Signal transmission among cells enables long-range coordination in biological systems. However, the scarcity of quantitative measurements hinders the development of theories that relate signal propagation to cellular heterogeneity and spatial organization. We address this problem in a bacterial community that employs electrochemical cell-to-cell communication. We developed a model based on percolation theory, which describes how signals propagate through a heterogeneous medium. Our model predicts that signal transmission becomes possible when the community is organized near a critical phase transition between a disconnected and a fully connected conduit of signaling cells. By measuring population-level signal transmission with single-cell resolution in wild-type and genetically modified communities, we confirm that the spatial distribution of signaling cells is organized at the predicted phase transition. Our findings suggest that at this critical point, the population-level benefit of signal transmission outweighs the single-cell level cost. The bacterial community thus appears to be organized according to a theoretically predicted spatial heterogeneity that promotes efficient signal transmission.

This work was in part supported by the San Diego Center for Systems Biology (NIHP50 GM085764, G.M.S), National Institute of General Medical Sciences (R01 GM121888, G.M.S and A.M.), the Howard Hughes Medical Institute-Simons Foundation Faculty Scholars program (G.M.S.), a Simons Foundation Fellowship of the Helen Hay Whitney Foundation (F1135, A.P.), the Simons Foundation Mathematical Modeling of Living Systems Program (376198, A.M.), the National Science Foundation Research Experiences for Undergraduates Program (PHY-1460899, S.G.), the Spanish Ministry of Economy and Competitiveness and FEDER (project FIS2015-66503-C3-1-P, J.G.O.), the ICREA Academia program (J.G.O.), the Maria de Maeztu Program for Units of Excellence in Research and Development (Spanish Ministry of Economy and Competitiveness, MDM-2014-0370, J.G.O.), and a Marie Curie MCCIG grant (no. 303561, A.M.W.).