5/31/2023 0 Comments Explicit equation calculatorThe cell alignment along the boundaries then forces the surrounding cells to align in the same direction at a scale of several hundred micrometres. Cells cultured in small domains tend to align along the boundaries of the domains. Recent studies have revealed that topological defects in spindle-shaped adhesive cells have different properties from other active nematic systems. Therefore, many experimental and theoretical studies of active nematic systems have focused on the characteristics of the topological defects. The non-uniformity of the alignment around the defects can cause mechanical imbalances among the components, which may play key roles in the active movement of living matter. These singular points are called topological defects. ![]() In these active nematic systems, the alignment of the spindle-shaped materials induces singular points at which the alignment angle cannot be defined. Many active nematic systems have been studied, including micro- and nano-biosystems such as microtubule-kinesin compounds, bacterial colonies, cell monolayers, macroscopic tissues and animals. Spindle- and rod-shaped living materials exhibit active behaviours as nematic liquid crystals, known as active nematics. The proposed calculation method is used to demonstrate a numerical prediction of multiple defects in circular and non-circular geometries, which are consistent with previous experimental results. Finally, the complex potential allows a calculation of the Frank elastic energy, which can be minimized with respect to the defect positions to predict their equilibrium state in the geometry. Then, the derived formula for the unit disc is extended to the case for non-circular geometries using a numerical conformal mapping. First, a complex potential is introduced to describe the alignment angles of cells, which is used to derive an explicit formula for cell alignment in a unit disc. ![]() This study proposes an explicit calculation method for predicting cell alignment and defect positions in non-circular geometries. To control defects related to biological roles such as cell apoptosis, calculation methods for predicting the defect positions are required. ![]() The alignment of spindle-shaped cells in two-dimensional geometries induces singular points called topological defects, at which the alignment angle of the cell cannot be defined.
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