The role of cell geometry and cell-cell communication in gradient sensing

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. Author summary Groups of cells collectively migrate in many biological processes, ranging from development to cancer metastasis. The migration is often driven by the gradient of a signaling molecule that can be shallow and noisy, raising the question of how cells can measure it reliably. 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. In this work, we generalize the existing mathematical models to investigate how short- and long-range cellular communication can increase gradient sensing in two-dimensional models of epithelial tissues. We analyze various cellular geometries and tissue size, and we identify the optimal setting that corresponds to different types of communication. Our findings will help pinpoint the communication mechanisms at work in a given tissue and the properties of the molecules that mediate the communication.