Tractions and stress fibers control cell shape and rearrangements in collective cell migration

Key to collective cell migration is the ability of cells to rearrange their position with respect to their neighbors. Recent theory and experiments demonstrated that cellular rearrangements are facilitated by cell shape, with cells having more elongated shapes and greater perimeters more easily sliding past their neighbors within the cell layer. Though it is thought that cell perimeter is controlled primarily by cortical tension and adhesion at each cell's periphery, experimental testing of this hypothesis has produced conflicting results. Here we studied collective cell migration in an epithelial monolayer by measuring forces, cell perimeters, and motion, and found all three to decrease with either increased cell density or inhibition of cell contraction. In contrast to previous understanding, the data suggest that cell shape and rearrangements are controlled not by cortical tension or adhesion at the cell periphery but rather by the stress fibers that produce tractions at the cell-substrate interface. This finding is confirmed by an experiment showing that increasing tractions reverses the effect of density on cell shape and rearrangements. Our study therefore reduces the focus on the cell periphery by establishing cell-substrate traction as a major physical factor controlling cell shape and motion in collective cell migration.Comment: 39 pages, 6 figure

A Model for Compression-Weakening Materials and the Elastic Fields due to Contractile Cells

We construct a homogeneous, nonlinear elastic constitutive law, that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material, than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.Comment: 18 pages, 2 figure

Analysis of nanoindentation of soft materials with an atomic force microscope

Nanoindentation is a popular experimental technique for characterization of the mechanical properties of soft and biological materials. With its force resolution of tens of pico-Newtons, the atomic force microscope (AFM) is well-suited for performing indentation experiments on soft materials. However, nonlinear contact and adhesion complicate such experiments. This paper critically examines the application of the Johnson-Kendall-Roberts (JKR) adhesion model to nanoindentation data collected with an AFM. The use of a nonlinear least-square error-fitting algorithm to calculate reduced modulus from the nanoindentation data using the JKR model is discussed. It is found that the JKR model fits the data during loading but does not fit the data during unloading. A fracture stability analysis shows that the JKR model does not fit the data collected during unloading because of the increased stability provided by the AFM cantilever

Dynamics of Cell–Matrix Mechanical Interactions in Three Dimensions

The forces cells apply to their surroundings control biological processes such as growth, adhesion, development, and migration. In the past 20 years, a number of experimental techniques have been developed to measure such cell tractions. These approaches have primarily measured the tractions applied by cells to synthetic two-dimensional substrates, which do not mimic in vivo conditions for most cell types. Many cell types live in a fibrous three-dimensional (3D) matrix environment. While studying cell behavior in such 3D matrices will provide valuable insights for the mechanobiology and tissue engineering communities, no experimental approaches have yet measured cell tractions in a fibrous 3D matrix. This thesis describes the development and application of an experimental technique for quantifying cellular forces in a natural 3D matrix. Cells and their surrounding matrix are imaged in three dimensions with high speed confocal microscopy. The cell-induced matrix displacements are computed from the 3D image volumes using digital volume correlation. The strain tensor in the 3D matrix is computed by differentiating the displacements, and the stress tensor is computed by applying a constitutive law. Finally, tractions applied by the cells to the matrix are computed directly from the stress tensor. The 3D traction measurement approach is used to investigate how cells mechanically interact with the matrix in biologically relevant processes such as division and invasion. During division, a single mother cell undergoes a drastic morphological change to split into two daughter cells. In a 3D matrix, dividing cells apply tensile force to the matrix through thin, persistent extensions that in turn direct the orientation and location of the daughter cells. Cell invasion into a 3D matrix is the first step required for cell migration in three dimensions. During invasion, cells initially apply minimal tractions to the matrix as they extend thin protrusions into the matrix fiber network. The invading cells anchor themselves to the matrix using these protrusions, and subsequently pull on the matrix to propel themselves forward. Lastly, this thesis describes a constitutive model for the 3D fibrous matrix that uses a finite element (FE) approach. The FE model simulates the fibrous microstructure of the matrix and matches the cell-induced matrix displacements observed experimentally using digital volume correlation. The model is applied to predict how cells mechanically sense one another in a 3D matrix. It is found that cell-induced matrix displacements localize along linear paths. These linear paths propagate over a long range through the fibrous matrix, and provide a mechanism for cell-cell signaling and mechanosensing. The FE model developed here has the potential to reveal the effects of matrix density, inhomogeneity, and anisotropy in signaling cell behavior through mechanotransduction.</p

Coordinated tractions increase the size of a collectively moving pack in a cell monolayer

Cells in an epithelial monolayer coordinate motion with their neighbors giving rise to collectively moving packs of sizes spanning multiple cell diameters. The physical mechanism controlling the pack size, however, remains unclear. A potential mechanism comes from assuming that cell-substrate traction forces persist over some time scale: with large enough persistence time, collective cell packs emerge. To test this hypothesis, we measured the velocity and net traction of each cell. The data showed that in addition to having some temporal persistence, tractions were spatially correlated, suggesting that cells coordinate with their neighbors to apply tractions in the same direction. Chemical inhibitors and activators of actomyosin contraction were used to determine effects of altering the traction persistence and alignment. Numerical simulations based on the self-propelled Voronoi model, augmented to include both traction persistence and alignment and calibrated against the experimental data, matched the experimentally measured pack size. The model identified that if there were no alignment of traction between neighboring cells, the size of the collective pack would be substantially smaller than observed in the experiments. Hence, combining experiments and a simple mechanical model, this study confirms the long-standing assumption of traction persistence and adds the notion of traction alignment between neighbors. Together, persistence and alignment are two factors controlling the size of a collectively moving cell pack

Microbuckling of fibrin provides a mechanism for cell mechanosensing

Biological cells sense and respond to mechanical forces, but how such a mechanosensing process takes place in a nonlinear inhomogeneous fibrous matrix remains unknown. We show that cells in a fibrous matrix induce deformation fields that propagate over a longer range than predicted by linear elasticity. Synthetic, linear elastic hydrogels used in many mechanotransduction studies fail to capture this effect. We develop a nonlinear microstructural finite-element model for a fibre network to simulate localized deformations induced by cells. The model captures measured cell-induced matrix displacements from experiments and identifies an important mechanism for long-range cell mechanosensing: loss of compression stiffness owing to microbuckling of individual fibres. We show evidence that cells sense each other through the formation of localized intercellular bands of tensile deformations caused by this mechanism

Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix

Through mechanical forces, biological cells remodel the surrounding collagen network, generating striking deformation patterns. Tethers—tracts of high densification and fibre alignment—form between cells, thinner bands emanate from cell clusters. While tethers facilitate cell migration and communication, how they form is unclear. Combining modelling, simulation and experiment, we show that tether formation is a densification phase transition of the extracellular matrix, caused by buckling instability of network fibres under cell-induced compression, featuring unexpected similarities with martensitic microstructures. Multiscale averaging yields a two-phase, bistable continuum energy landscape for fibrous collagen, with a densified/aligned second phase. Simulations predict strain discontinuities between the undensified and densified phase, which localizes within tethers as experimentally observed. In our experiments, active particles induce similar localized patterns as cells. This shows how cells exploit an instability to mechanically remodel the extracellular matrix simply by contracting, thereby facilitating mechanosensing, invasion and metastasis