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Polygonal motion and adaptable phototaxis via flagellar beat switching in the microswimmer Euglena gracilis

Nature Physicsvolume 14pages12161222 (2018) | Download Citation


Biological microswimmers exhibit versatile strategies for sensing and navigating their environment, such as run-and-tumble and curvature modulation. Here, we report a striking phototactic behaviour of the microswimmer Euglena gracilis, where these eukaryotic cells swim in polygonal trajectories due to a sudden increase in light intensity. While smoothly curved trajectories are common for microswimmers, such quantized ones have not been reported previously. We find that this polygonal behaviour emerges from periodic switching between the flagellar beating patterns of helical swimming and spinning behaviours. We develop and experimentally validate a biophysical model that describes the phase relationship between the eyespot, cell orientation, light detection and cellular reorientation, accounting for all three behavioural states. Coordinated switching between these behaviours selects for ballistic, superdiffusive, diffusive or subdiffusive motion (including tuning the effective diffusion constant over several orders of magnitude), thereby enabling navigation in spatially structured light fields, such as edge avoidance and gradient descent. This feedback control links multiple system scales (flagellar beats, cellular behaviours and phototaxis strategies), with implications for other natural and synthetic microswimmers.

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The data sets and computer codes generated during and analysed during the current study are available from the corresponding author on reasonable request.

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Change history

  • 09 October 2018

    In the version of this Article originally published, the angular oscillation of amplitude in Fig. 4a was incorrectly labelled ζ; it should have been ξ. Also, the blue line in the top-right corner of Fig. 6d should not have been dash-dotted but solid. These have now been corrected in all versions of the Article.


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We thank members of the Riedel-Kruse laboratory, B. Friedrich, J. Dunkel, N. Ouellette and A. Macdonald. This work was supported by NSF grant no. 1324753, the Stanford Discovery Innovation Fund and the Croucher Foundation (through a postdoctoral fellowship to A.C.H.T.).

Author information


  1. Department of Bioengineering, Stanford University, Stanford, CA, USA

    • Alan C. H. Tsang
    • , Amy T. Lam
    •  & Ingmar H. Riedel-Kruse


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A.C.H.T. and I.H.R.-K. were responsible for the project idea, the theory and manuscript preparation; A.C.H.T. was responsible for the modelling, the experiments and data analysis (except Fig. 6: A.C.H.T. and A.T.L.).

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Ingmar H. Riedel-Kruse.

Supplementary information

  1. Supplementary Information

    Supplementary Methods, Supplementary Figures 1–14, Supplementary Table 1, Supplementary References 1–4

  2. Reporting Summary

  3. Supplementary Video 1

    Euglena swimming in a polygonal trajectory at intermediate light intensity. The images were sampled at 200 fps and the video is replayed at 10 × slower than the real time

  4. Supplementary Video 2

    Euglena swimming in a helical trajectory at low light intensity, recorded at 400 fps. The images were sampled at 400 fps and the video is replayed at 20 × slower than the real time

  5. Supplementary Video 3

    Euglena spinning around locally at high light intensity, recorded at 400 fps. The images were sampled at 400 fps and the video is replayed at 20 × slower than the real time

  6. Supplementary Video 4

    Various Euglena flagellar beat patterns for helical swimming, spinning, and polygonal swimming. The images are sampled at 200 fps

  7. Supplementary Video 5

    Comparison of simulation and experiment for helical swimming

  8. Supplementary Video 6

    Comparison of simulation and experiment for spinning

  9. Supplementary Video 7

    Comparison of simulation and experiment for polygonal swimming

  10. Supplementary Video 8

    Experimental tracking of Euglena exhibiting light avoidance from a light barrier

  11. Supplementary Video 9

    Experimental tracking of Euglena exhibiting spinning behaviour initially, followed by swimming in polygonal paths of increasing order, thereby expanding the search radius to navigate the light edge

  12. Supplementary Video 10

    Experimental tracking of Euglena exhibiting biased run-and-tumble down the light gradient

  13. Supplementary Video 11

    Simulations of Euglena exhibiting light avoidance from a light barrier

  14. Supplementary Video 12

    Simulations of Euglena exhibiting polygonal paths of increasing order and navigating the light edge

  15. Supplementary Video 13

    Simulations of Euglena exhibiting biased run-and-tumble down the light gradient

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