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Collective Motion of Filamentous Bacteria

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Order and Fluctuations in Collective Dynamics of Swimming Bacteria

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Abstract

This chapter describes our experimental study on collective motion of long, filamentous, non-tumbling bacteria swimming in a thin fluid layer. The confinement in the quasi-two-dimensional plane and the high aspect ratio of the cells induce weak nematic alignment upon collision due to the weak excluded volume interactions, which, for sufficiently high density of cells, gives rise to global nematic order. This homogeneous but highly-fluctuating phase, observed on the largest experimentally-accessible scale of millimeters, exhibits the properties predicted by the standard flocking models, especially the Vicsek-style self-propelled rods: true long-range nematic order and non-trivial giant number fluctuations. Thus, our experimental system is recognized as the first unambiguous example that falls into the Vicsek universality class. Our results suggest necessary conditions for the Vicsek universality class in comparison with other experimental studies. This chapter is based on our publication [Nishiguchi et al., Physical Review E 95, 020601(R) (2017)] but also includes further detailed analysis of correlations and collisions.

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Notes

  1. 1.

    This is because particles cannot overlap in this model due to excluded volume but can overlap in the Vicsek-style point-like particles models.

  2. 2.

    We used a membrane filter, because concentrating suspensions by centrifugation does not work well. Centrifugation often damages such long filamentous bacteria, leading bacteria to die or to be almost non-motile.

  3. 3.

    Because we are trying to find GNF in the true long-range ordered states, both order parameter and number fluctuations have to be reliably quantified in the same images.

  4. 4.

    While, of course, on much larger (inaccessible) scales, this order may break down due to experimental limitations such as imperfectness or boundaries of our setup, our observation done in the area with true long-range order far away from boundaries can extract bulk properties that we are interested in.

  5. 5.

    When we did not apply binarization and just used calibrated intensity, we could not obtain normal fluctuations with the exponent \(\alpha =0.5\) but spurious giant fluctuations with \(\alpha >0.5\) even in the disordered state.

  6. 6.

    In equilibrium liquid crystals and in active nematics, this \(\sim q^{-2}\) fluctuations of director arising from the Nambu-Goldstone mode break the global order, leading to only quasi-long-range order.

  7. 7.

    In the following, we neglect the positional diffusion term, which is small in our experiment and does not affect the linear stability analysis.

  8. 8.

    Of course, at the onset of collective motion, there should be a strong correlation in the angles \(\theta _1\) and \(\theta _2\) of the two colliding particles. Taking this into account, in [37, 38], the angular correlations was given in the form of \(f^{(2)}(\varvec{r},\theta _1,\theta _2,t)=\left( 1+A/|\theta _{12}| \right) f(\varvec{r},\theta _1,t)f(\varvec{r},\theta _2,t)\). However, this dependence cannot be justified by experiments and, furthermore, this does not modify the obtained results qualitatively.

  9. 9.

    In the field of image analysis, the term ‘orientation’ is often used to represent the direction of images in which periodic patterns appear. The ‘orientation’ in this definition is different by \(90^\circ \) from the direction of nematic director field that we want to know.

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  1. Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo, Japan

    Dr. Daiki Nishiguchi

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Correspondence to Daiki Nishiguchi .

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Nishiguchi, D. (2020). Collective Motion of Filamentous Bacteria. In: Order and Fluctuations in Collective Dynamics of Swimming Bacteria. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-32-9998-6_3

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  • DOI: https://doi.org/10.1007/978-981-32-9998-6_3

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