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by Keyword: Rigidity

Clark, AG, Maitra, A, Jacques, C, Bergert, M, Perez-Gonzalez, C, Simon, A, Lederer, L, Diz-Munoz, A, Trepat, X, Voituriez, R, Vignjevic, DM, (2022). Self-generated gradients steer collective migration on viscoelastic collagen networks Nature Materials 21, 1200-1210

Growing evidence suggests that the physical properties of the cellular microenvironment influence cell migration. However, it is not currently understood how active physical remodelling by cells affects migration dynamics. Here we report that cell clusters seeded on deformable collagen-I networks display persistent collective migration despite not showing any apparent intrinsic polarity. Clusters generate transient gradients in collagen density and alignment due to viscoelastic relaxation of the collagen networks. Combining theory and experiments, we show that crosslinking collagen networks or reducing cell cluster size results in reduced network deformation, shorter viscoelastic relaxation time and smaller gradients, leading to lower migration persistence. Traction force and Brillouin microscopy reveal asymmetries in force distributions and collagen stiffness during migration, providing evidence of mechanical cross-talk between cells and their substrate during migration. This physical model provides a mechanism for self-generated directional migration on viscoelastic substrates in the absence of internal biochemical polarity cues.; Cell clusters mechanically reorganize viscoelastic collagen networks, resulting in transient gradients in collagen density, alignment and stiffness that promote spontaneous persistent migration.

JTD Keywords: Cell-migration, Design, Invasion, Limits, Mechanics, Microscopy, Morphogenesis, Motility, Rear, Rigidity


Beltrán G, Navajas D, García-Aznar JM, (2022). Mechanical modeling of lung alveoli: From macroscopic behaviour to cell mechano-sensing at microscopic level Journal Of The Mechanical Behavior Of Biomedical Materials 126, 105043

The mechanical signals sensed by the alveolar cells through the changes in the local matrix stiffness of the extracellular matrix (ECM) are determinant for regulating cellular functions. Therefore, the study of the mechanical response of lung tissue becomes a fundamental aspect in order to further understand the mechanosensing signals perceived by the cells in the alveoli. This study is focused on the development of a finite element (FE) model of a decellularized rat lung tissue strip, which reproduces accurately the mechanical behaviour observed in the experiments by means of a tensile test. For simulating the complex structure of the lung parenchyma, which consists of a heterogeneous and non-uniform network of thin-walled alveoli, a 3D model based on a Voronoi tessellation is developed. This Voronoi-based model is considered very suitable for recreating the geometry of cellular materials with randomly distributed polygons like in the lung tissue. The material model used in the mechanical simulations of the lung tissue was characterized experimentally by means of AFM tests in order to evaluate the lung tissue stiffness on the micro scale. Thus, in this study, the micro (AFM test) and the macro scale (tensile test) mechanical behaviour are linked through the mechanical simulation with the 3D FE model based on Voronoi tessellation. Finally, a micro-mechanical FE-based model is generated from the Voronoi diagram for studying the stiffness sensed by the alveolar cells in function of two independent factors: the stretch level of the lung tissue and the geometrical position of the cells on the extracellular matrix (ECM), distinguishing between pneumocyte type I and type II. We conclude that the position of the cells within the alveolus has a great influence on the local stiffness perceived by the cells. Alveolar cells located at the corners of the alveolus, mainly type II pneumocytes, perceive a much higher stiffness than those located in the flat areas of the alveoli, which correspond to type I pneumocytes. However, the high stiffness, due to the macroscopic lung tissue stretch, affects both cells in a very similar form, thus no significant differences between them have been observed. © 2021 The Authors

JTD Keywords: rat, scaffolds, stiffness, Afm, Animal cell, Animal experiment, Animal model, Animal tissue, Article, Biological organs, Cell function, Cells, Computational geometry, Cytology, Extracellular matrices, Extracellular matrix, Extracellular-matrix, Geometry, High stiffness, Human, Lung alveolus cell type 1, Lung alveolus cell type 2, Lung parenchyma, Lung tissue, Male, Mechanical behavior, Mechanical modeling, Mechanical simulations, Mechanosensing, Model-based opc, Nonhuman, Physical model, Rat, Rigidity, Stiffness, Stiffness matrix, Tensile testing, Thin walled structures, Three dimensional finite element analysis, Tissue, Type ii, Voronoi tessellations


Andreu, I, Falcones, B, Hurst, S, Chahare, N, Quiroga, X, Le Roux, AL, Kechagia, Z, Beedle, AEM, Elosegui-Artola, A, Trepat, X, Farre, R, Betz, T, Almendros, I, Roca-Cusachs, P, (2021). The force loading rate drives cell mechanosensing through both reinforcement and cytoskeletal softening Nature Communications 12, 4229

Cell response to force regulates essential processes in health and disease. However, the fundamental mechanical variables that cells sense and respond to remain unclear. Here we show that the rate of force application (loading rate) drives mechanosensing, as predicted by a molecular clutch model. By applying dynamic force regimes to cells through substrate stretching, optical tweezers, and atomic force microscopy, we find that increasing loading rates trigger talin-dependent mechanosensing, leading to adhesion growth and reinforcement, and YAP nuclear localization. However, above a given threshold the actin cytoskeleton softens, decreasing loading rates and preventing reinforcement. By stretching rat lungs in vivo, we show that a similar phenomenon may occur. Our results show that cell sensing of external forces and of passive mechanical parameters (like tissue stiffness) can be understood through the same mechanisms, driven by the properties under force of the mechanosensing molecules involved. Cells sense mechanical forces from their environment, but the precise mechanical variable sensed by cells is unclear. Here, the authors show that cells can sense the rate of force application, known as the loading rate, with effects on YAP nuclear localization and cytoskeletal stiffness remodelling.

JTD Keywords: Actin cytoskeleton, Actin filament, Actin-filament, Adhesion, Animal, Animals, Atomic force microscopy, Breathing, Cell, Cell adhesion, Cell culture, Cell nucleus, Cells, cultured, Cytoplasm, Extracellular-matrix, Fibroblast, Fibroblasts, Fibronectin, Frequency, Gene knockdown, Gene knockdown techniques, Genetics, Germfree animal, Integrin, Intracellular signaling peptides and proteins, Knockout mouse, Lung, Male, Mechanotransduction, Mechanotransduction, cellular, Metabolism, Mice, Mice, knockout, Microscopy, atomic force, Mouse, Optical tweezers, Paxillin, Physiology, Primary cell culture, Pxn protein, mouse, Rat, Rats, Rats, sprague-dawley, Respiration, Signal peptide, Softening, Specific pathogen-free organisms, Sprague dawley rat, Stress, Substrate, Substrate rigidity, Talin, Talin protein, mouse, Tln2 protein, mouse, Traction, Transmission, Ultrastructure, Yap1 protein, rat


Bennett, Mark, Cantini, Marco, Reboud, Julien, Cooper, Jonathan M., Roca-Cusachs, Pere, Salmeron-Sanchez, Manuel, (2018). Molecular clutch drives cell response to surface viscosity Proceedings of the National Academy of Sciences of the United States of America 115, (6), 1192-1197

Cell response to matrix rigidity has been explained by the mechanical properties of the actin-talin-integrin-fibronectin clutch. Here the molecular clutch model is extended to account for cell interactions with purely viscous surfaces (i.e., without an elastic component). Supported lipid bilayers present an idealized and controllable system through which to study this concept. Using lipids of different diffusion coefficients, the mobility (i.e., surface viscosity) of the presented ligands (in this case RGD) was altered by an order of magnitude. Cell size and cytoskeletal organization were proportional to viscosity. Furthermore, there was a higher number of focal adhesions and a higher phosphorylation of FAK on less-mobile (more-viscous) surfaces. Actin retrograde flow, an indicator of the force exerted on surfaces, was also seen to be faster on more mobile surfaces. This has consequential effects on downstream molecules; the mechanosensitive YAP protein localized to the nucleus more on less-mobile (more-viscous) surfaces and differentiation of myoblast cells was enhanced on higher viscosity. This behavior was explained within the framework of the molecular clutch model, with lower viscosity leading to a low force loading rate, preventing the exposure of mechanosensitive proteins, and with a higher viscosity causing a higher force loading rate exposing these sites, activating downstream pathways. Consequently, the understanding of how viscosity (regardless of matrix stiffness) influences cell response adds a further tool to engineer materials that control cell behavior.

JTD Keywords: Matrix rigidity, Molecular clutch, Surface viscosity, Mechanotransduction, Cell differentiation


Elosegui-Artola, A., Andreu, I., Beedle, A. E. M., Lezamiz, A., Uroz, M., Kosmalska, A. J., Oria, R., Kechagia, J. Z., Rico-Lastres, P., Le Roux, A. L., Shanahan, C. M., Trepat, X., Navajas, D., Garcia-Manyes, S., Roca-Cusachs, P., (2017). Force triggers YAP nuclear entry by regulating transport across nuclear pores Cell 171, (6), 1397-1410

YAP is a mechanosensitive transcriptional activator with a critical role in cancer, regeneration, and organ size control. Here, we show that force applied to the nucleus directly drives YAP nuclear translocation by decreasing the mechanical restriction of nuclear pores to molecular transport. Exposure to a stiff environment leads cells to establish a mechanical connection between the nucleus and the cytoskeleton, allowing forces exerted through focal adhesions to reach the nucleus. Force transmission then leads to nuclear flattening, which stretches nuclear pores, reduces their mechanical resistance to molecular transport, and increases YAP nuclear import. The restriction to transport is further regulated by the mechanical stability of the transported protein, which determines both active nuclear transport of YAP and passive transport of small proteins. Our results unveil a mechanosensing mechanism mediated directly by nuclear pores, demonstrated for YAP but with potential general applicability in transcriptional regulation. Force-dependent changes in nuclear pores control protein access to the nucleus.

JTD Keywords: Atomic force microscopy, Hippo pathway, Mechanosensing, Mechanotransduction, Molecular mechanical stability, Nuclear mechanics, Nuclear pores, Nuclear transport, Rigidity sensing, Transcription regulation


Melo, E., Cárdenes, N., Garreta, E., Luque, T., Rojas, M., Navajas, D., Farré, R., (2014). Inhomogeneity of local stiffness in the extracellular matrix scaffold of fibrotic mouse lungs Journal of the Mechanical Behavior of Biomedical Materials , 37, 186-195

Lung disease models are useful to study how cell engraftment, proliferation and differentiation are modulated in lung bioengineering. The aim of this work was to characterize the local stiffness of decellularized lungs in aged and fibrotic mice. Mice (2- and 24-month old; 14 of each) with lung fibrosis (N=20) and healthy controls (N=8) were euthanized after 11 days of intratracheal bleomycin (fibrosis) or saline (controls) infusion. The lungs were excised, decellularized by a conventional detergent-based (sodium-dodecyl sulfate) procedure and slices of the acellular lungs were prepared to measure the local stiffness by means of atomic force microscopy. The local stiffness of the different sites in acellular fibrotic lungs was very inhomogeneous within the lung and increased according to the degree of the structural fibrotic lesion. Local stiffness of the acellular lungs did not show statistically significant differences caused by age. The group of mice most affected by fibrosis exhibited local stiffness that were ~2-fold higher than in the control mice: from 27.2±1.64 to 64.8±7.1. kPa in the alveolar septa, from 56.6±4.6 to 99.9±11.7. kPa in the visceral pleura, from 41.1±8.0 to 105.2±13.6. kPa in the tunica adventitia, and from 79.3±7.2 to 146.6±28.8. kPa in the tunica intima. Since acellular lungs from mice with bleomycin-induced fibrosis present considerable micromechanical inhomogeneity, this model can be a useful tool to better investigate how different degrees of extracellular matrix lesion modulate cell fate in the process of organ bioengineering from decellularized lungs.

JTD Keywords: Ageing, Atomic force microscopy, Decellularization, Lung fibrosis, Tissue engineering, Atomic force microscopy, Biological organs, Peptides, Sodium dodecyl sulfate, Sodium sulfate, Tissue engineering, Ageing, Decellularization, Extracellular matrices, Healthy controls, Inhomogeneities, Lung fibrosis, Micro-mechanical, Statistically significant difference, Mammals, bleomycin, adventitia, animal experiment, animal model, article, atomic force microscopy, bleomycin-induced pulmonary fibrosis, cell fate, controlled study, extracellular matrix, female, intima, lung alveolus, lung fibrosis, lung mechanics, mechanical probe, microenvironment, mouse, nonhuman, pleura, priority journal, rigidity, tissue engineering


Nonaka, P. N., Uriarte, J. J., Campillo, N., Melo, E., Navajas, D., Farré, R., Oliveira, L. V. F., (2014). Mechanical properties of mouse lungs along organ decellularization by sodium dodecyl sulfate Respiratory Physiology & Neurobiology , 200, 1-5

Lung decellularization is based on the use of physical, chemical, or enzymatic methods to break down the integrity of the cells followed by a treatment to extract the cellular material from the lung scaffold. The aim of this study was to characterize the mechanical changes throughout the different steps of lung decellularization process. Four lungs from mice (C57BL/6) were decellularized by using a conventional protocol based on sodium dodecyl sulfate. Lungs resistance (RL) and elastance (EL) were measured along decellularization steps and were computed by linear regression fitting of tracheal pressure, flow, and volume during mechanical ventilation. Transients differences found were more distinct in an intermediate step after the lungs were rinsed with deionized water and treated with 1% SDS, whereupon the percentage of variation reached approximately 80% for resistance values and 30% for elastance values. In conclusion, although a variation in extracellular matrix stiffness was observed during the decellularization process, this variation can be considered negligible overall because the resistance and elastance returned to basal values at the final decellularization step.

JTD Keywords: Lung bioengineering, Lung decellularization, Organ scaffold, dodecyl sulfate sodium, animal tissue, article, artificial ventilation, compliance (physical), controlled study, enzyme chemistry, extracellular matrix, female, flow, lung, lung decellularization, lung pressure, lung resistance, mouse, nonhuman, positive end expiratory pressure, priority journal, rigidity, tissue engineering, trachea pressure


Vaca, R., Aranda, J., (2014). Triangular-fan-based algorithm for computing the closure conditions of planar linkages Advanced Numerical Methods IV 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI) , CIMNE (Barcelona, Spain) , 1-2

The position analysis of a planar mechanism is based on obtaining the roots of its characteristic polynomial. In general, this polynomial is the result of a system of kinematic equations which they are derived from closure condition of the mechanism, widely known as independent kinematic loop equations or loop closure equations . This way of solving the position analysis of kinematic chains introduces complex variable eliminations, and in general trigonometric substitutions. Recently, the use of methods based on bilateration to solve the position analysis, has been shown to avoid these variable eliminations and trigonometric substitutions in planar mechanism. In this work it is shown how this method based on bilateration can be use to automatically generate closure conditions of a planar mechanism.

JTD Keywords: Position analysis, Bilateration, Rigidity, Isomorphism, Kinematic