Conflicting Roles of Flagella in Planktonic Protists: Propulsion, Resource Acquisition, and Stealth

Flagellates are key components of aquatic microbial food webs. Their flagella propel the cell through the water and/or generate a feeding current from which bacterial prey is harvested, but the activity of the flagella also disturbs the ambient water, thereby attracting the flagellate's flow-sensing predators. Here we use computational fluid dynamics to explore the optimality and fluid dynamics of the diverse arrangements, beat patterns, and external morphologies of flagella found among free-living flagellates in light of the fundamental propulsion–foraging–predation-risk trade-off. We examine 5-$\mu \mathrm{m}$-sized representative model organisms with different resource acquisition modes: autotrophs relying on photosynthesis and uptake of nutrient molecules, phagotrophs that feed on bacteria, and mixotrophs that employ both strategies. For all types, the transport of inorganic molecules is diffusion dominated, and the flagellum in autotrophic species therefore mainly serves propulsion purposes. Flagellates with a single, naked flagellum found among nonforaging swarmer stages have a waveform (less than one wave) that is optimized for swimming and stealth but inefficient for feeding. Flagellates with a hairy flagellum typically have many waves, which optimizes swimming and stealth but is suboptimal for foraging, leading to a design trade-off. However, when compared with naked flagella, the presence of hairs allows a very efficient feeding current, making these primarily phagotrophic flagellates the most efficient and dominant bacterivores in the ocean. Autotrophic biflagellates have wave patterns optimized for both propulsion and foraging but conflicting weakly with stealth. Finally, the mixotrophic haptophytes are optimized for foraging, conflicting with both stealth and propulsion. This is largely due to the long, slender filament (haptonema) that improves prey collection but at the cost of stealth and propulsion. We use dimensional analysis to rationalize our findings. We conclude that phagotrophic flagellates must trade off stealth and propulsion for foraging efficiency, while in autotrophic flagellates stealth is traded off for propulsion and foraging efficiency.

Figure 1

Model organisms [(a)–(e)] and the associated model waveforms and morphologies [(f)–(j)]. (a) M. brevicollis, a predatory flagellate. The cell has one flagellum (long arrow) equipped with a vane (not visible) and a relatively short collar (short arrow) in this dispersal-swimming stage as compared with the feeding stage (Fig. S1). Image courtesy of Jasmine L. Mah. (b) Pseudobodo sp., also a predatory flagellate. The cell has a long and a short flagellum (long and short arrows, respectively), the long one bearing mastigonemes (hairs). (c) C. reinhardtii, a green alga with two active flagella. The cell shown here is held with a micropipette from below. Image courtesy of Kirsty Wan. (d) and (e) P. parvum and P. polylepis, respectively, are mixotroph haptophytes with two active flagella. The haptonema (arrow) is relatively short ($\sim 3\mu \mathrm{m}$) in P. parvum, while in P. polylepis it is much longer ($\sim 20\mu \mathrm{m}$). (f)–(j) Reconstruction of the flagellar waveform for different model organisms using dimensionless input parameters: $A_{\varphi }$, the amplitude of the angle; $N_w$, the number of waves; $C{L}_{fl}$, the maximum turning angle; and $C_0$, the turning angle measured from the symmetry line [dash-dotted line in (h)]. The blue curves show the flagellar waveform during the beat period, and the red curves correspond to the snapshots of the model organisms in (a)–(e). Prey capture happens on the cell surface and haptonema (green), and on the hairy flagellum for hairy flagellates. The rudimentary collar in M. brevicollis, the short flagellum in Pseudobodo sp., and the short haptonema in P. parvum are neglected in the model morphology. Scale bars, $10\mu \mathrm{m}$.

Figure 2

CFD results for uniflagellates. (a) Flagellum thrust ${\overline{F}}_{fl}$ as a function of the number of waves $N_w$ for cells with a naked flagellum (“naked”), a flagellum with a vane positioned perpendicular to the beat plane (“vaned”), and a flagellum with hairs positioned in the beat plane (“hairy”). The dashed curve is fitted to the CFD results for hairy flagellates (based on the mechanism of the produced thrust) with ${\overline{F}}_{fl}=a\sqrt{N_w}-b$, where $a$ and $b$ are positive constants. (b) Average swimming speed over a beat cycle as a function of the number of waves $N_w$, and (c) normalized extension of the fluid noise ($\frac{A_E}{\overline{U}}$) during a beat cycle as a function of the number of waves $N_w$. (d) and (e) Snapshots of the volume around the cell within which the fluid velocity exceeds the threshold velocity $U_{th}=50\mu \mathrm{m}/\mathrm{s}$ (d) and of the concentration field (e), with $r_p^{*}={10}^{-1}$ corresponding to 0.5-$\mu \mathrm{m}$ prey-sized particles, for the cells with the naked (left) and hairy (right) flagellum. (f) The Sherwood number, the ratio of advective to diffusive transport, for $r_p^{*}={10}^{-1}$ as a function of the number of waves $N_w$. The asterisk denotes $r_p^{*}={10}^{-5}$ (corresponding to small molecules); for this $r_p^{*}$ value the Sherwood number is nearly 1 for all cases indicating the predominance of the diffusion transport. Other relevant parameters: $N=7\mu {\mathrm{m}}^{-1}, l=1.5\mu \mathrm{m}, A_{\varphi }=1.25, L_{fl}^{*}=5$, and $\overline{P}=10\mathrm{fW}$.

Figure 3

Hair bundling and terminal filaments. (a) Hairs in flagellate Melkoniania moestrupii are often bundled together. (b) In addition, there are terminal filaments (arrow) on individual tubular hairs. (c) and (d) Spatial distribution of generated thrust ${\sigma }_y$ without (c) and with (d) terminal filaments. Here, hairs have a length of $l=0.9\mu \mathrm{m}$, and the terminal filaments have length $l_{tf}=1.0\mu \mathrm{m}$ and are positioned at distance $l_0=0.8\mu \mathrm{m}$ on the hairs (measured from the attachment point of the hairs to the flagellum), with an arbitrary orientation of $\vec{\mathbf{r}}=\vec{\mathbf{n}}+11\vec{\mathbf{b}}$, where $\vec{\mathbf{n}}$ and $\vec{\mathbf{b}}$ are normal (in the beat plane) and binormal (perpendicular to the beat plane) unit vectors. The addition of the terminal hairs increases the thrust by 100% for the same kinematics and by 34% for the same power input. Scale bars in (a) and (b) are 1 and $0.2\mu \mathrm{m}$, respectively. Other relevant parameters: $N=7\mu {\mathrm{m}}^{-1}, A_{\varphi }=1.25$, and $L^{*}=2.5$. Images courtesy of Robert A. Andersen.

Figure 4

CFD results for biflagellates' swimming and noise. Swimming speed (a) and normalized noise (d) as a function of number of waves $N_w$ for the cases with short flagella ($L_{fl}^{*}=2$) and no haptonema, and swimming speed (b) and normalized noise (e) as a function of number of waves $N_w$ for the cases with long flagella ($L_{fl}^{*}=5$) and no haptonema. For comparison, results for uniflagellates (uni-fl; black) and cells with haptonema (green) are also added. (c) and (f) Effect of length of the haptonema $L_h^{*}$ on swimming and noise with parameters $L_{fl}^{*}=5$ and $N_w=5$. (g) and (h) Snapshots of the velocity field for freely swimming flagellates with short flagella $[L_{fl}^{*}=2$ (left, $N_w=1$; right, $N_w=2$)] (g) and long flagella $[L_{fl}^{*}=5$ (left, $N_w=1$; right, $N_w=2$)] (h). Other relevant parameters: In (g), $A_{\varphi }=0.75, C_0=0.5\pi$, and $L_h^{*}=0.0$; in (h), $A_{\varphi }=1.00, C_0=0.5\pi$, and $L_h^{*}=4.0$. For all cases, $C{L}_{fl}^{*}=0.7\pi$ and $\overline{P}=10\mathrm{fW}$.

Figure 5

CFD results for biflagellates' feeding. (a)–(c) Snapshots of the concentration field (with $r_p^{*}={10}^{-1}$) with parameters corresponding to those of C. reinhardtii (a), P. parvum (b), and P. polylepis (c). (d) Variation in Sherwood number as a function of the number of waves $N_w$ for the three model organisms feeding on $\sim 0.5-\mu \text{m-sized}$ prey particles ($r_p^{*}={10}^{-1}$). For comparison, results for uniflagellates with long and short flagella are added as black dotted curves. The black dashed line shows the Sherwood numbers for small molecules ($r_p^{*}={10}^{-5}$, denoted in the key with an asterisk). (e) Effect of the length of the haptonema on the Sherwood number. For all cases, $\overline{P}=10\mathrm{fW}$.