed DOI

Yang Z, Lin JS, Chen J, Wang JHC. Determining substrate displacement and cell traction fields—a new approach. Journal of Theoretical Biology. 2006;242(3):607–616. doi: 10.1016/j.jtbi.2006.05.005 PubMed DOI

Sabass B, Gardel ML, Waterman CM, Schwarz US. High Resolution Traction Force Microscopy Based on Experimental and Computational Advances. Biophysical Journal. 2008;94(1):207–220. doi: 10.1529/biophysj.107.113670 PubMed DOI PMC

Tambe DT, Hardin CC, Angelini TE, Rajendran K, Park CY, Serra-Picamal X, et al.. Collective cell guidance by cooperative intercellular forces. Nat Mater. 2011;10(6):469–475. doi: 10.1038/nmat3025 PubMed DOI PMC

Tambe DT, Croutelle U, Trepat X, Park CY, Kim JH, Millet E, et al.. Monolayer Stress Microscopy: Limitations, Artifacts, and Accuracy of Recovered Intercellular Stresses. PLoS ONE. 2013;8(2):e55172. doi: 10.1371/journal.pone.0055172 PubMed DOI PMC

Tambe DT, Butler JP, Fredberg JJ. Comment on “Intracellular stresses in patterned cell assemblies” by M. Moussus et al., Soft Matter, 2014, 10, 2414. Soft Matter. 2014;10(39):7681–7682. doi: 10.1039/C4SM00597J PubMed DOI

Moussus M, der Loughian C, Fuard D, Courçon M, Gulino-Debrac D, Delanoë-Ayari H, et al.. Intracellular stresses in patterned cell assemblies. Soft Matter. 2013;10(14):2414–2423. doi: 10.1039/C3SM52318G PubMed DOI

Ng MR, Besser A, Brugge JS, Danuser G. Mapping the dynamics of force transduction at cell–cell junctions of epithelial clusters. eLife. 2014;3. doi: 10.7554/eLife.03282 PubMed DOI PMC

Gerum RC, Richter S, Fabry B, Zitterbart DP. ClickPoints: an expandable toolbox for scientific image annotation and analysis. Methods in Ecology and Evolution. 2016;8(6):750–756. doi: 10.1111/2041-210X.12702 DOI

Harris CR, Millman KJ, van der Walt SJ, Gommers R, Virtanen P, Cournapeau D, et al.. Array programming with NumPy. Nature. 2020;585(7825):357–362. doi: 10.1038/s41586-020-2649-2 PubMed DOI PMC

Behnel S, Bradshaw R, Citro C, Dalcin L, Seljebotn DS, Smith K. Cython: The Best of Both Worlds. Computing in Science Engineering. 2011;13(2):31–39. doi: 10.1109/MCSE.2010.118 DOI

Virtanen P, Gommers R, Oliphant TE, Haberland M, Reddy T, Cournapeau D, et al.. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods. 2020;17:261–272. doi: 10.1038/s41592-019-0686-2 PubMed DOI PMC

van der Walt S, Schönberger JL, Nunez-Iglesias J, Boulogne F, Warner JD, Yager N, et al.. scikit-image: image processing in Python. PeerJ. 2014;2:e453. doi: 10.7717/peerj.453 PubMed DOI PMC

Hunter JD. Matplotlib: A 2D graphics environment. Computing in Science & Engineering. 2007;9(3):90–95. doi: 10.1109/MCSE.2007.55 DOI

Landau LD. Theory of elasticity. Oxford England Burlington, MA: Butterworth-Heinemann; 1986.

Han SJ, Oak Y, Groisman A, Danuser G. Traction microscopy to identify force modulation in subresolution adhesions. Nature Methods. 2015;12(7):653–656. doi: 10.1038/nmeth.3430 PubMed DOI PMC

Trepat X, Wasserman MR, Angelini TE, Millet E, Weitz DA, Butler JP, et al.. Physical forces during collective cell migration. Nature Physics. 2009;5(6):426–430. doi: 10.1038/nphys1269 DOI

Gómez J, Guarín-Zapata N. SolidsPy: 2D-Finite Element Analysis with Python; 2018. Available from: https://github.com/AppliedMechanics-EAFIT/SolidsPy.

Bochev P, Lehoucq R. Energy Principles and Finite Element Methods for Pure Traction Linear Elasticity. Comput Methods Appl Math. 2011;11(2):173–191. doi: 10.2478/cmam-2011-0009 DOI

Boudou T, Ohayon J, Picart C, Tracqui P. An extended relationship for the characterization of Young’s modulus and Poisson’s ratio of tunable polyacrylamide gels. Biorheology. 2006;43 6:721–8. PubMed

Pritchard RH, Lava P, Debruyne D, Terentjev EM. Precise determination of the Poisson ratio in soft materials with 2D digital image correlation. Soft Matter. 2013;9(26):6037. doi: 10.1039/c3sm50901j DOI

Kim TK, Kim JK, Jeong OC. Measurement of nonlinear mechanical properties of PDMS elastomer. Microelectronic Engineering. 2011;88(8):1982–1985. doi: 10.1016/j.mee.2010.12.108 DOI

Boudou T, Ohayon J, Picart C, Pettigrew RI, Tracqui P. Nonlinear elastic properties of polyacrylamide gels: Implications for quantification of cellular forces. Biorheology. 2009;46(3):191–205. doi: 10.3233/BIR-2009-0540 PubMed DOI PMC

Wang N, Naruse K, Stamenović D, Fredberg JJ, Mijailovich SM, Tolić-Nørrelykke IM, et al.. Mechanical behavior in living cells consistent with the tensegrity model. Proc Natl Acad Sci USA. 2001;98(14):7765–7770. doi: 10.1073/pnas.141199598 PubMed DOI PMC

Martiel JL, Leal A, Kurzawa L, Balland M, Wang I, Vignaud T, et al.. Measurement of cell traction forces with ImageJ. In: Methods in Cell Biology. Elsevier; 2015. p. 269–287. Available from: 10.1016/bs.mcb.2014.10.008. PubMed DOI

Huang Y, Gompper G, Sabass B. A Bayesian traction force microscopy method with automated denoising in a user-friendly software package. arXiv. 2020;.

Zielinski R, Mihai C, Kniss D, Ghadiali SN. Finite Element Analysis of Traction Force Microscopy: Influence of Cell Mechanics, Adhesion, and Morphology. Journal of Biomechanical Engineering. 2013;135(7). doi: 10.1115/1.4024467 PubMed DOI PMC

Mechanics of cell sheets: plectin as an integrator of cytoskeletal networks

Plectin-mediated cytoskeletal crosstalk controls cell tension and cohesion in epithelial sheets