Microenvironmental entropy dynamics analysis reveals novel insights into Notch-Delta-Jagged decision-making mechanism

Notch-Delta-Jagged (NDJ) signaling among neighboring cells contributes crucially to spatiotemporal pattern formation and developmental decision-making. Despite numerous detailed mathematical models, their high-dimensionality parametric space limits analytical treatment, especially regarding local microenvironmental fluctuations. Using the low-dimensional dynamics of the recently postulated least microenvironmental uncertainty principle (LEUP) framework, we showcase how the LEUP formalism recapitulates a noisy NDJ spatial patterning. Our LEUP simulations show that local phenotypic entropy increases for lateral inhibition but decreases for lateral induction. This distinction allows us to identify a critical parameter that captures the transition from a Notch-Delta-driven lateral inhibition to a Notch-Jagged-driven lateral induction phenomenon and suggests random phenotypic patterning in the case of lack of dominance of either Notch-Delta or Notch-Jagged signaling. Our results enable an analytical treatment to map the high-dimensional dynamics of NDJ signaling on tissue-level patterning and can possibly be generalized to decode operating principles of collective cellular decision-making.