Traction patterns of tumor cells

When crawling on a flat substrate, living cells exert forces on it via adhesive contacts, enabling them to build up tension within their cytoskeleton and to change shape. The measurement of these forces has been made possible by traction force microscopy (TFM), a technique which has allowed us to obtain time-resolved traction force maps during cell migration. This cell 'footprint' is, however, not sufficient to understand the details of the mechanics of migration, that is how cytoskeletal elements (respectively, adhesion complexes) are put under tension and reinforce or deform (respectively, mature and/or unbind) as a result. In a recent paper, we have validated a rheological model of actomyosin linking tension, deformation and myosin activity. Here, we complement this model with tentative models of the mechanics of adhesion and explore how closely these models can predict the traction forces that we recover from experimental measurements during cell migration. The resulting mathematical problem is a PDE set on the experimentally observed domain, which we solve using a finite-element approach. The four parameters of the model can then be adjusted by comparison with experimental results on a single frame of an experiment, and then used to test the predictive power of the model for following frames and other experiments. It is found that the basic pattern of traction forces is robustly predicted by the model and fixed parameters as a function of current geometry only.

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“…ðxÞ (see [51] for details). V is chosen so that ju exp j is vanishingly small close to @V. In general, we note that ju …”

Section: Appendix a Methods (A) Cell Crawling Assays And Image Analysismentioning

confidence: 99%

Prediction of traction forces of motile cells

et al. 2016

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“…Experiments involving GFP-transfected RT112 cells (from bladder epithelial tissues, rather low invasiveness degree) have been performed on Polyacrylamide gels with Young modulus E = 10 kPa and Poisson ratio ν = 1/2. Measurements of fluorescent beads positions have been made using confocal microscopy and displacements were deduced using a technique previously described [3].…”

Section: Numerical Comparison Of Adjoint and P-fttc Methodsmentioning

confidence: 99%

“…So, the determination of the traction stress field from the (partial) knowledge u b of the induced displacements needs to solve an inverse elasticity problem. This method has been called Traction Force Microscopy (TFM) and has been considered using different formulations, the BEM (Boundary Element Method (BEM) [11], the Fourier Transform Traction Cytometry (FTTC) method [8], the Traction Recovery from Point Force (TRPF) [22], and finally the more recent Adjoint Method (AM) [2,3,25].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical framework for traction force microscopy

et al. 2013

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Résumé. Cet article est consacré au problème de la Microscopieà Force de Traction (TFM). Ce problème consisteà déterminer les contraintes exercées par une cellule lors de sa migration sur un substratélastiqueà partir d'une mesure expérimentale des déplacements induits dans ce substrat. Mathématiquement, il s'agit de résoudre un problème inverse pour lequel nous proposons une formulation abstraite de type optimisation sous contraintes. Les contraintes mathématiques expriment les constraintes biomécaniques que doit satisfaire le champ de contraintes exercé par la cellule. Ce cadre abstrait permet de retrouver deux des méthodes de résolution utilisées en pratique,à savoir la méthode adjointe (AM) et la méthode de Cytométrie de Traction par Transformée de Fourier (FTTC). Il permet aussi d'ameliorer la méthode FTTC. Les résultats numériques obtenus sont ensuite comparés et démontrent l'avantage de la méthode adjointe, en particulier par sa capacitéà capturer des détails avec une meilleure précision.Abstract. This paper deals with the Traction Force Microscopy (TFM) problem. It consists in obtaining stresses by solving an inverse problem in an elastic medium, from known experimentally measured displacements. In this article, the application is the determination of the stresses exerted by a living cell at the surface of an elastic gel. We propose an abstract framework which formulates this inverse problem as a constrained minimization one. The mathematical constraints express the biomechanical conditions that the stress field must satisfy. From this framework, two methods currently used can be derived, the adjoint method (AM) and the Fourier Transform Traction Cytometry (FTTC) method. An improvement of the FTTC method is also derived using this framework. The numerical results are compared and show the advantage of the AM, in particular its ability to capture details more accurately.

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“…The box size is given on vertical and lateral axes in µm. The cell is moving from bottom-right to top-left, is initially attached and develops a large lamellipodium to proceed [84].…”

Section: Understanding Cell Behaviour: Beyond Cell Rheological Propermentioning

confidence: 99%

Review: Rheological properties of biological materials

Verdier¹,

Etienne²,

Duperray

et al. 2009

Comptes Rendus. Physique

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Eucaryotic cells and biological materials are described from a rheological point of view. Single cell properties give rise to typical microrheological properties which can affect cell behaviour. Single cell properties are also important in the context of multicellular systems, i.e. in biological tissues. Results from experiments are analyzed and models proposed both at the cellular scale and the macroscopic scale.

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Traction patterns of tumor cells

Cited by 64 publications

References 28 publications

Prediction of traction forces of motile cells

Prediction of traction forces of motile cells

Mathematical framework for traction force microscopy

Review: Rheological properties of biological materials

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