A new approach to estimating speed of microorganisms uniform movement along a helical trajectory

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Abstract

Analysis of the motion of microscopic organisms is important for understanding their behavior, intrinsic state, and response to external conditions. Many free-swimming microorganisms move in three-dimensional space along a helical trajectory. When a three-dimensional trajectory is analyzed from video frames, it is transformed into a flat curve. This leads to loss of some of the motion data and, in particular, to errors in the estimates of the traveled path and true speed. We propose to estimate the length of a three-dimensional spiral path using the maximum length of the projection of the trajectory segment. The analysis showed that for rectilinear spiral trajectories, along which organisms move uniformly, this method in many cases allows us to correctly estimate the traveled path and true speed of movement, and to perform a correct comparison of the speeds of different microorganisms.

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A. M. Lyakh

Kovalevskii Institute of Biology of the Southern Seas, Russian Academy of Sciences

Author for correspondence.
Email: me@antonlyakh.ru
Russian Federation, Sevastopol, 299011

T. V. Rauen

Kovalevskii Institute of Biology of the Southern Seas, Russian Academy of Sciences

Email: antonlyakh@gmail.com
Russian Federation, Sevastopol, 299011

References

  1. Aragaki H., Ogoh K., Kondo Y., Aoki K. LIM Tracker: a software package for cell tracking and analysis with advanced interactivity // Sci. Rep. 2022. V. 12. 2702. https://doi.org/10.1038/s41598-022-06269-6
  2. Boakes D. E., Codling E. A., Thorn G. J., Steinke M. Analysis and modelling of swimming behaviour in Oxyrrhis marina // J. Plank. Res. 2011. V. 33. № 4. P. 641–649. https://doi.org/10.1093/plankt/fbq136
  3. Crenshaw H. C. A new look at locomotion in microorganisms: Rotating and translating // American Zoologist. 1996. V. 36. № 6. P. 608–618. https://doi.org/10.1093/icb/36.6.608
  4. Croze O. A., Martinez V. A., Jakuszeit T., Dell’Arciprete D., Poon W. C.K., Bees M. A. Helical and oscillatory microswimmer motility statistics from differential dynamic microscopy // New J. Phys. 2019. V. 21. 063012. https://doi.org/10.1088/1367-2630/ab241f
  5. Durante G., Roselli L., De Nunzio G., Piemomtese U., Marsella G., Basset A. Plankton Tracker: A novel integrated system to investigate the dynamic sinking behavior in phytoplankton // Ecological Informatic. 2020. V. 60. 101166. https://doi.org/10.1016/j.ecoinf.2020.101166
  6. Drescher K, Leptos K. C., Goldstein R. E. How to track protists in three dimensions // Rev. Sci. Instrum. 2009. V. 80. 014301. https://doi.org/10.1063/1.3053242
  7. Emami N., Sedaei Z., Ferdousi R. Computerized cell tracking: Current methods, tools and challenges // Visual Informatics. 2021. V. 5. № 1. P. 1–13. https://doi.org/10.1016/j.visinf.2020.11.003
  8. Ershov D., Phan M.-S., Pylvanainen J. W., Rigaud S. U., Le Blanc L., Charles-Orszag A., Conway J. R.W., Laine R. F., Roy N. H., Bonazzi D., Dumenil G., Jacquemet G., Tinevez J.-Y. TrackMate 7: integrating state-of-the-art segmentation algorithms into tracking pipelines // Nat. Methods. 2002. V. 19. P. 829–832. https://doi.org/10.1038/s41592-022-01507-1
  9. Fenchel T. How dinoflagellates swim // Protist. 2001. V. 152. № 4. P. 329–338. https://doi.org/10.1078/1434-4610-00071
  10. Gurarie E., Grunbawm D., Nishizaki M. T. Estimating 3D movements from 2D observations using a continuous model of helical swimming // Bull. Math. Biol. 2011. V. 73. P. 1358–1377. https://doi.org/10.1007/s11538-010-9575-7
  11. Rauen T. V., Mukhanov V. S., Baiandina I. S., Lyakh A. M. Influence of microplastics on the nutritional and locomotive activity of dinoflagellate Oxyrrhis marina under experimental conditions // Inland Water Biology. 2024. V. 17. № 2. P. 316–326. https://doi.org/10.1134/S1995082924020135
  12. Roberts E. C., Wootton E. C., Davidson K., Jeong H. J., Lowe C. D., Montagnes D. J.C. Feeding in the dinoflagellate Oxyrrhis marina: linking behaviour with mechanisms // J. Plankt. Res. 2011. V. 33. № 4. P. 603–614. https://doi.org/10.1093/PLANKT%2FFBQ118
  13. Vestergaard C. L., Pedersen J. N., Mortensen K. I., Flyvbjerg H. Estimation of motility parameters from trajectory data // Eur. Phys. J. Spec. Top. 2015. V. 224. P. 1151–1168. https://doi.org/10.1140/epjst/e2015-02452-5
  14. Yang Y., Qingxuan L, Yuezun L., Zhiqiang W., Junyu D. PhyTracker: an online tracker for phytoplankton // arXiv. 2024. arXiv:2407.00352.

Supplementary files

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2. Fig. 1. Relative errors between the maximum projection (ςmax) and true length of trajectory segments with different characteristics.

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3. Fig. 2. Relative difference, Δma, between the true velocity of motion, Va, and (a) the maximum projected velocity Vm or (b) the normal projected velocity Vp for trajectories with different characteristics: different turn ratios and different rotation angles. The same color is used to mark Δma calculated for the same turn ratios but different Vc.

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4. Fig. 3. Situations in which one absolute speed of movement corresponds to many projection speeds – normal (a) and maximum (b), equal to other absolute speeds. Each horizontal line shows a fixed value of absolute speed (or the true path traveled by the organism in a second). Each curved line shows the dynamics of change in projection speed (projection path traveled in a second), calculated for trajectories with different characteristics. A horizontal intersection of a line with curved lines indicates a coincidence of speed values that are initially different, i.e., signals an error. For convenience, we have depicted only the case when Vc = 1; for other values of Vc, the graphs are similar.

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