Motility of Colonial Choanoflagellates and the Statistics of Aggregate Random Walkers

We illuminate the nature of the three-dimensional random walks of microorganisms composed of individual organisms adhered together. Such aggregate random walkers are typified by choanoflagellates, eukaryotes that are the closest living relatives of animals. In the colony-forming species Salpingoeca rosetta we show that the beating of each flagellum is stochastic and uncorrelated with others, and the vectorial sum of the flagellar propulsion manifests as stochastic helical swimming. A quantitative theory for these results is presented and species variability discussed.

Figure 1

The choanoflagellate S. rosetta. (a) Bright field image ($5\mu \mathrm{m}$ scale) and (b) schematics of ‘slow-swimmer’ single cell, base angle $\theta$, and rosette colony.

Figure 2

Flagellar beating dynamics. (a,b) Time series of the base angle $\theta (t)$ on two flagella within a single colony. (c) Autocorrelation function of $\theta$ for one flagellum, with fit of the envelope to an exponential decay (dashed red). (d) Cross correlation of $\theta$ between two flagella on the same colony. (e) Peak frequencies of $n=23$ tracked flagella. (f) Decay time of autocorrelation in single flagella. (g) Magnitude of cross correlations between flagella in same colonies.

Figure 3

Random walks. (a) Long tracks of swimming S. rosetta. Inset scale bar is $10\mu \mathrm{m}$. (b) Projected mean squared displacement for individual walks (solid, error shaded) and fits of model (dashed). Inset shows a zoom-out with late-time linear behavior $\sim 4D_{\infty }t$ (dashed, gray). (c) Velocity autocorrelation (solid, error shaded) and model (dashed) with parameters as in (b). Fitted parameters (red curve): ${\omega }_0=1.63{\mathrm{s}}^{-1}$, $v_p=9.0\mu \mathrm{m}/\mathrm{s}$, $v_{\omega }=12.1\mu \mathrm{m}/\mathrm{s}$, $D_r=0.09{\mathrm{s}}^{-1}$.

Figure 4

Speed vs size for $\sim 750$ colonies. Colony size is estimated by median $xy$-projected area. Colonies are blue and green circles, green speed being $\sqrt{v_p^2+v_{\omega }^2}$ from model fits to the long tracks. Green crosses are single-celled fast swimmers [12]. Colored background indicates running mean and standard deviation.