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Mathematical Framework for Hierarchical Cell Identity Control by Collective Enhancer Dynamics

Anton Grishechkin, Abhirup Mukherjee, and Omer Karin

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PRX Life 3, 043007 – Published 23 October, 2025

DOI: https://doi.org/10.1103/dkmq-h4d9

Abstract

The hierarchical organization of cell identity, characterized by progenitor cells coexpressing multiple transcriptional 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 regulation 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.

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PRX Life 3, 043007– Published 23 October, 2025
  • Received 8 April 2025
  • Accepted 10 September 2025
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