Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Tracking phase synchronization between flagella in the time-frequency domain resolves photophobic response

Lucas Federspiel

Jorge Arrieta

Marco Polin

Françoise Argoul* and Antoine Allard†

  • *Contact author: francoise.argoul@u-bordeaux.fr
  • †Contact author: antoine.allard@u-bordeaux.fr

Phys. Rev. Research 8, 023294 – Published 15 June, 2026

DOI: https://doi.org/10.1103/xhvh-n796

Abstract

The unicellular microalga Chlamydomonas reinhardtii (CR) is well known for its biflagellated swimming in response to light stimuli. This work aims to study the resynchronization of CR flagella after a high light intensity stimulus, known as photoshock. The synchronization is estimated thanks to a quantity defined as the phase synchronization index (PSI). The originality of this approach is to perform a time-frequency computation of a complex PSI based on continuous wavelet transform. Thanks to this analysis, we distinguish three swimming stages involving different frequency bands and phase shifts: synchronized breaststroke swimming, undulatory backward swimming, and resynchronization. This approach also reveals the presence of signal harmonics that set the photoshock response, independently of cell variability. Our results suggest that CR modulates the balance between spectral beating modes, providing a mechanism for robust adaptation to sudden environmental stresses.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (49)

  1. M. Riedl, I. Mayer, J. Merrin, M. Sixt, and B. Hof, Synchronization in collectively moving inanimate and living active matter, Nat. Commun. 14, 5633 (2023).
  2. E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (The MIT Press, Cambridge, 2006).
  3. C. Schäfer, M. G. Rosenblum, H.-H. Abel, and J. Kurths, Synchronization in the human cardiorespiratory system, Phys. Rev. E 60, 857 (1999).
  4. U. Schibler, Steven A. Brown and the synchronization of circadian rhythms by body temperature cycles, Eur. J. Neurosci. 60, 3891 (2024).
  5. S. H. Strogatz and I. Stewart, Coupled oscillators and biological synchronization, Sci. Am. 269, 102 (1993).
  6. C. M. Denis and P. François, Unclocklike oscillators with frequency memory for the entrainment of biological clocks, PRX Life 2, 043008 (2024).
  7. C. Huygens and F. Muguet, Christiani Hugenii Zulichemi... Horologium oscillatorium sive De Motu pendulorum ad horologia aptato demonstrationes geometricae, Manuscripta; History of Science, 16th to 19th Century (Apud F. Muguet, 1673).
  8. A. Pikovsky, M. Rosenblum, J. Kurths, and R. C. Hilborn, Synchronization: A universal concept in nonlinear science, Am. J. Phys. 70, 655 (2002).
  9. B. Button, L.-H. Cai, C. Ehre, M. Kesimer, D. B. Hill, J. K. Sheehan, R. C. Boucher, and M. Rubinstein, A periciliary brush promotes the lung health by separating the mucus layer from airway epithelia, Science 337, 937 (2012).
  10. S. Hu and F. Meng, Multiflagellate swimming controlled by hydrodynamic interactions, Phys. Rev. Lett. 132, 204002 (2024).
  11. E. M. Holland, H. Harz, R. Uhl, and P. Hegemann, Control of phobic behavioral responses by rhodopsin-induced photocurrents in Chlamydomonas, Biophys. J. 73, 1395 (1997).
  12. A. Guillet and F. Argoul, Uncertainty and information in physiological signals: Explicit physical trade-off with log-normal wavelets, J. Franklin Inst. 361, 107201 (2024).
  13. B. Torrésani, Analyse Continue Par Ondelettes, Savoirs Actuels/Série Physique (CNRS Editions/EDP Sciences, France, 1995).
  14. C. Torrence and G. P. Compo, A practical guide to wavelet analysis, Bull. Am. Meteorol. Soc. 79, 61 (1998).
  15. R. Kronland-Martinet, J. Morlet, and A. Grossmann, Analysis of sound patterns through wavelet transforms, Int. J. Pattern Recognit. Artif. Intell. 01, 273 (1987).
  16. B. Schack and S. Weiss, Quantification of phase synchronization phenomena and their importance for verbal memory processes, Biol. Cybern. 92, 275 (2005).
  17. Z. Liang, Y. Bai, Y. Ren, and X. Li, Synchronization measures in EEG signals, in Signal Processing in Neuroscience, edited by X. Li (Springer Singapore, Singapore, 2016), Chap. 9, pp. 167–202.
  18. V. V. Grubov, A. K. Kuc, S. A. Kurkin, D. A. Andrikov, N. Utyashev, V. A. Maksimenko, O. E. Karpov, and A. E. Hramov, Harnessing long-range temporal correlations for advanced epilepsy classification, PRX Life 3, 013005 (2025).
  19. R. Adler, A study of locking phenomena in oscillators, Proc. IRE 34, 351 (1946).
  20. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer Series in Synergetics (Springer, Berlin, 1984).
  21. E. H. Harris, The Chlamydomonas Sourcebook: Introduction to Chlamydomonas and its Laboratory Use (Academic Press, 1989), Vol. 1.
  22. Y. Liu, R. Claydon, M. Polin, and D. R. Brumley, Transitions in synchronization states of model cilia through basal-connection coupling, J. R. Soc. Interface 15, 20180450 (2018).
  23. K. Y. Wan and R. E. Goldstein, Coordinated beating of algal flagella is mediated by basal coupling, Proc. Natl. Acad. Sci. USA 113, E2784 (2016).
  24. L. Zorrilla, A. Allard, K. Desai, and M. Polin, Role of hydrodynamics in the synchronization of Chlamydomonas flagella, Phys. Rev. Lett. 135, 218402 (2025).
  25. B. Friedrich, Hydrodynamic synchronization of flagellar oscillators, Eur. Phys. J.: Spec. Top. 225, 2353 (2016).
  26. R. E. Goldstein, M. Polin, and I. Tuval, Noise and synchronization in pairs of beating eukaryotic flagella, Phys. Rev. Lett. 103, 168103 (2009).
  27. P. Hegemann and B. Bruck, Light-induced stop response in Chlamydomonas reinhardtii: Occurrence and adaptation phenomena, Cell Motil. 14, 501 (1989).
  28. U. Rüffer and W. Nultsch, Flagellar photoresponses of Chlamydomonas cells held on micropipettes: II. Change in flagellar beat pattern, Cell Motil. 18, 269 (1991).
  29. J. Arrieta, A. Barreira, M. Chioccioli, M. Polin, and I. Tuval, Phototaxis beyond turning: Persistent accumulation and response acclimation of the microalga Chlamydomonas reinhardtii, Sci. Rep. 7, 3447 (2017).
  30. A. Ramamonjy, J. Dervaux, and P. Brunet, Nonlinear phototaxis and instabilities in suspensions of light-seeking algae, Phys. Rev. Lett. 128, 258101 (2022).
  31. P. Berthold, S. P. Tsunoda, O. P. Ernst, W. Mages, D. Gradmann, and P. Hegemann, Channelrhodopsin-1 initiates phototaxis and photophobic responses in Chlamydomonas by immediate light-induced depolarization, The Plant Cell 20, 1665 (2008).
  32. R. Jeanneret, M. Contino, and M. Polin, A brief introduction to the model microswimmer Chlamydomonas reinhardtii, Eur. Phys. J.: Spec. Top. 225, 2141 (2016).
  33. U. Rüffer and W. Nultsch, Flagellar coordination in Chlamydomonas cells held on micropipettes, Cell Motil. 41, 297 (1998).
  34. N. Ueki and K.-i. Wakabayashi, in Dyneins: Structure, Biology and Disease, edited by S. M. King, 2nd ed. (Academic Press, 2018), pp. 368–385.
  35. C. Brennen and H. Winet, Fluid mechanics of propulsion by cilia and flagella, Annu. Rev. Fluid Mech. 9, 339 (1977).
  36. A. K. Boggon, A. D. Hastewell, J. Dunkel, and K. Y. Wan, Embodied behavioural complexity in a ciliated microorganism, bioRxiv (2025).
  37. See Supplemental Material at http://link.aps.org/supplemental/10.1103/xhvh-n796 for additional experimental data and details regarding the wavelet transform and phase synchronization index.
  38. M. Riccomi, F. Alberini, E. Brunazzi, and D. Vigolo, Ghost particle velocimetry as an alternative to μPIV for micro/milli-fluidic devices, Chem. Eng. Res. Des. 133, 183 (2018).
  39. A. Rößler, Runge–Kutta methods for the strong approximation of solutions of stochastic differential equations, SIAM J. Numer. Anal. 48, 922 (2010).
  40. F. Roddier, Distributions et Transformation de Fourier: A l'usage des Physiciens et Des Ingénieurs (McGraw-Hill, New York, 1984).
  41. M. X. Cohen, A better way to define and describe Morlet wavelets for time-frequency analysis, NeuroImage 199, 81 (2019).
  42. A. Bruns, Fourier-, Hilbert- and wavelet-based signal analysis: Are they really different approaches? J. Neurosci. Methods 137, 321 (2004).
  43. A. Guillet, A. Arneodo, and F. Argoul, Tracking rhythms coherence from polysomnographic records: A time-frequency approach, Front. Appl. Math. Stat. 7, 624456 (2021).
  44. S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd ed. (Academic Press, New York, 2008).
  45. C. S. Pittendrigh and S. Daan, A functional analysis of circadian pacemakers in nocturnal rodents, J. Comput. Physiol. 106, 333 (1976).
  46. H. Brown, D. Difrancesco, and S. Noble, Cardiac pacemaker oscillation and its modulation by autonomic transmitters, J. Exp. Biol. 81, 175 (1979).
  47. R. Carmona, W. L. Hwang, and B. Torrésani, in Wavelets and Statistics, edited by A. Antoniadis and G. Oppenheim (Springer, New York, 1995), pp. 95–108.
  48. D. R. Brumley, K. Y. Wan, M. Polin, and R. E. Goldstein, Flagellar synchronization through direct hydrodynamic interactions, eLife 3, e02750 (2014).
  49. L. Federspiel, J. Arrieta Sanagustin, M. Polin, F. Argoul, and A. Allard, Tracking phase synchronization between flagella in the time-frequency domain resolves photophobic response [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.17406887.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation