Quantifying forces in cell biology

Cells exert, sense, and respond to physical forces through an astounding diversity of mechanisms. Here we review recently developed tools to quantify the forces generated by cells. We first review technologies based on sensors of known or assumed mechanical properties, and discuss their applicability and limitations. We then proceed to draw an analogy between these human-made sensors and force sensing in the cell. As mechanics is increasingly revealed to play a fundamental role in cell function we envisage that tools to quantify physical forces may soon become widely applied in life-sciences laboratories.

[1]  Francis Crick,et al.  The physical properties of cytoplasm: A study by means of the magnetic particle method Part I. Experimental , 1950 .

[2]  Taekjip Ha,et al.  Defining Single Molecular Forces Required to Activate Integrin and Notch Signaling , 2013, Science.

[3]  E. Paluch Biophysical methods in cell biology , 2015 .

[4]  J. Fredberg,et al.  Collective cell guidance by cooperative intercellular forces , 2010 .

[5]  Christian Eggeling,et al.  Super-Resolved Traction Force Microscopy (STFM) , 2016, Nano letters.

[6]  Philippe Marcq,et al.  Mechanical state, material properties and continuous description of an epithelial tissue , 2012, Journal of The Royal Society Interface.

[7]  Christian Franck,et al.  High Resolution, Large Deformation 3D Traction Force Microscopy , 2014, PloS one.

[8]  S. Iwai,et al.  Visualizing myosin–actin interaction with a genetically-encoded fluorescent strain sensor , 2008, Proceedings of the National Academy of Sciences.

[9]  G. Wayne Brodland,et al.  CellFIT: A Cellular Force-Inference Toolkit Using Curvilinear Cell Boundaries , 2014, PloS one.

[10]  J. Bechhoefer,et al.  Calibration of atomic‐force microscope tips , 1993 .

[11]  Hervé Rouault,et al.  A global pattern of mechanical stress polarizes cell divisions and cell shape in the growing Drosophila wing disc , 2013, Journal of Cell Science.

[12]  Kaoru Sugimura,et al.  Unified quantitative characterization of epithelial tissue development , 2015, eLife.

[13]  Guillem Singla-Buxarrais,et al.  Compressed sensing traction force microscopy. , 2015, Acta biomaterialia.

[14]  Christian Franck,et al.  Quantifying cellular traction forces in three dimensions , 2009, Proceedings of the National Academy of Sciences.

[15]  Eric Mazur,et al.  Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics. , 2006, Biophysical journal.

[16]  M. Dembo,et al.  Stresses at the cell-to-substrate interface during locomotion of fibroblasts. , 1999, Biophysical journal.

[17]  Gaudenz Danuser,et al.  Traction microscopy to identify force modulation in sub-resolution adhesions , 2015, Nature Methods.

[18]  David R. Liu,et al.  A DNA-based molecular probe for optically reporting cellular traction forces , 2014, Nature Methods.

[19]  Benjamin Geiger,et al.  Focal Contacts as Mechanosensors Externally Applied Local Mechanical Force Induces Growth of Focal Contacts by an Mdia1-Dependent and Rock-Independent Mechanism , 2001 .

[20]  G. Meacci,et al.  Cells test substrate rigidity by local contractions on submicrometer pillars , 2012, Proceedings of the National Academy of Sciences.

[21]  C. Verdier,et al.  Traction patterns of tumor cells , 2009, Journal of mathematical biology.

[22]  Shu Chien,et al.  Live Cells Exert 3-Dimensional Traction Forces on Their Substrata , 2009, Cellular and molecular bioengineering.

[23]  Long-lived, high-strength states of ICAM-1 bonds to beta2 integrin, II: lifetimes of LFA-1 bonds under force in leukocyte signaling. , 2010, Biophysical journal.

[24]  Xavier Trepat,et al.  Mapping forces and kinematics during collective cell migration. , 2015, Methods in cell biology.

[25]  S. Yonemura,et al.  α-Catenin as a tension transducer that induces adherens junction development , 2010, Nature Cell Biology.

[26]  Christopher S. Chen,et al.  Cells lying on a bed of microneedles: An approach to isolate mechanical force , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[27]  S. Grill,et al.  Anisotropies in cortical tension reveal the physical basis of polarizing cortical flows , 2010, Nature.

[28]  Teodor Gotszalk,et al.  Calibration of atomic force microscope , 2008 .

[29]  Christopher S. Chen,et al.  Magnetic microposts as an approach to apply forces to living cells , 2007, Proceedings of the National Academy of Sciences.

[30]  R. Firtel,et al.  Both contractile axial and lateral traction force dynamics drive amoeboid cell motility , 2014, The Journal of cell biology.

[31]  Manuel Théry,et al.  Measurement of cell traction forces with ImageJ. , 2015, Methods in cell biology.

[32]  Ulrich S Schwarz,et al.  Cell-ECM traction force modulates endogenous tension at cell–cell contacts , 2011, Proceedings of the National Academy of Sciences.

[33]  K. Salaita,et al.  Titin-Based Nanoparticle Tension Sensors Map High-Magnitude Integrin Forces within Focal Adhesions. , 2016, Nano letters.

[34]  M. Rief,et al.  Extracellular rigidity sensing by talin isoform–specific mechanical linkages , 2015, Nature Cell Biology.

[35]  G. Danuser,et al.  Mapping the dynamics of force transduction at cell–cell junctions of epithelial clusters , 2014, eLife.

[36]  G. Edwards,et al.  Forces for Morphogenesis Investigated with Laser Microsurgery and Quantitative Modeling , 2003, Science.

[37]  Hanry Yu,et al.  Mechanotransduction In Vivo by Repeated Talin Stretch-Relaxation Events Depends upon Vinculin , 2011, PLoS biology.

[38]  Enrico Gratton,et al.  Fluid Shear Stress on Endothelial Cells Modulates Mechanical Tension across VE-Cadherin and PECAM-1 , 2013, Current Biology.

[39]  Otger Campàs,et al.  A toolbox to explore the mechanics of living embryonic tissues. , 2016, Seminars in cell & developmental biology.

[40]  E. Fama,et al.  Migration , 2007 .

[41]  Jean-Léon Maître,et al.  Inferring cellular forces from image stacks , 2017, Philosophical Transactions of the Royal Society B: Biological Sciences.

[42]  Ben Fabry,et al.  Single-cell response to stiffness exhibits muscle-like behavior , 2009, Proceedings of the National Academy of Sciences.

[43]  Marion Ghibaudo,et al.  Traction forces and rigidity sensing regulate cell functions , 2008 .

[44]  Frank Jülicher,et al.  TissueMiner: A multiscale analysis toolkit to quantify how cellular processes create tissue dynamics , 2016, eLife.

[45]  Eric F. Wieschaus,et al.  Integration of contractile forces during tissue invagination , 2010, The Journal of cell biology.

[46]  Alberto Aliseda,et al.  Spatio-temporal analysis of eukaryotic cell motility by improved force cytometry , 2007, Proceedings of the National Academy of Sciences.

[47]  D. Speicher,et al.  Cysteine shotgun–mass spectrometry (CS-MS) reveals dynamic sequence of protein structure changes within mutant and stressed cells , 2011, Proceedings of the National Academy of Sciences.

[48]  Kaoru Sugimura,et al.  The mechanical anisotropy in a tissue promotes ordering in hexagonal cell packing , 2013, Development.

[49]  B. Ladoux,et al.  Techniques to measure pilus retraction forces. , 2012, Methods in molecular biology.

[50]  Donald E Ingber,et al.  Quantifying cell-generated mechanical forces within living embryonic tissues , 2013, Nature Methods.

[51]  K. Luby-Phelps,et al.  Physical properties of cytoplasm. , 1994, Current opinion in cell biology.

[52]  Jeffrey J. Fredberg,et al.  Monolayer Stress Microscopy: Limitations, Artifacts, and Accuracy of Recovered Intercellular Stresses , 2013, PloS one.

[53]  R. Austin,et al.  Force mapping in epithelial cell migration. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[54]  C. D. Murray,et al.  The Physiological Principle of Minimum Work: II. Oxygen Exchange in Capillaries. , 1926, Proceedings of the National Academy of Sciences of the United States of America.

[55]  G. Brodland,et al.  Practical aspects of the cellular force inference toolkit (CellFIT). , 2015, Methods in cell biology.

[56]  Dennis E. Discher,et al.  Nuclear Lamin-A Scales with Tissue Stiffness and Enhances Matrix-Directed Differentiation , 2013, Science.

[57]  J. Tinevez,et al.  Polar actomyosin contractility destabilizes the position of the cytokinetic furrow , 2011, Nature.

[58]  D. Weitz,et al.  Mechanical strain in actin networks regulates FilGAP and integrin binding to Filamin A , 2011, Nature.

[59]  Joachim P. Spatz,et al.  A molecular mechanotransduction pathway regulates collective migration of epithelial cells , 2015, Nature Cell Biology.

[60]  J. Grandl,et al.  Mechanical sensitivity of Piezo1 ion channels can be tuned by cellular membrane tension , 2015, eLife.

[61]  J. Theriot,et al.  Rickettsia Sca4 Reduces Vinculin-Mediated Intercellular Tension to Promote Spread , 2016, Cell.

[62]  Sami Alom Ruiz,et al.  Mechanical tugging force regulates the size of cell–cell junctions , 2010, Proceedings of the National Academy of Sciences.

[63]  G. Charras,et al.  The cytoplasm of living cells behaves as a poroelastic material , 2013, Nature materials.

[64]  Jean-Léon Maître,et al.  Adhesion Functions in Cell Sorting by Mechanically Coupling the Cortices of Adhering Cells , 2012, Science.

[65]  William J. Polacheck,et al.  Noncontact three-dimensional mapping of intracellular hydro-mechanical properties by Brillouin microscopy , 2015, Nature Methods.

[66]  Michael P. Sheetz,et al.  Stretching Single Talin Rod Molecules Activates Vinculin Binding , 2009, Science.

[67]  Lars Hufnagel,et al.  Supplementary Information for Mechanical Stress Inference for Two Dimensional Cell Arrays , 2012 .

[68]  Kaoru Sugimura,et al.  Bayesian inference of force dynamics during morphogenesis. , 2012, Journal of theoretical biology.

[69]  E. Farge Mechanical Induction of Twist in the Drosophila Foregut/Stomodeal Primordium , 2003, Current Biology.

[70]  Gaudenz Danuser,et al.  Mechanical Feedback through E-Cadherin Promotes Direction Sensing during Collective Cell Migration , 2014, Cell.

[71]  Marion Ghibaudo,et al.  Rigidity-driven growth and migration of epithelial cells on microstructured anisotropic substrates , 2007, Proceedings of the National Academy of Sciences.

[72]  Clare M Waterman,et al.  High resolution traction force microscopy based on experimental and computational advances. , 2008, Biophysical journal.

[73]  Ben Fabry,et al.  Traction fields, moments, and strain energy that cells exert on their surroundings. , 2002, American journal of physiology. Cell physiology.

[74]  Frederick Sachs,et al.  A fluorescence energy transfer‐based mechanical stress sensor for specific proteins in situ , 2008, The FEBS journal.

[75]  Viola Vogel,et al.  Mechanical forces regulate the interactions of fibronectin and collagen I in extracellular matrix , 2015, Nature Communications.

[76]  J. Prost,et al.  Cell-like pressure sensors reveal increase of mechanical stress towards the core of multicellular spheroids under compression , 2017, Nature Communications.

[77]  Kaden M. Southard,et al.  A Mechanogenetic Toolkit for Interrogating Cell Signaling in Space and Time , 2016, Cell.

[78]  Pere Roca-Cusachs,et al.  Finding the weakest link – exploring integrin-mediated mechanical molecular pathways , 2012, Journal of Cell Science.

[79]  D. Herschlag,et al.  Nanomechanical measurements of the sequence-dependent folding landscapes of single nucleic acid hairpins. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[80]  A. E. Ehret,et al.  Confocal reference free traction force microscopy , 2016, Nature Communications.

[81]  P. Hersen,et al.  Magnetic micropillars as a tool to govern substrate deformations. , 2011, Lab on a chip.

[82]  Jie Yan,et al.  Mechanical activation of vinculin binding to talin locks talin in an unfolded conformation , 2014, Scientific Reports.

[83]  M. Miodownik,et al.  Inter-Cellular Forces Orchestrate Contact Inhibition of Locomotion , 2015, Cell.

[84]  Sirio Dupont Role of YAP/TAZ in mechanotransduction , 2011 .

[85]  C. Lim,et al.  Inference of Internal Stress in a Cell Monolayer. , 2016, Biophysical journal.

[86]  M. Sheetz,et al.  Traction on Immobilized Netrin-1 Is Sufficient to Reorient Axons , 2009, Science.

[87]  G. Charras,et al.  Characterizing the mechanics of cultured cell monolayers , 2012, Proceedings of the National Academy of Sciences.

[88]  P. Lenne,et al.  Measuring forces and stresses in situ in living tissues , 2016, Development.

[89]  Beth L. Pruitt,et al.  For whom the cells pull: Hydrogel and micropost devices for measuring traction forces. , 2016, Methods.

[90]  Ulrich S Schwarz,et al.  Traction force microscopy on soft elastic substrates: A guide to recent computational advances. , 2015, Biochimica et biophysica acta.

[91]  J. Muñoz Non-regularised Inverse Finite Element Analysis for 3D Traction Force Microscopy , 2016, 1608.08197.

[92]  James Hone,et al.  Tropomyosin Controls Sarcomere-like Contractions for Rigidity Sensing and Suppressing Growth on Soft Matrices , 2015, Nature Cell Biology.

[93]  Jie Yan,et al.  The mechanical response of talin , 2016, Nature Communications.

[94]  M. Schwartz,et al.  Force regulated conformational change of integrin αVβ3. , 2017, Matrix biology : journal of the International Society for Matrix Biology.

[95]  Sriram Narasimhan,et al.  Video force microscopy reveals the mechanics of ventral furrow invagination in Drosophila , 2010, Proceedings of the National Academy of Sciences.

[96]  B. Fabry,et al.  Mechanotransduction: use the force(s) , 2015, BMC Biology.

[97]  Philippe Marcq,et al.  Mechanical Control of Morphogenesis by Fat/Dachsous/Four-Jointed Planar Cell Polarity Pathway , 2012, Science.

[98]  Robert G. Parton,et al.  Cells Respond to Mechanical Stress by Rapid Disassembly of Caveolae , 2011, Cell.

[99]  Margaret L. Gardel,et al.  Model-based Traction Force Microscopy Reveals Differential Tension in Cellular Actin Bundles , 2015, PLoS Comput. Biol..

[100]  Ulrich S Schwarz,et al.  United we stand – integrating the actin cytoskeleton and cell–matrix adhesions in cellular mechanotransduction , 2012, Journal of Cell Science.

[101]  John V. Small,et al.  Mechanosensing in actin stress fibers revealed by a close correlation between force and protein localization , 2009, Journal of Cell Science.

[102]  Manuela Schmidt,et al.  Piezo1 and Piezo2 Are Essential Components of Distinct Mechanically Activated Cation Channels , 2010, Science.

[103]  Jason Wu,et al.  Localized force application reveals mechanically sensitive domains of Piezo1 , 2016, Nature Communications.

[104]  Cheng Zhu,et al.  Mechanical regulation of a molecular clutch defines force transmission and transduction in response to matrix rigidity , 2016, Nature Cell Biology.

[105]  Beth L. Pruitt,et al.  E-cadherin is under constitutive actomyosin-generated tension that is increased at cell–cell contacts upon externally applied stretch , 2012, Proceedings of the National Academy of Sciences.

[106]  S. Sen,et al.  Matrix Elasticity Directs Stem Cell Lineage Specification , 2006, Cell.

[107]  Andreas Fouras,et al.  Cortical Tension Allocates the First Inner Cells of the Mammalian Embryo. , 2015, Developmental cell.

[108]  Anthony A. Hyman,et al.  Polarity controls forces governing asymmetric spindle positioning in the Caenorhabditis elegans embryo , 2001, Nature.

[109]  Robert W Style,et al.  Traction force microscopy in physics and biology. , 2014, Soft matter.

[110]  J. de Rooij,et al.  Converging and Unique Mechanisms of Mechanotransduction at Adhesion Sites. , 2016, Trends in cell biology.

[111]  Kristopher E Kubow,et al.  Fibronectin forms the most extensible biological fibers displaying switchable force-exposed cryptic binding sites , 2009, Proceedings of the National Academy of Sciences.

[112]  Pere Roca-Cusachs,et al.  Clustering of α5β1 integrins determines adhesion strength whereas αvβ3 and talin enable mechanotransduction , 2009, Proceedings of the National Academy of Sciences.

[113]  C. Heisenberg,et al.  Tension-oriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly , 2013, Nature Cell Biology.

[114]  Adam J. Engler,et al.  Matrix elasticity directs stem cell differentiation , 2006 .

[115]  A. Asnacios,et al.  Single-cell mechanics: the parallel plates technique. , 2015, Methods in cell biology.

[116]  Jagannathan Rajagopalan,et al.  MEMS sensors and microsystems for cell mechanobiology , 2011, Journal of micromechanics and microengineering : structures, devices, and systems.

[117]  J. Fredberg,et al.  Mechanical waves during tissue expansion , 2012, Nature Physics.

[118]  Ben Fabry,et al.  Three-dimensional force microscopy of cells in biopolymer networks , 2015, Nature Methods.

[119]  R. Chambers Microdissection studies. II. The cell aster: A reversible gelation phenomenon , 1917 .

[120]  J. Fredberg,et al.  Plithotaxis and emergent dynamics in collective cellular migration. , 2011, Trends in cell biology.

[121]  D. Stamenović,et al.  Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells. , 2002, American journal of physiology. Cell physiology.

[122]  V. Weaver,et al.  Tissue mechanics promote IDH1-dependent HIF1α–tenascin C feedback to regulate glioblastoma aggression , 2016, Nature Cell Biology.

[123]  K. Salaita,et al.  Lighting Up the Force: Investigating Mechanisms of Mechanotransduction Using Fluorescent Tension Probes , 2015, Molecular and Cellular Biology.

[124]  C. Lim,et al.  Adaptive rheology and ordering of cell cytoskeleton govern matrix rigidity sensing , 2015, Nature Communications.

[125]  Frank Jülicher,et al.  Increased Cell Bond Tension Governs Cell Sorting at the Drosophila Anteroposterior Compartment Boundary , 2009, Current Biology.

[126]  M. Davidson,et al.  Molecular mechanism of vinculin activation and nano-scale spatial organization in focal adhesions , 2015, Nature Cell Biology.

[127]  R. Dickinson,et al.  Nuclear forces and cell mechanosensing. , 2014, Progress in molecular biology and translational science.

[128]  A. Dunn,et al.  Molecular tension sensors report forces generated by single integrin molecules in living cells. , 2013, Nano letters.

[129]  William J Polacheck,et al.  Measuring cell-generated forces: a guide to the available tools , 2016, Nature Methods.

[130]  Sergey V. Plotnikov,et al.  Force Fluctuations within Focal Adhesions Mediate ECM-Rigidity Sensing to Guide Directed Cell Migration , 2012, Cell.

[131]  Daniel J. Muller,et al.  Single-cell force spectroscopy, an emerging tool to quantify cell adhesion to biomaterials. , 2014, Tissue engineering. Part B, Reviews.

[132]  D. Stamenović,et al.  Topographical control of multiple cell adhesion molecules for traction force microscopy. , 2014, Integrative biology : quantitative biosciences from nano to macro.

[133]  Dene L. Farrell,et al.  Spatiotemporal control of epithelial remodeling by regulated myosin phosphorylation , 2014, Proceedings of the National Academy of Sciences.

[134]  Taekjip Ha,et al.  Measuring mechanical tension across vinculin reveals regulation of focal adhesion dynamics , 2010, Nature.

[135]  J. Romero Non-regularised inverse finite element analysis for 3D traction force microscopy , 2016 .

[136]  David A. Weitz,et al.  Physical forces during collective cell migration , 2009 .

[137]  Cheng Zhu,et al.  JCB_200810002 1275..1284 , 2009 .

[138]  Jie Yan,et al.  Force-dependent conformational switch of α-catenin controls vinculin binding , 2014, Nature Communications.

[139]  Araxi O. Urrutia,et al.  YAP is essential for tissue tension to ensure vertebrate 3D body shape , 2015, Nature.

[140]  Wayne L. Rickoll,et al.  Multiple Forces Contribute to Cell Sheet Morphogenesis for Dorsal Closure in Drosophila , 2000, The Journal of cell biology.

[141]  D'arcy W. Thompson On growth and form i , 1943 .

[142]  Pierre-François Lenne,et al.  Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis , 2008, Nature Cell Biology.

[143]  B. Hodson,et al.  The effect of passage in vitro and in vivo on the properties of murine fibrosarcomas. II. Sensitivity to cell-mediated cytotoxicity in vitro. , 1985, British Journal of Cancer.

[144]  D. Leckband,et al.  Nanoscale mechanics guides cellular decision making. , 2016, Integrative biology : quantitative biosciences from nano to macro.

[145]  Lingzhou Xue,et al.  Cooperative unfolding of distinctive mechanoreceptor domains transduces force into signals , 2016, eLife.

[146]  J. Onuchic,et al.  Intercellular stress reconstitution from traction force data. , 2014, Biophysical journal.

[147]  Junghoon Lee,et al.  Cell motility regulation on stepped micro pillar array device (SMPAD) with discrete stiffness gradient , 2015, 2015 28th IEEE International Conference on Micro Electro Mechanical Systems (MEMS).

[148]  Ning Wang,et al.  Rapid signal transduction in living cells is a unique feature of mechanotransduction , 2008, Proceedings of the National Academy of Sciences.

[149]  Cheng Zhu,et al.  DNA-based digital tension probes reveal integrin forces during early cell adhesion , 2014, Nature Communications.

[150]  Michael P. Sheetz,et al.  Two-piconewton slip bond between fibronectin and the cytoskeleton depends on talin , 2003, Nature.

[151]  José Manuel García-Aznar,et al.  Collective cell durotaxis emerges from long-range intercellular force transmission , 2016, Science.

[152]  Xavier Trepat,et al.  Rigidity sensing and adaptation through regulation of integrin types , 2014, Nature materials.

[153]  Aleksandra K. Denisin,et al.  Single Molecule Force Measurements in Living Cells Reveal a Minimally Tensioned Integrin State. , 2016, ACS nano.

[154]  Xiaoyan Ma,et al.  Combining laser microsurgery and finite element modeling to assess cell-level epithelial mechanics. , 2009, Biophysical journal.

[155]  Pallav Kosuri,et al.  Work Done by Titin Protein Folding Assists Muscle Contraction. , 2016, Cell reports.

[156]  Wesley R. Legant,et al.  Measurement of mechanical tractions exerted by cells in three-dimensional matrices , 2010, Nature Methods.

[157]  Payam Rowghanian,et al.  In vivo quantification of spatially varying mechanical properties in developing tissues , 2016, Nature Methods.

[158]  Jennifer A Zallen,et al.  Myosin II dynamics are regulated by tension in intercalating cells. , 2009, Developmental cell.