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

Direct measurement of inertial impact and propulsive force in a eukaryotic swimmer

Katsuya Shimabukuro, Kosaku Horinaga, Kazumo Wakabayashi, and Hikaru Emoto

Noriko Ueki

Ken-ichi Wakabayashi

Noriyo Mitome*

  • *Contact author: mitome@sz.tokoha.ac.jp

Phys. Rev. Research 8, 023364 – Published 30 June, 2026

DOI: https://doi.org/10.1103/2b1s-z7t6

Abstract

Cilia and flagella are highly conserved biological motors that drive the motility of diverse eukaryotic cells. In the microscopic world, an organism's swimming kinematics are generally assumed to be a direct, instantaneous proxy for its underlying motor force output. However, as organisms scale in size—such as during the evolutionary transition to multicellularity—this fundamental assumption may break down. Using the multicellular alga Volvox as a model biophysical system, we perform direct, time-resolved force measurements during free-swimming collisions to deconvolve a swimmer's inertial impact force from its motor's propulsive force. We discover a ∼30Hz propulsive pulse, which serves as the mechanical signature of collective ciliary action and hydrodynamic synchronization. Crucially, we demonstrate that while this high-frequency motor output drives a fluctuating velocity in the smaller V. carteri, it is mechanically filtered by the inertia of the larger V. ferrisii, resulting in a smooth swimming trajectory. Our work reveals that as organisms grow larger, their own mass acts as a mechanical low-pass filter. This fundamentally decouples high-frequency motor dynamics from whole-organism swimming kinematics, highlighting how physical constraints shape the mechanobiology of motility as organisms evolve toward complex multicellularity.

View figure in article

Physics Subject Headings (PhySH)

Corrections

8 September, 2026

Correction: Errors in Refs. [10], [11], and [15] have been fixed.

Article Text

References (16)

  1. J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Associates, Sunderland, MA, 2001).
  2. D. R. Brumley, K. Y. Wan, M. Polin, and R. E. Goldstein, Flagellar synchronization through direct hydrodynamic interactions, eLife 3, e02750 (2014).
  3. R. E. Goldstein, Green algae as model organisms for biological fluid dynamics, Annu. Rev. Fluid Mech. 47, 343 (2015).
  4. D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, Hydrodynamic synchronization and metachronal waves on the surface of the colonial alga Volvox carteri, Phys. Rev. Lett. 109, 268102 (2012).
  5. D. R. Brumley, M. Polin, T. J. Pedley, and R. E. Goldstein, Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin, J. R. Soc. Interface 12, 20141358 (2015).
  6. E. M. Purcell, Life at low Reynolds number, Am. J. Phys. 45, 3 (1977).
  7. E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
  8. J. G. Umen, Volvox and volvocine green algae, EvoDevo 11, 13 (2020).
  9. D. L. Kirk, A twelve-step program for evolving multicellularity and a division of labor, BioEssays 27, 299 (2005).
  10. R. D. Schulman, M. Backholm, W. S. Ryu, and K. Dalnoki-Veress, Dynamic force patterns of an undulatory microswimmer, Phys. Rev. E 89, 050701(R) (2014).
  11. T. J. Böddeker, S. Karpitschka, C. T. Kreis, Q. Magdelaine, and O. Bäumchen, Dynamic force measurements on swimming Chlamydomonas cells using micropipette force sensors, J. R. Soc. Interface 17, 20190580 (2020).
  12. D. L. Kirk and M. M. Kirk, Protein synthetic patterns during the asexual life cycle of Volvox carteri, Dev. Biol. 96, 493 (1983).
  13. M. Krieg et al., Atomic force microscopy-based mechanobiology, Nat. Rev. Phys. 1, 41 (2019).
  14. K. Drescher, K. C. Leptos, I. Tuval, T. Ishikawa, T. J. Pedley, and R. E. Goldstein, Dancing Volvox: Hydrodynamic bound states of swimming algae, Phys. Rev. Lett. 102, 168101 (2009).
  15. C. A. Solari, S. Ganguly, J. O. Kessler, R. E. Michod, and R. E. Goldstein, Multicellularity and the functional interdependence of motility and molecular transport, Proc. Natl. Acad. Sci. U.S.A. 103, 1353 (2006).
  16. N. Ueki and K. Wakabayashi, Multicellularity and increasing reynolds number impact on the evolutionary shift in flash-induced ciliary response in Volvocales, BMC Ecol. Evol. 24, 119 (2024).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation