A computational model of fractal interface formation in bacterial biofilms

Bacteria benefit from cellular heterogeneity: cells differentiate into diverse gene expression states. As colonies grow, cellular phenotypes arrange into spatial patterns. To uncover the functional role of these emergent patterns, we must understand how they arise from cellular growth and mechanical interactions. Here we present a simple, agent-based model to predict patterns of motile and extracellular matrix-producing cells in biofilms of Bacillus subtilis. By incorporating phenotypic inheritance, mechanical interactions, and peripheral motile cell dispersal, our model predicts the emergence of a pattern: matrix cells surround a fractal-like interior motile population. We find that, while some properties of the motile-matrix interface depend on initial conditions, the motile distribution at large radii depends solely on the models growth mechanism. The phenotypic interface exhibits a fractal dimension that increases as biofilms grow but reaches a maximum as the peripheral layer of matrix cells exceeds the capacity of the inner cells to push it out of the way. By varying parameters, we find correlations between the interface fractal dimension and expansion of motile cells. We validate findings using experiments on B. subtilis biofilms in microfluidics. Our model demonstrates the emergence of colony-level phenotypes from single cell-level interactions and cells modifying their own environment.