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Epithelial tissues form physically integrated barriers against the external environment protecting organs from infection and invasion. Within each tissue, epithelial cells respond to different challenges that can potentially compromise tissue integrity. In particular, cells collectively respond by reorganizing their cell-cell junctions and migrating directionally towards the sites of injury. Notwithstanding, the mechanisms that define the spatiotemporal scales and driving forces of these collective responses remain poorly understood. To address this we first analyzed the collective response of epithelial monolayers to injury and compare the results with different computational models of epithelial cells. We found that a model that integrates the mechanics of cells at the cell-cell and cell-substrate interface as well as contact inhibition of locomotion predicts two key properties of epithelial response to injury as: 1) local relaxation of the tissue and 2) collective responses involving the elongation of cells (basal and apical regions) and extension of cryptic lamellipodia that extend up to < 3 cell diameters from the site of injury. Our results therefore highlight the integration between junctional biomechanics, cell substrate adhesion and contact inhibition of locomotion to guide the rapid collective rearrangements that are required to preserve the epithelial barrier in response to injury., Comment: 26 pages, 5 figures. Supplementary Movie 1 available upon request to the corresponding authors

We generated a computational approach to analyze the biomechanics of epithelial cell aggregates, either island or stripes or entire monolayers, that combines both vertex and contact-inhibition-of-locomotion models to include both cell-cell and cell-substrate adhesion. Examination of the distribution of cell protrusions (adhesion to the substrate) in the model predicted high order profiles of cell organization that agree with those previously seen experimentally. Cells acquired an asymmetric distribution of basal protrusions, traction forces and apical aspect ratios that decreased when moving from the edge to the island center. Our in silico analysis also showed that tension on cell-cell junctions and apical stress is not homogeneous across the island. Instead, these parameters are higher at the island center and scales up with island size, which we confirmed experimentally using laser ablation assays and immunofluorescence. Without formally being a 3-dimensional model, our approach has the minimal elements necessary to reproduce the distribution of cellular forces and mechanical crosstalk as well as distribution of principal stress in cells within epithelial cell aggregates. By making experimental testable predictions, our approach would benefit the mechanical analysis of epithelial tissues, especially when local changes in cell-cell and/or cell-substrate adhesion drive collective cell behavior., Comment: 39 pages, 8 Figures. Supplementary Information is included

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk., Comment: 9 pages