Hydrodynamic Interactions, Hidden Order, and Emergent Collective Behavior in an Active Bacterial Suspension

C. J. Pierce, H. Wijesinghe, E. Mumper, B. H. Lower, S. K. Lower, and R. Sooryakumar

Phys. Rev. Lett. 121, 188001 – Published 2 November 2018

Abstract

Spontaneous self-organization (clustering) in magnetically oriented bacteria arises from attractive pairwise hydrodynamics, which are directly determined through experiment and corroborated by a simple analytical model. Lossless compression algorithms are used to identify the onset of many-body self-organization as a function of experimental tuning parameters. Cluster growth is governed by the interplay between hydrodynamic attraction and magnetic dipole repulsion, leading to logarithmic time dependence of the cluster size. The dynamics of these complex, far-from-equilibrium structures are relevant to broader phenomena in condensed matter, statistical mechanics, and biology.

Received 20 July 2018
Revised 11 September 2018
Corrected 2 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.121.188001

Physics Subject Headings (PhySH)

Collective behavior Self-assembly

Bacteria Living matter & active matter Low Reynolds number swimmers

Hydrodynamics

Fluid DynamicsPhysics of Living SystemsCondensed Matter, Materials & Applied PhysicsPolymers & Soft Matter

Corrections

2 May 2019

Correction: Two references and their citations in text were missing and have been inserted. Three incorrect figure citations in text have been fixed. Errors in the author list and arXiv number in Ref. [32] have been straightened out.

Authors & Affiliations

C. J. Pierce¹, H. Wijesinghe¹, E. Mumper², B. H. Lower², S. K. Lower^2,3,4, and R. Sooryakumar¹

¹Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
²School of Environment and Natural Resources, The Ohio State University, Columbus, Ohio 43210, USA
³School of Earth Sciences, The Ohio State University, Columbus, Ohio 43210, USA
⁴Department of Microbial Infection and Immunity, The Ohio State University, Columbus, Ohio 43210, USA

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Vol. 121, Iss. 18 — 2 November 2018

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Images

Figure 1
(a) Schematic of oriented cells and resulting hydrodynamic interaction. (b) Flow field of a pure Stokeslet at height $h$ from a surface with image system (force monopole, force dipole, source dipole). Inset, profile of the velocity [Eq. (1)] derived from the flow field along the dashed line at height $h$ above surface. (c) Time of flight ( $t$ ) vs intercellular spacing ( $r$ ) for 87 cellular trajectories from three distinct pairs of cells, along with fit to model (in red) and power series (blue) revealing presence of lower order ( $1 / r$ ) terms. Vertical line indicates the minimum cell separation $d$ from fit. Inset, microscopy images of cells forming a rotating doublet. (d) Flow field of a rotlet dipole and image system, along with the singularities. (e) The angular velocity ( $ω$ ) vs $r$ with fit to rotlet dipole ( $1 / r^{3}$ ) model (red).
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Figure 2
(a) $f_{c} (t)$ for a population subjected to $10 - 100 G$ fields for 55 s (bold arrow indicates increasing magnetic field). The bolder, red curve shows the most dramatic drop in $f_{c}$ under a 100 G field. As the field is decreased (other colors), the extent of the decay in $f_{c}$ is reduced until at low values it remains nearly static in time. Inset: selected microscopy images from the self-organization process associated with the red (100 G) curve, taken at $t = 2.5$ , 5, 25, and 50 s. (b) initial (red) and final (black) values of the scaled CID ( $f_{c} / f_{0}$ ) as a function of field strength for various densities. As density decreases (left to right), the self-organization disappears at all field strengths (as seen in the decrease in the shaded area) Inset: selected images from 60 G field pulse showing initial (red outline) and final (black outline) representative configurations.
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Figure 3
Phase diagram illustrating the boundary between clustered states (closed circles) and disordered states (open circles). The color indicates the percentage drop in the scaled CID ( $f_{c} / f_{0}$ ). The black line is a approximate power law fit to the phase boundary. The gray line indicates the threshold beyond which the density may not be reliably determined optically. Hence, for these points, the recorded density should be interpreted as a lower bound.
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Figure 4
$g (r)$ , offset for clarity at $t = 0.1$ , 1.5, 10, and 50 s after application of a 100 Oe external field (corresponding with the images in Fig. 2. The dashed line corresponds with the value of $g (r)$ expected for a noninteracting gas (a flat distribution). Inset shows a logarithmic increase in the peak associated with clustered cells (red) and the logarithmic scaling of the CID(blue) in time. Vertical dashed line indicates the onset of logarithmic scaling at $t \sim 2 s$ after the initial transient.
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