Tumor invasion and metastasis are strongly regulated by biophysical interactions between tumor cells and the extracellular matrix (ECM). While the influence of ECM stiffness on cell migration, adhesion, and contractility has been extensively studied in 2D culture, extension of this concept to 3D cultures that more closely resemble tissue has proven challenging, because perturbations that change matrix stiffness often concurrently change cellular confinement. This coupling is particularly problematic given that matriximposed steric barriers can regulate invasion speed independent of mechanics. Here we introduce a matrix platform based on microfabrication of channels of defined wall stiffness and geometry that allows independent variation of ECM stiffness and channel width. For a given ECM stiffness, cells confined to narrow channels surprisingly migrate faster than cells in wide channels or on unconstrained 2D surfaces, which we attribute to increased polarization of cell-ECM traction forces. Confinement also enables cells to migrate increasingly rapidly as ECM stiffness rises, in contrast with the biphasic relationship observed on unconfined ECMs. Inhibition of nonmuscle myosin II dissipates this traction polarization and renders the relationship between migration speed and ECM stiffness comparatively insensitive to matrix confinement. We test these hypotheses in silico by devising a multiscale mathematical model that relates cellular force generation to ECM stiffness and geometry, which we show is capable of recapitulating key experimental trends. These studies represent a paradigm for investigating matrix regulation of invasion and demonstrate that matrix confinement alters the relationship between cell migration speed and ECM stiffness. microchannels | glioblastoma | cytoskeleton | mechanobiology | polyacrylamide

Physical forces generated by cells drive morphologic changes during development and can feedback to regulate cellular phenotypes. Because these phenomena typically occur within a 3-dimensional (3D) matrix in vivo, we used microelectromechanical systems (MEMS) technology to generate arrays of microtissues consisting of cells encapsulated within 3D micropatterned matrices. Microcantilevers were used to simultaneously constrain the remodeling of a collagen gel and to report forces generated during this process. By concurrently measuring forces and observing matrix remodeling at cellular length scales, we report an initial correlation and later decoupling between cellular contractile forces and changes in tissue morphology. Independently varying the mechanical stiffness of the cantilevers and collagen matrix revealed that cellular forces increased with boundary or matrix rigidity whereas levels of cytoskeletal and extracellular matrix (ECM) proteins correlated with levels of mechanical stress. By mapping these relationships between cellular and matrix mechanics, cellular forces, and protein expression onto a bio-chemo-mechanical model of microtissue contractility, we demonstrate how intratissue gradients of mechanical stress can emerge from collective cellular contractility and finally, how such gradients can be used to engineer protein composition and organization within a 3D tissue. Together, these findings highlight a complex and dynamic relationship between cellular forces, ECM remodeling, and cellular phenotype and describe a system to study and apply this relationship within engineered 3D microtissues.biomechanics ͉ cell mechanics ͉ collagen ͉ morphogenesis ͉ PDMS

Invasion of cancer cells into the extracellular matrix (ECM) is a key step in tumor infiltration and metastasis. While the strong influence of ECM stiffness in governing tumor cell migration has been well established in two-dimensional culture paradigms, investigation of this parameter in three-dimensional (3D) ECMs has proven considerably more challenging, in part because perturbations that change 3D ECM stiffness often concurrently change microscale matrix parameters that critically regulate cell migration, such as pore size, fiber architecture, and local material deformability. Here we review the potential importance of these parameters in the context of tumor cell migration in 3D ECMs. We begin by discussing biophysical mechanisms of cell motility in 3D ECMs, with an emphasis on the cell-matrix mechanical interactions that underlie this process and key signatures of mesenchymal and amoeboid modes of motility. We then consider microscale matrix physical properties that are particularly relevant to 3D culture and would be expected to regulate motility, including matrix microstructure and nonlinear elasticity. We also discuss how changes in 3D matrix properties might be expected to trigger transitions in subcellular mechanisms, which in turn contribute to mesenchymal-amoeboid transition (MAT) by imposing restrictions on 3D motility. We expect that the field will gain valuable insight into invasion and metastasis by deepening its understanding of microscale, biophysical interactions between tumor cells and matrix elements and by creating new 3D scaffolds that permit orthogonal manipulation of specific matrix parameters.

During morphogenesis and cancer metastasis, grouped cells migrate through tissues of dissimilar stiffness. Although the influence of matrix stiffness on cellular mechanosensitivity and motility are well-recognized, it remains unknown whether these matrix-dependent cellular features persist after cells move to a new microenvironment. Here, we interrogate whether priming of epithelial cells by a given matrix stiffness influences their future collective migration on a different matrix – a property we refer to as the ‘mechanical memory’ of migratory cells. To prime cells on a defined matrix and track their collective migration onto an adjoining secondary matrix of dissimilar stiffness, we develop a modular polyacrylamide substrate through step-by-step polymerization of different PA compositions. We report that epithelial cells primed on a stiff matrix migrate faster, display higher actomyosin expression, form larger focal adhesions, and retain nuclear YAP even after arriving onto a soft secondary matrix, as compared to their control behavior on a homogeneously soft matrix. Priming on a soft ECM causes a reverse effect. The depletion of YAP dramatically reduces this memory-dependent migration. Our results present a previously unidentified regulation of mechanosensitive collective cell migration by past matrix stiffness, in which mechanical memory depends on YAP activity.

The remodelling of the cytoskeleton and focal adhesion (FA) distributions for cells on substrates with micro-patterned ligand patches is investigated using a bio-chemo-mechanical model. We investigate the effect of ligand pattern shape on the cytoskeletal arrangements and FA distributions for cells having approximately the same area. The cytoskeleton model accounts for the dynamic rearrangement of the actin/myosin stress fibres. It entails the highly nonlinear interactions between signalling, the kinetics of tension-dependent stress-fibre formation/dissolution and stress-dependent contractility. This model is coupled with another model that governs FA formation and accounts for the mechano-sensitivity of the adhesions from thermodynamic considerations. This coupled modelling scheme is shown to capture a variety of key experimental observations including: (i) the formation of high concentrations of stress fibres and FAs at the periphery of circular and triangular, convex-shaped ligand patterns; (ii) the development of high FA concentrations along the edges of the V-, T-, Y- and U-shaped concave ligand patterns; and (iii) the formation of highly aligned stress fibres along the non-adhered edges of cells on the concave ligand patterns. When appropriately calibrated, the model also accurately predicts the radii of curvature of the non-adhered edges of cells on the concave-shaped ligand patterns.