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We ecological be trait-based observations. a to with feeders, results well filter microbial our very in accords of size that cell rates with prediction filtration fil- increases optimum the size how for mesh predict finally ter account We feeders. can filter we microbial flag- other model of a rate simple with filtration a model the using CFD predicts correctly A vane (sponges). observed ellar choanocytes sporadically some- related but (sheet), the visualize vane in to flagellar difficult fil- a notoriously different requires thing radically that a suggest mechanism for to tration discrepancies us motivate similar observations find paradox. Our enough apparent We an draw highlighting filter. species, to choanoflagellate fine other unable the simply mag- through is of water flagellum order an beating than the more nitude; by rates under- filtration approaches fluid observed Both computational estimate estimates. analytical with and inconsistent (CFD) of is dynamics understanding current feeding the filter that microbial demonstrate and will tracking, fine the suitably cle of too flow allow feeding filter choanoflagellate the will a filter-feeding quantify We whereas coarse resistance. flow unintercepted, too strong despite pass cause filter unexplored, to prey A remains sized spacing formulation: Also, filter water. simple the of its amounts in adequate feed- trade-off process filter the to microbial force generate what must poor, unknown ers is is feeding it filter biogeochem- importantly, microbial and and, of webs, understanding food Our 2017) 7, aquatic cycling. signif- June loop, ical grazers, review microbial for of the (received group 2017 to important 10, icant an July are approved and feeders CA, filter Berkeley, Microbial California, of University Koehl, R. A. M. by Edited Z CH-8092 Zentrum, www.pnas.org/cgi/doi/10.1073/pnas.1708873114 and Denmark; Lyngby, Kongens Denmark; Lyngby, DK-2800 Kongens Denmark, DK-2800 of Denmark, University of University Technical Engineering, Mechanical a Nielsen Tor feeding Lasse filter microbial of Hydrodynamics ainlIsiueo qai eore n etefrOenLf,TcnclUiest fDnak K20 ogn ygy Denmark; Lyngby, Kongens DK-2800 Denmark, of University Technical Life, Ocean for Centre and Resources Aquatic of Institute National ayuiellrflglae swl sclna pne and sponges colonial as well as flagellates unicellular Many niomn n hyne fcetfeigmcaim to mechanisms feeding dilute efficient a need they inhabit and oceans environment the in microorganisms eterotrophic | choanoflagellates rc,Switzerland urich, ¨ a,1 ee ae Asadzadeh Saeed Seyed , | le feeding filter ipaoc grandis Diaphanoeca | microswimmers b and grandis, D. ui D Julia , sn parti- using d | ws eea nttt fTcnlg Z Technology of Institute Federal Swiss olger ¨ c esH Walther H. Jens , h choanoflagellate the quantita- resolved 11). been (10, experiments not in has tively and understood poorly choanoflag- in is flow ellates feeding near-cell essential the choanoflagellate However, sessile (14). trans- the measured are for been modeled recently prey and have the choanoflagellates Far-field by where 12–16). (10, created from phagocytosed flows and filter surface to cell collar the prey to the ported bacteria-sized of transports sur- flagellum outside that beating that the current The 1). (lorica) feeding freely (Fig. a are structure filter creates others and basket-like flagellum, whereas a cell, surfaces rounds have solid and to and sessile of stalk are swimming up species a made flagellum Some with filter cell. single attach collar the a funnel-shaped from with a extending equipped microvilli by are surrounded They is 11). that 10, (1, feeders such through rates clearance observed filters? the the fine for sufficient drives account produce that even to flagellum flagellum force beating the a of Can current. production feeding force the to related l rcigt uniytefeigflw o oprsn euse we comparison, For opti- parti- flow. and the feeding videography the is quantify high-speed to what use tracking cle and We spacing? choanoflagellates, filter in mum capture particle of circum- not lorica. should the particles inside prey once filter and the with filter, vent large web func- internal supposedly has fine an therefore a as lorica filter collar tions by the The covered (13). of is sizes part pore part small lower upper The the 1). whereas openings, (Fig. lorica a carries 1073/pnas.1708873114/-/DCSupplemental at online information supporting contains article This Submission. 1 Direct PNAS a is article This interest. of conflict with no paper declare the authors wrote The A.A. J.H.W. and and J.D. T.K., J.D., L.T.N., simulations; S.S.A., and CFD from theory; conducted comments applied J.H.W. and and developed S.S.A. A.A. data; and analyzed A.A. and L.T.N. ments; uhrcnrbtos ... .. n ..dsge eerh ...promdexperi- performed L.T.N. research; designed A.A. and T.K., L.T.N., contributions: Author owo orsodnesol eadesd mi:[email protected]. Email: addressed. be should correspondence whom To nsi nihsaeipratt orcl nesadand understand webs. correctly food marine to in heterotrophs important microbial mech- model are that These spacing sizes. insights prey filter choanoflagellate anistic in predict trade-off to mecha- a us pumping allows demonstrate alternative of also an presence We suggest widespread nism. and the vanes for mor-flagellar argue the we of understanding Instead, current phology. hydrody- the on with based inconsistent filter-feeding theory is namic flow for feeding observed demonstrate life— the multicellular how we to higher relatives Here, under- closest to choanoflagellates—the poor. our energy which is of of standing mechanisms have ecosys- transfer They foraging cycles. aquatic different the biogeochemical evolved global in to to and life crucial levels trophic are of and majority tems the compose Microbes Significance samdlogns fmcoilfitrfees efcson focus we feeders, filter microbial of organism model a As filter unicellular of example prime the are Choanoflagellates Using ehr s:Wa r h mechanisms the are What ask: here we grandis, D. c PNAS eateto hsc n etefrOenLf,Technical Life, Ocean for Centre and Physics of Department b,d hmsKiørboe Thomas , | uut2,2017 29, August ipaoc grandis Diaphanoeca rc,Caro opttoa cec,ETH Science, Computational of Chair urich, ¨ . | a o.114 vol. www.pnas.org/lookup/suppl/doi:10. n nesAndersen Anders and , htsisfel and freely swims that | apnoc rosetta Salpingoeca o 35 no. b eatetof Department | 9373–9378 c

APPLIED PHYSICAL ECOLOGY SCIENCES ties in the annular region do not depend on the distance from the ABlongitudinal axis (Fig. S1A). To determine the clearance rate we −1 therefore use the average value vz = 7.3 ± 4.4 µm·s (mean ± SD) times the area of the annular region. We find Q = (1.22 ± 0.72) · 103 µm3·s−1, or 1.20 million cell volumes per day, where 3 the cell volume VC = 88 µm . The corresponding flagellar beat frequency is f = 7.3 ± 2.6 Hz (Fig. S1B).

Computational Fluid Dynamics and Theoretical Clearance. To ex- plore 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 0.05−0.5 µm (13), and for simplicity we treat it as an impermeable, rigid surface and neglect the ribs in the lower part of the lorica. D. grandis carries a standard eukary- Fig. 1. Morphology of D. grandis. (A) Microscopic image of freely swim- otic flagellum with diameter b = 0.3 µm (23), and high-speed ming choanoflagellate. (B) Model morphology with cell (orange), collar fil- videography showed that the flagellum beats, like most other ter (green surface and black lines), flagellum (blue), and lorica (red). The ribs eukaryotic flagella, in a single plane (Movie S2). For computa- (costae) in the lower (posterior) part of the lorica are indicated, whereas for tional simplicity we model the flagellum as a thin sheet of width b clarity the ribs in the finely netted, upper (anterior) part of the lorica are that is oriented perpendicular to the plane of beating and moving not shown. with a simple traveling wave motion in the positive z direction. Based on our validation of the CFD simulations, we estimate that this approach underestimates the flagellar forces by ∼20% computational fluid dynamic (CFD) simulations and simple esti- (Tables S2 and S3). The time-averaged CFD flow is an order mates of the filter resistance and the force production due to the of magnitude weaker than the flow observed experimentally for beating flagellum. Our analysis shows that modeling the beat- D. grandis (Fig. 2). The model leads to the time-averaged flag- ing flagellum as a simple, slender structure produces a force that ellum force in the z-direction F0.3 = 1.1 pN, the time-averaged is an order of magnitude too small to account for the observed 3 −1 power P0.3 = 0.31 fW, and the clearance rate Q0.3 = 95 µm ·s , clearance rate. This demonstrates the strong trade-off in small- which is ∼13 times lower than the clearance rate based on the scale filter feeding and leads us to suggest an alternative flagellar observed flow field. pumping mechanism. To generalize our CFD results and roughly estimate the clear- Results ance rates of other species of choanoflagellates, we model filter resistance and flagellum force. We describe the filter locally as a Observed Feeding Flow and Clearance Rate. We developed a row of parallel and equidistantly spaced solid cylinders, and we generic model morphology of D. grandis to collate particle model the flow far from the filter as uniform and perpendicular track observations from individual cells (Model Morphology and to the filter plane. For such simple filters we can express the flow Observed Flow, Table S1, and Fig. 1). The feeding flow is driven speed through the filter by the beating flagellum. The flow transports particles from the a region below the choanoflagellate, in through the large openings v = κ ∆p, [2] in the lower part of the lorica and up toward the collar filter µ on which the particles are caught (Fig. 2 and Movie S1). The where ∆p is the pressure drop across the filter, κ the dimension- detailed visualization reveals a true filtration flow that undoubt- less permeability of the filter, and µ the dynamic viscosity. The edly passes through the filter, confirming the current under- dimensionless permeability κ is a function only of the dimen- standing of filter feeding in choanoflagellates (11). However, our sionless filter spacing l/a. We model κ by combining previous results are for a loricate species, and it is uncertain whether, and theoretical work on closely and distantly spaced filter structures, to what extent, nonloricate species can filter the same way, since respectively (24, 25). The dimensionless permeability κ increases flow could pass along the filter on the outside and circumvent strongly with l/a and contributes to the filter spacing trade-off as the filter. From the flow field, one important function of the lor- discussed above (Fig. S6). For the model morphology we find the ica seems to be the separation of in- and exhalent flow, reducing average dimensionless permeability hκi = 0.41. With a flagellum refiltration. The clearance rate Q can be expressed as the volume of length L and diameter b we can estimate the flagellum force flow rate through the filter

Z FT = CF µLU = 4CF µLAf , [3] Q = v dA, [1] AF −3 where CF is the drag coefficient, µ = 1.0 · 10 Pa·s the viscos- where AF is the surface area of the filter and v is the normal ity, and A the amplitude of the flagellar beat. The average speed component of the flow velocity. The observed velocity field shows of the flagellum is estimated as U = 4Af . For simplicity we take that the water that passes the filter first passes the equator (z = 0) CF to be the drag coefficient of a slender spheroid that is moving in the annular region between the cell and the finely netted part sideways, CF = 4π/(ln(2L/b)+1/2) (26). The estimate neglects of the lorica. We determine the clearance rate as the volume flow the presence of filter and lorica structures surrounding the rate upward across the annular region in the equator plane. This flagellum and assumes that all (primarily transversal) drag on the procedure is more precise than directly using the flow through the flagellum is converted into longitudinal flow. The corresponding 2 2 filter. No-slip boundary conditions would suggest reduced flow power estimate is PT = FT U = 16CF µLA f . To estimate the velocities near the cell and lorica. At the spatial resolution of theoretical clearance rate we assume that the pressure drop is our experiment, however, the z components of the flow veloci- ∆p = F /AF and we obtain

9374 | www.pnas.org/cgi/doi/10.1073/pnas.1708873114 Nielsen et al. Downloaded by guest on September 23, 2021 Downloaded by guest on September 23, 2021 pnil lacustris Spongilla ∗∗ k # ¶ § cells. sessile ‡ † ∗ similar. or Eq. experiments on incubation based rate clearance of radius; microvillum species choanocyte and choanoflagellate selected for parameters kinematic and Species morphological Characteristic 1. Table tpaoc diplocostata Stephanoeca amphoridium Salpingoeca sp. Monosiga ovata Monosiga brevicollis Monosiga grandis Diaphanoeca grandis Diaphanoeca gracilis Codosiga botrytis Codosiga ile tal. et Nielsen cir- filter to subject potentially and nonloricate species the are Of rest water. The of species volumes two significant only only listed, filter and to realized, able the seem underestimates clearance grossly theoretical the rate species, (Eq. most In estimate 1). (Table analytical observations the from rate results. CFD the rate clearance F For i.2. Fig. h F oe ae ntesadr ecito fmrhlg n aelmpeit edn o hti oeta nodro antd weaker magnitude of order an than more is that rate. flow clearance feeding observed a the (C predicts for region. filtered account flagellum intake cannot The and the it from caught. morphology and separated of eventually flow, clearly description are observed and The standard to experimentally particles opposite tracking. the the the lorica particle than on where the on based of filter based “chimney” model collar field the CFD the of velocity The the out Average approach and in (B) and upward field openings. lorica flow velocity lorica jet the 10 CFD the concentrated enter The a toward choanoflagellate tracks. in particles the flow expelled particle below the net particles is Representative slow as The water (A) intervals. a dramatically (red). time display increase 0.1-s lorica and with the velocities positions motion and particle flow Brownian (blue), show to circles flagellum solid due the the randomly (green), and move tracks filter discrete collar 10 the to correspond (orange), colors cell different the shows morphology model The siae rmrf 10. ref. from Estimated on Data 18. ref. from Estimated siae rmrf 21. ref. from Estimated Sessile. oiae reyswimming. freely Loricate, esrduigoiia iesknl rvddb a ta.(20). al. et Mah by provided kindly videos original using Measured T Choanocyte. S,euvln peia aiso cell; of radius spherical equivalent ESR, o te haoaelt pce ecluaeteclearance the calculate we species choanoflagellate other For 2 = .grandis D. . bevdfeigflwgnrtdby generated flow feeding Observed 5 Q ± eeuaalbe n instead and unavailable, were A .grandis D. 0.9 ∗ ∗ Q ∗ Q ∗ N h power the pN, ∗∗ l itnebtencneso egbrn microvilli; neighboring of centers between distance , T T h siaepeit h aelmforce flagellum the predicts estimate the ∗ 75 = ¶ ¶ = xz and hκi ln stm vrgdoe h aelrba yl,adtevlct etr isd”fitradcinyaeoitdfrclarity. for omitted are chimney and filter “inside” vectors velocity the and cycle, beat flagellar the over averaged time is plane ¶ ∗ ± tpaoc diplocostata Stephanoeca µ a ESR, 26 4; F 2.00 .01. . . . .7 .4807 ,1 ,2 hsstudy This (13) 1,220 4,400 1,410 35 3,200 75 2.5 0.50 65 0.100 8.0 2.0 6.0 0.54 10.0 3.0 8.0 0.075 1.0 8.3 17.0 0.40 2.0 8.6 32.5 0.075 20.7 14.4 5.5 1.80 10.0 2.8 6.0 2.30 7.3 4.0 1.63 1.5 10.0 1.26 11.7 10.0 6.4 11.0 8.3 30.0 2.80 2.50 29.0 1.84 3.75 2.00 Q T µm µm V 4hκiC = laac aeetmt ae ntepeec favn codn oEq. to according vane a of presence the on based estimate rate clearance , # k P 3 ·s T −1 L Q 0 = 13.8 041. 1.5 11.0 10.4 , aelmlength; flagellum L, µm a siae s1mlincl oue e a 4.I pce ihdfeetmrhtps aaaefrsingle, for are data morphotypes, different with species In (4). day per volumes cell million 1 as estimated was .grandis D. nruhareetwith agreement rough in .20 n opr twith it compare and 4) F # aLAf ± f 00241. .5 .566476 6.6 0.45 0.055 12.2 2.4 50.0 Hz , 0.14 . n eoiyfil rmCDmdlbsdo h tnaddsrpino opooyadflagellum. and morphology of description standard the on based model CFD from field velocity and A, ar lorica. a carry W n the and fW, µm § § § † k k B f aelmba frequency; beat flagellum , λ, 2200001 . 2 3.1 0.18 0.060 12.2 7900007 3.8 0.70 0.050 17.9 5.5 10.3 0.54 0.075 0.25 0.088 10.3 17.5 18.5 . .7 .75.4 0.47 0.075 8.6 µm [4] W k imtro hme ratro le xas opening; exhaust filter anterior or chimney of diameter , a, .0 .84.4 0.28 0.100 µm hi w oyvlm 4.Ised h hoycno course of can theory times the million Instead, 1 (4). approximately volume of body volume time a own plankton same clear their heterotrophic the daily that at to notion and (13) need general observation the as earlier with an robust, mag- consistent to of seems similar order rate an is clearance than it more flow-field–derived by The field flow nitude. observed the rate clearance on the based underestimate estimates simple the and model Paradox. Filter-Feeder The Discussion filtered. be actually not would clearance the water reduce since potentially circumvention rate, but Filter rate, for. flow the account increase not would did we which cumvention, l , µm W , µm mltd fflgla beat; flagellar of amplitude A, § § † k § Q PNAS T , µm 1 ,7 600 3,470 716 40 2,600 34,600 42 64 | ,4 ,0 2,22) (21, 1,800 2,340 3 3 ·s u eut eelaprdx h CFD The paradox: a reveal results Our uut2,2017 29, August −1 and 5; Q C V , µm 60400 9660 9 0 (1) 600 490 3 ,0 1,19) (10, 4,400 930 19) (10, 1,000 850 2 400 620 bevdcernert from rate clearance observed Q, 3 ·s −1 | aelrwavelength; flagellar λ, o.114 vol. Q, Q T µm hoeia estimate theoretical , 3 | ·s ‡ ‡ ‡ ‡ −1 o 35 no. 1,18) (17, Source (20) (20) (10) | The ) 9375 a,

APPLIED PHYSICAL ECOLOGY SCIENCES 3 −1 be questioned, most obviously perhaps through the notion that rate Q5 = 898 µm ·s , slightly lower than the experimentally various types of flagellar hairs often line eukaryotic flagella and observed clearance rate. could increase the force output of the flagellum (23). How- To explore the vane-based pumping mechanism conjecture for ever, the force estimate is only weakly influenced by the flagel- other choanoflagellates we make a rough estimate of the clear- lum diameter (Eq. 3), as long as we neglect interaction between ance rate as the volume flow rate given by the simple model flagellum and filter, and simple flagellar hairs would have little Q = AW λ f , [5] influence on the clearance rate. It is thus difficult to see how V the flagellum would be able to deliver the force required to where W is the diameter of the chimney of the lorica and λ the account for the experimentally observed clearance rate, unless flagellar wavelength. We assume that the flagellum is moving some major aspect of its morphology or function has been in the central beat plane with amplitude A and that the flagel- overlooked. lar vane is attached to filter and chimney. The average peak-to- peak amplitude of the flagellar vane must therefore be A, and Pumping Mechanism Conjecture. A few choanoflagellate species we assume that a water volume AW λ is forced through the filter have been shown to have a so-called flagellar vane composed of a and out of the chimney per flagellar beat period. For D. grandis 3 3 −1 sheet-like structure along the length of the flagellum (17, 20, 27). we find the estimate QV = (1.41 ± 0.50) · 10 µm ·s in good Although a flagellar vane has been observed in a few choanoflag- agreement with the clearance rate based on the observed flow ellate species, the structure remains elusive. Leadbeater (27) field (Table 1). went so far as to call it a “mystery” because the structure is In fact, QV provides a solid prediction of the observed clear- notoriously difficult to visualize using electron microscopy. While ance rate Q in six of the seven species for which the naked a vane cannot account for the clearance rate due to increased flagellum clearance rate estimate QT cannot account for Q flagellum drag as long as interactions between flagellum and (Table 1). Thus, two species seem to use a simple flagellum to filter are neglected, this structure could still offer a satisfac- drive the feeding current, whereas six choanoflagellate species tory solution to the apparent paradox: With a vane, the dis- and the choanocyte rely on a flagellar vane. A narrow vane has tance between flagellum and the inside of the collar would be been observed in Monosiga brevicollis, but a vane this small would reduced, reducing transversal flow past the beating flagellum have only limited influence on the clearance rate (Fig. S5), and inside the collar. Instead, more fluid would be forced upward, the apparent discrepancy is certainly within estimate uncertain- and the resulting low pressure would have to be equalized by a ties. Only for Codosiga botrytis does neither of the two models flux through the filter. With a flagellar vane nearly as wide as adequately predict Q. This species has a long and rapidly beat- the collar, or even physically attached to the inside of the col- ing flagellum that extends far beyond the collar and also the finest lar, the pumping mechanism would be radically different. The of the choanoflagellate filters. Combined, this suggests that this highly similar choanocytes of aquatic sponges have been shown species may not perform actual filter feeding, but instead relies to have flagellar vanes that indeed are attached to the filter on cross-flow filtration in which the flow passes along and not or span its width (20, 28, 29). The flagellum together with its through the filter. The suggested pumping mechanism would also vane would function as a waving wall forming two adjacent peri- provide a means to avoid unwanted filter circumvention in lori- staltic pumps (30), one on each side of the vane, that draw cate as well as nonloricate species. If the vane spans most of the in water through the filter and expel it out of the chimney of collar width, a flagellum wavelength “traps” a package of water the lorica. To explore such a pumping mechanism we replace that has to be expelled with the flagellar beat. Furthermore, typ- the flagellum in the CFD model with a b = 5-µm-wide sheet ical flagellar beat frequencies of eukaryotic organisms are in the that spans almost the entire width of the filter (Movies S3– range 30–70 Hz (1, 18), and the low beat frequencies found in S5). The time-averaged CFD flow agrees well with the flow D. grandis and a number of other choanoflagellate species stand observed for D. grandis (Fig. 3). The model leads to the time- out (Table 1). We speculate that the low beat frequencies are the averaged flagellum force in the z-direction F5 = 12.1 pN, result of extensive flagellar vanes and their high force require- the time-averaged power P5 = 2.20 fW, and the clearance ments. While the dynein motor proteins themselves would easily

ABC

Fig. 3. Model morphology with a flagellar vane, observed average velocity field for D. grandis, and velocity field from CFD model including a 5-µm-wide flagellar vane. (A) The model morphology shows the cell (orange), the collar filter (green), the flagellum with a 5-µm-wide flagellar vane (blue), and the lorica (red). (B) Observed average velocity field. The velocity field is identical to the velocity field in Fig. 2B, and it is shown repeatedly to facilitate comparison with the CFD result. (C) The CFD velocity field in the xz plane is time averaged over the flagellar beat cycle, and the velocity vectors inside filter and chimney are omitted for clarity. The CFD model with a flagellar vane predicts a feeding flow in through the permeable lower part of the lorica and a clearance rate in good agreement with the experimental observations for D. grandis.

9376 | www.pnas.org/cgi/doi/10.1073/pnas.1708873114 Nielsen et al. Downloaded by guest on September 23, 2021 Downloaded by guest on September 23, 2021 le) eoti h piu iesols le spacing filter dimensionless optimum the obtain l we filter), for where (35), biomass of approx- amounts contain equal bins imately size particle logarithmic that accepted erally and particles, prey of centration ile tal. et Nielsen (1/3) to filtration. equal true than is rather is diameter line filtration predicted cross-flow prey the diam- maximum below prey outlier the dimensionless The that ESR. maximum assumed 1 the have Table of We in functions eter. choanoflagellates as blue) the circles, for the (solid and spacing red) filter line, (solid dimensionless spacing observed filter dimensionless pre- optimum theoretical the The for (B) spacing. diction filter dimensionless the of average (Eq. observed spacing filter dimensionless of 4. Fig. for relevant range the in size approximately prey increases maximum spacing the filter with optimum linearly The 4A). (Fig. filter size microbial prey aquatic maximum of the spacing With filter feeders. optimum the predict to force flagellum the as rate size prey gap maximum filter the siev- the by than greater captured diameter are efficiency, with collection particles 100% assume the can if we ing, Now, diameter. particle in where where can rate encounter The time. integral unit the as per expressed biomass rate be encounter The prey prey opti- of possible. the an terms as maximize in is will food that there much spacing that as filter mum suggests intercept trade-off to filter is above-mentioned filter the Filter. of Optimum pose the and Trade-Off Filter-Feeder The so. do acquiring to energy between investing feeders agreement and filter energy in microbial new demonstrates is for and trade-off This (34) strong choanocytes 33). a similar (32, the the ener- from belief of results the budget common with energy making to total magnitude, the contrary of of cell, fraction order significant a an costs by getic flagellum the pres- ing The structures. a vane beat of delicate flagellar for ence the much to too due be shear could the motion (31), force needed the provide AB /a .grandis D. 8 = E β C .4 none aea function as rate Encounter (A) filters. choanoflagellate Optimum 0 0 stecleto efficiency, collection the is ( = -ievn nrae h nrei ot fbeat- of costs energetic the increases vane 5-µm-wide ncoeareetwt h bevdaeaevalue average observed the with agreement close in stepril ascnetainwti ahdecade each within concentration mass particle the is a apoiaeyteoeig ftecas outer coarse the of openings the (approximately /µ)FC E F E = 0 n ehdo upn,i stu possible thus is it pumping, of method and C = = sidpnetof independent is d Q (s nti aew a rt h encounter the write can we case this In . E Q Z = ) 0 0 Z hκi ∞ l −2a d .Tevria ie(le niae the indicates (blue) line vertical The 8). C log β s 0 (s h atcedaee.I sgen- is It diameter. particle the C / ) s l C n10 ln (s /a C pcltdt eyon rely to speculated botrytis , C. d )ds h ieseicms con- mass size-specific the d /a (s − )ER=0.93 = ESR (1/3) = l l , ) 2 − and ds , 2a , β d n mle than smaller and needn of Independent . 1 = h anpur- main The o particles for , µm [7] [8] [6] E u ugsinta hsseismyntb refitrfeeder. filter true when a rate be encounter not the may approximate can species We this that suggestion our 4B). (Fig. species, observations One with consistent is it and choanoflagellates, soitdwt h rqec fteflgla eta h corresponding morphology, the model at average the beat was using track collated flagellar were particle the tracks Each particle of field. All time. frequency velocity of the the total A construct with ImageJ. to associated for used plugin were tracking tracks manual intervals, 73 the 1-s using fps), at sequences. video (10 video reduced–frame-rate noted sequences on 100-fps resolved was slowed-down flow-field were the tracks beat the particle of Two-dimensional in flagellar inspection use visual the for manual, of by selected frequency were The individual, analysis. unique a fielding each Analysis. Flow-Field clumping. avoid to use before sonicated and BSA of with Neu- concentration using a flagellum. to manually the added were ∼1 digitized in along beads frame points polystyrene was 300-nm 15 each position buoyant, trally approximately For flagellum identifying microscope. the by the beat cycle, ImageJ of flagellum beat plane the single focal with were a the oriented beat with were flagellar aligned that the plane the individuals of onto five amplitude settled on or average swimming estimated and free length were either Flagellum Cells slide. glass. objective cover an between a silicone and with slide mounted cm) 2 and (diameter fps ring 100 carbonate an of in rate done were frame vations a pixels 1,024 at of recorded resolution high-speed were a v210 Videos 1,920× Phantom system. of a video total using digital obtained a were provided IX- sequences lens Video Olympus magnifying fication. An U-ECA oil-immersion observed a UPLSAPO60XO/1.35 video. were a and digital cells with objective high-speed equipped flagellum, microscope a beating inverted using the 71 magnification, of motion high the at and field Flow. Feeding flow and Motion Flagellum of Videography 65-mL per substrate. added bacterial were as B1 grains serve rice in to autoclaved, flask dark grown, organically the few in a 10 and nonaxenically at grown 32) was (salinity medium 50111) no. Collection Culture Organisms. Experimental Methods and bud- Materials energy believed. total typically the otherwise of as percent cell few the a of get than that more process much costly up demonstrated energetically an takes instance, is feeding for filter have, microbial that We various modes. in involved mechanistic under- feeding trade-offs the microbial the the and of to general, quantification allow relevant in explored insights filtering are small-scale The estimates of feeding. model standing our filter and small-scale problems efficient choanoflagellates how perform explain choanoflagellate can can and spo- different the many radically mecha- of pumping is proposed nism in presence The vane. widespread flagellar observed a observed radically suggest account rates we cannot Instead, flagellum clearance species. naked the simple, a for that shown have We Conclusion filter measured the for sieving direct of with esti- by spacing compared are small collected effects be be these to but can mated deposition, spacing diffusional filter Par- or range. the interception size filter prey than the small smaller relatively when a ticles size to leading prey large, maximum approx- is is spacing the spacing to filter proportional optimum the imately that shows expression The filter optimum the of determination analytical spacing allows which · 10 6 mL a l .grandis D. −1 ≈ eitsfo hspten ossetwith consistent pattern, this from deviates botrytis, C. E ovsaietewtrflw h atce eepretreated were particles The flow. water the visualize to exp ≈ ae ncl lgmn,attlo 9vdosequences, video 19 of total a alignment, cell on Based PNAS  E + −1 0 -Lcabr osrce sa5m-ihpoly- 5-mm-high a as constructed chamber, ≈1-mL (36). l h choanoflagellate The 8π /a ◦ × | .Tecluewsdltdoc vr – wk, 2–3 every once diluted was culture The C. .Obser- pixels/µm. 10 provided This pixels. 800  uut2,2017 29, August ln(d 1 − 1 /a ln 2 ) + l 2π /a ln(2π [ln(d  | .grandis D. log o.114 vol. ) /a oepoetenear-cell the explore To − d l )] l 1/2 /a /a /a 2 | ,  Aeia Type (American  o 35 no. d a 1 . as magni- | [10] 9377 [9]

APPLIED PHYSICAL ECOLOGY SCIENCES and the velocity field in the xz plane was constructed using a square window were subsequently determined as the equally weighted average grid with 2-µm × 2-µm spatial resolution. The velocity field was assumed over all particle tracks within the window. to have rotational symmetry about the longitudinal axis of the cell, and the observed velocity field in the xz plane was therefore correspondingly ACKNOWLEDGMENTS. We thank Jasmine Mah for providing videos of M. brevicollis and Øjvind Moestrup and Helge Abildhauge Thomsen for assumed to have left–right reflection symmetry with respect to the longitu- helpful discussions. The Centre for Ocean Life is a Villum Kann Rasmussen dinal axis. Within each grid window the manually detected particle positions Centre of Excellence supported by the Villum Foundation, and S.S.A. were selected and for each particle track the average particle position and and J.H.W. were supported by a research grant (9278) from the Villum velocity were determined. Position and velocity associated with a given grid Foundation.

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