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Collective migration reveals mechanical flexibility of malaria parasites


Plasmodium sporozoites are the crescent-shaped forms of malaria parasites injected from the salivary glands of mosquitoes into the skins of their vertebrate hosts. To proceed towards the liver of the host, sporozoites individually migrate at very high speeds and with relatively few adhesive interactions. By contrast, in the mosquito sporozoites often exist as collectives. Here we study their motion in collectives extracted from salivary glands, a situation in which dozens of sporozoites form rotating vortices. Complementing our experiments with quantitative image analysis and agent-based computer simulations, we find that, owing to their mechanical flexibility, single sporozoites are sorted according to their curvatures and speeds, and that these effects increase with vortex size. We also find that the vortices undergo oscillatory breathing because the thrust from the motility force of the single sporozoites can be stored in their elastic energy. Our findings suggest that the malaria parasite has evolved flexibility as an essential means to adapt to its mechanical environment and to ensure efficient transmission. In general, our work demonstrates how single-particle shape and mechanics can determine the dynamics of large, active collectives.

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Fig. 1: Collectives of malaria parasites form rotating vortices.
Fig. 2: Quantitative image analysis reveals unexpected speed distributions.
Fig. 3: Agent-based computer simulations explain experimentally observed features by self-sorting.
Fig. 4: Simulations predict sporozoite self-sorting in rotating vortices.
Fig. 5: Mechanism of vortex size fluctuations.

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Data availability

All data necessary to reproduce Figs. 2–5 are available via Zenodo at Source data are provided with this paper.

Code availability

Custom codes that were used to analyse experimental data within this manuscript are available from the corresponding authors upon reasonable request. Python scripts to generate the plots in the figures are available via Zenodo at Our code for the agent-based computer simulations is available via GitHub at


  1. World Malaria Report 2020 (World Health Organization, 2020).

  2. Cowman, A. F., Healer, J., Marapana, D. & Marsh, K. Malaria: biology and disease. Cell 167, 610–624 (2016).

    Article  Google Scholar 

  3. Ménard, R. et al. Looking under the skin: the first steps in malarial infection and immunity. Nat. Rev. Microbiol. 11, 701–712 (2013).

    Article  Google Scholar 

  4. Amino, R. et al. Quantitative imaging of plasmodium transmission from mosquito to mammal. Nat. Med. 12, 220–224 (2006).

    Article  Google Scholar 

  5. Frischknecht, F. & Matuschewski, K. Plasmodium sporozoite biology. Cold Spring Harb. Perspect. Med. 7, a025478 (2017).

    Article  Google Scholar 

  6. Münter, S. et al. Plasmodium sporozoite motility is modulated by the turnover of discrete adhesion sites. Cell Host Microbe 6, 551–562 (2009).

    Article  Google Scholar 

  7. Battista, A., Frischknecht, F. & Schwarz, U. S. Geometrical model for malaria parasite migration in structured environments. Phys. Rev. E 90, 042720 (2014).

    Article  ADS  Google Scholar 

  8. Muthinja, M. J. et al. Microstructured blood vessel surrogates reveal structural tropism of motile malaria parasites. Adv. Healthc. Mater. 6, 1601178 (2017).

    Article  Google Scholar 

  9. Ripp, J. et al. Malaria parasites differentially sense environmental elasticity during transmission. EMBO Mol. Med. 13, e13933 (2021).

    Article  Google Scholar 

  10. Hegge, S. et al. Direct manipulation of malaria parasites with optical tweezers reveals distinct functions of Plasmodium surface proteins. ACS Nano 6, 4648–4662 (2012).

    Article  Google Scholar 

  11. Quadt, K. A., Streichfuss, M., Moreau, C. A., Spatz, J. P. & Frischknecht, F. Coupling of retrograde flow to force production during malaria parasite migration. ACS Nano 10, 2091–2102 (2016).

    Article  Google Scholar 

  12. Klug, D. & Frischknecht, F. Motility precedes egress of malaria parasites from oocysts. Elife 6, e19157 (2017).

    Article  Google Scholar 

  13. Vanderberg, J., Rdodin, J. & Yoelt, M. Electron microscopic and histochemical studies of sporozoite formation in Plasmodium berghei. J. Protozool. 14, 82–103 (1967).

    Article  Google Scholar 

  14. Frischknecht, F. et al. Imaging movement of malaria parasites during transmission by Anopheles mosquitoes. Cell. Microbiol. 6, 687–694 (2004).

    Article  Google Scholar 

  15. Vicsek, T. & Zafeiris, A. Collective motion. Phys. Rep. 517, 71–140 (2012).

    Article  ADS  Google Scholar 

  16. Couzin, I. D. & Krause, J. et al. Self-organization and collective behavior in vertebrates. Adv. Study Behav. 32, 1–75 (2003).

    Article  Google Scholar 

  17. Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).

    Article  ADS  Google Scholar 

  18. Zöttl, A. & Stark, H. Emergent behavior in active colloids. J. Phys. Condens. Matter 28, 253001 (2016).

    Article  ADS  Google Scholar 

  19. Gompper, G. et al. The 2020 motile active matter roadmap. J. Phys. Condens. Matter 32, 193001 (2020).

    Article  ADS  Google Scholar 

  20. Tunstrøm, K. et al. Collective states, multistability and transitional behavior in schooling fish. PLoS Comput. Biol. 9, e1002915 (2013).

    Article  MathSciNet  Google Scholar 

  21. Schaller, V., Weber, C., Semmrich, C., Frey, E. & Bausch, A. R. Polar patterns of driven filaments. Nature 467, 73–77 (2010).

  22. Sumino, Y. et al. Large-scale vortex lattice emerging from collectively moving microtubules. Nature 483, 448–452 (2012).

    Article  Google Scholar 

  23. Wioland, H., Woodhouse, F. G., Dunkel, J., Kessler, J. O. & Goldstein, R. E. Confinement stabilizes a bacterial suspension into a spiral vortex. Phys. Rev. Lett. 110, 268102 (2013).

    Article  ADS  Google Scholar 

  24. Loose, M. & Mitchison, T. J. The bacterial cell division proteins FtsA and FtsZ self-organize into dynamic cytoskeletal patterns. Nat. Cell Biol. 16, 38–46 (2014).

    Article  Google Scholar 

  25. Franks, N. R. et al. Social behaviour and collective motion in plant-animal worms. Proc. R. Soc. B 283, 20152946 (2016).

    Article  Google Scholar 

  26. J Delcourt N. W Bode M Denoël Collective vortex behaviors: diversity, proximate, and ultimate causes of circular animal group movements Q. Rev. Biol. 9, 1-24 2016.

  27. Suzuki, K., Miyazaki, M., Takagi, J., Itabashi, T. & Ishiwata, S. Spatial confinement of active microtubule networks induces large-scale rotational cytoplasmic flow. Proc. Natl Acad. Sci. USA 114, 2922–2927 (2017).

    Article  Google Scholar 

  28. Balagam, R. & Igoshin, O. A. Mechanism for collective cell alignment in Myxococcus xanthus bacteria. PLoS Comput. Biol. 11, e1004474 (2015).

    Article  ADS  Google Scholar 

  29. Balagam, R. et al. Emergent myxobacterial behaviors arise from reversal suppression induced by kin contacts. mSystems 6, e0072021 (2021).

    Article  Google Scholar 

  30. Peng, C., Turiv, T., Guo, Y., Wei, Q.-H. & Lavrentovich, O. D. Command of active matter by topological defects and patterns. Science 354, 882–885 (2016).

    Article  ADS  Google Scholar 

  31. Wu, K.-T. et al. Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science 355, eaal1979 (2017).

    Article  MathSciNet  Google Scholar 

  32. Souslov, A., Van Zuiden, B. C., Bartolo, D. & Vitelli, V. Topological sound in active-liquid metamaterials. Nat. Phys. 13, 1091–1094 (2017).

    Article  Google Scholar 

  33. Hamby, A. E., Vig, D. K., Safonova, S. & Wolgemuth, C. W. Swimming bacteria power microspin cycles. Sci. Adv. 4, eaau0125 (2018).

    Article  ADS  Google Scholar 

  34. Kokot, G. & Snezhko, A. Manipulation of emergent vortices in swarms of magnetic rollers. Nat. Commun. 9, 2344 (2018).

    Article  ADS  Google Scholar 

  35. Han, K. et al. Emergence of self-organized multivortex states in flocks of active rollers. Proc. Natl Acad. Sci. USA 117, 9706–9711 (2020).

    Article  MathSciNet  Google Scholar 

  36. Wan, L. Q. et al. Micropatterned mammalian cells exhibit phenotype-specific left-right asymmetry. Proc. Natl Acad. Sci. USA 108, 12295–12300 (2011).

    Article  ADS  Google Scholar 

  37. Lushi, E., Wioland, H. & Goldstein, R. E. Fluid flows created by swimming bacteria drive self-organization in confined suspensions. Proc. Natl Acad. Sci. USA 111, 9733–9738 (2014).

    Article  ADS  Google Scholar 

  38. Liu, S., Shankar, S., Marchetti, M. C. & Wu, Y. Viscoelastic control of spatiotemporal order in bacterial active matter. Nature 590, 80–84 (2021).

    Article  ADS  Google Scholar 

  39. Reinken, H. et al. Organizing bacterial vortex lattices by periodic obstacle arrays. Commun. Phys. 3, 76 (2020).

    Article  Google Scholar 

  40. Vanderberg, J. P. Studies on the motility of Plasmodium sporozoites. J. Protozool. 21, 527–537 (1974).

    Article  Google Scholar 

  41. Denk, J., Huber, L., Reithmann, E. & Frey, E. Active curved polymers form vortex patterns on membranes. Phys. Rev. Lett. 116, 178301 (2016).

    Article  ADS  Google Scholar 

  42. Suzuki, R., Weber, C. A., Frey, E. & Bausch, A. R. Polar pattern formation in driven filament systems requires non-binary particle collisions. Nat. Phys. 11, 839–843 (2015).

    Article  Google Scholar 

  43. Huber, L., Suzuki, R., Krüger, T., Frey, E. & Bausch, A. Emergence of coexisting ordered states in active matter systems. Science 361, 255–258 (2018).

    Article  ADS  Google Scholar 

  44. Abkenar, M., Marx, K., Auth, T. & Gompper, G. Collective behavior of penetrable self-propelled rods in two dimensions. Phys. Rev. E 88, 062314 (2013).

    Article  ADS  Google Scholar 

  45. Moore, J. M., Glaser, M. A. & Betterton, M. D. Chiral self-sorting of active semiflexible filaments with intrinsic curvature. Soft Matter 17, 4559–4565 (2021).

    Article  ADS  Google Scholar 

  46. Kan, A. et al. Quantitative analysis of Plasmodium ookinete motion in three dimensions suggests a critical role for cell shape in the biomechanics of malaria parasite gliding motility. Cell. Microbiol. 16, 734–750 (2014).

    Article  Google Scholar 

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We thank J. Ripp, M. Singer, S. Rossberger, H. Böhm, J. Spatz, C. Haubold and F. Hamprecht for stimulating discussions. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1129 (Projektnummer 240245660). P.P. acknowledges funding through an interdisciplinary postdoctoral fellowship of the cluster of excellence CellNetworks. U.S.S. is a member of the Interdisciplinary Center for Scientific Computing (IWR) at Heidelberg. F.F. and U.S.S. were supported by the Marsilius-Kolleg of Heidelberg University.

Author information

Authors and Affiliations



P.P. and A.B. wrote the simulation code. P.P. performed the simulations and analysed the experimental data. K.B. performed the experiments. A.J. and K.R. performed the image analysis. F.F. and U.S.S. designed and supervised the project. P.P., F.F. and U.S.S. wrote the manuscript. All authors approved the manuscript.

Corresponding authors

Correspondence to Friedrich Frischknecht or Ulrich S. Schwarz.

Ethics declarations

Competing interests

The authors declare no competing interests.

Ethics statement

All animal experiments were performed according to European guidelines and regulations and the German Animal Welfare Act (Tierschutzgesetz) and executed following the guidelines of the Society of Laboratory Animal Science (GV-SOLAS) and of the Federation of European Laboratory Animal Science Associations (FELASA). All experiments were approved by the responsible German authorities (Regierungspräsidium Karlsruhe).

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Peer review information

Nature Physics thanks Isabelle Tardieux, Daria Bonazzi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–6 and Sections A–E.

Supplementary Video 1

Video for data presented in Fig. 1b.

Supplementary Video 2

Video for data presented in Fig. 1d,e.

Supplementary Video 3

Video for data presented in Fig. 1f–i.

Supplementary Video 4

Videos of vortex formation from isolated sporozoites and the merging of two small vortices.

Supplementary Video 5

Videos of experimental vortices.

Supplementary Video 6

Video of simulation with identical sporozoites.

Supplementary Video 7

ad, Videos of simulations showing vortex formation from isolated sporozoites (a), a merger of two vortices (b), vortex re-organization in the presence of a repulsion zone (c) and splitting of a large vortex (d).

Supplementary Video 8

Video for data presented in Fig. 3.

Supplementary Video 9

Video for data presented in Fig. 4a,b.

Supplementary Video 10

Video for data presented in Fig. 4c.

Supplementary Video 11

Video for data presented in Fig. 5b,c.

Supplementary Video 12

Video of simulation of an isolated vortex with a rigid obstacle at the core.

Source data

Source Data Fig. 2

Zip file with all relevant data files for Fig. 2, together with the python script to plot it.

Source Data Fig. 3

Zip file with all relevant data files for Fig. 3, together with the python script to plot it.

Source Data Fig. 4

Zip file with all relevant data files for Fig. 4, together with the python script to plot it.

Source Data Fig. 5

Zip file with all relevant data files for Fig. 5, together with the python script to plot it.

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Patra, P., Beyer, K., Jaiswal, A. et al. Collective migration reveals mechanical flexibility of malaria parasites. Nat. Phys. 18, 586–594 (2022).

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