Introduction

The fitness of microorganisms depends critically on their ability to sense dynamic physico-chemical clues from the environment, elaborate the information and respond effectively. Environmental responses range from changes in gene expression1 (typical timescale ~10 min); to the activation/deactivation of biochemical processes like chloroplast photoprotection2 (~1 min); to fast movement regulation (~1 s), either active3, 4 or passive5. The best characterised motile response is currently chemotaxis of run-and-tumble bacteria like E. coli 6, a strategy based on the modulation of tumbling frequency7. Chemotaxis features (almost) perfect adaptation to persistent stimuli over intermediate timescales (~10–100 s)8, 9 and can stimulate/inhibit gene expression through a variety of chemosensory pathways10. This paradigmatic sensory system highlights the important crosstalk happening between responses acting across a wide spectrum of time intervals, and exemplifies the need for a consistent cross-timescale framework to understand motility regulation in microorganisms. In the case of phototaxis, a major response in eukaryotic microalgae11, this framework is lacking.

Among micro-eukaryotes, phototaxis is best characterised in the model system Chlamydomonas reinhardtii 12, a green microalga which swims along a helical trajectory by the synchronous breaststroke beating of its flagellar pair13, 14. Cell spinning15 induces a periodic modulation of the signal received by the eyespot, a rhodopsin-based light-sensitive organelle16 featuring a contrast-enhancing dielectric mirror17, 18. Eyespot stimulation is rapidly relayed via an action-potential-like signal to the flagella (ms)19, and triggers a Ca+2-dependent differential response of their beating20, 21 causing cells to steer either towards or away from light22, 23. Implementation within a minimal model24 confirmed that phototactic steering is robust and can indeed lead to both positive and negative taxis, a property that has been used to achieve photo-hydrodynamic focussing of microalgae25. What happens beyond phototactic steering, however, is not well understood. Phototaxis of microalgae can lead to persistent modification of bioconvective patterns26, 27, and should therefore contribute to the interplay between fluid flow and motility leading to microscale patchiness in the seas28, 29. At the single cell level, phototaxis will modulate cell irradiance and can therefore be expected to impact both cell metabolism -through chloroplast stimulation- and light-sensitive gene expression30. Studies of these links are currently limited to qualitative accounts of red-light31 or redox state32 control of phototactic sign, and switch from negative to positive phototaxis after prolonged illumination33. An integrative understanding of phototaxis and its impact on cell metabolism requires a quantitative characterisation and modelling of light-regulated swimming over long timescales.

Here we focus on phototactic behaviour of C. reinhardtii, as representative of green microalgae, for timescales beyond flagellar-initiated steering. Studying the accumulation dynamics around a localised source, we show that cells use tight circulation around the maximum light intensity as a strategy to maximise their overall light exposure before spontaneously leaving the illuminated region. Periodic exposure experiments reveal that this is accompanied by a decrease in the overall response to light stimuli. The quantitative modulation of phototactic response tracks the dynamics of chlorophyll fluorescence, used here as a proxy for the photosynthetic activity of the cells.

Material and Methods

Chlamydomonas reinhardtii wild type strain CC125 and mutant CC2905 (which lacks flagella) were grown axenically at 24 °C in Tris-Acetate-Phosphate medium (TAP)34 under fluorescent light illumination (OSRAM Fluora, 100 μmol/m2s PAR) following a 14 h/10 h light/dark diurnal cycle. Exponentially growing cells at ~2 × 106 cells/ml were resuspended in fresh TAP at the required concentration, loaded in the 7 mm diameter circular observation chamber cored out of a 1 mm thick agar pad sandwiched between coverslips. A CCD camera (Pike, AVT) hosted on a continuously focusable objective (InfiniVar CFM-2S, Infinity USA) recorded at 12.2 fps the phototactic motility of cells within the horizontal sample, visualised through darkfield illumination at 635 nm (FLDR-i70A-R24, Falcon Lighting). Actinic light was provided by a 470 nm LED (Thorlabs M470L2) through a 200 μm-diameter multimode optical fibre (FT200EMT, Thorlabs). Approximation of the fibre output I(x) by a Gaussian (σ I  = 667 μm, peak intensity 260 μmol/m2s) is excellent and will be used throughout the paper. An inverted microscope (TE2000-U, Nikon) fitted with a 10× Plan Apo objective (NA 0.45) and a EMCCD (Evolve, Photometrics) was used to record the chlorophyll fluorescence of CC2905, excited by the epiport-coupled blue LED.

Results and Discussion

We begin by examining single-cell phototaxis after the light was kept on for >10 min to ensure steady conditions (Fig. 1a). Cells further from the centre than 200 μm move inwards along almost radial trajectories as a result of active steering. As they approach the centre, however, individual cells turn sharply and start circulating around the maximum at an average distance of ρ c  = 139 ± 24 μm. This is confirmed by the azimuthally-averaged probability distribution function of swimming directions in Fig. 1b. Given the average swimming speed v s  = 78 ± 11 μm/s, we obtain an angular velocity ω c  = 0.56 ± 0.125 rad/s which compares well with the average value previously reported for sharp turns ($${\omega }_{m}\simeq 0.8$$ rad/s) where cells achieve their largest angular speeds35. Orbiting cells do not show the preference for a particular chirality characteristic of hydrodynamic interactions with the sample surface36, 37. Instead, the orbits have a fundamentally phototactic origin. Recorded only episodically in flagellates38,39,40, orientation perpendicular to light stimulus (diaphototaxis) was reported as an anecdotal curiosity in C. reinhardtii 17. It appears here as a specific modulation of phototaxis allowing cells to dwell in localised light spots.

The position x(t) of a cell swimming at constant speed v s along the direction p(t) will evolve according to

$$\dot{{\bf{x}}}(t)={v}_{s}{\bf{p}}(t);\dot{{\bf{p}}}(t)={\boldsymbol{\omega }}\wedge {\bf{p}}(t),$$
(1)

where the angular speed ω encodes the phototactic response through its (unknown) dependence on the light field. Absent detailed measurements, a common approach26, 27, 41 has been to assume proportionality to the local gradient in light intensity, ω = α p(t)I, where the phototactic parameter α, possibly dependent on I, represents the magnitude of the response.

For C. reinhardtii, the requirement ω ≤ ω m implies α ≤ α max = ω m /|I|max. This reasonable model predicts correctly the radial reorientation of cells far from the source, but the incoming trajectories are then expected to overshoot the centre and eventually describe trochoids like those seen in Fig. 1c. Similar trajectories are indeed seen both in phototactic colloids moving around a diverging laser beam42, and in sea-urchin sperm swimming around a local chemotactic cue43. Phototactic cells however, do not follow trochoids but fall instead onto the tightest closed loops they can achieve around the light source, at an average distance ρ c from the centre. This dynamics cannot be reproduced by changing α to include a transition between positive and negative phototaxis around ρ c (SI Appendix, Fig. S1): it is a fundamentally different type of behaviour that cells follow during positive phototaxis, which might be related to helical swimming of the cell44.

Our simulations in Fig. 1c and d show that circular dynamics would expose the microalgae to a ~30% larger path-averaged light intensity than the trochoidal case, and therefore appears to be better strategy to optimise light capture by a photosynthetic microswimmer. In our experiments, however, cells stop orbiting and leave the field of view after τ c  = 11.2 ± 2.5 s. Consistently observed across the 3290 tracks recorded, this behaviour reflects a clear adaptation of phototactic motility, turning here from positive to negative, and show that cells do not simply migrate to a region of the sample with a specific light intensity, but rather continuously navigate through the spatially varying light profile. Flagellar response to light-step-up/step-down stimuli is indeed known to depend -qualitatively- on the choice of pre-stimulus adaptation20. The adaptive dynamics observed here, however, is a consequence of a history of light-exposure selected autonomously by single cells through their motility.

We now turn to the phototactic behaviour of a population (Fig. 2) to investigate the effect of adaptation over timescales longer than those accessible from the limited field of view of single-cell experiments. Cell concentrations will be kept below 5 × 106 cells/ml to prevent effects on either the actinic light field perceived by the algae, or darkfield illumination22. The image brightness b(x, t) is then proportional to the 2D-projected concentration of algae c(x, t), which integrates the 3D one across approximately the depth of field of the imaging apparatus. Agreement between brightness profiles after prolonged light exposure (>35 s), and the distribution of cell positions from individual tracks (Fig. 2c) confirms the proportionality, and suggests that cell-cell interactions are not important here. Cell accumulation can be characterised through the integrated image brightness $$B(t;\rho )=2\pi {\int }_{0}^{\rho }b(\rho ,t)\rho \,{\rm{d}}\rho$$ where the maximum value ρ max = 958 μm is set by the image size. Initially uniformly distributed, the algae begin to accumulate around the fibre as the light is turned on, causing B(t; ρ) to increase linearly with time (Fig. 2a, blue solid line). This is a signature of a constant inward flux of cells, proportional to the product ρ 2 v p (ρ) of the net phototactic drift v p (ρ) at distance ρ, and the geometric factor ρ 2 which takes into account cells moving inwards from deep within the sample. The full curve v p (ρ) can then be measured from the initial increase up to a multiplicative constant (Fig. 2a, black dashed line). Figure 2b shows that this is well described by v p (ρ)  |I| with the exception of the core region $$\rho \lesssim 150\,\mu {\rm{m}}$$, where we already know that cell behaviour is different.

Switching the light off, the profile relaxes down to the original homogeneous value (Fig. 2a, blue solid line). This dynamics is well characterised by a simple diffusive spreading (Fig. 2b, magenta dashed line) with an effective diffusivity D which can be recovered from a one-parameter fit (Fig. 2b inset). The average value 〈D〉 = (3.9 ± 0.4) × 10−4 cm2/s is in reasonable agreement with the average diffusivity (4.7 ± 0.5) × 10−4 cm2/s reported previously35.

The coarse-grained phototactic drift and the effective diffusivity can be used in a Keller-Segel-like continuum model of the phototactic behaviour of a population of C. reinhardtii, in the spirit of previous effective descriptions of phototaxis41, 45, 46. In this model, valid sufficiently far from the source, the local concentration of cells c(ρ, t) moving in the fibre’s axisymmetric light field I(ρ) obeys the continuity equation

$$\frac{{\rm{\partial }}c}{{\rm{\partial }}t}=\frac{{\rm{\partial }}}{{\rm{\partial }}\rho }(D\frac{{\rm{\partial }}c}{{\rm{\partial }}\rho }-c\frac{\rho }{{h}^{\ast }}{v}_{p}(\rho )),$$
(2)

where the extra factor of ρ, non-dimensionalised by the effective thickness h * has been included to take into account three dimensional effects on our 2D description, as discussed previously. The local phototactic velocity v p (ρ) = βv s (∂I(ρ)/∂ρ)/(∂I(ρ)/∂ρ)max, which incorporates Weber’s law47, is characterised by the phototactic sensitivity of the population, β, setting the maximum phototactic drift (βv s ). To compare Eq. (2) with experiments, we fix the cell concentration at the sample boundary, c(x, t)|boundary = 1, and use the experimentally measured values for the mean swimming velocity and cell diffusivity, light field and phototactic sensitivity. The last parameter is derived from the distribution of single cells’ swimming directions at ρ = σ I (Fig. 1b), giving β = 0.14 ± 0.013. A one-parameter fit to the long-timescale profile in Fig. 2c (blue circles) sets the value of h *. The result (dashed blue line) shows that h * = 519 ± 27 μm provides an excellent description of the cell concentration, implying that cells within roughly half of the sample thickness take part in the phototactic accumulation. The model predicts also the presence of a depletion ring at $$\rho \simeq 1.1\,$$ mm responsible for the slight overshoot of B(t; ρ) experimentally observed right after light-off (Fig. 2a, green bar). Single cell experiments suggest, then, that the measured low phototactic sensitivity results from the balance between inwards/outwards swimming and dwell time, all present in the natural phototactic behaviour of each individual cell and modulated by its irradiation history (Fig. 1a).

Equipped with an appropriate description of the steady state, we now investigate the adaptation process by characterising the phototactic accumulation of a population of dark-adapted cells to a series of identical light-on/light-off cycles (15/90 s on/off; Movie S1 shows one cycle). Figure 3a presents the accumulation dynamics for a representative experiment out of 60, showing a clear dependence on history of light exposure. Accumulation and dispersal phases allow one to measure the time (and light) evolution of both β and D, and therefore pinpoint the dynamical features responsible for the adaptation. Figure 3a (inset) shows that over the whole experiment D increases slightly by ~15%, suggesting a ~7% increase in v s (i.e. photokinesis) which, by itself, would lead to an equivalent increase in β. Instead, this parameter displays a well defined decrease through the cycles (Fig. 3b, red squares), unequivocally assigning the adaptation to a change in the phototactic sensitivity alone. The evolution of the sensitivity parameter is well described by a single-time adaptation ∂ t β(t) = (β * − β(t))/τ β where the adaptation timescale τ β  = 31.84 ± 1.94 s and β */β(0) = 0.46 ± 0.19 are derived from the fit in Fig. 3b (black dashed line). In this analysis, we assumed that β evolves only during periods of illumination. Dark re-adaptation was not observed in the experiments; it must happen over significantly longer timescales and therefore was not considered here.

Phototactic adaptation operates on timescales clearly separated from those characterising adaptation of either flagellar photoshock (~1 s)16, 48 or eyespot signalling (~100 ms)49. Comparison with simulations shows also that the observed adaptation is not the result of a progressively higher proportion of negatively phototactic cells (SI Appendix, Fig. S2). Being directly related to cell irradiance, itself relevant for photosynthesis, we therefore wondered whether the dynamics of β would contain any signature of light-adaptation by C. reinhardtii’s photosynthetic apparatus. To investigate this, we exposed ~1500 dark adapted non-swimming cells (CC2905) to the sequence of light stimulation used previously (see Fig. 3a), and recorded the evolution of their average chlorophyll fluorescence Φchl (502 nm < λ < 538 nm), which can be used as a simple proxy for the activity of the photosynthetic apparatus50.

A homogeneous light field of intensity 540 μE/m2 s was used (identical results were obtained for 975 and 1320 μmol/m2s). Figure 3b shows the evolution of the mean Φchl(t) during each light-on period (blue circles). Light-off intervals did not induce appreciable dark-adaptation, in line with known differences between light- and dark-adaptation of the photosynthetic apparatus51, 52. Chlorophyll fluorescence evolution is well fitted by a simple two-timescale dynamics (Fig. 3b magenta dashed line) with an initial fast response (timescale $${\tau }_{{\rm{chl}}}^{f}=1.47\pm 0.21$$ s) followed by a slow adaptation with timescale $${\tau }_{{\rm{chl}}}^{s}=33.49\pm 5.2$$ s. The exceptional quantitative agreement between $${\tau }_{{\rm{chl}}}^{s}$$ and τ β suggests a connection between the two processes, a possibility which would also explain the slow dark-adaptation of phototaxis.

Phototaxis experiments under a simultaneous background illumination have shown that chloroplast stimulation can induce cells to qualitatively switch their phototactic sign (positive to negative)31. Our results suggest the intriguing possibility that phototaxis and photosynthesis are in fact connected quantitatively, perhaps through intracellular variations in redox poise32, 52. Although further experiments are needed to firmly establish this layer of control, we propose here the hypothesis that this connection is indeed the major determinant of the phototactic motility of eukaryotic microalgae.

Conclusions

The light-induced steering responses evolved by microorganisms like Chlamydomonas are complex, and have been studied extensively. Ultimately, however, flagellar activity must be integrated into a coherent navigation strategy combining physical stimuli and intracellular requirements: how this is achieved is currently not understood. By shifting the focus to long timescales we start addressing this gap. Our experiments have already revealed a surprisingly rich dynamics, from the ability to increase light exposure through diaphototaxis to the adaptive response of cells which reproduces the slow (re)adaptation of their chlorophyll fluorescence. Future experiments will be needed to systematically explore the role of light intensity and colour; to determine whether phototaxis shares any of the common properties of cellular sensory systems, like exact adaptation47, 53; and in particular how these properties are connected with photoprotective dynamics within the chloroplast2 and photosynthetic efficiency54.