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INTRODUCTION: Traction force microscopy (TFM) is a widely used technique to measure cell contractility on compliant substrates that mimic the stiffness of human tissues. For every step in a TFM workflow, users make choices which impact the quantitative results, yet many times the rationales and consequences for making these decisions are unclear. We have found few papers which show the complete experimental and mathematical steps of TFM, thus obfuscating the full effects of these decisions on the final output. METHODS: Therefore, we present this Field Guide with the goal to explain the mathematical basis of common TFM methods to practitioners in an accessible way. We specifically focus on how errors propagate in TFM workflows given specific experimental design and analytical choices. RESULTS: We cover important assumptions and considerations in TFM substrate manufacturing, substrate mechanical properties, imaging techniques, image processing methods, approaches and parameters used in calculating traction stress, and data-reporting strategies. CONCLUSIONS: By presenting a conceptual review and analysis of TFM-focused research articles published over the last two decades, we provide researchers in the field with a better understanding of their options to make more informed choices when creating TFM workflows depending on the type of cell being studied. With this review, we aim to empower experimentalists to quantify cell contractility with confidence. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s12195-024-00801-6.

Traction force microscopy (TFM) allows to estimate tractions on the surface of cells when they mechanically interact with hydrogel substrates that mimic the extracellular matrix (ECM). The field of mechanobiology has a strong interest in using TFM in 3D in vitro models. However, there are a number of challenges that hamper the accuracy of 3D TFM and that are often bypassed. In this study, the computational efficiency and accuracy of TFM, referred to traction reconstruction from synthetically generated (control) ground truth solutions, are assessed from four different perspectives: magnitude of cellular pulling force (and hence strain level achieved in the hydrogel), effect of the complexity of the cellular morphology, accuracy and computational efficiency of forward vs inverse traction recovery methods, and the effect of incorrectly selecting a constitutive model that describes the behavior of the ECM (i.e. linear/nonlinear). The main results showed: (i) traction reconstruction is more challenging for complex cell morphologies, (ii) there is no significant impact of the magnitude of cellular pulling force on the overall reconstruction accuracy, and (iii) modeling a nonlinear hydrogel with a linear constitutive model leads to non-negligible errors (up to 80% and 30% for forward and inverse methodologies, respectively) in traction reconstruction. This study expands the characterization of the accuracy and efficiency of 3D TFM, highlighting important factors to be considered in future 3D TFM in vitro applications.

To establish functional networks, neurons must migrate to their appropriate destinations and then extend axons toward their target cells. These processes depend on the advances of growth cones that located at the tips of neurites. Axonal growth cones generate driving forces by sensing their local microenvironment and modulating cytoskeletal dynamics and actin-adhesion coupling (clutch coupling). Decades of research have led to the identification of guidance molecules, their receptors, and downstream signaling cascades for regulating neuronal migration and axonal guidance; however, the molecular machineries required for generating forces to drive growth cone advance and navigation are just beginning to be elucidated. At the leading edge of neuronal growth cones, actin filaments undergo retrograde flow, which is powered by actin polymerization and actomyosin contraction. A clutch coupling between F-actin retrograde flow and adhesive substrate generates traction forces for growth cone advance. The present study describes a detailed protocol for monitoring F-actin retrograde flow by single speckle imaging. Importantly, when combined with an F-actin marker Lifeact, this technique can quantify 1) the F-actin polymerization rate and 2) the clutch coupling efficiency between F-actin retrograde flow and the adhesive substrate. Both are critical variables for generating forces for growth cone advance and navigation. In addition, the present study describes a detailed protocol of traction force microscopy, which can quantify 3) traction force generated by growth cones. Thus, by coupling the analyses of single speckle imaging and traction force microscopy, investigators can monitor the molecular mechanics underlying growth cone advance and navigation.

Traction force microscopy (TFM) allows to estimate tractions on the surface of cells when they mechanically interact with hydrogel substrates that mimic the extracellular matrix (ECM). The field of mechanobiology has a strong interest in using TFM in 3D in vitro models. However, there are a number of challenges that hamper the accuracy of 3D TFM and that are often bypassed. In this study, the computational efficiency and accuracy of TFM, referred to traction reconstruction from synthetically generated (control) ground truth solutions, are assessed from four different perspectives: magnitude of cellular pulling force (and hence strain level achieved in the hydrogel), effect of the complexity of the cellular morphology, accuracy and computational efficiency of forward vs inverse traction recovery methods, and the effect of incorrectly selecting a constitutive model that describes the behavior of the ECM (i.e. linear/nonlinear). The main results showed: (i) traction reconstruction is more challenging for complex cell morphologies, (ii) there is no significant impact of the magnitude of cellular pulling force on the overall reconstruction accuracy, and (iii) modeling a nonlinear hydrogel with a linear constitutive model leads to non-negligible errors (up to 80% and 30% for forward and inverse methodologies, respectively) in traction reconstruction. This study expands the characterization of the accuracy and efficiency of 3D TFM, highlighting important factors to be considered in future 3D TFM in vitro applications.

The influence of the biophysical environment in known models of cell patterning is an area of growing interest to determine how to properly control cell fate and recapitulate tissue organization. This dissertation uses BMP4-induced human embryonic stem cells (hESCs) on gels of defined soft stiffness as a model of gastrulation-stage embryos. Additionally, to probe how mechanical cues affect the regulation of cell fate, traction force microscopy is leveraged to measure stress distributions in tissues. The findings here described indicate that areas of higher tension correlate with early mesoderm differentiation, emphasizing a critical role for tissue architecture in early development. The elevated tension promotes the release of beta-catenin from adhesion junctions and further Wnt signaling through a force-dependent conformational exposure of the tyrosine 654 (Y654) of cadherin-bound beta-catenin. By using a dephosphomimetic mutant for beta-catenin (Y654F), expression of the early mesodermal marker Brachyury (T) is severely affected, indicating a mechanism whereby high cell-cell tension initiates and spatially restrict a release of beta-catenin from junctions to promote mesoderm specification. Furthermore, in order to understand how the mesodermal T signal becomes spatially restricted, this dissertation explored an underappreciated aspect of developmental systems, programmed cell death (PCD). The findings indicate that not only apoptosis may play a mechanical role in equilibrating tissue-level forces, but also that apoptotic cell recognition may play an inhibitory role in the expression of the mesoderm marker T and regulate the boundary of its signal through the phagocytic receptor MERTK. These results provide a framework to understand how mechanical cues and PCD can work in tandem to regulate the self-organization of tissues in developmental processes, such as gastrulation.

Cardiotoxicity is one of the major reasons for withdrawal of drugs from the market. Hence, assessing the cardiotoxicity of drug candidates with high efficacy and accuracy during the drug development process is essential to reduce the withdrawal risk of new drugs. Excitation-contraction coupling in cardiomyocytes orchestrates the cardiac function, but the inability to record electrical and mechanical signals simultaneously has hindered the acquisition of synchronous and correlative information between the electrical and mechanical properties of cardiomyocytes. Herein, a high-throughput, easy to use, minimally invasive, accurate, and combined measurement platform for iPSC-CM action potential and contraction force is demonstrated using a Nano-electrode array, and Fluorescent nanospheres that help construct contraction forces using Traction Force Microscopy technique. This platform represents a multimodal analysis technique that can easily reach sub-cellular resolution with simultaneous use of nano-electrode array and nanospheres. First, the platform was developed and characterized without the use of cells, that included optimization of PDMS thickness, characterization of its stiffness, and optimization of nanosphere distribution density on the PDMS substrate. After optimization of measurement acquisition, separate action potential and contraction force were obtained from iPSC derived cardiomyocytes. And, the dynamic response of cardiomyocytes to caffeine was recorded and analyzed. Obtained results indicate that the platform has tremendous potential in simultaneous recording and application in patient specific cardiotoxicity screening.

The capacity of cells to adhere to, exert forces upon and migrate through their surrounding environment governs tissue regeneration and cancer metastasis. The role of the physical contractile forces that cells exert in this process, and the underlying molecular mechanisms are not fully understood. We, therefore, aimed to clarify if the extracellular forces that cells exert on their environment and/or the intracellular forces that deform the cell nucleus, and the link between these forces, are defective in transformed and invasive fibroblasts, and to indicate the underlying molecular mechanism of control. Confocal, Epifluorescence and Traction force microscopy, followed by computational analysis, showed an increased maximum contractile force that cells apply on their environment and a decreased intracellular force on the cell nucleus in the invasive fibroblasts, as compared to normal control cells. Loss of HDAC6 activity by tubacin-treatment and siRNA-mediated HDAC6 knockdown also reversed the reduced size and more circular shape and defective migration of the transformed and invasive cells to normal. However, only tubacin-mediated, and not siRNA knockdown reversed the increased force of the invasive cells on their surrounding environment to normal, with no effects on nuclear forces. We observed that the forces on the environment and the nucleus were weakly positively correlated, with the exception of HDAC6 siRNA-treated cells, in which the correlation was weakly negative. The transformed and invasive fibroblasts showed an increased number and smaller cell-matrix adhesions than control, and neither tubacin-treatment, nor HDAC6 knockdown reversed this phenotype to normal, but instead increased it further. This highlights the possibility that the control of contractile force requires separate functions of HDAC6, than the control of cell adhesions, spreading and shape. These data are consistent with the possibility that defective force-transduction from the extracellula, QC 20230824

Traction force microscopy (TFM) allows to estimate tractions on the surface of cells when they mechanically interact with hydrogel substrates that mimic the extracellular matrix (ECM). The field of mechanobiology has a strong interest in using TFM in 3D in vitro models. However, there are a number of challenges that hamper the accuracy of 3D TFM and that are often bypassed. In this study, the computational efficiency and accuracy of TFM, referred to traction reconstruction from synthetically generated (control) ground truth solutions, are assessed from four different perspectives: magnitude of cellular pulling force (and hence strain level achieved in the hydrogel), effect of the complexity of the cellular morphology, accuracy and computational efficiency of forward vs inverse traction recovery methods, and the effect of incorrectly selecting a constitutive model that describes the behavior of the ECM (i.e. linear/nonlinear). The main results showed: (i) traction reconstruction is more challenging for complex cell morphologies, (ii) there is no significant impact of the magnitude of cellular pulling force on the overall reconstruction accuracy, and (iii) modeling a nonlinear hydrogel with a linear constitutive model leads to non-negligible errors (up to 80% and 30% for forward and inverse methodologies, respectively) in traction reconstruction. This study expands the characterization of the accuracy and efficiency of 3D TFM, highlighting important factors to be considered in future 3D TFM in vitro applications.

Traction force microscopy (TFM) allows to estimate tractions on the surface of cells when they mechanically interact with hydrogel substrates that mimic the extracellular matrix (ECM). The field of mechanobiology has a strong interest in using TFM in 3D in vitro models. However, there are a number of challenges that hamper the accuracy of 3D TFM and that are often bypassed. In this study, the computational efficiency and accuracy of TFM, referred to traction reconstruction from synthetically generated (control) ground truth solutions, are assessed from four different perspectives: magnitude of cellular pulling force (and hence strain level achieved in the hydrogel), effect of the complexity of the cellular morphology, accuracy and computational efficiency of forward vs inverse traction recovery methods, and the effect of incorrectly selecting a constitutive model that describes the behavior of the ECM (i.e. linear/nonlinear). The main results showed: (i) traction reconstruction is more challenging for complex cell morphologies, (ii) there is no significant impact of the magnitude of cellular pulling force on the overall reconstruction accuracy, and (iii) modeling a nonlinear hydrogel with a linear constitutive model leads to non-negligible errors (up to 80% and 30% for forward and inverse methodologies, respectively) in traction reconstruction. This study expands the characterization of the accuracy and efficiency of 3D TFM, highlighting important factors to be considered in future 3D TFM in vitro applications.

A main challenge in biology is to understand the development of the human body, namely how cell and tissue shape transitions occur. Our organism is riddled with curved cell layers that withstand stress and react to it depending on their function, and this is where physics plays an important role, trying to unveil the forces and mechanical properties of these tissues. Thus, the study hereby presented aims to characterize human pluripotent stem cell monolayer curling transitions, and tries to set the fine line that separates them from the dewetting transitions. For controlling these changes in form, we apply different geometrical constraints by varying the size and shape of the islands using photopatterning of extracellular matrix (ECM) proteins on dishes, and apart from that, we subject the cell monolayers to different external chemical and physical stimuli: we inhibit or activate contractility of the cells by using Y27 drug, we control apical constriction optogenetically, or we vary the cell-substrate adhesion by either using dispase or creating ECM protein gradients. In order to gain control over the curling and dewetting transitions, the role of the different geometrical constraints and external stimuli is assessed. This work shows the contribution of each variable by measuring some mechanical and physical properties of the monolayers, such as curvatures, velocities and traction forces exerted by the tissues. These magnitudes, which change with the stimuli, hold the key that governs the transition, and after assessing the relations between them, we are able of programming the dewetting and curling transitions at will. Finally, the potential of this system as a biological actuator is evaluated, by trying to make a hand-like monolayer curl and grab a bead or a cell spheroid., Uno de los principales desafíos en biología es comprender el desarrollo del cuerpo humano, en particular cómo ocurren las transiciones en la forma de las células y los tejidos. Nuestro organismo está lleno de capas de células curvas que resisten el estrés y reaccionan ante él según su función, y aquí es donde la física desempeña un papel importante, tratando de analizar las fuerzas y propiedades mecánicas de estos tejidos. Por lo tanto, el estudio que se presenta aquí tiene como objetivo caracterizar las transiciones de monocapas de células madre pluripotentes humanas que se curvan y trata de establecer la línea que las separa de las transiciones de ''dewetting''. Para controlar estos cambios en la forma, aplicamos diferentes restricciones geométricas al variar el tamaño y la forma de las islas. Además de eso, sometemos las monocapas celulares a diferentes estímulos químicos y físicos externos: inhibimos o activamos la contractilidad de las células utilizando el fármaco Y27, controlamos la constricción apical de forma optogenética o variamos la adhesión célula-sustrato mediante el uso de dispasa o la creación de gradientes de proteínas de la matriz extracelular. Para obtener el control sobre las transiciones de ''curling'' y ''dewetting'', evaluamos el papel de las diferentes restricciones geométricas y estímulos externos. Este trabajo muestra la contribución de cada variable al medir algunas propiedades mecánicas y físicas de las monocapas, como curvaturas, velocidades y fuerzas de tracción ejercidas por los tejidos. Estas magnitudes, que cambian con los estímulos, son la clave para gobernar la transición, y después de evaluar las relaciones entre ellas, somos capaces de programar las transiciones de "dewetting" y "curling" a voluntad. Finalmente, se evalúa el potencial de este sistema como actuador biológico, tratando de hacer que una monocapa con forma de asterisco se pliegue y agarre un esferoide celular. User traduce also to catalan ChatGPT Un dels reptes princ, Un dels reptes principals en biologia és entendre el desenvolupament del cos humà, concretament com ocorren les transicions en la forma de les cèl·lules i els teixits. El nostre organisme està ple de capes de cèl·lules corbades que resisteixen l'estrès i hi reaccionen segons la seva funció, i aquí és on la física juga un paper important, tractant de desxifrar les forces i les propietats mecàniques d'aquests teixits. Per tant, l'estudi que es presenta aquí té com a objectiu caracteritzar les transicions d'enrollament de monocapes de cèl·lules mare pluripotents humanes i tracta d'establir la línia que les separa de les transicions de "dewetting". Per controlar aquests canvis en la forma, apliquem diferents restriccions geomètriques variant la mida i la forma de les illes. A més a més, sotmetem les monocapes cel·lulars a diferents estímuls químics i físics externs: inhibim o activem la contractilitat de les cèl·lules mitjançant l'ús del fàrmac Y27, controlem la constricció apical de forma optogenètica o variem la adhesió cèl·lula-substrat utilitzant dispasa o creant gradients de proteïnes de la matriu extracel·lular. Per obtenir el control sobre les transicions de "curling" i "dewetting", avaluem el paper de les diferents restriccions geomètriques i estímuls externs. Aquest treball mostra la contribució de cada variable mitjançant la mesura de diverses propietats mecàniques i físiques de les monocapes, com ara la curvatura, velocitats i forces de tracció exercides pels teixits. Aquestes magnituds, que canvien amb els estímuls, són clau per a governar la transició, i després d'avaluar les relacions entre elles, som capaços de programar les transicions de "dewetting" i "curling" a voluntat. Finalment, s'avalua el potencial d'aquest sistema com a actuador biològic, tractant de fer que una monocapa amb forma de asterisc s'enrotlli i agafi un esferoide cel·lular.

In the last decade, cellular forces in three-dimensional hydrogels that mimic the extracellular matrix have been calculated by means of Traction Force Microscopy (TFM). However, characterizing the accuracy limits of a traction recovery method is critical to avoid obscuring physiological information due to traction recovery errors. So far, 3D TFM algorithms have only been validated using simplified cell geometries, bypassing image processing steps or arbitrarily simulating focal adhesions. Moreover, it is still uncertain which of the two common traction recovery methods, i.e., forward and inverse, is more robust against the inherent challenges of 3D TFM. In this work, we established an advanced in silico validation framework that is applicable to any 3D TFM experimental setup and that can be used to correctly couple the experimental and computational aspects of 3D TFM. Advancements relate to the simultaneous incorporation of complex cell geometries, simulation of microscopy images of varying bead densities and different focal adhesion sizes and distributions. By measuring the traction recovery error with respect to ground truth solutions, we found that while highest traction recovery errors occur for cases with sparse and small focal adhesions, our implementation of the inverse method improves two-fold the accuracy with respect to the forward method (average error of 23% vs. 50%). This advantage was further supported by recovering cellular tractions around angiogenic sprouts in an in vitro model of angiogenesis. The inverse method recovered higher traction peaks and a clearer pulling pattern at the sprout protrusion tips than the forward method. Statement of significance: Biomaterial performance is often studied by quantifying cell-matrix mechanical interactions by means of Traction Force Microscopy (TFM). However, 3D TFM algorithms are often validated in simplified scenarios, which do not allow to fully assess errors that could obscure physiological information. Her

We present TFMLAB, a MATLAB software package for 4D (x;y;z;t) Traction Force Microscopy (TFM). While various TFM computational workflows are available in the literature, open-source programs that are easy to use by researchers with limited technical experience and that can analyze 4D in vitro systems do not exist. TFMLAB integrates all the computational steps to compute active cellular forces from confocal microscopy images, including image processing, cell segmentation, image alignment, matrix displacement measurement and force recovery. Moreover, TFMLAB eases usability by means of interactive graphical user interfaces. This work describes the package's functionalities and analyzes its performance on a real TFM case

We present TFMLAB, a MATLAB software package for 4D (x;y;z;t) Traction Force Microscopy (TFM). While various TFM computational workflows are available in the literature, open-source programs that are easy to use by researchers with limited technical experience and that can analyze 4D in vitro systems do not exist. TFMLAB integrates all the computational steps to compute active cellular forces from confocal microscopy images, including image processing, cell segmentation, image alignment, matrix displacement measurement and force recovery. Moreover, TFMLAB eases usability by means of interactive graphical user interfaces. This work describes the package's functionalities and analyzes its performance on a real TFM case

To establish functional networks, neurons must migrate to their appropriate destinations and then extend axons toward their target cells. These processes depend on the advances of growth cones that located at the tips of neurites. Axonal growth cones generate driving forces by sensing their local microenvironment and modulating cytoskeletal dynamics and actin-adhesion coupling (clutch coupling). Decades of research have led to the identification of guidance molecules, their receptors, and downstream signaling cascades for regulating neuronal migration and axonal guidance; however, the molecular machineries required for generating forces to drive growth cone advance and navigation are just beginning to be elucidated. At the leading edge of neuronal growth cones, actin filaments undergo retrograde flow, which is powered by actin polymerization and actomyosin contraction. A clutch coupling between F-actin retrograde flow and adhesive substrate generates traction forces for growth cone advance. The present study describes a detailed protocol for monitoring F-actin retrograde flow by single speckle imaging. Importantly, when combined with an F-actin marker Lifeact, this technique can quantify 1) the F-actin polymerization rate and 2) the clutch coupling efficiency between F-actin retrograde flow and the adhesive substrate. Both are critical variables for generating forces for growth cone advance and navigation. In addition, the present study describes a detailed protocol of traction force microscopy, which can quantify 3) traction force generated by growth cones. Thus, by coupling the analyses of single speckle imaging and traction force microscopy, investigators can monitor the molecular mechanics underlying growth cone advance and navigation.

We present TFMLAB, a MATLAB software package for 4D (x;y;z;t) Traction Force Microscopy (TFM). While various TFM computational workflows are available in the literature, open-source programs that are easy to use by researchers with limited technical experience and that can analyze 4D in vitro systems do not exist. TFMLAB integrates all the computational steps to compute active cellular forces from confocal microscopy images, including image processing, cell segmentation, image alignment, matrix displacement measurement and force recovery. Moreover, TFMLAB eases usability by means of interactive graphical user interfaces. This work describes the package's functionalities and analyzes its performance on a real TFM case

In the last decade, cellular forces in three-dimensional hydrogels that mimic the extracellular matrix have been calculated by means of Traction Force Microscopy (TFM). However, characterizing the accuracy limits of a traction recovery method is critical to avoid obscuring physiological information due to traction recovery errors. So far, 3D TFM algorithms have only been validated using simplified cell geometries, bypassing image processing steps or arbitrarily simulating focal adhesions. Moreover, it is still uncertain which of the two common traction recovery methods, i.e., forward and inverse, is more robust against the inherent challenges of 3D TFM. In this work, we established an advanced in silico validation framework that is applicable to any 3D TFM experimental setup and that can be used to correctly couple the experimental and computational aspects of 3D TFM. Advancements relate to the simultaneous incorporation of complex cell geometries, simulation of microscopy images of varying bead densities and different focal adhesion sizes and distributions. By measuring the traction recovery error with respect to ground truth solutions, we found that while highest traction recovery errors occur for cases with sparse and small focal adhesions, our implementation of the inverse method improves two-fold the accuracy with respect to the forward method (average error of 23% vs. 50%). This advantage was further supported by recovering cellular tractions around angiogenic sprouts in an in vitro model of angiogenesis. The inverse method recovered higher traction peaks and a clearer pulling pattern at the sprout protrusion tips than the forward method. Statement of significance: Biomaterial performance is often studied by quantifying cell-matrix mechanical interactions by means of Traction Force Microscopy (TFM). However, 3D TFM algorithms are often validated in simplified scenarios, which do not allow to fully assess errors that could obscure physiological information. Her

To establish functional networks, neurons must migrate to their appropriate destinations and then extend axons toward their target cells. These processes depend on the advances of growth cones that located at the tips of neurites. Axonal growth cones generate driving forces by sensing their local microenvironment and modulating cytoskeletal dynamics and actin-adhesion coupling (clutch coupling). Decades of research have led to the identification of guidance molecules, their receptors, and downstream signaling cascades for regulating neuronal migration and axonal guidance; however, the molecular machineries required for generating forces to drive growth cone advance and navigation are just beginning to be elucidated. At the leading edge of neuronal growth cones, actin filaments undergo retrograde flow, which is powered by actin polymerization and actomyosin contraction. A clutch coupling between F-actin retrograde flow and adhesive substrate generates traction forces for growth cone advance. The present study describes a detailed protocol for monitoring F-actin retrograde flow by single speckle imaging. Importantly, when combined with an F-actin marker Lifeact, this technique can quantify 1) the F-actin polymerization rate and 2) the clutch coupling efficiency between F-actin retrograde flow and the adhesive substrate. Both are critical variables for generating forces for growth cone advance and navigation. In addition, the present study describes a detailed protocol of traction force microscopy, which can quantify 3) traction force generated by growth cones. Thus, by coupling the analyses of single speckle imaging and traction force microscopy, investigators can monitor the molecular mechanics underlying growth cone advance and navigation., journal article

We present TFMLAB, a MATLAB software package for 4D (x;y;z;t) Traction Force Microscopy (TFM). While various TFM computational workflows are available in the literature, open-source programs that are easy to use by researchers with limited technical experience and that can analyze 4D in vitro systems do not exist. TFMLAB integrates all the computational steps to compute active cellular forces from confocal microscopy images, including image processing, cell segmentation, image alignment, matrix displacement measurement and force recovery. Moreover, TFMLAB eases usability by means of interactive graphical user interfaces. This work describes the package's functionalities and analyzes its performance on a real TFM case

Motile cells can use and switch between different modes of migration. Here, we use traction force microscopy and fluorescent labeling of actin and myosin to quantify and correlate traction force patterns and cytoskeletal distributions in Dictyostelium discoideum cells that move and switch between keratocyte-like fan-shaped, oscillatory, and amoeboid modes. We find that the wave dynamics of the cytoskeletal components critically determine the traction force pattern, cell morphology, and migration mode. Furthermore, we find that fan-shaped cells can exhibit two different propulsion mechanisms, each with a distinct traction force pattern. Finally, the traction force patterns can be recapitulated using a computational model, which uses the experimentally determined spatiotemporal distributions of actin and myosin forces and a viscous cytoskeletal network. Our results suggest that cell motion can be generated by friction between the flow of this network and the substrate.

En la consecución de este trabajo se ha estudiado la viabilidad del empleo de tres modelos constitutivos hiperelásticos en la caracterización de hidrogeles de colágeno: modelo Neo-Hookeano, modelo de Holzapfel y modelo de Steinwachs. Estos geles son utilizados en mecanobiología para simular las características de la matriz extracelular, siendo de gran importancia en el marco de la Microscopía de Fuerza de Tracción (TFM, por sus siglas en inglés). En dicho estudio, se ha efectuado la implementación de los modelos en MATLAB, y sirviéndose de las herramientas que el programa ofrece, se han realizado ajustes por mínimos cuadrados de los parámetros gobernantes de dichos modelos a curvas experimentales enviadas por colaboradores de la Universidad KU Leuven. El modelo que mejor aproxima el comportamiento de los geles es el modelo de Steinwachs, seguido por el de Holzapfel, siendo el Neo-Hookeano el que peores resultados ofrece. Por último, se ha desarrollado una sub-rutina UMAT que implementa el modelo de Steinwachs en el entorno de Análisis por Elementos Finitos Simulia ABAQUS, con el objetivo de ser empleada en el futuro en la resolución de problemas de mayor relevancia en el contexto de TFM., This master’s thesis is devoted to the study of the viability of the application of three hyperelastic constitutive models for the characterization of collagen hydrogels. The considered models are: Neo-Hookean model, Holzapfel model and Steinwachs model. The gels to be characterized are used in mechanobiology to simulate the characteristics of the extracellular matrix, being of great importance in the framework of Traction Force Microscopy (TFM). In such a study, the implementation of the models has been carried out in MATLAB, and using the tools offered by the software, it has been performed a least squares fitting of the experimental curves, sent by collaborators from the KU Leuven University, to the mentioned models. The model that best approximates the behaviour of the gels is the Steinwachs model, followed by Holzapfel’s, with the Neo-Hookean model offering the worst results. Finally, a UMAT subroutine aimed for the implementation of the Steinwachs model in the Finite Element Analysis environment Simulia ABAQUS, has been developed, which could be used in the future in relevant problems in the framework of TFM.

En la consecución de este trabajo se ha estudiado la viabilidad del empleo de tres modelos constitutivos hiperelásticos en la caracterización de hidrogeles de colágeno: modelo Neo-Hookeano, modelo de Holzapfel y modelo de Steinwachs. Estos geles son utilizados en mecanobiología para simular las características de la matriz extracelular, siendo de gran importancia en el marco de la Microscopía de Fuerza de Tracción (TFM, por sus siglas en inglés). En dicho estudio, se ha efectuado la implementación de los modelos en MATLAB, y sirviéndose de las herramientas que el programa ofrece, se han realizado ajustes por mínimos cuadrados de los parámetros gobernantes de dichos modelos a curvas experimentales enviadas por colaboradores de la Universidad KU Leuven. El modelo que mejor aproxima el comportamiento de los geles es el modelo de Steinwachs, seguido por el de Holzapfel, siendo el Neo-Hookeano el que peores resultados ofrece. Por último, se ha desarrollado una sub-rutina UMAT que implementa el modelo de Steinwachs en el entorno de Análisis por Elementos Finitos Simulia ABAQUS, con el objetivo de ser empleada en el futuro en la resolución de problemas de mayor relevancia en el contexto de TFM., This master’s thesis is devoted to the study of the viability of the application of three hyperelastic constitutive models for the characterization of collagen hydrogels. The considered models are: Neo-Hookean model, Holzapfel model and Steinwachs model. The gels to be characterized are used in mechanobiology to simulate the characteristics of the extracellular matrix, being of great importance in the framework of Traction Force Microscopy (TFM). In such a study, the implementation of the models has been carried out in MATLAB, and using the tools offered by the software, it has been performed a least squares fitting of the experimental curves, sent by collaborators from the KU Leuven University, to the mentioned models. The model that best approximates the behaviour of the gels is the Steinwachs model, followed by Holzapfel’s, with the Neo-Hookean model offering the worst results. Finally, a UMAT subroutine aimed for the implementation of the Steinwachs model in the Finite Element Analysis environment Simulia ABAQUS, has been developed, which could be used in the future in relevant problems in the framework of TFM.

Traction Force Microscopy (TFM) is a technique used to determine the tensions that a biological cell conveys to the underlying surface. Typically, TFM requires culturing cells on gels with fluorescent beads, followed by bead displacement calculations. We present a new method allowing to predict those forces from a regular fluorescent image of the cell. Using Deep Learning, we trained a Bayesian Neural Network adapted for pixel regression of the forces and show that it generalises on different cells of the same strain. The predicted forces are computed along with an approximated uncertainty, which shows whether the prediction is trustworthy or not. Using the proposed method could help estimating forces when calculating non-trivial bead displacements and can also free one of the fluorescent channels of the microscope. Code is available at https://github.com/wahlby-lab/InSilicoTFM.

Human embryonic stem cells demonstrate a unique ability to respond to morphogens in vitro by self-organizing patterns of cell fate specification that correspond to primary germ layer formation during embryogenesis. Thus, these cells represent a powerful tool with which to examine the mechanisms that drive early human development. We have developed a method to culture human embryonic stem cells in confined colonies on compliant substrates that provides control over both the geometry of the colonies and their mechanical environment in order to recapitulate the physical parameters that underlie embryogenesis. The key feature of this method is the ability to generate polyacrylamide hydrogels with defined patterns of extracellular matrix ligand at the surface to promote cell attachment. This is achieved by fabricating stencils with the desired geometric patterns, using these stencils to create patterns of extracellular matrix ligand on glass coverslips, and transferring these patterns to polyacrylamide hydrogels during polymerization. This method is also compatible with traction force microscopy, allowing the user to measure and map the distribution of cell-generated forces within the confined colonies. In combination with standard biochemical assays, these measurements can be used to examine the role mechanical cues play in fate specification and morphogenesis during early human development.

Cell migration is a crucial aspect of many biological processes ranging from development, to cancer cell metastasis. One very important process is the inflammatory response, where neutrophils must migrate through a diverse set of environments as they travel from the bloodstream, across cell monolayers and through the extravascular space which contains other cells and extracellular matrix before reaching locations of injury or infection. Although many studies have focused on the biochemical and molecular signaling events involved in the entire process, little is know about the role of mechanics in the last step, which is essentially migration through a 3-dimensional (3-D) confined environment. Extracellular matrix structure and stiffness have been shown to affect 3-D cell migration. However, it is unclear whether an optimal balance must exist between these factors for neutrophils to navigate and migrate complex 3-D environments in the presence of a chemoattractant. In the present thesis, we aim to investigate whether matrix porosity and stiffness play a determinant role in 3-D neutrophil chemotaxis. Using novel assays, imaging and computational analysis techniques, we found that although neutrophils are able to engage in directed migration in a range of matrix environments, optimal migration occurs at low densities and stiffnesses. Also, we see that these cells engage in periodic shape and motion changes that are independent of the nature of their matrix. However, unique forces are exerted on their surrounding environments in matrices with high porosities and low stiffnesses. These results demonstrate that although 3-D neutrophil migration is a robust process, the mechanical environment plays a very important role on the ability of these cells to move in 3-D spaces.

Cell migration is a crucial aspect of many biological processes ranging from development, to cancer cell metastasis. One very important process is the inflammatory response, where neutrophils must migrate through a diverse set of environments as they travel from the bloodstream, across cell monolayers and through the extravascular space which contains other cells and extracellular matrix before reaching locations of injury or infection. Although many studies have focused on the biochemical and molecular signaling events involved in the entire process, little is know about the role of mechanics in the last step, which is essentially migration through a 3-dimensional (3-D) confined environment. Extracellular matrix structure and stiffness have been shown to affect 3-D cell migration. However, it is unclear whether an optimal balance must exist between these factors for neutrophils to navigate and migrate complex 3-D environments in the presence of a chemoattractant. In the present thesis, we aim to investigate whether matrix porosity and stiffness play a determinant role in 3-D neutrophil chemotaxis. Using novel assays, imaging and computational analysis techniques, we found that although neutrophils are able to engage in directed migration in a range of matrix environments, optimal migration occurs at low densities and stiffnesses. Also, we see that these cells engage in periodic shape and motion changes that are independent of the nature of their matrix. However, unique forces are exerted on their surrounding environments in matrices with high porosities and low stiffnesses. These results demonstrate that although 3-D neutrophil migration is a robust process, the mechanical environment plays a very important role on the ability of these cells to move in 3-D spaces.

The aim of this work is to quantify the spatio-temporal dynamics of flow-driven amoeboid locomotion in small (~100 µm) fragments of the true slime mold Physarum polycephalum. In this model organism, cellular contraction drives intracellular flows, and these flows transport the chemical signals that regulate contraction in the first place. As a consequence of these non-linear interactions, a diversity of migratory behaviors can be observed in migrating Physarum fragments. To study these dynamics, we measure the spatio-temporal distributions of the velocities of the endoplasm and ectoplasm of each migrating fragment, the traction stresses it generates on the substratum, and the concentration of free intracellular calcium. Using these unprecedented experimental data, we classify migrating Physarum fragments according to their dynamics, finding that they often exhibit spontaneously coordinated waves of flow, contractility and chemical signaling. We show that Physarum fragments exhibiting symmetric spatio-temporal patterns of endoplasmic flow migrate significantly slower than fragments with asymmetric patterns. In addition, our joint measurements of ectoplasm velocity and traction stress at the substratum suggest that forward motion of the ectoplasm is enabled by a succession of stick-slip transitions, which we conjecture are also organized in the form of waves. Combining our experiments with a simplified convection-diffusion model, we show that the convective transport of calcium ions may be key for establishing and maintaining the spatiotemporal patterns of calcium concentration that regulate the generation of contractile forces.

The aim of this work is to quantify the spatio-temporal dynamics of flow-driven amoeboid locomotion in small (~100 µm) fragments of the true slime mold Physarum polycephalum. In this model organism, cellular contraction drives intracellular flows, and these flows transport the chemical signals that regulate contraction in the first place. As a consequence of these non-linear interactions, a diversity of migratory behaviors can be observed in migrating Physarum fragments. To study these dynamics, we measure the spatio-temporal distributions of the velocities of the endoplasm and ectoplasm of each migrating fragment, the traction stresses it generates on the substratum, and the concentration of free intracellular calcium. Using these unprecedented experimental data, we classify migrating Physarum fragments according to their dynamics, finding that they often exhibit spontaneously coordinated waves of flow, contractility and chemical signaling. We show that Physarum fragments exhibiting symmetric spatio-temporal patterns of endoplasmic flow migrate significantly slower than fragments with asymmetric patterns. In addition, our joint measurements of ectoplasm velocity and traction stress at the substratum suggest that forward motion of the ectoplasm is enabled by a succession of stick-slip transitions, which we conjecture are also organized in the form of waves. Combining our experiments with a simplified convection-diffusion model, we show that the convective transport of calcium ions may be key for establishing and maintaining the spatiotemporal patterns of calcium concentration that regulate the generation of contractile forces.

While performing several functions, adherent cells deform their surrounding substrate via stable adhesions that connect the intracellular cytoskeleton to the extracellular matrix. The traction forces that deform the substrate are studied in mechanotrasduction because they are affected by the mechanics of the extracellular milieu. We review the development and application of two methods widely used to measure traction forces generated by cells on 2D substrates: (i) traction force microscopy with polyacrylamide hydrogels and (ii) calculation of traction forces with arrays of deformable microposts. Measuring forces with these methods relies on measuring substrate displacements and converting them into forces. We describe approaches to determine force from displacements and elaborate on the necessary experimental conditions for this type of analysis. We emphasize device fabrication, mechanical calibration of substrates and covalent attachment of extracellular matrix proteins to substrates as key features in the design of experiments to measure cell traction forces with polyacrylamide hydrogels or microposts. We also report the challenges and achievements in integrating these methods with platforms for the mechanical stimulation of adherent cells. The approaches described here will enable new studies to understand cell mechanical outputs as a function of mechanical inputs and advance the understanding of mechanotransduction mechanisms.

While performing several functions, adherent cells deform their surrounding substrate via stable adhesions that connect the intracellular cytoskeleton to the extracellular matrix. The traction forces that deform the substrate are studied in mechanotrasduction because they are affected by the mechanics of the extracellular milieu. We review the development and application of two methods widely used to measure traction forces generated by cells on 2D substrates: (i) traction force microscopy with polyacrylamide hydrogels and (ii) calculation of traction forces with arrays of deformable microposts. Measuring forces with these methods relies on measuring substrate displacements and converting them into forces. We describe approaches to determine force from displacements and elaborate on the necessary experimental conditions for this type of analysis. We emphasize device fabrication, mechanical calibration of substrates and covalent attachment of extracellular matrix proteins to substrates as key features in the design of experiments to measure cell traction forces with polyacrylamide hydrogels or microposts. We also report the challenges and achievements in integrating these methods with platforms for the mechanical stimulation of adherent cells. The approaches described here will enable new studies to understand cell mechanical outputs as a function of mechanical inputs and advance the understanding of mechanotransduction mechanisms.

This study focuses on the application of inverse finite element methods and computational mechanic techniques in order to simulate the spinal cord s contraction described in the previous section. Specifically, the aim is to know which forces lead to some imposed displacements and boundary conditions and to know the state of deformation of the full body due to the input data. In order to acquire this objective, the TFM experiment will be discretized in an appropriate way in order to apply the inverse finite element method. The scope of this study is to determine the uniqueness of the solution and it s stability for different sets of external or internal forces and imposed displacements. This parameters will be studied through numerical analysis and theoretical results will be attempted. The results of the numerical computations will be physically interpreted and illustrated.

While performing several functions, adherent cells deform their surrounding substrate via stable adhesions that connect the intracellular cytoskeleton to the extracellular matrix. The traction forces that deform the substrate are studied in mechanotrasduction because they are affected by the mechanics of the extracellular milieu. We review the development and application of two methods widely used to measure traction forces generated by cells on 2D substrates: (i) traction force microscopy with polyacrylamide hydrogels and (ii) calculation of traction forces with arrays of deformable microposts. Measuring forces with these methods relies on measuring substrate displacements and converting them into forces. We describe approaches to determine force from displacements and elaborate on the necessary experimental conditions for this type of analysis. We emphasize device fabrication, mechanical calibration of substrates and covalent attachment of extracellular matrix proteins to substrates as key features in the design of experiments to measure cell traction forces with polyacrylamide hydrogels or microposts. We also report the challenges and achievements in integrating these methods with platforms for the mechanical stimulation of adherent cells. The approaches described here will enable new studies to understand cell mechanical outputs as a function of mechanical inputs and advance the understanding of mechanotransduction mechanisms.

This work examines the relationship between spatio-temporal coordination of intracellular flow and traction stress and the speed of amoeboid locomotion of microplasmodia of Physarum polycephalum. We simultaneously perform particle image velocimetry and traction stress microscopy to measure the velocity of cytoplasmic flow and the stresses applied to the substrate by migrating Physarum microamoebae. In parallel, we develop a mathematical model of a motile cell which includes forces from the viscous cytosol, a poro-elastic, contractile cytoskeleton and adhesive interactions with the substrate. Our experiments show that flow and traction stress exhibit back-to-front-directed waves with a distinct phase difference. The model demonstrates that the direction and speed of locomotion are determined by this coordination between contraction, flow and adhesion. Using the model, we identify forms of coordination that generate model predictions consistent with experiments. We demonstrate that this coordination produces near optimal migration speed and is insensitive to heterogeneity in substrate adhesiveness. While it is generally thought that amoeboid motility is robust to changes in extracellular geometry and the nature of extracellular adhesion, our results demonstrate that coordination of adhesive forces is essential to producing robust migration.

Fundamental biological processes including morphogenesis and tissue repair require cells to migrate collectively. In these processes, epithelial or endothelial cells move in a cooperative manner coupled by intercellular junctions. Ultimately, the movement of these multicellular systems occurs through the generation of cellular forces, exerted either on the substrate via focal adhesions (cell–substrate forces) or on neighboring cells through cell–cell junctions (cell–cell forces). Quantitative measurements of multicellular forces and kinematics with cellular or subcellular resolution have become possible only in recent years. In this chapter, we describe some of these techniques, which include particle image velocimetry to map cell velocities, traction force microscopy to map forces exerted by cells on the substrate, and monolayer stress microscopy to map forces within and between cells. We also describe experimental protocols to perform these measurements. The combination of these techniques with high-resolution imaging tools and molecular perturbations will lead to a better understanding of the mechanisms underlying collective cell migration in health and disease., Peer Reviewed, Postprint (author's final draft)

Olfactory ensheathing cell (OEC) transplantation emerged some years ago as a promising therapeutic strategy to repair injured spinal cord. However, inhibitory molecules are present for long periods of time in lesioned spinal cord, inhibiting both OEC migration and axonal regrowth. Two families of these molecules, chondroitin sulphate proteoglycans (CSPG) and myelin-derived inhibitors (MAIs), are able to trigger inhibitory responses in lesioned axons. Mounting evidence suggests that OEC migration is inhibited by myelin. Here we demonstrate that OEC migration is largely inhibited by CSPGs and that inhibition can be overcome by the bacterial enzyme Chondroitinase ABC. In parallel, we have generated a stable OEC cell line overexpressing the Nogo receptor (NgR) ectodomain to reduce MAI-associated inhibition in vitro and in vivo. Results indicate that engineered cells migrate longer distances than unmodified OECs over myelin or oligodendrocyte-myelin glycoprotein (OMgp)-coated substrates. In addition, they also show improved migration in lesioned spinal cord. Our results provide new insights toward the improvement of the mechanisms of action and optimization of OEC-based cell therapy for spinal cord lesion.

Physical processes play an important role in many biological phenomena, such as wound healing, organ development, and tumor metastasis. During these processes, cells constantly interact with and adapt to their environment by exerting forces to mechanically probe the features of their surroundings and generating appropriate biochemical responses. The mechanisms underlying how cells sense the physical properties of their environment are not well understood. In this thesis, I present my studies to investigate cellular responses to the stiffness and topography of the environment. In order to sense the physical properties of their environment, cells dynamically reorganize the structure of their actin cytoskeleton, a dynamic network of biopolymers, altering the shape and spatial distribution of protein assemblies. Several observations suggest that proteins that crosslink actin filaments may play an important role in cellular mechanosensitivity. Palladin is an actin-crosslinking protein that is found in the lamellar actin network, stress fibers and focal adhesions, cellular structures that are critical for mechanosensing of the physical environment. By virtue of its close interactions with these structures in the cell, palladin may play an important role in cell mechanics. However, the role of actin crosslinkers in general, and palladin in particular, in cellular force generation and mechanosensing is not well known. I have investigated the role of palladin in regulating the plasticity of the actin cytoskeleton and cellular force generation in response to alterations in substrate stiffness. I have shown that the expression levels of palladin modulate the forces exerted by cells and their ability to sense substrate stiffness. Perturbation experiments also suggest that palladin levels in cells altered myosin motor activity. These results suggest that the actin crosslinkers, such as palladin, and myosin motors coordinate for optimal cell function and to prevent aberrant behav

The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.

The ability of cells to adhere and to exert contractile forces governs their capacity to move within an organism. The cytoskeletal regulators of the Rho GTPase proteins are involved in control of the contractile forces of cells. To elucidate the basis of cell migration, we analyzed contractile forces and nanoscale adhesion-related particles in single cells expressing constitutively active variants of Rho GTPases by using traction-force microscopy and ultra-high-resolution stimulated emission depletion microscopy, respectively. RhoAV14 induced large increases in the contractile forces of single cells, with Rac1L61 and RhoDV26 having more moderate effects. The RhoAV14- and RhoDV26-induced forces showed similar spatial distributions and were accompanied by reduced or unaltered cell spreading. In contrast, the Rac1L61-induced force had different, scattered, force distributions that were linked to increased cell spreading. All three of these Rho GTPase activities caused a loss of thick stress fibers and focal adhesions and a more homogenous distribution of nanoscale adhesion-related particles over the ventral surface of the cells. Interestingly, only RhoAV14 increased the density of these particles. Our data suggest a Rac1-specific mode for cells to generate contractile forces. Importantly, increased density and a more homogenous distribution of these small adhesion-related particles promote cellular contractile forces.-Gad, A. K. B., Ronnlund, D., Spaar, A., Savchenko, A. A., Petranyi, G., Blom, H., Szekely, L., Widengren, J., Aspenstrom, P. Rho GTPases link cellular contractile force to the density and distribution of nanoscale adhesions., QC 20120703

Newly generated olfactory receptor axons grow from the peripheral to the central nervous system aided by olfactory ensheathing cells (OECs). Thus, OEC transplantation has emerged as a promising therapy for spinal cord injuries and for other neural diseases. However, these cells do not present a uniform population, but instead a functionally heterogeneous population that exhibits a variety of responses including adhesion, repulsion, and crossover during cell–cell and cell–matrix interactions. Some studies report that the migratory properties of OECs are compromised by inhibitory molecules and potentiated by chemical gradients. Here, we demonstrated that rodent OECs express all the components of the Nogo receptor complex and that their migration is blocked by myelin. Next, we used cell tracking and traction force microscopy to analyze OEC migration and its mechanical properties over myelin. Our data relate the decrease of traction force of OEC with lower migratory capacity over myelin, which correlates with changes in the F-actin cytoskeleton and focal adhesion distribution. Lastly, OEC traction force and migratory capacity is enhanced after cell incubation with the Nogo receptor inhibitor NEP1-40.