Abstract
Cells can measure shallow gradients of external signals to initiate and accomplish a migration or a morphogenetic process. Recently, starting from mathematical models like the local-excitation global-inhibition (LEGI) model and with the support of empirical evidence, it has been proposed that cellular communication improves the measurement of an external gradient. However, the mathematical models that have been used have over-simplified geometries (e.g., they are uni-dimensional) or assumptions about cellular communication, which limit the possibility to analyze the gradient sensing ability of more complex cellular systems. Here, we generalize the existing models to study the effects on gradient sensing of cell number, geometry and of long- versus short-range cellular communication in 2D systems representing epithelial tissues. We find that increasing the cell number can be detrimental for gradient sensing when the communication is weak and limited to nearest neighbour cells, while it is beneficial when there is long-range communication. We also find that, with long-range communication, the gradient sensing ability improves for tissues with more disordered geometries; on the other hand, an ordered structure with mostly hexagonal cells is advantageous with nearest neighbour communication. Our results considerably extend the current models of gradient sensing by epithelial tissues, making a step further toward predicting the mechanism of communication and its putative mediator in many biological processes.
Highlights
Collective migration of epithelial cells is central in plenty of biological processes, ranging from development, to wound healing and cancer [1–11]
Cellular communication has recently been suggested to play a key role in gradient sensing, and mathematical models with simplified cellular geometries have been developed to help interpret and design experiments
The local reporter remains confined in the cell and represents a local measurement of the signal; the global reporter is exchanged between neighbour cells, allowing the system to perform a spatial average of the signal concentration
Summary
Collective migration of epithelial cells is central in plenty of biological processes, ranging from development, to wound healing and cancer [1–11]. Each cell can estimate local deviations of the signal from the overall spatial average by combining the information encoded in the levels of the two reporters [18]. This model has been successfully used to describe branching morphogenesis of the epithelial tissue in mammary glands [18], and its physical limits in terms of the properties of the external signal, the cell size and the typical length scale of cellular communication (which in turn depends on the kinetic rates of the LEGI global reporter), have been derived [19]
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