Inferring intraciliary dynamics from the gliding motility of Chlamydomonas reinhardtii

TL;DR

It is shown that, while gliding, the cells exhibit anomalous-diffusive features, including Lorentzian-like distributions of displacements, which are reminiscent of enhanced search strategies, which may be exploited by the cells to facilitate colony formation and by organisms possessing an intraciliary-transport machinery for the transport of cargo molecules and signaling.

Abstract

The unicellular microalga Chlamydomonas reinhardtii is widely recognized as a premier model living microswimmer for physicists and biophysicists. However, the interest around C. reinhardtii goes beyond its swimming capabilities. In fact, light can drastically alter its behavior: under blue illumination, the cell attaches to a nearby surface and intermittently glides on it. Such a gliding motility is powered by molecular-motor proteins operating on the cell's cilia, and the related machinery has established the cell as a prime reference for the study of intraciliary-transport mechanisms. This is what we focus on in the present work, by combining in-line holographic microscopy -which leads to unprecedented spatial and temporal resolutions on the gliding dynamics -and statistical inference. We show that, while gliding, the cells exhibit anomalous-diffusive features, including Lorentzian-like distributions of displacements, which are reminiscent of enhanced search strategies. The latter may be exploited by the cells to facilitate colony formation, or, more broadly, by organisms possessing an intraciliary-transport machinery for the transport of cargo molecules and signaling. Furthermore, gliding trajectories, by being intermittent, are valid candidates to infer forces at the molecular-motor scale that are necessary for the cells to move, or symetrically, to transport cargo molecules. We report a gliding threshold of about 20 pN, compatible with the activity of single molecular motors.

Figures (4)

• Figure 1: Gliding motility of the unicellular microalga C. reinhardtii. (A) Illustration of a gliding cell within the experimental setup. Plane and spherical waves represent the incident and scattered lights, respectively. (B) Picture showing cells in the gliding configuration (scale bar: $10 \, \mathrm{\mu m}$). (C) Schematic (not to scale) of the inside of a cell's cilium to highlight the mechanism driving gliding motility (see text). (D) Hologram corresponding to a gliding cell (scale bar: $10 \, \mathrm{\mu m}$). (E) Radial intensity profile $I$ (normalized by the incident intensity $I_0$) as a function of the distance $\rho$ from the center of the hologram. The purple solid line depicts an experimental profile (orthoradial average), with the light-shaded purple area representing the related error (orthoradial standard deviation). The black dashed line depicts the corresponding theoretical profile, i.e. the best fit to the Mie theory lavaud2021stochastic of the two-dimensional image shown in panel D, leading to: $a = 4.2 \, \mathrm{\mu m}$ (alga's effective radius), $n_\mathrm{p} = 1.40$ (alga's effective refractive index), and $z = 75.1 \, \mathrm{\mu m}$ (distance between the cell's center and the focal plane of the objective). (F) Trajectory of a gliding cell. The top line corresponds to the in-plane $r$-coordinate, with $r = \sqrt{(x - x(0))^2 + (y-y(0))^2}$, and the bottom line to the $z$-coordinate. The right-hand-side column of the panel corresponds to a zoom on one gliding event. (G) Violin plot showing the distribution of in-plane gliding speeds $v_\mathrm{g}$ of cells. The dashed line represents the average velocity, which is about $0.9 \, \mathrm{\mu m / s}$ (measured over 343 gliding events).
• Figure 2: Anomalous super-diffusive-like behavior of gliding cells. (A) In-plane mean squared displacements (MSDs) $\langle \delta_\tau r^2 \rangle_t$ as a function of the lag time $\tau$. Colored lines correspond to experimental MSDs from individual trajectories, either (red) when the cells exhibit the intermittent gliding motility (8 cells) displayed in Fig. \ref{['fig:intro']}F or (blue) for one cell that stays at a given location, without actively gliding, for more than 500 seconds (1 cell). The dashed lines are guides to the eye. (B) Probability distribution function (PDF) $P(\delta_\tau r)$ of observing in-plane displacements $\delta_\tau r$ over a time lag $\tau$. The red disks correspond to intermittent trajectories, and the black solid (resp. dashed) line is a Lorentzian (resp. Gaussian) guide to the eye. The inset shows the PDF of in-plane displacements corresponding to an cell pausing at a given location, and the black solid line is a Gaussian guide to the eye. In both panels, the black hexagons correspond to the simulations combining Brownian motion and Lévy flights as described in the Materials and Methods.
• Figure 3: The cells glide in a double-well potential. (A) Potential $U$, normalized by the thermal energy $k_\mathrm{B}T$, as a function of the in-plane position $r$. Blue disks correspond to experimental data. Colored lines are guides to the eye. The inset shows a zoom on the left-hand-side well. The black line corresponds to the best fit to $k(r-r_\mathrm{well})^2/2$, leading to $k= 234 \, \mathrm{nN/m}$ and $r_\mathrm{well} = 1.0 \, \mathrm{\mu m}$. (B) Box plot showing springs constants $k$ obtained as in panel A, for 6 different wells (3 cells).
• Figure 4: Inference of forces acting on single cells. (A) In-plane coordinate $r$ as a function of time. The colors highlight periods of motion (red) and periods of pausing at a given location (blue). (B) In-plane MSDs $\langle \delta_\tau r ^2\rangle_t$ as functions of the time lag $\tau$, in both of the aforementioned regimes. The MSDs correspond to one cell. The lines correspond to single intervals, either gliding or pausing. The disks correspond to the average of the lines, in both of the aforementioned regimes. (C) Box plot showing the in-plane forces $F$ measured according to Eq. (\ref{['eq:force']}) in both of the aforementioned regimes (8 cells). The orange (resp. purple) dashed line corresponds to the average force measured when the cells glide (resp. pause at a given location). The stars indicate the result of an independent t-test with a p-value of $3\cdot 10^{-10}$.