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Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes

  1. Antonio DeSimonea,2
  1. aMathLab, International School for Advanced Studies, 34136 Trieste, Italy;
  2. bInstitute of Fluid Mechanics and Aerodynamics, Bundeswehr University Munich, 85577 Neubiberg, Germany;
  3. cSezione Oceanografia, Istituto Nazionale di Oceanografia e di Geofisica Sperimentale, 34151 Trieste, Italy
  1. Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved October 16, 2017 (received for review May 16, 2017)


Active flagella provide the propulsion mechanism for a large variety of swimming eukaryotic microorganisms, from protists to sperm cells. Planar and helical beating patterns of these structures are recurrent and widely studied. The fast spinning motion of the locomotory flagellum of the alga Euglena gracilis constitutes a remarkable exception to these patterns. We report a quantitative description of the 3D flagellar beating in swimming E. gracilis. Given their complexity, these shapes cannot be directly imaged with current microscopy techniques. We show how to overcome these limitations by developing a method to reconstruct in full the 3D kinematics of the cell from conventional 2D microscopy images, based on the exact characterization of the helical motion of the cell body.


The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement.


  • ?1M.R. and G.C. contributed equally to this work.

  • ?2To whom correspondence should be addressed. Email: desimone{at}sissa.it.
  • Author contributions: M.R., G.N., and A.D. designed research; M.R., G.C., G.N., and A.D. performed research; M.R. analyzed data; M.R. and G.N. designed experiments; A.B. grew cells and shared expertise on microscopy; G.C. and A.D. developed the theoretical model; and M.R., G.C., A.B., G.N., and A.D. 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.danielhellerman.com/lookup/suppl/doi:10.1073/pnas.1708064114/-/DCSupplemental.

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