How simple cell to cell communication rules can generate and maintain scale invariant gradients of signalling activity across a multicellular population

This paper shows computationally and conceptually how gradients of signalling activity can be generated and dynamically maintained across a population of cells using very simple cell to cell communication rules. The rules work on the basis of cells regulating their production rate of a signalling molecule according to the production rates of their immediate neighbours. Highly stable, scale invariant signalling gradients can be formed across the population, with highest rates at the centre and lowest at the periphery. The cell to cell communication behaviour that causes gradient formation is first explained in a descriptive, thought experiment type manner. It is then defined more formally using a conceptual, mathematically discrete computational model, which provides a network or graph type framework in which it is easy to analyse and control discrete signals that are sent between neighbouring cells. This provides an intuitive method of explaining how the signalling gradient emerges as a result of local cell to cell communication. Finally, examples of gradient formation are shown using software implementations of the model.