Edited by M. A. R. Koehl, University of California, Berkeley, CA, and approved July 10, 2017 (received for review June 7, 2017)
Microbes compose the majority of life in aquatic ecosystems and are crucial to the transfer of energy to higher trophic levels and to global biogeochemical cycles. They have evolved different foraging mechanisms of which our understanding is poor. Here, we demonstrate for filter-feeding choanoflagellates—the closest relatives to multicellular life—how the observed feeding flow is inconsistent with hydrodynamic theory based on the current understanding of the morphology. Instead, we argue for the widespread presence of flagellar vanes and suggest an alternative pumping mechanism. We also demonstrate a trade-off in filter spacing that allows us to predict choanoflagellate prey sizes. These mechanistic insights are important to correctly understand and model microbial heterotrophs in marine food webs.
Microbial filter feeders are an important group of grazers, significant to the microbial loop, aquatic food webs, and biogeochemical cycling. Our understanding of microbial filter feeding is poor, and, importantly, it is unknown what force microbial filter feeders must generate to process adequate amounts of water. Also, the trade-off in the filter spacing remains unexplored, despite its simple formulation: A filter too coarse will allow suitably sized prey to pass unintercepted, whereas a filter too fine will cause strong flow resistance. We quantify the feeding flow of the filter-feeding choanoflagellate Diaphanoeca grandis using particle tracking, and demonstrate that the current understanding of microbial filter feeding is inconsistent with computational fluid dynamics (CFD) and analytical estimates. Both approaches underestimate observed filtration rates by more than an order of magnitude; the beating flagellum is simply unable to draw enough water through the fine filter. We find similar discrepancies for other choanoflagellate species, highlighting an apparent paradox. Our observations motivate us to suggest a radically different filtration mechanism that requires a flagellar vane (sheet), something notoriously difficult to visualize but sporadically observed in the related choanocytes (sponges). A CFD model with a flagellar vane correctly predicts the filtration rate of D. grandis, and using a simple model we can account for the filtration rates of other microbial filter feeders. We finally predict how optimum filter mesh size increases with cell size in microbial filter feeders, a prediction that accords very well with observations. We expect our results to be of significance for small-scale biophysics and trait-based ecological modeling.
Heterotrophic microorganisms in the oceans inhabit a dilute environment and they need efficient feeding mechanisms to acquire enough food to sustain growth (1, 2). At the microscale the Reynolds number is low and viscous forces govern hydrodynamical interactions. This implies extensive, long-range flow disturbances around moving particles and microswimmers, impeding cell–cell contact and prey capture (3, 4). However, to encounter enough food, purely heterotrophic plankton that rely solely on prey capture typically need to clear a volume of water for prey corresponding to 1 million times their own body volume per day (4). Thus, heterotrophic microbes face a difficult challenge, and the prevailing viscous forces must strongly influence prey capture and shape the various feeding modes through evolution.
Many unicellular flagellates as well as colonial sponges and metazoans, e.g., tunicates, use filter feeding to catch bacteria-sized prey (1, 5⇓–7). They establish a feeding current, from which prey particles are sieved using filter structures. Such filter feeders benefit from having filters with small mesh size that allow the organisms to capture small prey (5, 8). However, filter spacing involves a trade-off: The finer the mesh size is, the higher the availability of food but the lower the clearance rate due to a dramatic decrease in filter permeability (9). An optimum mesh size must therefore exist. While microbial filter feeding has been studied regarding the pressure drop across the filter and the observed clearance rates (5), clearance rates have never been related to the force production of the flagellum that drives the feeding current. Can a beating flagellum even produce sufficient force to account for the observed clearance rates through such fine filters?
Choanoflagellates are the prime example of unicellular filter feeders (1, 10, 11). They are equipped with a single flagellum that is surrounded by a funnel-shaped collar filter made up of microvilli extending from the cell. Some species are sessile and attach with a stalk to solid surfaces whereas others are freely swimming and have a basket-like structure (lorica) that surrounds cell, flagellum, and filter (Fig. 1). The beating flagellum creates a feeding current that transports bacteria-sized prey to the outside of the collar filter from where the prey are transported to the cell surface and phagocytosed (10, 12⇓⇓⇓–16). Far-field flows created by choanoflagellates have recently been measured and modeled for the sessile choanoflagellate Salpingoeca rosetta (14). However, the essential near-cell feeding flow in choanoflagellates is poorly understood and has not been resolved quantitatively in experiments (10, 11).
Morphology of D. grandis. (A) Microscopic image of freely swimming choanoflagellate. (B) Model morphology with cell (orange), collar filter (green surface and black lines), flagellum (blue), and lorica (red). The ribs (costae) in the lower (posterior) part of the lorica are indicated, whereas for clarity the ribs in the finely netted, upper (anterior) part of the lorica are not shown.
As a model organism of microbial filter feeders, we focus on the choanoflagellate Diaphanoeca grandis that swims freely and carries a lorica (Fig. 1). The lower part of the lorica has large openings, whereas the upper part is covered by a fine web with small pore sizes (13). The collar filter therefore supposedly functions as an internal filter, and prey particles should not circumvent the filter once inside the lorica.
Using D. grandis, we here ask: What are the mechanisms of particle capture in choanoflagellates, and what is the optimum filter spacing? We use high-speed videography and particle tracking to quantify the feeding flow. For comparison, we use computational fluid dynamic (CFD) simulations and simple estimates of the filter resistance and the force production due to the beating flagellum. Our analysis shows that modeling the beating flagellum as a simple, slender structure produces a force that is an order of magnitude too small to account for the observed clearance rate. This demonstrates the strong trade-off in small-scale filter feeding and leads us to suggest an alternative flagellar pumping mechanism.
We developed a generic model morphology of D. grandis to collate particle track observations from individual cells (Model Morphology and Observed Flow, Table S1, and Fig. 1). The feeding flow is driven by the beating flagellum. The flow transports particles from the region below the choanoflagellate, in through the large openings in the lower part of the lorica and up toward the collar filter on which the particles are caught (Fig. 2 and Movie S1). The detailed visualization reveals a true filtration flow that undoubtedly passes through the filter, confirming the current understanding of filter feeding in choanoflagellates (11). However, our results are for a loricate species, and it is uncertain whether, and to what extent, nonloricate species can filter the same way, since flow could pass along the filter on the outside and circumvent the filter. From the flow field, one important function of the lorica seems to be the separation of in- and exhalent flow, reducing refiltration. The clearance rate
Observed feeding flow generated by D. grandis and velocity field from CFD model based on the standard description of morphology and flagellum. The model morphology shows the cell (orange), the collar filter (green), the flagellum (blue), and the lorica (red). (A) Representative particle tracks. The 10 different colors correspond to 10 discrete tracks and the solid circles show particle positions with 0.1-s time intervals. The particles below the choanoflagellate move randomly due to Brownian motion and display a slow net flow toward the lorica openings. (B) Average velocity field based on particle tracking. The flow velocities increase dramatically as the particles enter the lorica and approach the collar filter where the particles are eventually caught. The filtered water is expelled in a concentrated jet flow upward and out of the “chimney” of the lorica opposite to and clearly separated from the intake region. (C) The CFD velocity field in the
Average morphology parameters that describe both size
Flow velocities as function of the distance
To explore the feeding flow theoretically we numerically solve the Navier–Stokes equation and the equation of continuity for the incompressible Newtonian flow due to the beating flagellum with the known morphology (CFD Simulations and Figs. S2–S5). The collar filter consists of ∼50 evenly distributed microvilli (13), with a fairly uniform filter spacing and permeability along most of their length (Fig. 1). The finely netted upper part of the lorica has pore sizes in the range
Model geometry and computational domain. (A) The model organism consisting of cell (blue), flagellum (light gray), filter (green), upper part of lorica (red), and chimney (dark gray). The coordinate system is defined so that the flagellum is beating in the
The computational cells in the discretized computational domain with 4.8 million computational cells for a flagellum of width
Mesh size independence of the time-averaged force
Time-averaged flagellum force in the
Independence of the time-averaged force
Drag coefficients
To generalize our CFD results and roughly estimate the clearance rates of other species of choanoflagellates, we model filter resistance and flagellum force. We describe the filter locally as a row of parallel and equidistantly spaced solid cylinders, and we model the flow far from the filter as uniform and perpendicular to the filter plane. For such simple filters we can express the flow speed through the filter
Filter characteristics. (A) The drag coefficient
For other choanoflagellate species we calculate the clearance rate from the analytical estimate (Eq. 4) and compare it with observations (Table 1). In most species, the theoretical clearance rate grossly underestimates the realized, and only two species seem able to filter significant volumes of water. Of the species listed, only D. grandis and Stephanoeca diplocostata carry a lorica. The rest are nonloricate and potentially subject to filter circumvention, which we did not account for. Filter circumvention would increase the flow rate, but potentially reduce the clearance rate, since water would not actually be filtered.
Characteristic morphological and kinematic parameters for selected choanoflagellate and choanocyte species
The Supporting Information is mainly devoted to our CFD simulations, including verification, validation, results, and movies with flow animations. Additionally, we present movies of observed particle tracks and flagellar beats, details of the model morphology, and details of the analytical modeling of the filter resistance.
To collate particle tracks from the different individuals and to set up the CFD simulation geometry, we construct a generic morphology model to which all observations are scaled. We focus on six individuals that are viewed from the side with the longitudinal axis of the cell in the focal plane. To good approximation the cell surface and the outline of the lorica have rotational symmetry about the longitudinal axis, and we therefore describe them as surfaces of revolution. In spherical polar coordinates we write
To model the outline of the filter we use the interpolation
We apply the commercial CFD program STAR-CCM+ (12.02.010-R8) to numerically solve the Navier–Stokes equation and the equation of continuity for incompressible Newtonian flow using the finite-volume approach. Both the frequency parameter and the Reynolds number are much smaller than unity, and the flow is therefore a quasi-steady Stokes flow (37). We use the model morphology and a spherical computational domain with the model cell held stationary at the center (Fig. S2). With this approach we disregard the slow swimming motion and the periodic rocking motion of the cell during the flagellar beat, which we presume to have negligible effect on the feeding flow. The no-slip boundary condition is applied at the surfaces of the cell and the microvilli. The upper part of the lorica and the chimney of height
We treat the beating flagellum as a thin sheet of width
We take advantage of mesh morphing to avoid reconstructing the mesh geometry at the different flagellum positions during the flagellar beat. The morphing motion redistributes mesh vertices in response to the movement of the flagellum at each time step. Therefore, between two time steps, the mesh is morphed in response to the flagellar movement and at each time step, the discretized forms of the governing equations are solved inside the entire computational domain. We use polyhedral cells for the discretization since they allow mesh morphing and flexibility when representing the complex geometry of the model organism (Fig. S3).
We make sure that the four governing equations are satisfied with negligible error and that the flagellum force converges for each time step during the computational iteration process. To verify that the solutions for the time-averaged flagellum force and the time-averaged clearance rate do not depend on the mesh size, we discretize the computational domain with different mesh sizes. For meshes with more than 4 million computational cells we find ∼1% variation, and in the result simulations we use 4.8 million computational cells (Fig. S4). We use two different time steps to check the time-step independence, and we conclude that 24 time steps per flagellar beat period are sufficient (Table S2). To make sure that the solution is independent of the size of the computational domain, we solve the governing equations inside domains with different sizes. We find minute differences between domains with radii
To validate the computational approach we use it to numerically calculate the drag forces on a slender cylinder and a slender thin sheet in steady flow at Reynolds numbers comparable to the low Reynolds number for the flagellar motion. Our goal is both to validate the results for the slender cylinder against known analytical theory and to validate the approximation of a beating cylindrical flagellum using a thin sheet. We consider the drag force components
The main simulation results are the time-averaged flagellum forces in the
Our results reveal a paradox: The CFD model and the simple estimates underestimate the clearance rate based on the observed flow field by more than an order of magnitude. The flow-field–derived clearance rate seems robust, as it is similar to an earlier observation (13) and at the same time consistent with the general notion that heterotrophic plankton need to daily clear a volume of approximately 1 million times their own body volume (4). Instead, the theory can of course be questioned, most obviously perhaps through the notion that various types of flagellar hairs often line eukaryotic flagella and could increase the force output of the flagellum (23). However, the force estimate is only weakly influenced by the flagellum diameter (Eq. 3), as long as we neglect interaction between flagellum and filter, and simple flagellar hairs would have little influence on the clearance rate. It is thus difficult to see how the flagellum would be able to deliver the force required to account for the experimentally observed clearance rate, unless some major aspect of its morphology or function has been overlooked.
A few choanoflagellate species have been shown to have a so-called flagellar vane composed of a sheet-like structure along the length of the flagellum (17, 20, 27). Although a flagellar vane has been observed in a few choanoflagellate species, the structure remains elusive. Leadbeater (27) went so far as to call it a “mystery” because the structure is notoriously difficult to visualize using electron microscopy. While a vane cannot account for the clearance rate due to increased flagellum drag as long as interactions between flagellum and filter are neglected, this structure could still offer a satisfactory solution to the apparent paradox: With a vane, the distance between flagellum and the inside of the collar would be reduced, reducing transversal flow past the beating flagellum inside the collar. Instead, more fluid would be forced upward, and the resulting low pressure would have to be equalized by a flux through the filter. With a flagellar vane nearly as wide as the collar, or even physically attached to the inside of the collar, the pumping mechanism would be radically different. The highly similar choanocytes of aquatic sponges have been shown to have flagellar vanes that indeed are attached to the filter or span its width (20, 28, 29). The flagellum together with its vane would function as a waving wall forming two adjacent peristaltic pumps (30), one on each side of the vane, that draw in water through the filter and expel it out of the chimney of the lorica. To explore such a pumping mechanism we replace the flagellum in the CFD model with a
Model morphology with a flagellar vane, observed average velocity field for D. grandis, and velocity field from CFD model including a
To explore the vane-based pumping mechanism conjecture for other choanoflagellates we make a rough estimate of the clearance rate as the volume flow rate given by the simple model
In fact,
The main purpose of the filter is to intercept as much food as possible. The above-mentioned filter trade-off suggests that there is an optimum filter spacing that will maximize the prey encounter rate
Optimum choanoflagellate filters. (A) Encounter rate as function of dimensionless filter spacing (Eq. 8). The vertical line (blue) indicates the observed average of the dimensionless filter spacing. (B) The theoretical prediction for the optimum dimensionless filter spacing (solid line, red) and the observed dimensionless filter spacing for the choanoflagellates in Table 1 (solid circles, blue) as functions of the maximum dimensionless prey diameter. We have assumed that the maximum prey diameter is equal to (1/3) ESR. The outlier below the predicted line is C. botrytis, speculated to rely on cross-flow filtration rather than true filtration.
We have shown that a simple, naked flagellum cannot account for the clearance rates observed in many choanoflagellate species. Instead, we suggest a widespread presence of the sporadically observed flagellar vane. The proposed pumping mechanism is radically different and can explain how choanoflagellates can perform efficient small-scale filter feeding. The explored problems and our model estimates are relevant to the understanding of small-scale filtering in general, and the mechanistic insights allow quantification of the trade-offs involved in various microbial feeding modes. We have, for instance, demonstrated that microbial filter feeding is an energetically costly process that takes up much more than a few percent of the total energy budget of the cell as otherwise typically believed.
The choanoflagellate D. grandis (American Type Culture Collection no. 50111) was grown nonaxenically in the dark in B1 medium (salinity 32) at
To explore the near-cell flow field and the motion of the beating flagellum, cells were observed at high magnification, using a high-speed digital video. An Olympus IX-71 inverted microscope equipped with a UPLSAPO60XO/1.35 oil-immersion objective and a U-ECA magnifying lens provided a total of
Based on cell alignment, a total of 19 video sequences, each fielding a unique individual, were selected for use in the flow-field analysis. The frequency of the flagellar beat was noted at 1-s intervals, by manual, visual inspection of the slowed-down 100-fps video sequences. Two-dimensional particle tracks were resolved on reduced–frame-rate video sequences (10 fps), using the manual tracking plugin for ImageJ. A total of 73 tracks were used to construct the velocity field. Each particle track was associated with the frequency of the flagellar beat at the corresponding time. All particle tracks were collated using the average model morphology, and the velocity field in the
For the drag force per unit length
We thank Jasmine Mah for providing videos of M. brevicollis and Øjvind Moestrup and Helge Abildhauge Thomsen for helpful discussions. The Centre for Ocean Life is a Villum Kann Rasmussen Centre of Excellence supported by the Villum Foundation, and S.S.A. and J.H.W. were supported by a research grant (9278) from the Villum Foundation.
Author contributions: L.T.N., T.K., and A.A. designed research; L.T.N. performed experiments; L.T.N. and A.A. analyzed data; S.S.A. and J.H.W. conducted CFD simulations; J.D. and A.A. developed and applied theory; and L.T.N., T.K., and A.A. wrote the paper with comments from S.S.A., J.D., and J.H.W.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1708873114/-/DCSupplemental.
