Microenvironmental Entropy Dynamics Analysis Reveals Novel Insights in 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.