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Various molecules exclusively accumulate at the front or back of migrating eukaryotic cells in response to a shallow gradient of extracellular signals. Directional sensing and signal amplification highlight the essential properties in the migrating cells, known as cell polarity. In addition to these, such properties of cell polarity involve unique determination of migrating direction (uniqueness of axis) and localized gradient sensing at the front edge (localization of sensitivity), both of which may be required for smooth migration. Here we provide the mass conservation system based on the reaction-diffusion system with two components, where the mass of the two components is always conserved. Using two models belonging to this mass conservation system, we demonstrate through both numerical simulation and analytical approximations that the spatial pattern with a single peak (uniqueness of axis) can be generally observed and that the existent peak senses a gradient of parameters at the peak position, which guides the movement of the peak. We extended this system with multiple components, and we developed a multiple-component model in which cross-talk between members of the Rho family of small GTPases is involved. This model also exhibits the essential properties of the two models with two components. Thus, the mass conservation system shows properties similar to those of cell polarity, such as uniqueness of axis and localization of sensitivity, in addition to directional sensing and signal amplification.
Cells crawling through tissues migrate inside a complex fibrous environment called the extracellular matrix (ECM), which provides signals regulating motility. Here we investigate one such well-known pathway, involving mutually antagonistic signalling
Cell polarization and directional cell migration can display random, persistent and oscillatory dynamic patterns. However, it is not clear if these polarity patterns can be explained by the same underlying regulatory mechanism. Here, we show that ran
The polarisation of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganisati
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than that estimat
Massive single-cell profiling efforts have accelerated our discovery of the cellular composition of the human body, while at the same time raising the need to formalise this new knowledge. Here, we review current cell ontology efforts to harmonise an