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Edited by Harry L. Swinney, University of Texas at Austin, Austin, TX, and approved June 2, 2014 (received for review March 28, 2014)
Significance
The collective dynamics of swimming microorganisms exhibits a complex interplay with the surrounding fluid: the motile cells stir the fluid, which in turn can reorient and advect them. This feedback loop can result in long-range interactions between the cells, an effect whose significance remains controversial. We present a computational model that takes into account these cell–fluid interactions and cell–cell forces and that predicts counterintuitive cellular order driven by long-range flows. This prediction is confirmed with experimental studies that track the orientation of cells in a confined, dense bacterial suspension.
Abstract
Concentrated suspensions of swimming microorganisms and other forms of active matter are known to display complex, self-organized spatiotemporal patterns on scales that are large compared with those of the individual motile units. Despite intensive experimental and theoretical study, it has remained unclear the extent to which the hydrodynamic flows generated by swimming cells, rather than purely steric interactions between them, drive the self-organization. Here we use the recent discovery of a spiral-vortex state in confined suspensions of Bacillus subtilis to study this issue in detail. Those experiments showed that if the radius of confinement in a thin cylindrical chamber is below a critical value, the suspension will spontaneously form a steady single-vortex state encircled by a counter-rotating cell boundary layer, with spiral cell orientation within the vortex. Left unclear, however, was the flagellar orientation, and hence the cell swimming direction, within the spiral vortex. Here, using a fast simulation method that captures oriented cell–cell and cell–fluid interactions in a minimal model of discrete particle systems, we predict the striking, counterintuitive result that in the presence of collectively generated fluid motion, the cells within the spiral vortex actually swim upstream against those flows. This prediction is then confirmed by the experiments reported here, which include measurements of flagella bundle orientation and cell tracking in the self-organized state. These results highlight the complex interplay between cell orientation and hydrodynamic flows in concentrated suspensions of microorganisms.
Footnotes
- ↵1To whom correspondence should be addressed. E-mail: R.E.Goldstein{at}damtp.cam.ac.uk.
Author contributions: E.L., H.W., and R.E.G. designed research, performed research, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1405698111/-/DCSupplemental.
Freely available online through the PNAS open access option.
- aSchool of Engineering, Brown University, Providence, RI 02912; and
- bDepartment of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom
Edited by Harry L. Swinney, University of Texas at Austin, Austin, TX, and approved June 2, 2014 (received for review March 28, 2014)
Significance
The collective dynamics of swimming microorganisms exhibits a complex interplay with the surrounding fluid: the motile cells stir the fluid, which in turn can reorient and advect them. This feedback loop can result in long-range interactions between the cells, an effect whose significance remains controversial. We present a computational model that takes into account these cell–fluid interactions and cell–cell forces and that predicts counterintuitive cellular order driven by long-range flows. This prediction is confirmed with experimental studies that track the orientation of cells in a confined, dense bacterial suspension.
Abstract
Concentrated suspensions of swimming microorganisms and other forms of active matter are known to display complex, self-organized spatiotemporal patterns on scales that are large compared with those of the individual motile units. Despite intensive experimental and theoretical study, it has remained unclear the extent to which the hydrodynamic flows generated by swimming cells, rather than purely steric interactions between them, drive the self-organization. Here we use the recent discovery of a spiral-vortex state in confined suspensions of Bacillus subtilis to study this issue in detail. Those experiments showed that if the radius of confinement in a thin cylindrical chamber is below a critical value, the suspension will spontaneously form a steady single-vortex state encircled by a counter-rotating cell boundary layer, with spiral cell orientation within the vortex. Left unclear, however, was the flagellar orientation, and hence the cell swimming direction, within the spiral vortex. Here, using a fast simulation method that captures oriented cell–cell and cell–fluid interactions in a minimal model of discrete particle systems, we predict the striking, counterintuitive result that in the presence of collectively generated fluid motion, the cells within the spiral vortex actually swim upstream against those flows. This prediction is then confirmed by the experiments reported here, which include measurements of flagella bundle orientation and cell tracking in the self-organized state. These results highlight the complex interplay between cell orientation and hydrodynamic flows in concentrated suspensions of microorganisms.
Footnotes
- ↵1To whom correspondence should be addressed. E-mail: R.E.Goldstein{at}damtp.cam.ac.uk.
Author contributions: E.L., H.W., and R.E.G. designed research, performed research, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1405698111/-/DCSupplemental.
Freely available online through the PNAS open access option.
Fluid flows and bacterial self-organization
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