Passive cell body plays active roles in microalgal swimming via nonreciprocal interactions

The cell body of flagellated microalgae is commonly considered to act merely as a passive load during swimming, and a larger body size would simply reduce the speed. In this work, we use numerical simulations based on a boundary element method to investigate the effect of body-flagella hydrodynamic interactions (HIs) on the swimming performance of the biflagellate, \textit{C. reinhardtii}. We find that body-flagella HIs significantly enhance the swimming speed and efficiency. As the body size increases, the competition between the enhanced HIs and the increased viscous drag leads to an optimal body size for swimming. Based on the simplified three-sphere model, we further demonstrate that the enhancement by body-flagella HIs arises from an effective non-reciprocity: the body affects the flagella more strongly during the power stroke, while the flagella affect the body more strongly during the recovery stroke. Our results have implications for both microalgal swimming and laboratory designs of biohybrid microrobots.

💡 Research Summary

In this study the authors investigate how the hydrodynamic interactions (HIs) between the cell body and the two anterior flagella of the biflagellate alga Chlamydomonas reinhardtii affect its swimming performance. Using a hybrid boundary‑element method (BEM) combined with regularized Stokeslets, they directly incorporate experimentally measured flagellar waveforms into a three‑dimensional model consisting of a spheroidal cell body (semi‑minor axis a, semi‑major axis b) and two planar flagella. By varying the body’s major axis length b while keeping the flagellar kinematics fixed, they quantify the dependence of average swimming speed ⟨U_b⟩ and swimming efficiency η on the dimensionless size ratio b/L (L = flagellum length).

The simulations reveal a non‑monotonic relationship: as b/L increases, both ⟨U_b⟩ and η first rise, reach a maximum at an intermediate body size (≈0.2–0.3 L for the model, close to the experimentally observed mean b/L≈0.38), and then decline for larger bodies. The initial increase is attributed to strengthening body‑flagellum HIs, which augment the forward thrust generated during the power stroke. Beyond the optimum, the viscous drag of the larger body (characterized by the friction coefficient ζ_b) outweighs the HI‑driven thrust, causing a drop in performance. Inter‑flagellar HIs are found to be largely screened by the body and have only a minor effect on the overall swimming metrics.

To uncover the physical origin of the enhancement, the authors construct a minimal three‑sphere model: a central sphere representing the cell body and two smaller spheres representing the flagella. They explicitly enforce the no‑slip condition on the body surface using the spherical image system (Kim & Karrila). In this reduced system, the body‑to‑flagellum (B‑to‑F) interaction consists of a static component (image Stokeslet) and a dynamic component (flow induced by the moving body). Analysis shows that during the power stroke the dynamic B‑to‑F force dominates, pulling the flagella forward and increasing the instantaneous body speed. During the recovery stroke the static image force dominates, pushing the flagella backward and reducing the backward slip of the body. This asymmetry—stronger body‑to‑flagellum coupling in the power stroke and stronger flagellum‑to‑body coupling in the recovery stroke—creates an effective non‑reciprocal interaction that doubles the net forward displacement per cycle compared with a system lacking body‑flagellum HIs.

The authors test the robustness of these findings by applying several experimentally measured flagellar waveforms that differ in curvature, wavelength, and amplitude. In all cases the non‑monotonic dependence on b/L persists and the optimal body size remains within the same range, confirming that the effect is governed primarily by the large‑scale approach and retreat motions of the body relative to the flagella rather than fine details of the flagellar shape.

The paper concludes that the cell body of C. reinhardtii is not a passive load but an active participant in propulsion through non‑reciprocal hydrodynamic coupling with its flagella. This insight explains why natural populations exhibit a relatively narrow distribution of body sizes and suggests that evolutionary pressures have tuned body geometry to maximize swimming efficiency. Moreover, the identified mechanism offers a design principle for bio‑hybrid microrobots: by appropriately scaling the body relative to the actuation length and timing the power/recovery strokes, artificial swimmers can achieve higher speeds and efficiencies with minimal energy consumption. Future work should aim at experimental validation (e.g., high‑speed imaging of body‑flagellum flow fields) and explore how external factors such as fluid viscosity, confinement, or external flow fields modulate the optimal body size and non‑reciprocal interaction.