A topological approach to describing multicellular network structures in bacterial biofilms

Bacterial biofilms are paradigmatic examples of prokaryotic multicellular collectives. Here, we describe a mathematical framework, based on algebraic topology, for describing the structure of multicellular networks formed via differential cell-cell adhesion within subpopulations of a developing biofilm. We describe the structure of a multicellular network within the biofilm in terms of a dynamic 3D simplicial complex, for which can identify a minimal basis for the first homology group—which localizes the "holes" in the network—as well as other topological information, such as the Betti numbers. Using this approach, we show that a biofilm of cells that switch between matrix-producing and non-producing states can form robust networks of matrix-producing cells, whose topological features depend on the strength of cell-cell adhesion. We also discuss how these features depend on the nature of cell-cell interactions within the biofilm, other phenotypes such as growth rate and cell shape, and aspects of the biofilm life cycle. This lays the groundwork for a general, rigorous approach to describing the internal organization of multicellular collectives.