Feeding flow and membranelle filtration in ciliates

Ciliates are ubiquitous in the marine environment and important consumers of phytoplankton and flagellates. The feeding on suspended food particles in ciliates is complex and relies typically on coordinated motion in bands of transversal rows of cilia known as membranelles. Many ciliates are upstream collectors that use a single membranelle band to generate feeding flow, retain food particles, and transport them to the mouth region. To explore a representative upstream collector, we consider the ciliate Euplotes vannus. We determine the clearance rate using particle tracking and estimate the flow-generating force by fitting a point force model to the observed flow. To obtain a mechanistic understanding of feeding flow and particle retention, we use high-speed video microscopy. The cilia move parallel to the membranelle band towards the mouth region in the power strokes, and a metachronal wave propagates away from the mouth region parallel to the band and outwards along the membranelles. A gap, therefore, opens between neighboring membranelles from the inner side of the band where the mouth region is located, and while food particles are retained, water is drawn in and pushed outwards across the membranelle band as the gap closes from the inner side. We suggest a model that rationalizes our observations and quantifies the mechanism by which the membranelle band can both generate feeding flow and retain food particles. The model compares favorably with our observations and suggests a trade-off between the clearance rate and the membranelle gap that determines the lower cutoff in the prey size spectrum. We quantify the trade-off and discuss the ecological significance of our findings.

Figure 1

Microscope images of Euplotes vannus. (a) Ventral view of an individual walking on the coverslip. The membranelle band is to the right, starting at the front of the cell (up) and twisting towards the mouth region at the center of the cell. The flow along the inner side of the band towards the mouth region and the flow outwards through the band are indicated by green and red arrows, respectively. Large cirri are visible on the back. (b) Profile view of an individual walking on a lump of material using its large cirri. The feeding flow is towards the front of the cell as indicated by the green arrow. (c) Freely swimming individual with helical trajectory. The instantaneous swimming direction is indicated by the green arrow.

Figure 2

Representative particle tracks visualizing the feeding flow. The tracer particles are carried past the ciliate (red), interact with the frontal membranelles but are lost and not carried along the membranelle band towards the mouth region (yellow), or are transported to the mouth region (green). (a) Ventral view of an individual on the coverslip with flow from right to left. (b) Profile view of an individual on a lump of material with flow from left to right. The particles are 4 $\mu \mathrm{m}$ in diameter and the particle positions are shown with 10-ms time intervals. The individual slowly rotates by $25{}^{\circ }$ in the video sequence used for panel (a), and each track has been oriented to match the cell orientation when the particle reaches the mouth region or its point of closest approach.

Figure 3

Velocity profile of the feeding flow. (a) Ventral view of an individual on the coverslip with flow in the positive $x$ direction. The tracks are color coded as in Fig. 2, and the blue lines delimit the clearance zone. The particles are 4 $\mu \mathrm{m}$ in diameter and the particle positions are shown with 20-ms time intervals. To take into account that the individual slowly rotates during the video sequence, each track has been oriented to match the cell orientation when the particle reaches the mouth region or its point of closest approach. (b) Velocity profile along the transect with $x=-50$ $\mu \mathrm{m}$. The particle velocities are shown as dots, and the stepwise averaged velocity profile is left-right symmetrized and made with 10-$\mu \mathrm{m}$ steps.

Figure 4

Point force model and estimation of the flow-generating force. (a) Profile view of an individual showing the assumed posture when sitting on a flat surface. The red arrow indicates the point force position and direction and the green line indicates the focal plane. (b) Model streamlines (blue) in the $xz$ plane with $h=30$ $\mu \mathrm{m}$. (c) and (d) Flow velocity components along the transect at $x=-50$ $\mu \mathrm{m}$. The selected tracer particles are in the focal plane when $x=-20$ $\mu \mathrm{m}$, and using model streamlines in the $xz$ plane, we estimate that they are at $z=30$ $\mu \mathrm{m}$ when $x=-50$ $\mu \mathrm{m}$. Measurements (red dots) and least-squares fit (blue lines) with the force magnitude as the only free parameter.

Figure 5

Visualization of the membranelle flow. Tracer particles are transported along the inner side of the membranelle band to the mouth region (green) or outwards through the membranelle band (red). The particles are 2 $\mu \mathrm{m}$ in diameter and the particle positions are shown with 2-ms time intervals. The particle tracks are shown relative to a coordinate system with the origin positioned in the mouth region and the $x$ axis oriented in the main flow direction along the membranelle band.

Figure 6

Velocity components in the membranelle flow. (a) Simple model of membranelle flow and particle retention. Particles with a diameter smaller than the distance between neighboring membranelles can pass outwards between the membranelles, whereas large particles are retained and transported along the inner side of the membranelle band to the mouth region. (b) and (c) Velocity components in the flow based on particle tracks (green and red) and model results (blue) based on Eqs. (3) and (4). The tracer particles are all 2 $\mu \mathrm{m}$ in diameter. Some of the particles pass through the membranelle band, whereas others are retained and transported to the mouth region.

Figure 7

Metachronal motion in the membranelle band for ten beat cycles. (a) Membranelle tip positions superimposed on a still image from the video. (b) The $x$ components of the outermost tip positions as functions of time. (c) The $x$ components of the innermost tip positions as functions of time. The membranelles are colored using a sequence of seven different colors, since the phase of the beat motion is repeated after approximately seven membranelle gaps. The inner membranelle positions correspond to the outer membranelle positions with identical color coding closest to the mouth region, and the data set has gaps since the cilia could only be identified during the power strokes. The metachronal wave velocity along the membranelle band and the phase difference between the inner- and outermost cilia of the individual membranelles are described by the two blue theory lines. (See Fig. 11 for details.)

Figure 8

Phase difference across an individual membranelle. (a)–(c) Innermost (blue) and outermost (dark red) tip positions during the power stroke, and three snapshots of the tips when the innermost cilia start the power stroke (green), the innermost cilia finish and the outermost cilia start (yellow), and the outermost cilia finish (red). The arrows indicate the direction of motion in the power stroke. (d) and (e) The $x$ and $y$ components of the innermost (blue) and the outermost (dark red) tip positions as functions of time. The snapshots in panels (a)–(c) correspond to the solid lines, and the beat period is indicated by the dashed lines in panels (d) and (e).

Figure 9

Time series of two neighboring membranelles through one beat cycle. A tracer particle is moved by the two membranelles outwards through the membranelle band during the beat cycle. The particle is 1 $\mu \mathrm{m}$ in diameter and marked by a red dot, and the membranelles are highlighted in orange and blue. The arrows indicate the directions of motion of the inner- and outermost cilia, and they are shown in the frames in which the cilia start the power and the return stroke, respectively. The beat period is $T=42$ ms, and the time instant of each frame is shown in its lower right corner.

Figure 10

Geometry of membranelle band model. The cilia in the membranelles (red) are assumed to move periodically with the power stroke (green arrows) in the $x$ direction, and the water flow (blue arrows) goes along the membranelle band towards the mouth region on the inner side and outwards through the membranelle band in between the membranelles.

Figure 11

Model of the metachronal motion in the membranelle band. (a) The outermost and (b) innermost ciliary beat positions as functions of time with the parameter values $T=42$ ms, $\alpha =1/3$, $\beta =0.7$, $N=7$, $d=2.3$ $\mu \mathrm{m}$, and $W=12$ $\mu \mathrm{m}$. The blue lines are based on Eq. (11) and the observed phase difference between the inner- and outermost cilia of the individual membranelles. The slope of the blue lines, $dx/dt=-0.4$ mm ${\mathrm{s}}^{-1}$, models the metachronal wave velocity along the membranelle band. See Fig. 7 for comparison of the theoretical lines and the observed membranelle motion.

Figure 12

Time series of two neighboring membranelles and a tracer particle through one beat cycle in the experiment (gray images) and the model with the parameter values $T=42$ ms, $\alpha =1/3$, $\beta =0.7$, $N=7$, $d=2.3$ $\mu \mathrm{m}$, and $W=12$ $\mu \mathrm{m}$. The particle is 1 $\mu \mathrm{m}$ in diameter and marked by a red dot, and the membranelles are highlighted in orange and blue. The phase shift is chosen so that the rightmost membranelle (blue) starts the power stroke on the inner side when $t=0$.