Roughening instability of growing three-dimensional bacterial colonies*

How do growing bacterial colonies get their shape? While this process of morphogenesis is well-studied in 2D, many bacterial colonies inhabit 3D environments, such as gels and tissues in the body, or soils, sediments, and subsurface media. Here, we describe a morphological instability exhibited by dense colonies of non-motile bacteria growing in 3D. Using experiments in transparent 3D media, we show that colonies of Escherichia coli and Vibrio cholerae generically roughen as they consume nutrients and grow, eventually forming branched, finger-like patterns. This behavior reflects a key difference between 2D and 3D colonies: while 2D colonies can more easily access the nutrients needed for growth, the 3D colonies inevitably become nutrient-limited in their interior, driving a transition to rough, branched growth. We elucidate this behavior using linear stability analysis and numerical simulations of a continuum active fluid model, which indeed reveal that when the size of the growing colony far exceeds the nutrient penetration length, nutrient depletion drives a transition to roughening with a characteristic universal shape that can be compared with experiments.