An iterative method to calculate forces exerted by single cells and multicellular assemblies from the detection of deformations of flexible substrates

Measurement of cell traction force with a thin film PDMS cantilever

Adherent cells produce cellular traction force (CTF) on a substrate to maintain their physical morphologies, sense external environment, and perform essential cellular functions. Precise characterization of the CTF can expand our knowledge of various cellular processes as well as lead to the development of novel mechanical biomarkers. However, current methods that measure CTF require special substrates and fluorescent microscopy, rendering them less suitable in a clinical setting. Here, we demonstrate a rapid and direct approach to measure the combined CTF of a large cell population using thin polydimethylsiloxane (PDMS) cantilevers. Cells attached to the top surface of the PDMS cantilever produce CTF, which causes the cantilever to bend. The side view of the cantilever was imaged with a low-cost camera to extract the CTF. We characterized the CTF of fibroblasts and breast cancer cells. In addition, we were able to directly measure the contractile force of a suspended cell sheet, which is similar to the CTF of the confluent cell layer before detachment. The demonstrated technique can provide rapid and real-time measurement of the CTF of a large cell population and can directly characterize its temporal dynamics. The developed thin film PDMS cantilever can be fabricated affordably and the CTF extraction technique does not require expensive equipment. Thus, we believe that the developed method can provide an easy-to-use and affordable platform for CTF characterization in clinical settings and laboratories.

Analysis of Calcium Transients and Uniaxial Contraction Force in Single Human Embryonic Stem Cell-Derived Cardiomyocytes on Microstructured Elastic Substrate with Spatially Controlled Surface Chemistries

The mechanical activity of cardiomyocytes is the result of a process called excitation-contraction coupling (ECC). A membrane depolarization wave induces a transient cytosolic calcium concentration increase that triggers activation of calcium-sensitive contractile proteins, leading to cell contraction and force generation. An experimental setup capable of acquiring simultaneously all ECC features would have an enormous impact on cardiac drug development and disease study. In this work, we develop a microengineered elastomeric substrate with tailor-made surface chemistry to measure simultaneously the uniaxial contraction force and the calcium transients generated by single human cardiomyocytes in vitro. Microreplication followed by photocuring is used to generate an array consisting of elastomeric micropillars. A second photochemical process is employed to spatially control the surface chemistry of the elastomeric pillar. As result, human embryonic stem cell-derived cardiomyocytes (hESC-CMs) can be confined in rectangular cell-adhesive areas, which induce cell elongation and promote suspended cell anchoring between two adjacent micropillars. In this end-to-end conformation, confocal fluorescence microscopy allows simultaneous detection of calcium transients and micropillar deflection induced by a single-cell uniaxial contraction force. Computational finite elements modeling (FEM) and 3D reconstruction of the cell-pillar interface allow force quantification. The platform is used to follow calcium dynamics and contraction force evolution in hESC-CMs cultures over the course of several weeks. Our results show how a biomaterial-based platform can be a versatile tool for in vitro assaying of cardiac functional properties of single-cell human cardiomyocytes, with applications in both in vitro developmental studies and drug screening on cardiac cultures.

The performance of discrete models of low Reynolds number swimmers

Swimming by shape changes at low Reynolds number is widely used in biology and understanding how the performance of movement depends on the geometric pattern of shape changes is important to understand swimming of microorganisms and in designing low Reynolds number swimming models. The simplest models of shape changes are those that comprise a series of linked spheres that can change their separation and/or their size. Herein we compare the performance of three models in which these modes are used in different ways.

Physically based principles of cell adhesion mechanosensitivity in tissues

The minimal structural unit that defines living organisms is a single cell. By proliferating and mechanically interacting with each other, cells can build complex organization such as tissues that ultimately organize into even more complex multicellular living organisms, such as mammals, composed of billions of single cells interacting with each other. As opposed to passive materials, living cells actively respond to the mechanical perturbations occurring in their environment. Tissue cell adhesion to its surrounding extracellular matrix or to neighbors is an example of a biological process that adapts to physical cues. The adhesion of tissue cells to their surrounding medium induces the generation of intracellular contraction forces whose amplitude adapts to the mechanical properties of the environment. In turn, solicitation of adhering cells with physical forces, such as blood flow shearing the layer of endothelial cells in the lumen of arteries, reinforces cell adhesion and impacts cell contractility. In biological terms, the sensing of physical signals is transduced into biochemical signaling events that guide cellular responses such as cell differentiation, cell growth and cell death. Regarding the biological and developmental consequences of cell adaptation to mechanical perturbations, understanding mechanotransduction in tissue cell adhesion appears as an important step in numerous fields of biology, such as cancer, regenerative medicine or tissue bioengineering for instance. Physicists were first tempted to view cell adhesion as the wetting transition of a soft bag having a complex, adhesive interaction with the surface. But surprising responses of tissue cell adhesion to mechanical cues challenged this view. This, however, did not exclude that cell adhesion could be understood in physical terms. It meant that new models and descriptions had to be created specifically for these biological issues, and could not straightforwardly be adapted from dead matter. In this review, we present physical concepts of tissue cell adhesion and the unexpected cellular responses to mechanical cues such as external forces and stiffness sensing. We show how biophysical approaches, both experimentally and theoretically, have contributed to our understanding of the regulation of cellular functions through physical force sensing mechanisms. Finally, we discuss the different physical models that could explain how tissue cell adhesion and force sensing can be coupled to internal mechanosensitive processes within the cell body.

Macroscopic stiffening of embryonic tissues via microtubules, RhoGEF and the assembly of contractile bundles of actomyosin

During morphogenesis, forces generated by cells are coordinated and channeled by the viscoelastic properties of the embryo. Microtubules and F-actin are considered to be two of the most important structural elements within living cells accounting for both force production and mechanical stiffness. In this paper, we investigate the contribution of microtubules to the stiffness of converging and extending dorsal tissues in Xenopus laevis embryos using cell biological, biophysical and embryological techniques. Surprisingly, we discovered that depolymerizing microtubules stiffens embryonic tissues by three- to fourfold. We attribute tissue stiffening to Xlfc, a previously identified RhoGEF, which binds microtubules and regulates the actomyosin cytoskeleton. Combining drug treatments and Xlfc activation and knockdown lead us to the conclusion that mechanical properties of tissues such as viscoelasticity can be regulated through RhoGTPase pathways and rule out a direct contribution of microtubules to tissue stiffness in the frog embryo. We can rescue nocodazole-induced stiffening with drugs that reduce actomyosin contractility and can partially rescue morphogenetic defects that affect stiffened embryos. We support these conclusions with a multi-scale analysis of cytoskeletal dynamics, tissue-scale traction and measurements of tissue stiffness to separate the role of microtubules from RhoGEF activation. These findings suggest a re-evaluation of the effects of nocodazole and increased focus on the role of Rho family GTPases as regulators of the mechanical properties of cells and their mechanical interactions with surrounding tissues.

Traction forces exerted by epithelial cell sheets

Whereas the adhesion and migration of individual cells have been well described in terms of physical forces, the mechanics of multicellular assemblies is still poorly understood. Here, we study the behavior of epithelial cells cultured on microfabricated substrates designed to measure cell-to-substrate interactions. These substrates are covered by a dense array of flexible micropillars whose deflection enables us to measure traction forces. They are obtained by lithography and soft replica molding. The pillar deflection is measured by video microscopy and images are analyzed with home-made multiple particle tracking software. First, we have characterized the temporal and spatial distributions of traction forces of cellular assemblies of various sizes. The mechanical force balance within epithelial cell sheets shows that the forces exerted by neighboring cells strongly depend on their relative position in the monolayer: the largest deformations are always localized at the edge of the islands of cells in the active areas of cell protrusions. The average traction stress rapidly decreases from its maximum value at the edge but remains much larger than the inherent noise due to the force resolution of our pillar tracking software, indicating an important mechanical activity inside epithelial cell islands. Moreover, these traction forces vary linearly with the rigidity of the substrate over about two decades, suggesting that cells exert a given amount of deformation rather than a force. Finally, we engineer micropatterned substrates supporting pillars with anisotropic stiffness. On such substrates cellular growth is aligned with respect to the stiffest direction in correlation with the magnitude of the applied traction forces.

Microfabricated substrates as a tool to study cell mechanotransduction

Mechanical cell-substrate interactions affect many cellular functions such as spreading, migration, and even differentiation. These interactions can be studied by incorporating micro- and nanotechnology-related tools. The design of substrates based on these technologies offers new possibilities to probe the cellular responses to changes in their physical environment. The investigations of the mechanical interactions of cells and their surrounding matrix can be carried out in well-defined and near physiological conditions. In particular, this includes the transmission of forces as well as rigidity and topography sensing mechanisms. Here, we review techniques and tools based on nano- and micro-fabrication that have been developed to analyze the influence of the mechanical properties of the substrate on cell functions. We also discuss how microfabrication methods have improved our knowledge on cell adhesion and migration and how they could solve remaining problems in the field of mechanobiology.

Local friction at a sliding interface between an elastomer and a rigid spherical probe

This paper reports on spatially resolved measurements of the shear stress distribution at a frictional interface between a flat rubber substrate and a glass lens. Silicone rubber specimens marked close to their surface by a colored pattern have been prepared in order to measure the surface displacement field induced by the steady-state friction of the spherical probe. The deconvolution of this displacement field then provides the actual shear stress distribution at the contact interface. When a smooth glass lens is used, a nearly constant shear stress is achieved within the contact. On the other hand, a bell-shaped shear stress distribution is obtained with rough lenses. These first results suggest that simple notions of real contact area and constant interface shear stress cannot account for the observed changes in local friction when roughness is varied.

Changes in the magnitude and distribution of forces at different Dictyostelium developmental stages

The distribution of forces exerted by migrating Dictyostelium amebae at different developmental stages was measured using traction force microscopy. By using very soft polyacrylamide substrates with a high fluorescent bead density, we could measure stresses as small as 30 Pa. Remarkable differences exist both in term of the magnitude and distribution of forces in the course of development. In the vegetative state, cells present cyclic changes in term of speed and shape between an elongated form and a more rounded one. The forces are larger in this first state, especially when they are symmetrically distributed at the front and rear edge of the cell. Elongated vegetative cells can also present a front-rear asymmetric force distribution with the largest forces in the crescent-shaped rear of the cell (uropod). Pre-aggregating cells, once polarized, only present this last kind of asymmetric distribution with the largest forces in the uropod. Except for speed, no cycle is observed. Neither the force distribution of pre-aggregating cells nor their overall magnitude are modified during chemotaxis, the later being similar to the one of vegetative cells (F(0) approximately 6 nN). On the contrary, both the force distribution and overall magnitude is modified for the fast moving aggregating cells. In particular, these highly elongated cells exert lower forces (F(0) approximately 3 nN). The location of the largest forces in the various stages of the development is consistent with the myosin II localization described in the literature for Dictyostelium (Yumura et al.,1984. J Cell Biol 99:894-899) and is confirmed by preliminary experiments using a GFP-myosin Dictyostelium strain.

Spatio-temporal analysis of eukaryotic cell motility by improved force cytometry

Cell motility plays an essential role in many biological systems, but precise quantitative knowledge of the biophysical processes involved in cell migration is limited. Better measurements are needed to ultimately build models with predictive capabilities. We present an improved force cytometry method and apply it to the analysis of the dynamics of the chemotactic migration of the amoeboid form of Dictyostelium discoideum. Our explicit calculation of the force field takes into account the finite thickness of the elastic substrate and improves the accuracy and resolution compared with previous methods. This approach enables us to quantitatively study the differences in the mechanics of the migration of wild-type (WT) and mutant cell lines. The time evolution of the strain energy exerted by the migrating cells on their substrate is quasi-periodic and can be used as a simple indicator of the stages of the cell motility cycle. We have found that the mean velocity of migration v and the period of the strain energy T cycle are related through a hyperbolic law v = L/T, where L is a constant step length that remains unchanged in mutants with adhesion or contraction defects. Furthermore, when cells adhere to the substrate, they exert opposing pole forces that are orders of magnitude higher than required to overcome the resistance from their environment.