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, 8 (2), 026008

Buckling Instability in Ordered Bacterial Colonies

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Buckling Instability in Ordered Bacterial Colonies

Denis Boyer et al. Phys Biol.

Abstract

Bacterial colonies often exhibit complex spatio-temporal organization. This collective behavior is affected by a multitude of factors ranging from the properties of individual cells (shape, motility, membrane structure) to chemotaxis and other means of cell-cell communication. One of the important but often overlooked mechanisms of spatio-temporal organization is direct mechanical contact among cells in dense colonies such as biofilms. While in natural habitats all these different mechanisms and factors act in concert, one can use laboratory cell cultures to study certain mechanisms in isolation. Recent work demonstrated that growth and ensuing expansion flow of rod-like bacteria Escherichia coli in confined environments leads to orientation of cells along the flow direction and thus to ordering of cells. However, the cell orientational ordering remained imperfect. In this paper we study one mechanism responsible for the persistence of disorder in growing cell populations. We demonstrate experimentally that a growing colony of nematically ordered cells is prone to the buckling instability. Our theoretical analysis and discrete-element simulations suggest that the nature of this instability is related to the anisotropy of the stress tensor in the ordered cell colony.

Figures

Figure 1
Figure 1
Two snapshots with superimposed local order parameter from the experimental run in a 100×90 μm2 side trap in which buckling instability was observed: (a) t = 0 min, (b) t = 25 min. Solid blue lines show the solid walls of the trap and the dashed blue lines show the open side. Red indicates low values of the local order parameter.
Figure 2
Figure 2
Spacetime diagram of the local order parameter η averaged over the width of the trap for the run illustrated by figure 1.
Figure 3
Figure 3
(a) First five eigenvalues corresponding to odd (dashed) and even (solid) modes of equation (17) as functions of a*. (b) Two fastest growing eigenmodes (even w0e(x) and odd w0o(x)) for a* = 2500 corresponding to almost identical positive (unstable) eigenvalues s0 = 3.4737 … × 105.
Figure 4
Figure 4
(ac) Three still frames from a simulation of a growing colony in a 40 × 80 open trap at times (a) t = 19.5, (b) t = 20.5, (c) t = 30. The growth rate a = 0.71, maximum aspect ratio of cells A = 6 and the bottom friction μ = 10 were turned on at t = 20. Coloring of the rods indicates rod’s angle with respect to the x-axis: green φ = 0, red φ = ±π/2. (d) Spacetime diagram of the magnitude of the order parameter averaged over the y dimension for the simulation exemplified in figure 4.
Figure 5
Figure 5
Still frames at time t = 50 (a, b) and spacetime diagrams (c, d) of the order parameter η (averaged over the transversal y coordinate) from simulations of a growing colony in a 40 × 80 side trap: (a, c) x-dependent mean cell size (c = 0.5); (b, d) x-independent mean cell size (c = 0).

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