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Over the last decade, a large number of pioneering studies have been conducted to understand complex mechanisms that regulate the internal and external behavior of cells. The entanglement among these mechanisms has been unraveled by performing experiments combining quantitative modeling that demonstrate cell behavior in a spatio-temporal way. Systematic understanding via modeling provides positive feedback to the experiments and more experiment and theory converge. How different mechanobiochemical pathways are entangled controlling cellular function is full of fascinating questions. Some aspects in this area we would like to discuss in this chapter. We will start with the filamentous network embedded in the cell cytoplasm, commonly known as cytoskeleton. We will discuss some of the biomechanial properties of cytoskeletal filaments and show how cell cytoskeleton changes from a uniform, homogeneous network to a non-homogeneous and polarized network that built and control the cell shape. The topology of the network depends on the focal adhesion through which cells anchor, sense mechanical properties of the extra cellular matrix, and respond actively. We will demonstrate that stress distribution along the cell periphery is a function of the instantaneous cell shape. Characteristic profile of stress determines the cell shape during migration leading to keratocyte-shaped morphology for a circular cell and fan-shape morphology for an elliptical cell. Finally, we will focus on the pattern formation by a group of cells seeded on a two-dimensional extra cellular matrix. Our results suggest that a string-like pattern of cells is favorable if the matrix stiffness and ambience temperatures are optimal.

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