Spatial patterns of cellular growth generate mechanical stresses that help to push, fold, expand, and deform tissues into their specific forms. Genetic factors are thought to specify patterns of growth and other behaviors to drive morphogenesis. Here, we show that tissue form itself can feed back to regulate patterns of proliferation. Using microfabrication to control the organization of sheets of cells, we demonstrated the emergence of stable patterns of proliferative foci. Regions of concentrated growth corresponded to regions of high tractional stress generated within the sheet, as predicted by a finite-element model of multicellular mechanics and measured directly by using a micromechanical force sensor array. Inhibiting actomyosin-based tension or cadherin-mediated connections between cells disrupted the spatial pattern of proliferation. These findings demonstrate the existence of patterns of mechanical forces that originate from the contraction of cells, emerge from their multicellular organization, and result in patterns of growth. Thus, tissue form is not only a consequence but also an active regulator of tissue growth. Spatial patterning of the behaviors of individual cells generates global changes in tissue architecture that drive morphogenesis (1, 2). Several morphogenic mechanisms likely collaborate to direct tissue form, including local changes in cell adhesion, cell shape, and cell proliferation. Qualitative and quantitative differences in cellular adhesiveness can lead to the segregation and layering of tissues (3); ordered changes in cell shape appear to direct gastrulation (4), epithelial folding (5), and tubulogenesis (6); and differentials in cell growth can locally alter tissue form (7,8). Although the molecular basis for these behaviors has been under intense study, the mechanical nature of morphogenesis also has been recognized since the late 19th century (9): Specific patterns of cellular growth (in which some cells proliferate but other cells do not) create mechanical stresses that help drive the buckling, budding, pinching, and branching processes of morphogenesis. Complex forms, such as the regular fractal structure of the branching organs, can thus arise from simple embryonic sheets (reviewed in refs. 10 and 11).What causes such localized patterns is one of the central puzzles of biology and has fascinated scientists from numerous disciplines for at least two millennia (12). Perhaps most well described are concentration gradients of diffusible factors, known as morphogens, which can drive spatial patterns of cellular behaviors (13-15). In addition to soluble factors, adhesion to extracellular matrix and mechanical forces also are known to modulate cell functions, including proliferation (10,16,17).Although spatial patterning of these cues can certainly explain spatial patterning of cellular behaviors, it remains unclear what initiates or maintains patterns. One theory suggests that these gradients (e.g., of morphogens) are entirely driven by prespecified genetic programs. A more tracta...

Endothelial cells possess a mechanical network connecting adhesions on the basal surface, the cytoskeleton, and the nucleus. Transmission of force at adhesions via this pathway can deform the nucleus, ultimately resulting in an alteration of gene expression and other cellular changes (mechanotransduction). Previously, we measured cell adhesion area and apparent nuclear stretch during endothelial cell rounding. Here, we reconstruct the stress map of the nucleus from the observed strains using finite-element modeling. To simulate the disruption of adhesions, we prescribe displacement boundary conditions at the basal surface of the axisymmetric model cell. We consider different scenarios of the cytoskeletal arrangement, and represent the cytoskeleton as either discrete fibers or as an effective homogeneous layer When the nucleus is in the initial (spread) state, cytoskeletal tension holds the nucleus in an elongated, ellipsoidal configuration. Loss of cytoskeletal tension during cell rounding is represented by reactive forces acting on the nucleus in the model. In our simulations of cell rounding, we found that, for both representations of the cytoskeleton, the loss of cytoskeletal tension contributed more to the observed nuclear deformation than passive properties. Since the simulations make no assumption about the heterogeneity of the nucleus, the stress components both within and on the surface of the nucleus were calculated. The nuclear stress map showed that the nucleus experiences stress on the order of magnitude that can be significant for the function of DNA molecules and chromatin fibers. This study of endothelial cell mechanobiology suggests the possibility that mechanotransduction could result, in part, from nuclear deformation, and may be relevant to angiogenesis, wound healing, and endothelial barrier dysfunction.

We investigated the mechanotransduction pathway in endothelial cells between their nucleus and adhesions to the extracellular matrix. First, we measured nuclear deformations in response to alterations of cell shape as cells detach from a flat surface. We found that the nuclear deformation appeared to be in direct and immediate response to alterations of the cell adhesion area. The nucleus was then treated as a neo-Hookean compressible material, and we estimated the stress associated with the cytoskeleton and acting on the nucleus during cell rounding. With the obtained stress field, we estimated the magnitude of the forces deforming the nucleus. Considering the initial and final components of this adhesion-cytoskeleton-nucleus force transmission pathway, we found our estimate for the internal forces acting on the nucleus to be on the same order of magnitude as previously measured traction forces, suggesting a direct mechanical link between adhesions and the nucleus.

ABSTRACT--The outer hair cell is a specialized cell in the mammalian cochlea, believed to amplify incoming sound waves. This amplification is associated with the outer hair cell's electromotility, a unique cellular phenomenon of voltagedependent length changes. Outer hair cell properties can be described in terms of the piezoelectric relationships, and the elastic moduli are a key part of them. We revisit the problem of estimating the elastic moduli of the outer hair cell composite membrane (wall) where two methods have previously been proposed. We analyze the two methods, while taking into account experimental ranges of the measured parameters. We have shown that cell stiffness is the critical parameter that determines the difference between the method predictions, and we have found a range of stiffness where the results are reasonably close. The elastic moduli corresponding to this range can be recommended for estimation of the characteristics of the piezoelectric model.