Signal transmission in a heterogeneous bacterial population

Biological systems such as tissues or bacterial communities often require reliable signal transmission among cells to coordinate actions at a distance. One of the key obstacles for such signal propagation is the spatial heterogeneity that arises when only a fraction of cells contributes to signal transmission. This cell-to-cell heterogeneity can cause signal propagation to die out before reaching its desired target. Motivated by electrochemical signaling within bacterial biofilms, in which only a fraction of cells participates in the signaling, we develop a model of signal propagation in a heterogeneous community. We integrate percolation theory, which describes the structure of the heterogeneity, with the FitzHugh-Nagumo model, which describes the excitable dynamics of signaling at the single-cell level. We find that the transition between signal propagation and signal failure is determined not only by the structural properties (e.g., the percolation threshold), but also by the dynamic properties (e.g., the excitation threshold) of the model. Our integrated model provides predictions that we test using gene-deletion strains that modify the fraction of participating cells in the biofilm.