Generalized receptor law governs phototaxis in the phytoplankton Euglena gracilis

Abstract

Phototaxis, the process through which motile organisms direct their swimming toward or away from light, is implicated in key ecological phenomena (including algal blooms and diel vertical migration) that shape the distribution, diversity, and productivity of phytoplankton and thus energy transfer to higher trophic levels in aquatic ecosystems. Phototaxis also finds important applications in biofuel reactors and microbiopropellers and is argued to serve as a benchmark for the study of biological invasions in heterogeneous environments owing to the ease of generating stochastic light fields. Despite its ecological and technological relevance, an experimentally tested, general theoretical model of phototaxis seems unavailable to date. Here, we present accurate measurements of the behavior of the alga Euglena gracilis when exposed to controlled light fields. Analysis of E. gracilis' phototactic accumulation dynamics over a broad range of light intensities proves that the classic Keller-Segel mathematical framework for taxis provides an accurate description of both positive and negative phototaxis only when phototactic sensitivity is modeled by a generalized "receptor law," a specific nonlinear response function to light intensity that drives algae toward beneficial light conditions and away from harmful ones. The proposed phototactic model captures the temporal dynamics of both cells' accumulation toward light sources and their dispersion upon light cessation. The model could thus be of use in integrating models of vertical phytoplankton migrations in marine and freshwater ecosystems, and in the design of bioreactors.

Keywords: microbial motility; photoaccumulation; photoresponse; phototactic potential; sensory system.

Fig. 1.

Sketch of the experimental setup. A LED point source (not to scale) was placed below the linear channels. Individuals of E. gracilis (green dots; not to scale) accumulated in the presence of light through phototaxis. Shown are distances from the LED and angles of light propagation in water, computed using Snell’s law. The light direction component orthogonal to the channel was disregarded here, because the cells’ movement dynamics in the vertical direction was dominated by gravitaxis (41), which resulted in the accumulation of cells at the top of the channel (SI Materials and Methods and Fig. S6).

Fig. 2.

Phototaxis of E. gracilis toward blue and red light of different intensities. Shown are normalized stationary cell density profiles $\overline{\rho }\left(x\right)$ around a light source located at $x=0$ cm for various peak intensities I₀ in the blue (A–G; $\lambda =469$ nm) and red (H and I; $\lambda =627$ nm) regions of the visible spectrum. The colored curves in A–G are the experimental cell density distributions (five replicates for each value of I₀), and the dashed black lines denote the mean. The grayscale bars below A–G show the imposed blue light intensity profiles $I\left(x\right)$, where the gray level scales linearly (upper bar) or logarithmically (lower bar) with I; white corresponds to $I=31$ W⋅m⁻² and black to $I=0.001$ W⋅m⁻². Positive phototaxis (directed movement toward the light source) is observed with blue light up to $I\simeq I_m=5.5$ W⋅m⁻², which is the value of light intensity that causes the highest attraction of algae compared with both lower and higher values (E–G) of I. For $I>I_m$, negative phototaxis (directed movement away from the light source) is observed. No phototactic behavior is discernible with red light (H and I) (three replicates for each value of $I_0$).

Fig. 3.

Temporal dynamics of accumulation around a light source at $x=0$ cm (A–C) and relaxation of cell density peaks upon removal of light (D–H). (A–F) Experimental cell density profiles at different times. The shaded gray area is delimited by the maximum and minimum cell densities of three replicate experiments and the black line denotes the mean. The red dashed line shows the theoretical prediction, Eq. 1, using the experimentally determined $\varphi \left(I\right)$ and $I\left(x\right)$ (Fig. 4 A and B) and D (Table 1) determined experimentally from the relaxation of density peaks (D–H). Density profiles are renormalized to display the same mean abundance. The grayscale bars below A–C show the light intensity profile imposed during the accumulation; the gray level scales linearly (upper panels) or logarithmically (lower panels) with the intensity I, with white corresponding to $I=5.2$ W⋅m⁻² and black to $I=0.001$ W⋅m⁻². The temporal decay of Fourier modes (G) during the relaxation of density peaks (D–F) is exponential [$\log \left|\widehat{\rho }\left(k,t\right)/\widehat{\rho }\left(k,t\right)\right|=-D{k}^{2}t$; data in black and linear fit in red], and the decay rate is a quadratic function of the wave number k (H; data in black and parabolic fit in red), proving the diffusive behavior in the absence of light gradients.

Fig. 4.

Computation of the phototactic potential $\varphi \left(I\right)$. (A) Light intensity profiles for different peak intensities $I_0$. (B) Phototactic potential $\varphi \left(I\right)$ computed from Eq. 2 via inversion of the light intensity profile $I\left(x\right)$ (A). The solid black line is the mean value of $\varphi \left(I\right)$ over the stationary density profiles for the various $I_0$, whereas the blue and gray regions represent the $68\text{\%}$ and $95\text{\%}$ confidence intervals, respectively. The dashed red line is the best fit of the phototactic potential predicted by the modified receptor law, Eq. 3. (Inset) The phototactic potential calculated from each of the stationary density profiles (color-coded by light intensity regime; see A and Fig. 2 A–G) at different $I_0$ collapse on the same curve [displayed on the y axis is the quantity $\varphi \left(I\right)=D\log \langle \overline{\rho }\left(I\right)\rangle$, where the mean is over the five replicates with same $I_0$], proving the applicability of Eq. 1. Axes labels and ticks are as in the enclosing figure. (C and D) Mean cell density profiles measured at steady state (solid lines) and predicted from Eq. 2 (dashed lines), color-coded according to the light intensity regime (see A and Fig. 2 A–G).