Roughening instability of growing 3D bacterial colonies

How do growing bacterial colonies get their shapes? While colony morphogenesis is well-studied in 2D, many bacteria grow as large colonies in 3D environments, such as gels and tissues in the body, or soils, sediments, and subsurface porous media. Here, we describe a morphological instability exhibited by large colonies of bacteria growing in 3D. Using experiments in transparent 3D granular hydrogel matrices, we show that dense colonies of four different species of bacteria--Escherichia coli, Vibrio cholerae, Pseudomonas aeruginosa, and Komagataeibacter sucrofermentans--generically roughen as they consume nutrients and grow beyond a critical size, eventually adopting a characteristic branched, broccoli-like, self-affine morphology independent of variations in the cell type and environmental conditions. This behavior reflects a key difference between 2D and 3D colonies: while a 2D colony may access the nutrients needed for growth from the third dimension, a 3D colony inevitably becomes nutrient-limited in its interior, driving a transition to rough growth at its surface. We elucidate the onset of roughening using linear stability analysis and numerical simulations of a continuum model that treats the colony as an active fluid whose dynamics are driven by nutrient-dependent cellular growth. We find that when all dimensions of the growing colony substantially exceed the nutrient penetration length, nutrient-limited growth drives a 3D morphological instability that recapitulates essential features of the experimental observations. Our work thus provides a framework to predict and control the organization of growing colonies--as well as other forms of growing active matter, such as tumors and engineered living materials--in 3D environments.