Speaker
Description
Waddington’s epigenetic landscape has long served as a central metaphor for cellular differentiation, depicting mature cell types as stable valley floors. Boolean networks, introduced by Kauffman in 1969, provide a mathematical formalization in which attractors represent phenotypes and basins correspond to developmental valleys. Traditional stability measures assess robustness via perturbations of arbitrary states, although biological systems typically reside at attractors. Here we formalize and analyze attractor coherence – a stability measure Kauffman envisioned but never rigorously developed – which quantifies the likelihood that perturbations of attractor states induce phenotype switching. Across 122 curated biological Boolean models, we uncover a paradox: attractors representing mature cell types are consistently less stable than the trajectories leading to them. Simulations of random networks show that this coherence gap arises from canalization, where specific genes dominate regulation. While canalization increases overall stability, it disproportionately stabilizes transient states, placing attractors near basin boundaries. The gap is almost perfectly predicted by network bias, itself shaped by canalization. These results revise Waddington’s landscape: canalization creates robust developmental valleys while flattening ridges near attractors, enabling phenotypic plasticity.
