Topological Structure of Epigenetic Forests in Flower Morphogenesis

Understanding how stable developmental patterns emerge from complex gene regulatory networks remains a central problem in developmental biology. Here, we compare wild-type and mutant epigenetic landscapes of the floral gene regulatory network of Arabidopsis thaliana using global basin statistics (entropy, effective number of fates, inequality of basin sizes, convergence times) and distributional distances (Jensen–Shannon divergence). The landscape is modeled as an Epigenetic Forest: a collection of rooted trees induced by the state transition graph of a Boolean gene regulatory network, where each tree represents the basin of attraction of a stable gene expression pattern associated with a floral or meristematic identity. We apply this framework to three classical single homeotic mutants (ap1, pi, and ag) and three double mutants (ap3–pi, ag–pi, and ap1–ag). Single mutants induce qualitatively distinct modes of landscape deformation, including restricted accessibility, redistribution of identity-specific basins, and increased fate diversity associated with defective meristem termination. In particular, ap1 strongly increases canalization, whereas ag increases structural diversity despite loss of reproductive identity. One pair of perturbations yields landscapes that are indistinguishable across all reported metrics (ap3–pi and pi), reflecting functional redundancy of the B-function partners AP3 and PI, while other combinations (ag–pi and ap1–ag) diverge sharply from the wild-type landscape. The framework reproduces canonical floral identities and experimentally observed mutant phenotypes, and treats the epigenetic landscape as a finite, computable object determined by regulatory logic encoded in the global topology of the state transition graph. Mathematics Subject Classification (2020) Primary: 92B05, 37N25. Secondary: 92C42, 05C20, 94A17