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

The unicellular microalga Chlamydomonas reinhardtii (CR) is well known for its bi-flagellated 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.

💡 Research Summary

This paper investigates how the two flagella of the unicellular green alga Chlamydomonas reinhardtii (CR) lose and regain synchrony after a sudden high‑intensity light stimulus, known as a photoshock. Traditional phase‑synchronization metrics based on stationary Fourier analysis cannot capture the rapid, non‑stationary dynamics of this response. To overcome this limitation, the authors develop a time‑frequency version of the Phase Synchronization Index (PSI) by embedding the continuous wavelet transform (CWT) into the PSI formulation. The complex PSI, denoted ΥΨ(t,f), is computed directly from the complex wavelet coefficients of the two signals, normalizing out amplitude at each time‑frequency point so that only phase relationships are retained. This yields a value between 0 (no synchrony) and 1 (perfect synchrony) that varies with both time and frequency.

Experimentally, 13 individual CR cells were immobilized in a micro‑pipette and recorded at 1000 fps for 25 s while a high‑intensity (≈10 W m⁻²) 470 nm LED delivered 50 ms light pulses every 3–5 s. The surrounding flow field was measured with ghost‑particle velocimetry using 250 nm polystyrene beads, and velocity signals were extracted from three regions of interest: two lateral windows (Y = ±1) capturing the flow generated by each flagellum, and a central window (Y = 0) representing the bulk swimming flow. These velocity components serve as proxies for the flagellar beating signals.

The authors first validate the method with numerical simulations of two coupled phase oscillators governed by a stochastic Adler equation, exploring strong/weak and positive/negative coupling regimes. The simulations demonstrate that the time‑frequency PSI correctly identifies in‑phase, anti‑phase, and transient synchronization states, even in the presence of Gaussian white noise.

Applying the wavelet‑based PSI to the experimental data reveals three distinct dynamical stages:

1. Pre‑stimulus forward swimming – Both flagella beat synchronously at ~40 Hz. The PSI magnitude |ΥΨ| is high (≈0.9) and the phase difference Φ(t,f) stays near zero, indicating a stable in‑phase “breaststroke” mode.

2. Photoshock‑induced backward swimming – Immediately after the light pulse, the dominant frequency band shifts upward to 60–80 Hz. Although |ΥΨ| briefly drops, a strong anti‑phase relationship (Φ≈π) emerges at ~80 Hz, signifying a high‑frequency undulatory mode that reverses swimming direction. Harmonic analysis shows that the first harmonic (≈80 Hz) becomes the principal energy carrier during this stage.

3. Resynchronization – Over the next 200–300 ms the PSI magnitude recovers and the dominant frequency returns to ~40 Hz. The phase difference again settles around zero, indicating a gradual return to the original breaststroke rhythm. Throughout this recovery, the relative power of the fundamental and its harmonics evolves smoothly, suggesting a continuous re‑balancing of spectral modes rather than an abrupt switch between discrete beating patterns.

The authors argue that the presence of persistent harmonics, especially the first harmonic that dominates during the backward‑swimming phase, points to a mechanism where CR modulates the relative amplitudes of co‑existing spectral modes to adapt rapidly to environmental stress. This spectral re‑weighting provides robustness against cell‑to‑cell variability and may underlie the organism’s ability to survive sudden light shocks.

In conclusion, the study introduces a novel, wavelet‑based complex PSI that can resolve phase relationships in non‑stationary biological oscillators. By applying it to flagellar dynamics, the authors uncover a nuanced picture of photoshock response: rather than a binary switch between two beating patterns, CR employs a dynamic redistribution of energy across fundamental and harmonic frequency bands, enabling rapid yet controlled reversal and recovery of swimming direction. The methodology has broad applicability to other systems featuring transient coupling, such as neuronal spike trains, cardiac pacemaker cells, or ciliary arrays.