Collective Stop-and-Go Dynamics of Active Bacteria Swarms

Editors' Suggestion

Collective Stop-and-Go Dynamics of Active Bacteria Swarms

Daniel Svenšek, Harald Pleiner, and Helmut R. Brand

Phys. Rev. Lett. 111, 228101 – Published 25 November 2013

Abstract

We set up a macroscopic model of bacterial growth and transport based on a dynamic preferred direction—the collective velocity of the bacteria. This collective velocity is subject to the isotropic-nematic transition modeling the density-controlled transformation between immotile and motile bacterial states. The choice of the dynamic preferred direction introduces a distinctive coupling of orientational ordering and transport not encountered otherwise. The approach can also be applied to other systems spontaneously switching between individual (disordered) and collective (ordered) behavior and/or collectively responding to density variations, e.g., bird flocks, fish schools, etc. We observe a characteristic and robust stop-and-go behavior. The inclusion of chirality results in a complex pulsating dynamics.

Received 1 March 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.228101

Authors & Affiliations

Daniel Svenšek^1,*, Harald Pleiner², and Helmut R. Brand³

¹Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
²Max-Planck-Institute for Polymer Research, Post Office Box 3148, 55021 Mainz, Germany
³Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany

^*Corresponding author. daniel.svensek@fmf.uni-lj.si

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 111, Iss. 22 — 27 November 2013

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Top: Growth of the colony after the point inoculation with $ρ = 0.2$ . (a)–(d) Density snapshots [26] (bright regions represent high density) of achiral population. Bottom: The time dependence of the sample-average magnitude of the velocity demonstrates the steplike growth dynamics.Reuse & Permissions
Figure 2
Density snapshots [26] (bright regions represent high density) [compare with Fig. 3a] of the growing colony after a slightly randomly perturbed line inoculation with $ρ = 0.2$ . Because of the periodic boundary conditions, in (f) the front, after passing the left boundary, reenters the system from the right. Note the internal waves in (e) and (g) advancing toward the front and pushing it ahead afterward. In (h), the whole system is about to be populated; subsequently, the front moves continuously.Reuse & Permissions
Figure 3
Growth of the colony after the perturbed line inoculation: the time dependence of the sample-average magnitude of the velocity demonstrates clear-cut pulses and almost no dynamics between them. (a) No chirality and (b) $K_{c} = 0.0034$ .Reuse & Permissions
Figure 4
Density snapshots [26] (bright regions represent high density) [compare with Fig. 3b] of the growing colony after a slightly randomly perturbed line inoculation [the same as in Fig. 2a] in a chiral system with $K_{c} = 0.0034$ [compare with Fig. 6f to locate it in the chirality diagram]. (a)–(c) The front typically moves back and forth across the populated region. (d)–(g) Two fronts are interestingly passing next to each other. (h) The last calm stage before the whole system gets populated.Reuse & Permissions
Figure 5
Density profile snapshots [26] (horizontal central cross sections of density fields like in Fig. 2). (a) Reposing phase with the static front (the peak on the left) and (b) active phase showing an internal density wave traveling toward the front. The threshold density $ρ^{*}$ is shown as a dashed line.Reuse & Permissions
Figure 6
Dynamograms showing the growth dynamics morphology (bright regions represent active stages) as a function of time (horizontal axis) and the model parameters (vertical axis). (a),(b) Dependence on $1 / γ$ , the responsiveness of the velocity field, for two values of the inoculation density (a) $ρ = 0.2$ and (b) $ρ = 0.02$ ; note the time shift in (b). (c) Dependence on the velocity scale $v_{0}$ , (d) dependence on $L$ , (e) the role of compressibility, and (f) the influence of chirality. Late stages (shown partially) exhibit an increased activity after the whole area has been populated. Taking horizontal cross sections produces velocity profiles like in Fig. 3.Reuse & Permissions

Physical Review Letters