Macroscopic waves, biological clocks and morphogenesis driven by light in a giant unicellular green alga

A free-falling ball follows a trajectory determined by external forces. When we aim to catch the ball, in contrast, our dynamics follows an intrinsic predictive model of the world, exhibiting anticipatory behaviour. Such behaviour has been observed in living systems down to cellular levels. Time-keeping and synchronisation with the external world, as well as within the organism, seem to be essential for homeostasis, the ability of living systems to maintain essential variables within physiological limits. This is one of the ways by which living organisms manifest self-organisation, defined here as networks of processes that are self-stabilizing far from thermodynamic equilibrium. Biological oscillators are found throughout the living world, constituting a mechanism for organismal synchronisation. Their manifestations, such as pulse rate and pressure, are none other than homeostasis. Biological oscillators are amenable to analytic approaches from dynamical systems. Here we study active rhythmic transport in Caulerpa brachypus, a marine green alga which presents complex morphology while being a giant single cell. Caulerpa challenges central paradigms in developmental biology, as it exhibits...

The study developed protocols for algal culture and propagation, automated illumination, live imaging, spatial coarse-graining, and power spectral analysis to quantify self-organised green-wave dynamics in Caulerpa racemosa/brachypus. Culture and propagation: Caulerpa brachypus samples (single origin) were cut into 1–3 cm segments and regenerated in 8-well dishes (7 ml Erdschreiber’s Medium per well). Over 1–2 months each regenerating sample could yield ~20 new segments, improving homogeneity of genetic background and initial morphologies. Prior to cutting, samples were triple-washed in filtered artificial seawater (35‰ Instant Ocean, 0.1 μm PES filters). Illumination and imaging: Custom 3D-printed rigs held dishes, LED strips (5000 K SM5050 12 V), Raspberry Pi Zero W and camera (SIMP Camera v2). Raspberry Pi controlled both time-lapse imaging (RPi-Cam-Web-Interface) and illumination via PWM (pigpio). Exposure and gain were auto-set to accommodate varying intensities. Reference illumination I0 ≈ 4.5 μmol·s−1·m−2 at dish lid level; spectrum featured peaks at ~545 nm (FWHM ~505–614 nm) and ~440 nm (FWHM ~428–449 nm). Incubators maintained 22.5–24.5 °C. Experimental driving protocols included 12h light:12h dark (T = 24 h), with dark ~1/200 of I0, as well as a range of driving periods (e.g., T = 18–30 h near-circadian and far-from-circadian T = 1.5, 3, 6, 9, 48, 54, 94 h). Constant-in-time illumination experiments spanned intensities from 2^−5 to 2^1 × I_L. Imaging cadence was typically every 15 s over weeks, enabling high-throughput concurrent tracking of tens of samples. Spatial coarse-graining and time-series extraction: For each well (region of interest), the fraction of pixels below a blue-channel threshold (value < 70/255) was computed to estimate apparent green area fraction (chlorophyll absorbs strongly in blue). This reduced the high-dimensional spatiotemporal dynamics to a single macroscopic observable per well. Post-processing: Outliers were identified using rolling windows (1 h) with criteria based on interquartile range (1.5× IQR) and a 75% window rule; limited outliers were replaced by nearest-neighbor forward/backward propagation. Datasets with >2% unrepaired outliers within analysis intervals were excluded. Power spectral analysis: Power spectra were estimated using Welch’s method with Hann-tapered segments (85.5 days; 4896 points), 50% overlap, zero-padding to improve frequency resolution (reported as 1 ν_s × 24 h^−1), no detrending. Local maxima (dominant frequencies) were detected via a two-step procedure: prominence at least twice baseline, then refined by log-scale parabolic fitting over 5-point neighborhoods. Analysis windows typically started 2 days after switching from baseline 12h:12h to the new protocol and spanned 35 days. Sample sizes: Examples include for near-24 h driving T ∈ {18, 21, 22.5, 24, 25.5, 27, 30 h} with sample sizes {5, 5, 7, 3, 8, 4, 5}; for far-from-24 h driving T ∈ {1.5, 3, 12, 24, 48, 54, 94 h} with sample sizes {6, 7, 6, 27, 8, 4, 5}. Data and code: Data deposited at figshare (10.6084/m9.figshare.2379027). Analysis used Scientific Python stack (SciPy, pandas, NumPy, JupyterLab, dask, xarray, HoloViz, Matplotlib).

- Self-organised waves of greenness (chloroplast-rich regions) propagate over centimeters within hours across the entire giant single-celled alga and anticipate external light-dark transitions. - Under 12h:12h (T = 24 h), power spectra show a strong fundamental at ~1/24 h with higher harmonics reflecting non-sinusoidal waveforms. Despite variability in individual time series, spectral decomposition consistently reveals common structure. - Driving periods within ~18–30 h produce fundamental response frequencies matching the driving (1:1 entrainment), and spectra collapse under appropriate rescaling, indicating dynamical equivalence near circadian periods. - For driving periods far from ~24 h (e.g., T = 48 h, 9 h, 3 h, 1.5 h, 54 h), spectra show signatures of coupling to an intrinsic oscillator: in addition to peaks at the driving frequency, local maxima appear near the intrinsic circadian frequency (~1/24 h). Time series under fast driving (e.g., T = 3 h) show rapid undulations superimposed on a slower ~24 h modulation. - Evidence for synchronization regions (Arnold tongues) indicates higher-order n:m entrainment near rational ratios of the intrinsic natural frequency, with a robust 1:1 entrainment range around 24 h. - Under constant illumination (free-running), the system exhibits intensity-dependent dynamics: (i) the response fundamental frequency f0 increases as illumination intensity decreases; (ii) at higher intensities, spectral peaks become less distinct, drowning in a broadband continuum indicative of increased temporal disorder; (iii) harmonic content is weaker than in entrained states. Low intensity (e.g., I ≈ 2.5×10^−2 of reference) yields sustained but reduced-amplitude oscillations over weeks; high intensity (e.g., ~2.2×10^−1) leads to intermittent/irregular oscillations. - Morphology depends on the temporal pattern of light: samples with identical mean photon flux but time-varying illumination (12h:12h) differ morphologically from those under constant illumination (e.g., crown size and aspect ratio), implying that temporal structure of light, not just average flux, shapes development. - Growth rates (population-level central tendency and dispersion) increase with illumination intensity; higher flux promotes faster area recovery on average but with greater individual unpredictability. - Experimental parameters and references: reference intensity I0 ≈ 4.5 μmol·s−1·m−2; dark level ~I0/200; constant-illumination intensities ranged ~2^−5 to 2^1 × I_L; multiple driving periods tested with sample sizes per protocol reported.

The findings reveal that the macroscopic chlorophyll waves constitute or are coupled to a self-sustained intrinsic oscillator that can be entrained by periodic illumination. This explains the apparent anticipatory onset of waves relative to external light transitions. Near circadian driving (around 24 h), the system exhibits 1:1 entrainment and dynamical equivalence, while far-from-circadian driving exposes coexistence of driven and intrinsic frequencies and higher-order entrainment, consistent with nonlinear oscillator theory and Arnold tongues. Under constant illumination, the dependence of the natural frequency on photon flux and the transition toward temporal disorder at high intensities demonstrate nonlinear, possibly chaotic dynamics and confirm the oscillator’s self-sustained nature independent of external cycling. The link between illumination temporal structure and organismal morphology suggests that these waves couple biological timekeeping to metabolism and morphogenesis. Given that Caulerpa derives energy from photons, photosynthetic metabolism likely mediates the coupling between light and the oscillator, analogous to known interactions between energy metabolism and circadian oscillators in cyanobacteria. Equivalence in average photon flux between 12h:12h and constant illumination but divergent dynamics indicates that dark-phase relaxation is important for typical organismal dynamics.

This work demonstrates self-organised, organism-scale greenness waves in a giant unicellular alga and shows they are governed by a self-sustained oscillator entrained by light. The study quantifies entrainment (including 1:1 and higher-order regimes), documents intensity-dependent free-running dynamics and transitions to temporal disorder under constant illumination, and establishes that illumination temporal structure influences development and morphology. These results connect biological timekeeping with metabolism and morphogenesis at macroscopic, single-cell scales. Potential future directions implied by the findings include identifying the biochemical and biophysical mechanisms coupling photosynthesis/metabolism to the oscillator, determining molecular components underpinning the intrinsic clock, and dissecting how wave dynamics causally influence morphogenetic patterning under different light regimes.

- Individual time series exhibit high variability, though spectral analysis reveals common features; variability may limit predictability at the single-sample level. - All algal material was derived from a single origin, potentially limiting generalizability across genotypes or environmental histories. - Coarse-graining via blue-channel thresholding reduces complex spatiotemporal structure to a single scalar metric per well, which may obscure spatial details. - Developmental differences between temporal light distributions (constant vs 12h:12h) are less apparent in growth curves, limiting some quantitative morphological comparisons. - The study focuses on laboratory illumination and temperature regimes; ecological relevance under natural fluctuating conditions was not tested.