Abstract:The ability of cells to follow gradients of extracellular matrix stiffnessdurotaxis-has been implicated in development, fibrosis and cancer. Durotaxis is established as a single cell phenomenon but whether it can direct the motion of cell collectives is unknown. Here we found that multicellular clusters exhibited durotaxis even if isolated constituent cells did not. This emergent mode of directed collective cell migration applied to a variety of epithelial cell types, and required the action of myosin motors and the integrity of cell-cell junctions. By extending traction microscopy to extracellular matrices of arbitrary stiffness profiles we showed that collective durotaxis originated from supracellular transmission of contractile physical forces. To explain the observed phenomenology, we developed a generalized clutch model in which local stickslip dynamics of cell-matrix adhesions is integrated to the tissue level through cell-cell junctions. Collective durotaxis is far more efficient than single cell durotaxis; it thus emerges as a robust mechanism to direct cell migration during development, wound healing, and collective cancer cell invasion. One Sentence Summary: Mechanical cooperation between cells enables an emergent mode of collective movement -3- Main Text:The ability of living cells to migrate following environmental gradients underlies a broad range of phenomena in development, homeostasis, and disease (1, 2). The best understood mode of directed cell migration is chemotaxis, the well-established ability of cells to follow gradients of soluble chemical cues (1). Some cell types are also able to follow gradients in the stiffness of their extracellular matrix (ECM), a process known as durotaxis (3-10).Durotaxis has been implicated in development (11), fibrosis (12) and cancer (13), but its underlying mechanisms remain unclear.Most of our understanding of directed cell migration has been obtained in single isolated cells. However, fundamental processes during development, wound healing, tissue regeneration, and some forms of cancer cell invasion are driven by directed migration of cell groups (14-16). Cell-cell interactions within these groups provide cooperative mechanisms of cell guidance that are altogether inaccessible to single cells (14-20). Here we investigated whether cell groups undergo collective durotaxis, and the cooperative nature of underlying mechanisms.Using stencils of magnetic PDMS, we micropatterned rectangular clusters (500 µm width) of human mammary epithelial cells (MCF-10A) on fibronectin-coated polyacrylamide gel substrates exhibiting uniform stiffness or a stiffness gradient (51 ± 17 kPa/mm, Fig. S1) (21). Upon removal of the PDMS stencil, clusters migrating on uniform gels displayed symmetric expansion (Fig. 1A,C,E,G, Fig. S2, Movie S1), whereas clusters migrating on stiffness gradients displayed a robust asymmetry characterized by faster, more persistent expansion towards the stiff edge (Fig. 1B-D-F-H, Fig. S2, Movie S1). This result was also -4-observed in clusters of...

Cells can sense the density and distribution of extracellular matrix (ECM) molecules by means of individual integrin proteins and larger, integrin-containing adhesion complexes within the cell membrane. This spatial sensing drives cellular activity in a variety of normal and pathological contexts. Previous studies of cells on rigid glass surfaces have shown that spatial sensing of ECM ligands takes place at the nanometre scale, with integrin clustering and subsequent formation of focal adhesions impaired when single integrin-ligand bonds are separated by more than a few tens of nanometres. It has thus been suggested that a crosslinking 'adaptor' protein of this size might connect integrins to the actin cytoskeleton, acting as a molecular ruler that senses ligand spacing directly. Here, we develop gels whose rigidity and nanometre-scale distribution of ECM ligands can be controlled and altered. We find that increasing the spacing between ligands promotes the growth of focal adhesions on low-rigidity substrates, but leads to adhesion collapse on more-rigid substrates. Furthermore, disordering the ligand distribution drastically increases adhesion growth, but reduces the rigidity threshold for adhesion collapse. The growth and collapse of focal adhesions are mirrored by, respectively, the nuclear or cytosolic localization of the transcriptional regulator protein YAP. We explain these findings not through direct sensing of ligand spacing, but by using an expanded computational molecular-clutch model, in which individual integrin-ECM bonds-the molecular clutches-respond to force loading by recruiting extra integrins, up to a maximum value. This generates more clutches, redistributing the overall force among them, and reducing the force loading per clutch. At high rigidity and high ligand spacing, maximum recruitment is reached, preventing further force redistribution and leading to adhesion collapse. Measurements of cellular traction forces and actin flow speeds support our model. Our results provide a general framework for how cells sense spatial and physical information at the nanoscale, precisely tuning the range of conditions at which they form adhesions and activate transcriptional regulation.

Collective cell migration is regulated by a complex set of mechanical interactions and cellular mechanisms. Collective migration emerges from mechanisms occurring at single cell level, involving processes like contraction, polymerization and depolymerization, of cell-cell interactions and of cell-substrate adhesion. Here, we present a computational framework which simulates the dynamics of this emergent behavior conditioned by substrates with stiffness gradients. The computational model reproduces the cell's ability to move toward the stiffer part of the substrate, process known as durotaxis. It combines the continuous formulation of truss elements and a particle-based approach to simulate the dynamics of cell-matrix adhesions and cell-cell interactions. Using this hybrid approach, researchers can quickly create a quantitative model to understand the regulatory role of different mechanical conditions on the dynamics of collective cell migration. Our model shows that durotaxis occurs due to the ability of cells to deform the substrate more in the part of lower stiffness than in the stiffer part. This effect explains why cell collective movement is more effective than single cell movement in stiffness gradient conditions. In addition, we numerically evaluate how gradient stiffness properties, cell monolayer size and force transmission between cells and extracellular matrix are crucial in regulating durotaxis.

The formation of gaps in the endothelium is a crucial process underlying both cancer and immune cell extravasation, contributing to the functioning of the immune system during infection, the unfavorable development of chronic inflammation and tumor metastasis. Here, we present a stochastic-mechanical multiscale model of an endothelial cell monolayer and show that the dynamic nature of the endothelium leads to spontaneous gap formation, even without intervention from the transmigrating cells. These gaps preferentially appear at the vertices between three endothelial cells, as opposed to the border between two cells. We quantify the frequency and lifetime of these gaps, and validate our predictions experimentally. Interestingly, we find experimentally that cancer cells also preferentially extravasate at vertices, even when they first arrest on borders. This suggests that extravasating cells, rather than initially signaling to the endothelium, might exploit the autonomously forming gaps in the endothelium to initiate transmigration.

The formation of gaps in the endothelium is a crucial process underlying both cancer and immune cell extravasation, contributing to the functioning of the immune system during infection, the unfavorable development of chronic inflammation and tumor metastasis. Here, we present a stochastic-mechanical multiscale model of an endothelial cell monolayer and show that the dynamic nature of the endothelium leads to spontaneous gap formation, even without intervention from the transmigrating cells. These gaps preferentially appear at the vertices between three endothelial cells, as opposed to the border between two cells. We quantify the frequency and lifetime of these gaps, and validate our predictions experimentally. Interestingly, we find experimentally that cancer cells also preferentially extravasate at vertices, even when they first arrest on borders. This suggests that extravasating cells, rather than initially signaling to the endothelium, might exploit the autonomously forming gaps in the endothelium to initiate transmigration.

During recent years the interaction between the extracellular matrix and the cytoskeleton of the cell has been object of numerous studies due to its importance in cell migration processes. These interactions are performed through protein clutches, known as focal adhesions. For migratory cells these focal adhesions along with force generating processes in the cytoskeleton are responsible for the formation of protrusion structures like lamellipodia or filopodia. Much is known about these structures: the different proteins that conform them, the players involved in their formation or their role in cell migration. Concretely, growth-cone filopodia structures have attracted significant attention because of their role as cell sensors of their surrounding environment and its complex behavior. On this matter, a vast myriad of mathematical models has been presented to explain its mechanical behavior. In this work, we aim to study the mechanical behavior of these structures through a discrete approach. This numerical model provides an individual analysis of the proteins involved including spatial distribution, interaction between them, and study of different phenomena, such as clutches unbinding or protein unfolding.

The formation and recovery of gaps in the vascular endothelium governs a wide range of physiological and pathological phenomena, from angiogenesis to tumor cell extravasation. However, the interplay between the mechanical and signaling processes that drive dynamic behavior in vascular endothelial cells is not well understood. In this study, we propose a chemo-mechanical model to investigate the regulation of endothelial junctions as dependent on the feedback between actomyosin contractility, VE-cadherin bond turnover, and actin polymerization, which mediate the forces exerted on the cell-cell interface. Simulations reveal that active cell tension can stabilize cadherin bonds, but excessive RhoA signaling can drive bond dissociation and junction failure. While actin polymerization aids gap closure, high levels of Rac1 can induce junction weakening. Combining the modeling framework with experiments, our model predicts the influence of pharmacological treatments on the junction state and identifies that a critical balance between RhoA and Rac1 expression is required to maintain junction stability. Our proposed framework can help guide the development of therapeutics that target the Rho family of GTPases and downstream active mechanical processes.

Cell migration is crucial in a wide variety of biological process like development, homeostasis or tissue regeneration. In particular, the interaction between the extracellular matrix and the cytoskeleton is a recurrent topic, due to its important role in this process. These interactions are built through protein clutches, generally known as focal adhesions or focal contacts. For migratory cells, these focal adhesions together with force generating processes in the cytoskeleton are responsible of the formation of protrusion structures like lamellipodia or filopodia, that determine the cell migration path. This phenomenon has been deeply studied in two-dimensional (2D) cases; however, the knowledge we have in the three-dimensional (3D) case is limited. In this work, we simulate different local extracellular matrix properties in order to unravel the fundamental mechanisms that regulate the formation of cell-matrix adhesions in 3D. We aim to study the mechanical interaction of these biological structures through a three dimensional discrete approach, reproducing the transmitting pattern force between the cytoskeleton and the extracellular matrix and how both parts are interplaying by them. This numerical model provides a discrete analysis of the proteins involved including spatial distribution, interaction between them, and study of the different phenomena, such as protein clutches unbinding or protein unfolding. * Corresponding authorEmail address: jmgaraz@unizar.es (J.M. García-Aznar) November 6, 2014 Keywords: Actin, myosin, focal adhesion, 3D discrete model, extracellular matrix reorganization. Preprint submitted to Journal of Theoretical Biology Highlights• A discrete computational model in 3D is proposed for reproducing the focal adhesion building phenomenon.• The proposed model analyze the importance of the alignment between the matrix fiber and the cell protrusion on the size of the adhesion.• The influence of different extracellular matrix properties on the size of the adhesion is also studied.2