Cross-feeding percolation phase transitions of intercellular metabolic networks.

Intercellular cross-talk is essential for the adaptation capabilities of populations of cells. While direct diffusion-driven cell-to-cell exchanges are difficult to map, current nanotechnology enables one to probe single-cell exchanges with the medium. We introduce a mathematical method to reconstruct the dynamic unfolding of intercellular exchange networks from these data, applying it to an experimental coculture system. The exchange network, initially dense, progressively fragments into small disconnected clusters. To explain these dynamics, we develop a maximum-entropy multicellular metabolic model with diffusion-driven exchanges. The model predicts a transition from a dense network to a sparse one as nutrient consumption shifts. We characterize this crossover both numerically, revealing a power-law decay in the cluster-size distribution, and analytically, by connecting to percolation theory. Comparison with data suggests that populations evolve toward the sparse phase by remaining near the crossover. These findings offer insights into the collective organization driving the adaptive dynamics of cell populations.