In cancer metastasis and other physiological processes, cells migrate through the three-dimensional (3D) extracellular matrix of connective tissue and must overcome the steric hindrance posed by pores that are smaller than the cells. It is currently assumed that low cell stiffness promotes cell migration through confined spaces, but other factors such as adhesion and traction forces may be equally important. To study 3D migration under confinement in a stiff (1.77 MPa) environment, we use soft lithography to fabricate polydimethylsiloxane (PDMS) devices consisting of linear channel segments with 20 μm length, 3.7 μm height, and a decreasing width from 11.2 to 1.7 μm. To study 3D migration in a soft (550 Pa) environment, we use self-assembled collagen networks with an average pore size of 3 μm. We then measure the ability of four different cancer cell lines to migrate through these 3D matrices, and correlate the results with cell physical properties including contractility, adhesiveness, cell stiffness, and nuclear volume. Furthermore, we alter cell adhesion by coating the channel walls with different amounts of adhesion proteins, and we increase cell stiffness by overexpression of the nuclear envelope protein lamin A. Although all cell lines are able to migrate through the smallest 1.7 μm channels, we find significant differences in the migration velocity. Cell migration is impeded in cell lines with larger nuclei, lower adhesiveness, and to a lesser degree also in cells with lower contractility and higher stiffness. Our data show that the ability to overcome the steric hindrance of the matrix cannot be attributed to a single cell property but instead arises from a combination of adhesiveness, nuclear volume, contractility, and cell stiffness.

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.

Migrating cells generate traction forces to counteract the movement-resisting forces arising from cell-internal stresses and matrix adhesions. In the case of collective migration in a cell colony, or in the case of 3-dimensional migration through connective tissue, movement-resisting forces arise also from external stresses. Although the deformation of a stiffer cell or matrix causes larger movement-resisting forces, at the same time a larger stiffness can also promote cell migration due to a feedback between forces, deformations, and deformation speed that is mediated by the acto-myosin contractile machinery of cells. This mechanical feedback is also important for stiffness sensing, durotaxis, plithotaxis, and collective migration in cell colonies.

The pore size of biopolymer networks governs their mechanical properties and strongly impacts the behavior of embedded cells. Confocal reflection microscopy and second harmonic generation microscopy are widely used to image biopolymer networks; however, both techniques fail to resolve vertically oriented fibers. Here, we describe how such directionally biased data can be used to estimate the network pore size. We first determine the distribution of distances from random points in the fluid phase to the nearest fiber. This distribution follows a Rayleigh distribution, regardless of isotropy and data bias, and is fully described by a single parameter--the characteristic pore size of the network. The bias of the pore size estimate due to the missing fibers can be corrected by multiplication with the square root of the visible network fraction. We experimentally verify the validity of this approach by comparing our estimates with data obtained using confocal fluorescence microscopy, which represents the full structure of the network. As an important application, we investigate the pore size dependence of collagen and fibrin networks on protein concentration. We find that the pore size decreases with the square root of the concentration, consistent with a total fiber length that scales linearly with concentration.

We describe a quantitative, high-precision, high-throughput method for measuring the mechanical properties of cells in suspension with a microfluidic device, and for relating cell mechanical responses to protein expression levels. Using a high-speed (750 fps) charge-coupled device camera, we measure the driving pressure Δp, maximum cell deformation ε, and entry time t of cells in an array of microconstrictions. From these measurements, we estimate population averages of elastic modulus E and fluidity β (the power-law exponent of the cell deformation in response to a step change in pressure). We find that cell elasticity increases with increasing strain ε according to E ∼ ε, and with increasing pressure according to E ∼ Δp. Variable cell stress due to driving pressure fluctuations and variable cell strain due to cell size fluctuations therefore cause significant variability between measurements. To reduce measurement variability, we use a histogram matching method that selects and analyzes only those cells from different measurements that have experienced the same pressure and strain. With this method, we investigate the influence of measurement parameters on the resulting cell elastic modulus and fluidity. We find a small but significant softening of cells with increasing time after cell harvesting. Cells harvested from confluent cultures are softer compared to cells harvested from subconfluent cultures. Moreover, cell elastic modulus increases with decreasing concentration of the adhesion-reducing surfactant pluronic. Lastly, we simultaneously measure cell mechanics and fluorescence signals of cells that overexpress the GFP-tagged nuclear envelope protein lamin A. We find a dose-dependent increase in cell elastic modulus and decrease in cell fluidity with increasing lamin A levels. Together, our findings demonstrate that histogram matching of pressure, strain, and protein expression levels greatly reduces the variability between measurements and enables us to reproducibly detect small differences in cell mechanics.