  Lateral inhibition patterns mediated by the Notch-Delta signaling system
occur in diverse developmental contexts. These systems are based on an
intercellular feedback loop in which Notch activation leads to down-regulation
of Delta. However, even in relatively well-characterized systems, the pathway
leading from Notch activation to Delta repression often remains elusive. Recent
work has shown that cis-interactions between Notch and Delta lead to mutual
inactivation of both proteins. Here we show that this type of cis-interaction
enables a simpler and more direct mechanism for lateral inhibition feedback
than those proposed previously. In this mechanism, Notch signaling directly
up-regulates Notch expression, thereby inactivating Delta through the mutual
inactivation of Notch and Delta proteins. This mechanism, which we term
Simplest Lateral Inhibition by Mutual Inactivation (SLIMI), can implement
patterning without requiring any additional genes or regulatory interactions.
Moreover, the key interaction of Notch expression in response to Notch
signaling has been observed in some systems. Stability analysis and simulation
of SLIMI mathematical models show that this lateral inhibition circuit is
capable of pattern formation across a broad range of parameter values. These
results provide a simple and plausible explanation for lateral inhibition
pattern formation during development.
