A spin glass representation of hierarchical gene regulation and the partial resolution of frustration

A nonreciprocal multicellular Ising model shows frustration in six nine-gene regulatory networks is only partially resolved: stronger cell-cell coupling lowers intercellular frustration while raising intracellular frustration.

• Why it matters: Gene regulatory loops can create conflicting demands that no expression state satisfies, but existing spin-glass tissue models assume symmetric regulation and single-cell studies miss multicellular effects.
• What they did: The authors couple a directed intracellular network in each cell to random symmetric signalling between neighbours, define intracellular and intercellular frustration densities, and analyze six nine-gene exemplars with shared downstream cascades.
• The result: In isolated cells, the upstream three-gene motif sets frustration, while negative feedback loops keep switching and incoherent feedforward loops freeze it; with communication, shared expression forms clusters and conflict concentrates at boundaries, with a transition near the coupling where eight-neighbour input matches one regulatory interaction.

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