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Cell-to-cell information at a feedback-induced bifurcation point

A ubiquitous way that cells share information is by exchanging molecules. Yet, the fundamental ways that this information exchange is influenced by intracellular dynamics remain unclear. Here we use information theory to investigate a simple model of two interacting cells with internal feedback. We show that cell-to-cell molecule exchange induces a collective two-cell critical point and that the mutual information between the cells peaks at this critical point. Information can remain large far from the critical point on a manifold of cellular states, but scales logarithmically with the correlation time of the system, resulting in an information-correlation time tradeoff. This tradeoff is strictly imposed, suggesting the correlation time as a proxy for the mutual information.