Mechanisms and fluid dynamics of foraging in heterotrophic nanoflagellates

Heterotrophic nanoflagellates are the main consumers of bacteria and picophytoplankton in the ocean. In their micro-scale world, viscosity impedes predator-prey contact, and the mechanisms that allow flagellates to daily clear a volume of water for prey corresponding to 106 times their own volume is unclear. It is also unclear what limits observed maximum ingestion rates of about 104 bacterial prey per day. We used high-speed video-microscopy to describe feeding flows, flagellum kinematics, and prey searching, capture, and handling in four species with different foraging strategies. In three species, prey-handling times limit ingestion rates and account well for their reported maximum values. Similarly, observed feeding flows match reported clearance rates. Simple point-force models allowed us to estimate the forces required to generate the feeding flows, between 4-13 pN, and consistent with the force produced by the hairy (hispid) flagellum, as estimated using resistive force theory. Hispid flagella can produce a force that is much higher than the force produced by a naked flagellum with similar kinematics, and the hairy flagellum is therefore key to foraging in most nanoflagellates. Our findings provide a mechanistic underpinning of observed functional responses of prey ingestion rates in nanoflagellates.


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Heterotrophic nanoflagellates play a key role in microbial food webs in the oceans by feeding on phytoplankton and 29 bacteria and by transferring primary production to higher trophic levels when. Their top-down control shapes the 30 structure and function of microbial communities and mediate essential biogeochemical cycles in the sea [1][2][3][4].

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Despite their importance, the mechanisms of prey capture and the processes limiting their ingestion rates are not 32 fully understood [5,6].

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Flagellates live in a low Reynolds number world where viscosity impedes predator-prey contact [7]. Yet, 34 nanoflagellates are capable of daily clearing a volume of water for prey that corresponds to about one million times 35 their cell volume [8,9]. In the nutritionally dilute ocean, this is the clearance rate needed to sustain a viable 36 population in the face of predation mortality [10]. How the flagellates overcome the impeding effect of viscosity is 37 unclear for many forms.

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Most flagellates use their flagella to swim, to generate feeding currents, and to capture prey. Many studies have 39 examined the fluid dynamics of flagellates from the perspective of swimming, but few have done so from the 40 perspective of food acquisition [11][12][13][14][15][16], even though feeding is likely a more fundamental component of the fitness 41 than propulsion per se. In a few cases, the flagellum forces have been estimated indirectly from swimming speeds   with separate power and recovery phases to create a slightly erratic feeding current parallel to the attachment 142 surface (Fig. 4a). As previously observed [25], prey particles are intercepted by the cell, not the flagellum (Fig. 4b).
143 Upon prey contact on the sensitive frontal side of the predator, the anterior flagellum stops beating and rapidly arches fully extended against the prey. Thus, food is physically retained between the flagellum and the cell, close to 145 where phagocytosis takes place (Fig. 4c). If the prey establishes first contact elsewhere on the cell, the flagellum 146 continues beating while the food is transported along the cell surface, upstream towards the frontal area. When the 147 prey gets near the ingestion site, the flagellum stops beating to capture the prey and initiate phagocytosis (Fig. 4d).

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The anterior flagellum resumes its initial beating behavior while or after the prey is phagocytized (Fig. 4e). The 149 flagellate can reject captured prey by returning the flagellum to its original position and releasing the food (Fig. 4f 150 and 4g). Handling times for C. roenbergensis are shorter for rejected than for ingested prey (Fig. 3), and durations 151 were uncorrelated with the prey size ( Supplementary Fig. S1). anterior flagellum resembling a lasso loop (Fig. 5a). The flagellum beats (36 ± 10 Hz) and creates a feeding flow 161 through the loop as briefly described previously [19]. The flow direction can vary from parallel to perpendicular to 162 the surface; and distance between loop and cell (5.7 ± 2.8 µm) is variable during the searching mode. Food particles 163 are intercepted by the anterior flagellum (Fig. 5b). Prey contact triggers an increase in beating frequency (63 ± 15 164 Hz) at a reduced wave amplitude, and a shorter helical pitch. The prey is retained between the cell and the flagellum 165 and transported towards the body (Fig. 5c), either for ingestion ( Fig. 5d-e) or rejection. Pseudobodo sp. has two ways 166 to actively reject a particle: 1) the quick release and 2) the lash rejection. While the particle is captured between the flagellum and the body, it can be quickly released by reducing the beating frequency and returning the flagellum to 168 its original position (Fig. 5f). Then, the feeding flow is rapidly restored (Fig. 5g). In the lash rejection, the flagellum 169 stops beating for an instant before starting to 'uncoil' from base to end, sometimes finalizing fully extended and 170 straight (Fig. 5h). Then it slowly starts beating (6 ± 3 Hz) with a higher wavelength and amplitude (2.2 ± 0.4 µm). In 171 this rejection mode the prey is physically pushed away by the flagellate after being captured. Once the prey is 172 released, the flagellum slowly coils back and recovers the initial 'loop' beating pattern (Fig. 5i). Pseudobodo sp.
173 rejected particles with diameter smaller than 3 µm with a quick release or a lash rejection, in contrast to particles 174 with diameter larger than 5 µm that were only discriminated with the later strategy ( Supplementary Fig. S1). The  (3) were 3.7 -12.5 pN, with flows perpendicular to the surface (P. danica and P. foraminifera) requiring a 202 slightly stronger force than the cases of parallel feeding currents (Pseudobodo sp. and C. roenbergensis) (Tab. 1).

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The forces required to drive the observed flow can be compared with estimates of the force generated by the 204 flagellum. Pteridomonas danica beats its flagellum in a plane with a roughly sinusoidal beat pattern, allowing us to 205 apply the resistive force theory expression in equation (5) to directly estimate the force produced by the flagellum.

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We have our observed parameters = 11.5 m, and 2 = 2.9 m, and we find = 15 pN using the force coefficients in equation (7) for the flagellum with hairs. Similar estimates 210 are not possible for the other species that have three-dimensional beat patterns.  I  II  I  II  I  II  I

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In the species examined here, prey encounter is facilitated by the generation of a feeding current produced by the 267 activity of one hairy flagellum that propels water towards the cell. We identified three different modes of prey

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Particle tracking allowed us to characterize the flow field generated by the feeding flagellates, to identify the 283 extension of the prey capture zone, and to estimate maximum clearance rates. Our estimates of cell-volume specific 284 maximum clearance rates varied between both individuals and species, between 10 6 -10 7 d -1 . This magnitude is again 285 similar to that obtained in incubation experiments, where estimates vary between species and range between 10 5 -286 10 7 d -1 (reviewed in [8,9]

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Particle tracking and clearance rates 371 Flow fields were mapped by particle tracking. A particle was followed from a minimum distance of one cell length 372 from the body, until it was either captured or it had gone well past the flagellate. We recorded 11 -15 tracks per 373 individual, studying two individuals per species. Most flagellates slightly shift their orientation while foraging 374 (Supplementary Tab. S3), and the particle tracks are therefore shown relative to the observed flagellum coordinates.

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An imaginary, circular filtering area (clearance disc) for prey capture was assumed in front of the cell and perpendicular to the feeding flow. The size of the disc was defined by the tracks of particles that were captured or 377 strongly interacted with the flagellate. A five-point, centered finite difference scheme was applied to the measured 378 particle positions to minimize noise and discretization errors when calculating the particle velocities. The average 379 velocity component perpendicular to the clearance disc was used to calculate the clearance rate.

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Model of the feeding flow

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To describe the flow fields and estimate the flow-generating forces from the observed feeding currents we use a 382 point force model [12,[27][28][29]. The low-Reynolds-number model describes the flow due to a point force above a 383 plane no-slip surface. We examined two situations in which the force direction is either perpendicular (P. danica, P. ( 1 where denotes the viscosity, the radial distance from the axis of symmetry, and the height above the surface 391 [30,31]. Using the stream function, we can derive the clearance rate, , through a circular clearance disc centered 392 on the axis of symmetry and oriented perpendicular to it: 393 394 = 2 4 ( 1 √ 2 + ( − ℎ) 2 − 1 √ 2 + ( + ℎ) 2 − 2 ℎ ( 2 + ( + ℎ) 2 ) 3/2 ) , where denotes the radius of the clearance disc and its height above the surface [29]. The equation allows us to 397 estimate the magnitude of the point force, , using our clearance rate estimate obtained with particle tracking. In 398 the parallel case, the flow does not have rotational symmetry and a Stokes stream function does not exist. We 399 therefore integrate the velocity field numerically to obtain streamlines [28,29]. To estimate the clearance rate 400 through a circular clearance disc that is perpendicular to the direction of the point force and positioned the distance 401 ℎ above the surface in the symmetry plane of the flow, we assume that ≪ ℎ and approximate the effect of the 402 image system that ensures that the no-slip boundary condition is satisfied [29]. We find the approximation: 403 404 ≈ 2 4 ( 1 √ 2 + 2 − 2 (4 ℎ 2 + 2 ) 3/2 − 12 ℎ 4 (4 ℎ 2 + 2 ) 5/2 ) ,    substrate to the attached cell. Flagellum features correspond to flagella creating a feeding current, i.e. not 565 interacting with prey. The flagellum amplitude was measured from peak-to-peak of the wave (note that for 566 Pseudobodo sp. it is the length of the 2D projection from the 3D beating wave to disc) from the species individual. As a method validation, the flow rate through more than one clearance disc per 585 individual was estimated and compared. Variations within each species (Paraphysomonas foraminifera,