The hierarchical organization of cell identity, characterized by progenitor cells coexpressing multiple tran scriptional programs, is a hallmark of animal development with well-documented experimental phenomenology.
However, the mechanisms underlying its emergence remain unclear. Here we investigate the origin and regu lation of progenitor states using a mechanistic mathematical framework based on transcription factor-enhancer
interactions. This framework maps the regulation of cell identity genes to the dynamics of a continuous Modern
Hopfield network, governed by an inverse-temperature-like parameter, β, representing epigenetic modifier
activity, and an input field, w, reflecting signaling activity. We propose that multilineage-primed progenitor states
emerge from the interplay between enhancer competition for epigenetic readers and the activation of overlapping
transcriptional programs. Mathematically, these progenitor states correspond to mixed attractor patterns in the
network at intermediate β values. We introduce an analytical approach to characterize the identity, stability, and
basins of attraction of progenitor states, including their emergence and destabilization at specific β thresholds.
Applying this approach, we explain how signaling can instruct differentiation, reconstruct the complex blood
progenitor landscape from terminal lineages, and identify potential mechanisms of differentiation dysregulation
in cancer. We propose that nonspecific modulation of enhancer competition is a key regulatory axis underlying
cell identity transitions.