Voronoi tessellation captures very early clustering of single primary cells as induced by interactions in nascent biofilms.

Biofilms dominate microbial life in numerous aquatic ecosystems, and in engineered and medical systems, as well. The formation of biofilms is initiated by single primary cells colonizing surfaces from the bulk liquid. The next steps from primary cells towards the first cell clusters as the initial step of biofilm formation remain relatively poorly studied. Clonal growth and random migration of primary cells are traditionally considered as the dominant processes leading to organized microcolonies in laboratory grown monocultures. Using Voronoi tessellation, we show that the spatial distribution of primary cells colonizing initially sterile surfaces from natural streamwater community deviates from uniform randomness already during the very early colonisation. The deviation from uniform randomness increased with colonisation--despite the absence of cell reproduction--and was even more pronounced when the flow of water above biofilms was multidirectional and shear stress elevated. We propose a simple mechanistic model that captures interactions, such as cell-to-cell signalling or chemical surface conditioning, to simulate the observed distribution patterns. Model predictions match empirical observations reasonably well, highlighting the role of biotic interactions even already during very early biofilm formation despite few and distant cells. The transition from single primary cells to clustering accelerated by biotic interactions rather than by reproduction may be particularly advantageous in harsh environments--the rule rather than the exception outside the laboratory.