Tilt-induced polar order and topological defects in growing bacterial populations

Abstract: Rod-shaped bacteria, such as Escherichia coli, commonly live forming mounded colonies. They initially grow two-dimensionally on a surface and finally achieve three-dimensional growth. While it was recently reported that three-dimensional growth is promoted by topological defects of winding number $+1/2$ in populations of motile bacteria, how cellular alignment plays a role in non-motile cases is largely unknown. Here, we investigate the relevance of topological defects in colony formation processes of non-motile E. coli populations, and found that both $\pm 1/2$ topological defects contribute to the three-dimensional growth. Analyzing the cell flow in the bottom layer of the colony, we observe that $+1/2$ defects attract cells and $-1/2$ defects repel cells, in agreement with previous studies on motile cells, in the initial stage of the colony growth. However, later, cells gradually flow toward $-1/2$ defects as well, exhibiting a sharp contrast to the existing knowledge. By investigating three-dimensional cell orientations by confocal microscopy, we find strong vertical tilting of cells near the defects. Crucially, this leads to the emergence of a polar order in the otherwise nematic two-dimensional cell orientation. We extend the theory of active nematics by incorporating this polar order and the vertical tilting, which successfully explains the influx toward $-1/2$ defects in terms of a polarity-induced force. Our work reveals that three-dimensional cell orientations may result in drastic changes in properties of active nematics, especially those of topological defects, which may be generically relevant in active matter systems driven by cellular growth instead of self-propulsion.