Collective forces of tumor spheroids in three-dimensional biopolymer networks.

We describe a method for quantifying the contractile forces that tumor spheroids collectively exert on highly nonlinear three-dimensional collagen networks. While three-dimensional traction force microscopy for single cells in a nonlinear matrix is computationally complex due to the variable cell shape, here we exploit the spherical symmetry of tumor spheroids to derive a scale-invariant relationship between spheroid contractility and the surrounding matrix deformations. This relationship allows us to directly translate the magnitude of matrix deformations to the total contractility of arbitrarily sized spheroids. We show that our method is accurate up to strains of 50% and remains valid even for irregularly shaped tissue samples when considering only the deformations in the far field. Finally, we demonstrate that collective forces of tumor spheroids reflect the contractility of individual cells for up to 1 hr after seeding, while collective forces on longer timescales are guided by mechanical feedback from the extracellular matrix.

Three-dimensional force microscopy of cells in biopolymer networks.

We describe a technique for the quantitative measurement of cell-generated forces in highly nonlinear three-dimensional biopolymer networks that mimic the physiological situation of living cells. We computed forces of MDA-MB-231 breast carcinoma cells from the measured network deformations around the cells using a finite-element approach based on a constitutive equation that captures the complex mechanical properties of diverse biopolymers such as collagen gels, fibrin gels and Matrigel. Our measurements show that breast carcinoma cells cultured in collagen gels generated nearly constant forces regardless of the collagen concentration and matrix stiffness. Furthermore, time-lapse force measurements showed that these cells migrated in a gliding motion with alternating phases of high and low contractility, elongation, migratory speed and persistence.

Vinculin is required for cell polarization, migration, and extracellular matrix remodeling in 3D collagen.

Vinculin is filamentous (F)-actin-binding protein enriched in integrin-based adhesions to the extracellular matrix (ECM). Whereas studies in 2-dimensional (2D) tissue culture models have suggested that vinculin negatively regulates cell migration by promoting cytoskeleton-ECM coupling to strengthen and stabilize adhesions, its role in regulating cell migration in more physiologic, 3-dimensional (3D) environments is unclear. To address the role of vinculin in 3D cell migration, we analyzed the morphodynamics, migration, and ECM remodeling of primary murine embryonic fibroblasts (MEFs) with cre/loxP-mediated vinculin gene disruption in 3D collagen I cultures. We found that vinculin promoted 3D cell migration by increasing directional persistence. Vinculin was necessary for persistent cell protrusion, cell elongation, and stable cell orientation in 3D collagen, but was dispensable for lamellipodia formation, suggesting that vinculin-mediated cell adhesion to the ECM is needed to convert actin-based cell protrusion into persistent cell shape change and migration. Consistent with this finding, vinculin was necessary for efficient traction force generation in 3D collagen without affecting myosin II activity and promoted 3D collagen fiber alignment and macroscopical gel contraction. Our results suggest that vinculin promotes directionally persistent cell migration and tension-dependent ECM remodeling in complex 3D environments by increasing cell-ECM adhesion and traction force generation.

Microconstriction arrays for high-throughput quantitative measurements of cell mechanical properties.

We describe a method for quantifying the mechanical properties of cells in suspension with a microfluidic device consisting of a parallel array of micron-sized constrictions. Using a high-speed charge-coupled device camera, we measure the flow speed, cell deformation, and entry time into the constrictions of several hundred cells per minute during their passage through the device. From the flow speed and the occupation state of the microconstriction array with cells, the driving pressure across each constriction is continuously computed. Cell entry times into microconstrictions decrease with increased driving pressure and decreased cell size according to a power law. From this power-law relationship, the cell elasticity and fluidity can be estimated. When cells are treated with drugs that depolymerize or stabilize the cytoskeleton or the nucleus, elasticity and fluidity data from all treatments collapse onto a master curve. Power-law rheology and collapse onto a master curve are predicted by the theory of soft glassy materials and have been previously shown to describe the mechanical behavior of cells adhering to a substrate. Our finding that this theory also applies to cells in suspension provides the foundation for a quantitative high-throughput measurement of cell mechanical properties with microfluidic devices.

Superstatistical analysis and modelling of heterogeneous random walks.

Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.

Biphasic response of cell invasion to matrix stiffness in three-dimensional biopolymer networks.

When cells come in contact with an adhesive matrix, they begin to spread and migrate with a speed that depends on the stiffness of the extracellular matrix. On a flat surface, migration speed decreases with matrix stiffness mainly due to an increased stability of focal adhesions. In a three-dimensional (3-D) environment, cell migration is thought to be additionally impaired by the steric hindrance imposed by the surrounding matrix. For porous 3-D biopolymer networks such as collagen gels, however, the effect of matrix stiffness on cell migration is difficult to separate from effects of matrix pore size and adhesive ligand density, and is therefore unknown. Here we used glutaraldehyde as a crosslinker to increase the stiffness of self-assembled collagen biopolymer networks independently of collagen concentration or pore size. Breast carcinoma cells were seeded onto the surface of 3-D collagen gels, and the invasion depth was measured after 3 days of culture. Cell invasion in gels with pore sizes >5 µm increased with higher gel stiffness, whereas invasion in gels with smaller pores decreased with higher gel stiffness. These data show that 3-D cell invasion is enhanced by higher matrix stiffness, opposite to cell behavior in two dimensions, as long as the pore size does not fall below a critical value where it causes excessive steric hindrance. These findings may be important for optimizing the recellularization of soft tissue implants or for the design of 3-D invasion models in cancer research.