The Notch signalling pathway is one of a handful of key regulators of cell differentiation in vertebrate and invertebrate animals. It serves to couple the cell-fate choice made by an individual cell to the cell-fate choices made by its next-door neighbours, through binding of the cell-surface ligand Delta (or its relative, Serrate) to the cell-surface receptor Notch. Activated Notch behaves as a regulator of gene transcription, driving a cell down one pathway of cell differentiation or another according to the nature of the tissue. Most importantly, activated Notch also regulates the expression of Delta. Thus the strength of signal that a cell receives from its neighbours governs the strength of signal that that cell delivers back to them. This feedback loop creates short-range correlations between the fates of adjacent cells: it is a generator of fine-grained spatial pattern. Two cases can be distinguished: in lateral inhibition, activated Notch down-regulates Delta; in lateral induction, it up-regulates Delta.
Lateral inhibition is the most famous form of Notch signalling and has the effect of forcing neighbouring cells to become different. Mathematical modelling shows that a homogeneous system of cells is unstable against the formation of a pepper-and-salt pattern of differentiation, provided that the level of Delta production in a given cell is regulated sufficiently steeply (differential coefficient < -1) by the level of Delta in neighbouring cells. This is analogous to anti-ferromagnetism. In vertebrate embryos, the central nervous system and the inner ear provide striking examples of the operation of this mechanism, which can serve not only to generate pepper-and-salt patterns, but also to single out an isolated cell for a unique fate and to maintain a balanced mixture of stem cells and differentiating cells in a stem-cell system.
Lateral induction has an opposite effect: it tends to make neighbours behave alike. This form of Notch signalling has been shown to occur at the developing wing margin of Drosophila, and may also operate in vertebrates. Mathematical modelling shows that lateral induction leads to the existence of alternative homogeneous stable states (with Delta everywhere high or everywhere low) provided again that the level of Delta production in a given cell is regulated sufficiently steeply (differential coefficient > +1) by the level of Delta in neighbouring cells. This is analogous to ferromagnetism. With suitable boundary conditions, a Delta-high domain can be generated adjacent to a Delta-low domain, with an abrupt (~1 cell diameter) transition between them, analogous to a domain boundary in a ferromagnet. Experimental evidence suggests that the formation of the sharp boundaries between somites may depend on this mechanism.