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On ciliary sieving and pumping in bryozoans
Journal of Sea Research 48 (2002) 181 – 195 www.elsevier.com/locate/seares
On ciliary sieving and pumping in bryozoans Poul S. Larsen a,*, Hans Ulrik Riisga˚rd b a
Department of Energy Engineering, Fluid Mechanics Section, Technical University of Denmark, Building 403, DK-2800 Kgs. Lyngby, Denmark b Marine Biological Research Centre (Institute of Biology, University of Southern Denmark), Hindsholmvej 11, DK-5300 Kerteminde, Denmark Received 17 January 2002; accepted 18 April 2002
Abstract Based on video-microscope observations of trajectories of particles in the feeding currents of individual isolated bryozoans Bowerbankia imbricata, Flustrellidra hispida and Electra pilosa the velocity fields above and in the lophophore have been determined. The flow into the lophophore, which is a result of water currents driven out between tentacles by the water pumping lateral cilia, is characterised by nearly parabolic profiles with highest velocity along the centreline of the lophophore. In intact animals, the centreline velocity first increases from its value at the inlet to a maximal value about 20 to 25% down into the lophophore and then decreases to low values as the flow stagnates at the mouth. In a narcotised animal, whose laterofrontal filter was inactive, the centreline velocity was found to decrease monotonously from its inlet value. An approximate expression is derived for the relation between velocity distribution in the lophophore and variation of pumping rate along tentacles. Typical variations are given and compared to those obtained by a more accurate two-dimensional numerical solution. Based on observed velocity distributions in the lophophore, particle tracks and tentacle flicks, a description is given of the feeding mechanisms. Particles entering the central region are brought to the mouth by the high velocity feeding current in the central part of the lophophore. Particles entering further out either escape between tentacles or are stopped by the laterofrontal cilia sieve and, in the distal region of tentacles, are brought back into the central feeding current by flicks of tentacles. The relative velocity between fluid and particle during a flick recovery phase ensures particle release. Particles stopped in the proximal region of the lophophore appear to be transferred to and conveyed by the frontal cilia bands on tentacles. The added load on laterofrontal cilia from viscous drag on a food particle retained by the cilia is found to be of the same order of magnitude or greater than the ‘background load’ of viscous drag from fluid passing the laterofrontal cilia in the absence of a particle. This is hypothesised to stimulate the sensing mechanism triggering observed flicks. The energy cost of pumping is estimated at 1 to 4% of the metabolic power of a ‘standard’ zooid. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Feeding in bryozoans; Flow in lophophore; Ciliary sieving; Particle retention; Bryozoan model
1. Introduction All bryozoans (‘moss-animals’), also known as the phylum Ectoprocta, are colonial, and in most cases the *
Corresponding author. E-mail address: [email protected] (P.S. Larsen).
units of the colony (zooids) secrete tubes or boxes partially encasing the soft parts. When feeding, the zooid extends its lophophore, a ring of ciliated tentacles with the mouth at the centre of its base, into the adjacent water. In the gymnolaemate bryozoans each tentacle has a tract of lateral cilia on each side, a tract of frontal cilia facing the mouth located at the apex of
1385-1101/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 5 - 11 0 1 ( 0 2 ) 0 0 1 3 6 - 3
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the conical lophophore, and between the lateral and frontal cilia a row of stiff laterofrontal cilia (Mukai et al., 1997). Cyclostomatous bryozoans lack frontal cilia (Nielsen and Riisga˚rd, 1998), but otherwise the basic particle capture mechanism seems to be identical in all bryozoans. When the lateral cilia beat in a coordinated metachronal rhythm, currents are generated which pass straight down the lophophore towards the mouth and out between the tentacles (Atkins, 1932; Bullivant, 1968a,b; Ryland, 1976; Riisga˚rd and Manrı´quez, 1997). Food particles, mainly phytoplankton, in the incoming stream either follow the central current and pass directly to the mouth or are restrained by the stiff laterofrontal ciliary filter (‘ciliary sieving’) and then either transported downwards on the tentacles by means of the frontal cilia, or the particles are transferred to the central current by means of tentacle flicks triggered by the restrained particles (Riisga˚rd and Manrı´quez, 1997; Nielsen and Riisga˚rd, 1998). Similar phenomena have recently been described for another lophophorate, Phoronis muelleri (phylum Phoronida) by Riisga˚rd (2002), who also discussed the possible role of localised disruption of the beat of the lateral cilia during capture of a particle as observed in a bryozoan by Strathmann (1982). Although structure, size and shape of the bryozoan lophophore have been thoroughly examined over the years (e.g. Atkins, 1932; Ryland, 1976; Winston, 1977, 1978; McKinney, 1990; Mukai et al., 1997; Shunatova and Ostrovsky, 2001), only few studies have so far been concerned with hydromechanical aspects of bryozoan feeding (Gru¨nbaum, 1995, 1997; Eckman and Okamura, 1998; Larsen et al., 1998; Larsen and Riisga˚rd, 2001). Obviously, both particle capture and water flow are closely related to the morphology of the lophophore, but the physical and hydromechanical conditions of ciliary-sieving and pump design have not yet been examined thoroughly enough to understand the function and energy cost of the integrated lophophore pump- and filtersystem. This paper, including video-microscope observations of three bryozoan species with different lophophore design, further describes the ‘ciliary sieving’ particle capture mechanism and physical conditions related to this process, and water pumping and flow pattern is characterised and modelled in order to interpret the functional morphology of the bryozoan lophophore in regard to pump-design.
2. Material and methods The gymnolaemate bryozoans Bowerbankia imbricata (Adams), Flustrellidra hispida (Fabricius) and Electra pilosa (Linnaeus) were selected as examples because of their different lophophore design. The two first species both have long tentacles (0.7 and 0.8 mm, respectively), but B. imbricata has only 10 tentacles forming a bell with a short diameter (0.6 mm) and a small apex angle, whereas F. hispida has 28 tentacles forming a bell with a wide diameter (1.2 mm) and a large apex angle. E. pilosa has 12 short tentacles (0.4 mm) forming a bell with a short diameter (0.4 mm). The ctenostomes B. and F. hispida were collected in September 1996 from the rocky intertidal in Menai Strait near Menai Bridge, North Wales, UK. In the laboratory (School of Biological Sciences, University of Wales, Bangor, UK) the bryozoans were kept in containers placed in a thermo-regulated bath (15 jC) with filtered (0.2 Am) and aerated seawater (34xS) until video observations could take place during the following days. For video-observations of the filterpump of F. hispida, lophophores were dissected out and narcotised with 7.5% MgCl2. It is well known that isolated and narcotised lophophores return to the normal funnel-shape probably due to the elastic properties of the thick basement membrane (Nielsen and Riisga˚rd, 1998). The cheilostome E. pilosa was collected in spring 2001 in Kerteminde Fjord, close to the Marine Biological Research Centre (University of Southern Denmark), Kerteminde, Denmark. Colonies grown on microscope glass slides (about 22xS) according to Hermansen et al. (2001) were used for video observations in November 2001. 2.1. Video observations Tentacle flicking and particle paths were recorded using a video camera (Kappa CF 11/1) attached to an inversed microscope (Labovert FS), and a 50 halfframes per second video recorder (Panasonic NVFS200 HQ). The bryozoans were put on the bottom of a cylindrical observation chamber placed on the microscope. The seawater in the observation chamber contained 6 Am diameter flagellates Rhinomonas reticulata at a concentration of 2800 cells cm 3, except for E. pilosa where 11 Am diameter Tetraselmis sp. were used. Video frames could be copied by
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means of a video graphic printer (Sony UP – 860 CE). Tentacle flickings and capture of food particles were traced from their position in successive frames. This was done by mounting a transparent plastic sheet onto the video screen so that the tentacle contours as well as the position of suspended particles could be marked with a pen directly on the sheet frame by frame.
3. Results and discussion 3.1. Video observations The particle capture process and downward transport in the lophophore of Bowerbankia imbricata are illustrated by means of Figs. 1 – 3, which show series of video graphic prints. Particles entering near the centre of the lophophore move directly towards the mouth, occasionally interacting with tentacles in the lower part. Some particles entering in the outer region
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of the lophophore escape between tentacles in the distal region while other particles are captured. When a particle is captured on the distal part of a tentacle this triggers a tentacle flicking that brings the particle into the central core and down towards the mouth. Most transport of captured particles towards the mouth seems to be dependent on such flicking-assisted transport, but particles may also be conveyed downwards on the frontal surface of the tentacles (Fig. 3). Particles in the central current are usually trapped deep down in the lophophore, but this does not trigger a noticeable tentacle flick. Rather a quick displacement, possibly by cilia action (cf Gordon, 1974), brings a trapped particle back into the central current. The velocity profiles of water flow at different depths in the lophophore of B. imbricata, characterised by a small apex half-angle of about 17.5j, are approximately parabolic with the highest velocity in the central core, and this velocity attains its largest
Fig. 1. Bowerbankia imbricata. Particle arrival and capture on a tentacle (A to D) followed by an individual tentacle flick (E, F) which takes the particle into the central current and thus further down towards the mouth (G, H). Particle (6 Am diameter Rhinomonas) indicated by arrow; 0.02 s between video graphic prints.
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Fig. 2. Bowerbankia imbricata. Particle capture (A to F) followed by a tentacle flick (G to L). Particle indicated by arrow; 0.02 s between video graphic prints.
value about 25% down the lophophore (inserted plot in Fig. 4). This velocity distribution may explain the observed particle paths. Particles should stay near the core to reach the mouth. This occurs when particles enter the lophophore near its centre, but when particles enter further out the various interactions with the tentacle structure apparently tend to bring them back into the downward-directed core flow. Fig. 5 shows particle trajectories in untreated and in narcotised (non-flicking) lophophores of Flustrellidra hispida, both characterised by a larger apex halfangle of about 30j. Again, particles entering near the centre of the lophophore move directly towards the
mouth in both cases. However, for the narcotised specimen, particles entering further out move towards tentacles and escape. This indicates that the waterpumping lateral cilia were not seriously influenced by the treatment whereas the laterofrontal cilia filter apparently had become inactive. The velocity profiles of water flow at different depths in the lophophore are again approximately parabolic with the highest velocity in the central core, but now this velocity decreased from its largest value at the inlet of the lophophore (at 0% down; see inserted plot in Fig. 5). For the untreated specimen, however, the highest velocity in the central core attains its maximum value about 20 to
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Fig. 3. Bowerbankia imbricata. Capture for particle conveyed downwards on the frontal surface of the tentacles (A to M). Particle indicated by arrow; 0.02 s between video graphic prints.
25% down the lophophore (Fig. 5, upper left). The inactivity of the laterofrontal cilia filter in the narcotised case apparently changes the variation of the pump flow per unit length of tentacles from root to tip because this variation affects the velocity distribution in the lophophore as appears from the section on cilia pumping below.
Fig. 6 shows the flow pattern and velocity distribution in the lophophore of Electra pilosa. In the periphery of the lophophore inlet, incoming particles are captured by a close interaction between the sensory laterofrontal ciliary filter (which cannot be seen on the video film) and tentacle flicks, as indicated on the figure by abrupt, inward changes of particle paths.
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Fig. 4. Bowerbankia imbricata. Drawings: Examples of particle trajectories in lophophore. Particles captured on the distal part of a tentacle may trigger a tentacle flick (I, II and III indicated by dotted tentacles). Flow lines and velocities (mm s 1) based on a time interval of 0.02 s between subsequent video frames of particles. Plot, right bottom: Velocity profile at different depths in lophophore. Highest velocity occurs about 25% down.
Only particles in the stagnant central current are captured without making contact with the tentacles. 3.2. Ciliary sieving 3.2.1. Particle retention The distance between the stiff laterofrontal cilia, which act as a sieve, determines the lower size of particles that can be retained by the ciliary filter-
feeding bryozoans. The particle retention efficiency of the laterofrontal filter has previously been measured in two other bryozoans and it was found that particles >5 Am in diameter are retained with near 100% efficiency in both Celleporella hyalina (Riisga˚rd and Manrı´quez, 1997) and Electra crustulenta (Riisga˚rd and Goldson, 1997). This shows that the spacing between the stiff 0.2 Am diameter laterofrontal cilia (Llfc f 15 to 20 Am long) may be about 5.5
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Fig. 5. Flustrellidra hispida. Upper left: Particle trajectories in lophophore of intact animal. Highest velocity occurs about 20 to 25% down. Flow lines and velocities (mm s 1) based on a time interval of 0.02 s between subsequent video frames of particles. Upper right: Particle trajectories in ‘leaky’ lophophore dissected out and narcotised with MgCl2 to prevent tentacle flicking. Lower: Velocity profile at different depths in narcotised lophophore. Highest velocity occurs at inlet, 0% down.
Am in these bryozoans. But the spacing seems to vary between groups and species: in cyclostome bryozoans the spacing varies between 2.5 and 4 Am (Nielsen and Riisga˚rd, 1998). The spacing observed on SEM pictures presented by Nielsen (2002) is about 2 Am in F.
hispida and about 3 Am in Alcyonidium gelatinosum. The fact that particles are still seen to escape between tentacles in the outer (distal) region (Fig. 4) is due to the increased spacing between tentacles in this region where the opposing laterofrontal cilia do not meet.
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For an approximate estimate of the pressure drop across the laterofrontal filter in bryozoans a screen of parallel cylinders with a mean diameter of d and spacing b may be a usable model. For a flat screen consisting of parallel cylinders forming a mesh of infinite extent, the pressure drop (DH in mm H2O) is given by the equation of Tamada and Fujikawa (1957), see also Riisga˚rd and Larsen (1995, their Eq.(16)) DH ¼ Kvul =gd
ð3Þ
where K = 8H /(1 – 2lnH + H 2 /6), H = k(d/b), u l = velocity of upstream flow, g = acceleration of gravity (9.807 m s 2), and v = kinematic viscosity of water (1.1 10 6 m2 s 1). Assuming d = 0.2 Am, b = 3.5 Am, and ul c um = 0.5 mm s 1 the pressure drop across the laterofrontal ciliary filter is DH = 0.09 mm H2O, or Dp = UgDH f 0.9 Pa. In the case of spacing b = 5.5 Am the pressure drop is estimated at DH = 0.05 mm H2O, or Dp f 0.5 Pa.
Fig. 6. Electra pilosa. Flow lines and velocities (mm s 1) based on a time interval of 0.02 s between subsequent video frames of particles. Highest velocity occurs close to inlet.
3.2.2. Pressure drop across laterofrontal ciliary filter The pressure drop across the laterofrontal filter cannot be determined in a simple way because of its geometry and because the water is not leaking through the ciliary filter array with the same velocity along the length of the cilia, from tip to base. For an estimate, however, we assume a uniform mean velocity (um) determined from a simple analysis of the lateral cilia pump (Riisga˚rd et al., 2000), um ¼ 0:5 utip ðTa =T Þ
ð1Þ
where T is the full period of beat and Ta is the period of active beat of lateral cilia of length L through angle u (degrees), giving the tip velocity utip ¼ ðu=360Þ2pL=Ta
3.2.3. Drag force and deflection of laterofrontal cilia We now evaluate how much the drag of a food particle captured by the laterofrontal cilia may deflect the about 20 Am long, but only 0.2 Am thick ‘filter’ cilia, as well as the force and moment exerted locally on the tentacle (see Fig. 7). A similar analysis for cilia spaced far apart was given by Riisga˚rd et al. (2000). The force of friction ( F = ‘drag force’) on a stationary
ð2Þ
Using L = 15 Am, 1/T = 25 Hz, Ta = 0.2 T, and u = 150j, gives utip = 4.9 mm s 1 and um = 0.5 mm s 1.
Fig. 7. Ciliary sieving. (Upper) Cross section of three tentacles of a lophophore with frontal cilia (fc), water pumping lateral cilia (lc), stiff laterofrontal cilia (lfc) acting as a mechanical sieve, and a stopped particle subject to downward water velocity u. (Lower) Laterofrontal cilium subject to load from (A) drag on particle and (B) ‘background’ drag on cilium from water velocity, increasing linearly from root to tip, both giving rise to force F, bending moment M at point of fixation to tentacle, and deflection of cilium tip X.
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sphere of diameter (D) placed in a fluid with undisturbed velocity (u) may be calculated according to Stokes’ law for creeping flow, F ¼ 3pDAu
ð4Þ
where A is the dynamic viscosity (1.1 10 3 N s m 2). The predicted deflection (X) of a cilium at the point of loading at a certain distance (l) from the base of the cilium is given by (Strathmann and McEdward, 1986), X ¼ Fc l 3 =3S
ð5Þ
where Fc is the force acting on one cilium and S is the flexural stiffness of the cilium (found to be about 2 10 19 N m2; Baba, 1972). At the point of fixation to the tentacle will act the force Fc and a bending moment of Mp = Fcl. For a realistic case example consider a 6 Am diameter particle that has been stopped by two laterofrontal cilia which ensures that the drag force on the particle is distributed on both cilia. Due to the actively beating lateral cilia the water flow past the particle may vary from u f 1 mm s 1 near the tip to 0 near the base of the laterofrontal ciliary filter, and further the loading point may vary between 0 and 20 Am. For an estimate of the maximum possible drag force, bending moment, and deflection caused by a stopped particle (at u = 1 mm s 1, l = 20 Am, S = 2 10 19 N m2) it is found that Fc = F/2 = 3 10 11 N, Mp = 6 10 16 N m, and X = 0.4 Am. The 0.4 Am deflection of the cilium tip due to drag on the stopped particle is negligible and indicates that the laterofrontal ciliary array has a sufficient stiffness to act as a sieve (‘mechanical filter’). 3.2.4. Trigger mechanism of tentacle flicking Each stiff laterofrontal cilium is situated in a depression surrounded by a collar of microvilli, which suggests that they are sensory (Lutaud, 1973; Mukai et al., 1997; Nielsen and Riisga˚rd, 1998), i.e. they may be able to trigger a tentacle flicking when a particle is retained by the ciliary filter. Further, according to Gordon (1974) the stiff laterofrontal cilia, observed in a single tentacle of a live Cryptosula pallasiana using a negative-field phase-contrast microscope, ‘‘are not rigid, but capable of occasional flicking movements’’.
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The exact mechanism that triggers such a flick is unknown, but it is reasonable to suggest that a certain extra drag force, besides the ‘background’ force exerted on the laterofrontal cilia due to the moving water, may be a prerequisite for triggering a tentacle flick. This is illustrated by the following considerations. An estimate of the ciliary-root moment (Mf) from the loading due to viscous flow (see Fig. 7) may be obtained from the pressure drop of Dp = 0.5 Pa across the laterofrontal filter (see previous section), which implies a force on each laterofrontal cilium of Fc = DpbL, where b = 3.5 Am is the centre distance between two cilia, and L = 20 Am is the length of laterofrontal cilia. Considering each cilium to be a lever arm the bending moment is estimated to be Mf = 2FcL/3 = 2DpbL2/3 = 4 10 16 N m, which is about identical to the above bending moment Mp due to a captured particle. This shows that the drag force of a captured particle is likely to be sufficiently strong to transfer a perceptible force and moment via the clamped root of the laterofrontal cilia affixed to the tentacle, i.e. the laterofrontal cilia may have a sensory function. If this is actually the case it implies that particles too small to be retained by the laterofrontal ciliary filter should not be able to trigger the flick mechanism. So far, however, this assumption has not been supported by experimental evidence. The dynamics of the trigger event should also be considered. As a tentacle is triggered it moves quickly a distance towards the centre of the lophophore with an estimated velocity of Vflick f 2.4 mm s 1 in B. imbricata and 10.7 mm s 1 in Flustrellidra hispida (Riisga˚rd and Manrı´quez, 1997, Table 3). Being retained by the stiff laterofrontal cilia the particle necessarily follows this motion and the fluid velocity relative to the particle may therefore increase from the value u f 1 mm s 1 (see above) to a value of u + Vflick. Since linear in approach velocity, all loads calculated previously will increase by a factor of 1 + Vflick/u f 3.4 to 11.7. Apparently, the laterofrontal cilia can handle such increased loads. Subsequently the tentacle moves back from the region of increased downward flow in a recovery stroke, which lasts 2.3 to 7.7 times longer than the active stroke (Riisga˚rd and Manrı´quez, 1997). During this event the fluid velocity relative to the particle, due to both pump action and tentacle motion, is probably negative or
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close to zero, which may explain why the particle is released to the core flow.
coordinate along the tentacle, ttip being the length of tentacles (Fig. 8), Eq.(6) becomes
3.3. Ciliary pumping
dðg2 sinbVm Þ=dg ¼ 4gVn
3.3.1. Pumping rate along tentacle The observed velocity distributions in the lophophore may be related to the pumping rate along tentacles by a simple mass balance. Plots in Figs. 4 and 5 show that radial distributions of downward velocity in the lophophore may be approximated by parabolas, hence the mean velocity equals one-half the maximum at the centreline, 1/2 Vm. Using this and equating the change in downward flow to loss between tentacles, the steady, one-dimensional form of conservation of mass for incompressible flow yields
According to this relation, a constant pumping rate along tentacles, V n f constant, would lead to Vm f constant, which is not observed (recall Figs. 4 and 5) so Vn must vary along tentacles. The velocity distribution in the lophophore, with the highest velocity at the centreline, Vm, is easily understood because the laminar streamlines for downward flow in the lophophore are being compressed along the centreline according to the apex angle. Thus, the maximum centreline velocity tends to be higher in a lophophore with long tentacles and a small apex angle than in a lophophore with short tentacles and a wide apex angle. Less obvious is the depth at which the maximum centreline velocity appears in a lophophore of a certain morphometry. To complete a general description of water flow and velocity distribution in a specific lophophore, the consequences of variable space between adjacent tentacles must also be taken into account. The form of the lophophore is constrained within certain limits: the number of tentacles may vary from 8 to 31, the length of tentacles may vary from 0.124 to 0.929 mm, the lophophore diameter from 0.187 to 1.226 mm, and the distance between the tips of the tentacles from 0.077 to 0.142 mm (Ryland, 1975, 1976; Winston, 1978; Gordon et al., 1987), and further, the distance between the tentacle tips determines the axillary angle which may vary between 10.5j and 30.8j (Ryland, 1976, Fig. 18 therein). The axillary angle is of great significance for the intertentacular gap and thus the distance between the water pumping lateral cilia on the opposing sides of the tentacles. The width of the intertentacular gap determines the velocity profile driven by the lateral cilia, and as the intertentacular gap vanishes downward the lateral cilia get more and more close, eventually impeding their pump efficiency. The intertentacular gap and the length of the lateral cilia have been measured in F. hispida by Markham and Ryland (1991). It was found that the lengths of the lateral cilia decrease proximally toward the mouth from a sub-distal maximum of about 23 Am to only 14 Am near the mouth so that the cilia completely span the gap for 25% of its length.
dðprt2 1=2Vm Þ ¼ 2prt Vn dz=cosb
ð6Þ
where rt denotes the radius of the lophophore at any location z, Vn the mean velocity normal to tentacles over the full circumference, and h the apex half-angle (see Fig. 8). Changing variables to D = t/ttip, noting dz = cosh dt, rt = t sinh where t is a convenient local
Fig. 8. Radial section of axisymmetric lophophore of apex halfangle h (schematic), showing velocity profile in lophophore with maximum Vm at axis, and variation of pumping rate, Vn, along tentacle having local coordinates (t,n).
ð7Þ
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Therefore, the mean velocity referred to area between tentacles may vary along tentacles. Since this value is greater than Vn in Eq.(6) by a factor 2krt /(2krt-ntdt) where nt denotes the number of tentacles and dt their diameter (or width), it is clear that the velocity normal to the tentacles may vary along the tentacle and possibly influence the depth at which the maximum centreline velocity appears in the lophophore. In order to examine how different variations Vn affect the variation of maximum downward velocity in the lophophore, consider two possible variations along tentacles of the pumping rate: linearly increasing, and parabolic with vanishing pumping rate at root and tip, i.e. Vn(D)/Vn(1) = D and D(1 D), respectively. Using (7) for these cases gives the results Vm(D)/ Vm(1) = D and D(4– 3D), respectively. In Fig. 9 the two cases are compared to experimental observations (from Figs. 4 –6). Data for B. imbricata (Vm(1) f 4 mm s 1), the untreated F. hispida (Vm(1) f 2.5 mm s 1), and E. pilosa (Vm(1) f 3.4 mm s 1) appear to follow a parabolic variation with a maximal value near 20 to 25% into the lophophore, while those of the narcotised F. hispida (Vm(1) f 4 mm s 1) show a nearly linear variation.
Fig. 9. Normalised centreline velocity Vm(D)/Vm(1) in lophophore versus position in terms of % from inlet, 100(1 D). Experiment: Bowerbankia imbricata (+); Flustrellidra hispida (o) narcotised and ( ) untreated; Electra pilosa (D). Approximate theory assuming the distribution of pumping rate along tentacle to be linear, D ( – – – ), and parabolic, D(1 D) (- - - -). Two-dimensional model, case D(1 D), h = 17.5j of Fig. 10 (——).
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To evaluate the approximate one-dimensional model of (6)-(7) a numerical solution has been made to the equations governing low-Reynolds number creeping flow in a two-dimensional axisymmetric model of a single, isolated lophophore with prescribed pumping rate Vn along tentacles (recall Fig. 8). Fig. 10 (upper) shows the computational domain in the r,z-plane, which extends to r = 10L and z = 10L, where L denotes the height of both lophophore and stem. For the cases of h = 17.5j and 30j, and Vn f D(1 D), Fig. 10 (lower) shows the resulting streamlines of the recirculating flow in the proximity of the lophophore set up by the pumps, which gives an idea of the extent of the flow. Given the streamline solution, the radial and vertical components of velocity are known, particularly the downward velocity in the lophophore. The computed maximal velocity, Vm, along the centreline of the lophophore is shown in Fig. 9 for the cases of h = 17.5j to illustrate the differences between the approximate one-dimensional model and a twodimensional numerical model. Although the normalized distribution of Vm is similar for the two models their magnitudes are different, in part because the former does not account for viscous effects. Once captured by the lophophore, the particles accumulate above the open, circular mouth where the muscular pharynx acts as a suction pump (Atkins, 1932). Occasional and rapid pharyngeal dilation, which is not included into the model, results in ingestion of the particles. For B. imbricata in the present work, it has been estimated that during ingestion a water volume of about 4 10 4 mm3 is sucked into the pharynx through the open mouth (diameter 50 Am) within 0.02 s resulting in a suction speed of 10 mm s 1 through the mouth. As the pharynx ‘slowly’ (during the following about 0.8 s) returns to its relaxed state, surplus water is drained back through the mouth while the particles remain in the pharynx and eventually are swallowed through the esophagus into the stomach. Particles entering the lophophore along the centreline may be carried directly to the mouth; but ingestion seems to be dependent on action of the pharynx suction pump. Particle capture in the central water current is a normal part of the feeding process in all bryozoans, but the quantitative importance for food uptake seems to be insignificant, only about 5% (Nielsen and Riisga˚rd, 1998).
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Fig. 10. Upper: Axisymmetric computational domain for model of single, isolated bryozoan with cone-shaped lophophore of height L formed by a large number of tentacles, each forming apex half-angle h with axis. Lower: Computed streamlines showing the recirculating flow driven by specified pumping rate, Vn f D(1 D), h = 17.5j and 30j. (Only part of the computational domain near lophophore is shown).
3.3.2. Energy cost of pumping Hunter et al. (1996) measured the oxygen uptake in Celleporella hyalina to be 2.2 F 1.5 10 6 cm3 O2 h 1 zooid 1 (after correction of a printing error; R.N. Hughes pers. comm., 1997). The oxygen uptake in Schizoporella bifrons and Membranipora hyadesi was measured by Moyano et al. (1974) to be 6.15 and 3.45 10 6 cm3 O2 h 1 zooid 1, respectively, and in Bugula turrita Magnum and Schopf (1967) measured the respiration to be 4.25 10 6 cm3 O2 h 1 zooid 1. For the present purpose, a mean respiration rate of 4 10 6 cm3 O2 h 1 zooid 1 may be applied, and using a conversion factor (Elliott and Davison, 1975) 1 cm3 O2 h 1 = 20 J h 1 = 5555 AW, the metabolic power for a ‘standard’ zooid is estimated at R = 0.02 AW.
The present measurements for an isolated B. imbricata showed a mean velocity of w0 f 2.0 mm s 1 at the entrance to the lophophore of diameter di f 0.5 mm (Fig. 4), hence the volume flow through a zooid is about Q = Ai w0=(k/4)di2 w0 f 0.39 mm3 s 1. Using the estimated pump pressure of Dp f 0.5 Pa, the pumping power supplied to the water is PP = Q Dp f 0.0002 AW, which is 1% of the above metabolic power of the ‘standard’ zooid. The corresponding values for F. hispida are w 0 f 1.9 mm s 1 , di f 1.1 mm (Fig. 5) and Dp f 0.5 Pa, yielding Q f 1.8 mm3 s 1 and PP f 0.0009 AW, which is 4.5% of the metabolic power of the ‘standard’ zooid. These results may be compared to those presented by Larsen and Riisga˚rd (2001) in modelling the chimney spacing in encrusting bryozoan colonies of
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Membranipora membranacea. Here the backpressure characteristic was modelled as Dp ¼ pmax ð1 w=wmax Þ
ð8Þ 1
inferred with pmax f 2.2 Pa and wmax f 3 mm s from the model of Gru¨nbaum (1995). Using Eq.(8) and noting that the volume flow per zooid is Q = Ai w0, the pumping power may be expressed as PP ¼ QDp ¼ wmax Ai pmax w=wmax ð1 w=wmax Þ
ð9Þ
The experimental observations of isolated zooids by Larsen and Riisga˚rd (2001, Fig. 2 therein) gave the values w f 1.2 – 1.3 mm s 1, di f 0.6– 0.7 mm, hence Dp = 1.28 Pa and PP f 0.00043 AW or about 2% of the metabolic power of the ‘standard’ zooid, which is in reasonable agreement with the present results. 3.4. Functional integration and hydromechanical aspects The present work is primarily based on observations and modelling of individual bryozoan zooids feeding in stagnant water. Although such simple, standardised laboratory conditions may be profitable for revealing basic functions and flow patterns, it is clear that the feeding success of the individual zooid is dependent on external water flow and mixing to supply food particles and to prevent recirculation of once filtered water. Although all bryozoans are colonial, the individual feeding zooids may be arranged in such a way that the hydrodynamic influence of the neighbouring zooids is rather insignificant, as may be the case in colonies forming erect slender branches of zooids (e.g. Crisia sp.), or colonies with more or less solitary zooids along a stolon (e.g. Bowerbankia sp.). However, in other colonies, such as Membranipora membranacea, forming extensive encrusting sheets of close-set zooids, the water currents generated by the individuals is indistinct, but co-ordinated to create benefits for the whole colony. Crowding of individuals reduces the feeding flow to individuals in the interior of the colony (Gru¨nbaum, 1995) and could mean a scarcity of food, but linked together in a colony zooids form a structurally and physiologically integrated compound organism with new properties. Colony morphology may thus have profound consequences for feeding. Thus, closely packed zooids in encrusting bryozoan colonies pump water against
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friction in the canopy region below the lophophores in order to drive the filtered water to either the rim of the colony or to so-called chimneys (areas without lophophores) for exhalant water from a larger number of zooids. The chimneys are arranged at regular intervals and appear to develop in a given area when the feeding rate of the zooids becomes less than a certain minimum value (Larsen and Riisga˚rd, 2001). Strong exhalant jets may prevent recirculation (Lidgard, 1981), and closely packed lophophores may be an advantage in the benthic boundary layer in which flow speeds increase with height above the surface. Fig. 11 shows the flow pattern and velocity distribution in the region above two neighbouring lophophores of E. pilosa. It is seen that the combined feeding currents produced by the two lophophores are faster and more vertically directed than the bending ‘recirculating’ currents of the isolated lophophore (cf. streamlines in Fig. 10). This is in agreement with the assumption that colonies with tightly packed lophophores develop
Fig. 11. Electra pilosa. Flow pattern and velocity distribution in the region above two neighbouring lophophores. Flow lines and velocities of particles (mm s 1) based on a time interval of either 0.02 s between subsequent video frames (crosses) or 0.1 s (dots).
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cylindrical feeding zones which divert water into the lophophore from a greater height than widely spaced lophophores (Eckman and Okamura, 1998; Okamura et al., 2001). Thus, colonies with tightly packed lophophores and exhalant chimney jets may have a higher feeding rate than colonies with more scattered lophophores. 4. Conclusion Over the years, the objective of many experimental and morphological studies has been to understand the method by which suspended particles are being captured by bryozoans. The present work, based on new insight provided during recent years’ research, has in detail described the particle capture mechanism and aspects of water flow related to the morphology of the bryozoan lophophore. The physical conditions related to the capture process have been examined, and the pump-design analysed by modelling. It has been found that water flow and velocity distribution in the lophophore is a consequence of the morphometry of variable space between adjacent tentacles and that the low energy pump is a necessary requisite for the ciliary sieving mechanism to operate in bryozoans. The bryozoan lophophore is a highly integrated pump- and filter system in which the particle-capture mechanism is based on a close and sophisticated interplay between a sensory ciliary filter that triggers an inward tentacle flick, which brings the arrested particle closer to the axis of the lophophore, and a centrally focused, downward stagnating current caused by the special pump design. Acknowledgements H.U.R. was supported by a grant from the Danish Natural Research Council (no. 28– 808). Thanks are due to the reviewers, who waived anonymity (Dr. Frank K. McKinney and Dr. Judith E. Winston). References Atkins, D., 1932. The ciliary feeding mechanism of the entoproct Polyzoa, and a comparison with that of the ectoproct Polyzoa. Q. J. Microsc. Sci. 75, 393 – 423.
Baba, S.A., 1972. Flexural rigidity and elastic constant of cilia. J. Exp. Biol. 56, 459 – 467. Bullivant, J.S., 1968a. The rate of feeding of the bryozoan, Zoobotryon verticillatum. N.Z. J. Mar. Freshwat. Res. 2, 111 – 134. Bullivant, J.S., 1968b. The method of feeding of lophophorates (Bryozoa, Phoronida, Brachiopoda). N.Z. J. Mar. Freshwat. Res. 2, 135 – 146. Eckman, J., Okamura, B., 1998. A model of particle capture by bryozoans in turbulent flow: significance of colony form. Am. Nat. 156, 861 – 880. Elliott, J.M., Davison, W., 1975. Energy equivalents of oxygen consumption in animal energetics. Oecologia (Berl.) 19, 195 – 201. Gordon, D.P., 1974. Microarchitecture and function of the lophophore in the bryozoan Cryptosula pallasiana. Mar. Biol. 27, 147 – 163. Gordon, D.P., Clark, A.G., Harper, J.F., 1987. Bryozoa. In: Pandian, T.J., Vernberg, F.J. (Eds.), Animal Energetics, vol. 2, Academic Press, London, pp. 173 – 199. Gru¨nbaum, D., 1995. A model of feeding currents in encrusting bryozoans shows interference between zooids with a colony. J. Theor. Biol. 174, 409 – 425. Gru¨nbaum, D., 1997. Hydromechanical mechanisms of colony organization and cost of defence in an encrusting bryozoan, Membranipora membranacea. Limnol. Oceanogr. 42, 741 – 752. Hermansen, P., Larsen, P.S., Riisga˚rd, H.U., 2001. Colony growth rate of encrusting marine bryozoans (Electra pilosa and Celleporella hyalina). J. Exp. Mar. Biol. Ecol. 263, 1 – 23. Hunter, E., Hughes, R.N., Goldson, A., 1996. Environmental and genetic control of somatic and sexual performance in Celleporella hyalina (L.). In: Gordon, D.P., Smith, A.M., Grant-Mackie, J.A. (Eds.), Bryozoans in Space and Time. Proc. 10th Int. Bryozool. Conf., Wellington, New Zealand, 1995. National Institute of Water and Atmospheric Research, Wellington, pp. 149 – 156. Larsen, P.S., Riisga˚rd, H.U., 2001. Chimney spacing in encrusting bryozoan colonies (Membranipora membranacea): video observations and hydrodynamic modeling. Ophelia 54, 167 – 176. Larsen, P.S., Matlok, S.S., Riisga˚rd, H.U., 1998. Bryozoan filter feeding in laminar wall layers: flume experiments and computer simulation. Vie Milieu 48, 309 – 319. Lidgard, S., 1981. Water flow, feeding, and colony form in an encrusting cheilostome. In: Larwood, G.P., Nielsen, C. (Eds.), Recent and Fossil Bryozoa. Olsen & Olsen, Fredensborg, Denmark, pp. 135 – 142. Lutaud, G., 1973. L’innervation du lophophore chez le Bryozoaire chilostome Electra pilosa (L.). Z. Zellforsch Mikrosk. Anal. 140, 217 – 234. Magnum, C.O., Schopf, T.J.M., 1967. Is an ectoproct possible? Nature (London) 213, 264 – 266. Markham, J.B., Ryland, J., 1991. Morphometry and function in the lophophore of Flustrellidra hispida (Bryozoa). In: Bigey, F.P. (Ed.), Bryozoa Living and Fossil. Bryoz Bull. Soc. Sci. Nat. Ouest Fr., Me´m. HS 1 Nantes (France), 237 – 242. McKinney, F., 1990. Feeding and associated colonial morphology in marine bryozoans. Rev. Aquat. Sci. 2, 255 – 288. Moyano, G.H., Marin, O.E., Salamanca, M.A., 1974. Estudio preliminar sobre el consumo de oxigeno de Schizoporella bifons y
P.S. Larsen, H.U. Riisga˚rd / Journal of Sea Research 48 (2002) 181–195 Membranipora hyadesi (Bryozoa, Cheilostomata). Bol. Soc. Biol. Concepcion 48, 123 – 126. Mukai, H., Terakado, K., Reed, C.G., 1997. Bryozoa. In: Harrison, F.W. (Ed.), Microscopic Anatomy of Invertebrates, vol. 13, Wiley-Liss, New York, pp. 45 – 206. Nielsen, C., 2002. Ciliary filter-feeding structures in adult and larval gymnolaemate bryozoans. Invertebrate Biol., in press. Nielsen, C., Riisga˚rd, H.U., 1998. Tentacle structure and filter-feeding in Crisia eburnea and other cyclostomatous bryozoans, with a review of upstream-collecting mechanisms. Mar. Ecol. Prog. Ser. 168, 163 – 186. Okamura, B., Harmelin, J.-G., Jackson, J.B.C., 2001. Refuges revisited. Enemies versus flow and feeding as determinants of sessile animal distribution and form. In: Jackson, J.B.C., Lidgard, S., McKinney, F. (Eds.), Evolutionary Patterns. Growth, Form, and Tempo in the Fossil Record. University of Chicago Press, Chicago, pp. 61 – 93. Riisga˚rd, H.U., 2002. The methods of ciliary filter feeding in the adult Phoronis muelleri (phylum Phoronida) and its free swimming actinotrocha larva. Mar. Biol., in press. Riisga˚rd, H.U., Goldson, A., 1997. Minimal scaling of the lophophore filter-pump in ectoprocts (Bryozoa) excludes physiological regulation of filtration rate to nutritional needs. Test of hypothesis. Mar. Ecol. Prog. Ser. 156, 109 – 120. Riisga˚rd, H.U., Larsen, P.S., 1995. Filter-feeding in marine macroinvertebrates: pump characteristics, modelling and energy cost. Biol. Rev. Camb. Phil. Soc. 70, 67 – 106. Riisga˚rd, H.U., Manrı´quez, P., 1997. Filter-feeding in fifteen marine ectoprocts (Bryozoa): particle capture and water pumping. Mar. Ecol. Prog. Ser. 154, 223 – 239.
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Riisga˚rd, H.U., Nielsen, C., Larsen, P.S., 2000. Downstream collecting in ciliary suspension feeders: the catch-up principle. Mar. Ecol. Prog. Ser. 207, 33 – 51. Ryland, J.S., 1975. Parameters of the lophophore in relation to population structure in a bryozoan community. In: Barnes, H. (Ed.), Proc. 9th EMBS. Aberdeen University Press, Aberdeen, pp. 363 – 393. Ryland, J.S., 1976. Physiology and ecology of marine bryozoans. Adv. Mar. Biol. 14, 285 – 443. Shunatova, N.N., Ostrovsky, A.N., 2001. Individual autozooidal behaviour and feeding in marine bryozoans. Sarsia 86, 113 – 142. Strathmann, R.R., 1982. Cinefilms of particle capture by an induced local change of beat of lateral cilia of a bryozoan. J. Exp. Mar. Biol. Ecol. 62, 225 – 236. Strathmann, R.R., McEdward, L.R., 1986. Cyphonautes’ ciliary sieve breaks a biological rule of inference. Biol. Bull. 171, 694 – 700. Tamada, K., Fujikawa, H., 1957. The steady two-dimensional flow of viscous fluid at low Reynolds numbers passing through an infinite row of equal parallel circular cylinders. Q. J. Mech. Appl. Math. 10, 426 – 432. Winston, J.E., 1977. Feeding in marine bryozoans. In: Woollacott, R.M., Zimmer, R.L. (Eds.), Biology of Bryozoans. Academic Press, New York, pp. 233 – 271. Winston, J.E., 1978. Polypide morphology and feeding behavior in marine ectoprocts. Bull. Mar. Sci. 28, 1 – 31.
On ciliary sieving and pumping in bryozoans Poul S. Larsen a,*, Hans Ulrik Riisga˚rd b a
Department of Energy Engineering, Fluid Mechanics Section, Technical University of Denmark, Building 403, DK-2800 Kgs. Lyngby, Denmark b Marine Biological Research Centre (Institute of Biology, University of Southern Denmark), Hindsholmvej 11, DK-5300 Kerteminde, Denmark Received 17 January 2002; accepted 18 April 2002
Abstract Based on video-microscope observations of trajectories of particles in the feeding currents of individual isolated bryozoans Bowerbankia imbricata, Flustrellidra hispida and Electra pilosa the velocity fields above and in the lophophore have been determined. The flow into the lophophore, which is a result of water currents driven out between tentacles by the water pumping lateral cilia, is characterised by nearly parabolic profiles with highest velocity along the centreline of the lophophore. In intact animals, the centreline velocity first increases from its value at the inlet to a maximal value about 20 to 25% down into the lophophore and then decreases to low values as the flow stagnates at the mouth. In a narcotised animal, whose laterofrontal filter was inactive, the centreline velocity was found to decrease monotonously from its inlet value. An approximate expression is derived for the relation between velocity distribution in the lophophore and variation of pumping rate along tentacles. Typical variations are given and compared to those obtained by a more accurate two-dimensional numerical solution. Based on observed velocity distributions in the lophophore, particle tracks and tentacle flicks, a description is given of the feeding mechanisms. Particles entering the central region are brought to the mouth by the high velocity feeding current in the central part of the lophophore. Particles entering further out either escape between tentacles or are stopped by the laterofrontal cilia sieve and, in the distal region of tentacles, are brought back into the central feeding current by flicks of tentacles. The relative velocity between fluid and particle during a flick recovery phase ensures particle release. Particles stopped in the proximal region of the lophophore appear to be transferred to and conveyed by the frontal cilia bands on tentacles. The added load on laterofrontal cilia from viscous drag on a food particle retained by the cilia is found to be of the same order of magnitude or greater than the ‘background load’ of viscous drag from fluid passing the laterofrontal cilia in the absence of a particle. This is hypothesised to stimulate the sensing mechanism triggering observed flicks. The energy cost of pumping is estimated at 1 to 4% of the metabolic power of a ‘standard’ zooid. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Feeding in bryozoans; Flow in lophophore; Ciliary sieving; Particle retention; Bryozoan model
1. Introduction All bryozoans (‘moss-animals’), also known as the phylum Ectoprocta, are colonial, and in most cases the *
Corresponding author. E-mail address: [email protected] (P.S. Larsen).
units of the colony (zooids) secrete tubes or boxes partially encasing the soft parts. When feeding, the zooid extends its lophophore, a ring of ciliated tentacles with the mouth at the centre of its base, into the adjacent water. In the gymnolaemate bryozoans each tentacle has a tract of lateral cilia on each side, a tract of frontal cilia facing the mouth located at the apex of
1385-1101/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 5 - 11 0 1 ( 0 2 ) 0 0 1 3 6 - 3
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the conical lophophore, and between the lateral and frontal cilia a row of stiff laterofrontal cilia (Mukai et al., 1997). Cyclostomatous bryozoans lack frontal cilia (Nielsen and Riisga˚rd, 1998), but otherwise the basic particle capture mechanism seems to be identical in all bryozoans. When the lateral cilia beat in a coordinated metachronal rhythm, currents are generated which pass straight down the lophophore towards the mouth and out between the tentacles (Atkins, 1932; Bullivant, 1968a,b; Ryland, 1976; Riisga˚rd and Manrı´quez, 1997). Food particles, mainly phytoplankton, in the incoming stream either follow the central current and pass directly to the mouth or are restrained by the stiff laterofrontal ciliary filter (‘ciliary sieving’) and then either transported downwards on the tentacles by means of the frontal cilia, or the particles are transferred to the central current by means of tentacle flicks triggered by the restrained particles (Riisga˚rd and Manrı´quez, 1997; Nielsen and Riisga˚rd, 1998). Similar phenomena have recently been described for another lophophorate, Phoronis muelleri (phylum Phoronida) by Riisga˚rd (2002), who also discussed the possible role of localised disruption of the beat of the lateral cilia during capture of a particle as observed in a bryozoan by Strathmann (1982). Although structure, size and shape of the bryozoan lophophore have been thoroughly examined over the years (e.g. Atkins, 1932; Ryland, 1976; Winston, 1977, 1978; McKinney, 1990; Mukai et al., 1997; Shunatova and Ostrovsky, 2001), only few studies have so far been concerned with hydromechanical aspects of bryozoan feeding (Gru¨nbaum, 1995, 1997; Eckman and Okamura, 1998; Larsen et al., 1998; Larsen and Riisga˚rd, 2001). Obviously, both particle capture and water flow are closely related to the morphology of the lophophore, but the physical and hydromechanical conditions of ciliary-sieving and pump design have not yet been examined thoroughly enough to understand the function and energy cost of the integrated lophophore pump- and filtersystem. This paper, including video-microscope observations of three bryozoan species with different lophophore design, further describes the ‘ciliary sieving’ particle capture mechanism and physical conditions related to this process, and water pumping and flow pattern is characterised and modelled in order to interpret the functional morphology of the bryozoan lophophore in regard to pump-design.
2. Material and methods The gymnolaemate bryozoans Bowerbankia imbricata (Adams), Flustrellidra hispida (Fabricius) and Electra pilosa (Linnaeus) were selected as examples because of their different lophophore design. The two first species both have long tentacles (0.7 and 0.8 mm, respectively), but B. imbricata has only 10 tentacles forming a bell with a short diameter (0.6 mm) and a small apex angle, whereas F. hispida has 28 tentacles forming a bell with a wide diameter (1.2 mm) and a large apex angle. E. pilosa has 12 short tentacles (0.4 mm) forming a bell with a short diameter (0.4 mm). The ctenostomes B. and F. hispida were collected in September 1996 from the rocky intertidal in Menai Strait near Menai Bridge, North Wales, UK. In the laboratory (School of Biological Sciences, University of Wales, Bangor, UK) the bryozoans were kept in containers placed in a thermo-regulated bath (15 jC) with filtered (0.2 Am) and aerated seawater (34xS) until video observations could take place during the following days. For video-observations of the filterpump of F. hispida, lophophores were dissected out and narcotised with 7.5% MgCl2. It is well known that isolated and narcotised lophophores return to the normal funnel-shape probably due to the elastic properties of the thick basement membrane (Nielsen and Riisga˚rd, 1998). The cheilostome E. pilosa was collected in spring 2001 in Kerteminde Fjord, close to the Marine Biological Research Centre (University of Southern Denmark), Kerteminde, Denmark. Colonies grown on microscope glass slides (about 22xS) according to Hermansen et al. (2001) were used for video observations in November 2001. 2.1. Video observations Tentacle flicking and particle paths were recorded using a video camera (Kappa CF 11/1) attached to an inversed microscope (Labovert FS), and a 50 halfframes per second video recorder (Panasonic NVFS200 HQ). The bryozoans were put on the bottom of a cylindrical observation chamber placed on the microscope. The seawater in the observation chamber contained 6 Am diameter flagellates Rhinomonas reticulata at a concentration of 2800 cells cm 3, except for E. pilosa where 11 Am diameter Tetraselmis sp. were used. Video frames could be copied by
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means of a video graphic printer (Sony UP – 860 CE). Tentacle flickings and capture of food particles were traced from their position in successive frames. This was done by mounting a transparent plastic sheet onto the video screen so that the tentacle contours as well as the position of suspended particles could be marked with a pen directly on the sheet frame by frame.
3. Results and discussion 3.1. Video observations The particle capture process and downward transport in the lophophore of Bowerbankia imbricata are illustrated by means of Figs. 1 – 3, which show series of video graphic prints. Particles entering near the centre of the lophophore move directly towards the mouth, occasionally interacting with tentacles in the lower part. Some particles entering in the outer region
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of the lophophore escape between tentacles in the distal region while other particles are captured. When a particle is captured on the distal part of a tentacle this triggers a tentacle flicking that brings the particle into the central core and down towards the mouth. Most transport of captured particles towards the mouth seems to be dependent on such flicking-assisted transport, but particles may also be conveyed downwards on the frontal surface of the tentacles (Fig. 3). Particles in the central current are usually trapped deep down in the lophophore, but this does not trigger a noticeable tentacle flick. Rather a quick displacement, possibly by cilia action (cf Gordon, 1974), brings a trapped particle back into the central current. The velocity profiles of water flow at different depths in the lophophore of B. imbricata, characterised by a small apex half-angle of about 17.5j, are approximately parabolic with the highest velocity in the central core, and this velocity attains its largest
Fig. 1. Bowerbankia imbricata. Particle arrival and capture on a tentacle (A to D) followed by an individual tentacle flick (E, F) which takes the particle into the central current and thus further down towards the mouth (G, H). Particle (6 Am diameter Rhinomonas) indicated by arrow; 0.02 s between video graphic prints.
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Fig. 2. Bowerbankia imbricata. Particle capture (A to F) followed by a tentacle flick (G to L). Particle indicated by arrow; 0.02 s between video graphic prints.
value about 25% down the lophophore (inserted plot in Fig. 4). This velocity distribution may explain the observed particle paths. Particles should stay near the core to reach the mouth. This occurs when particles enter the lophophore near its centre, but when particles enter further out the various interactions with the tentacle structure apparently tend to bring them back into the downward-directed core flow. Fig. 5 shows particle trajectories in untreated and in narcotised (non-flicking) lophophores of Flustrellidra hispida, both characterised by a larger apex halfangle of about 30j. Again, particles entering near the centre of the lophophore move directly towards the
mouth in both cases. However, for the narcotised specimen, particles entering further out move towards tentacles and escape. This indicates that the waterpumping lateral cilia were not seriously influenced by the treatment whereas the laterofrontal cilia filter apparently had become inactive. The velocity profiles of water flow at different depths in the lophophore are again approximately parabolic with the highest velocity in the central core, but now this velocity decreased from its largest value at the inlet of the lophophore (at 0% down; see inserted plot in Fig. 5). For the untreated specimen, however, the highest velocity in the central core attains its maximum value about 20 to
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Fig. 3. Bowerbankia imbricata. Capture for particle conveyed downwards on the frontal surface of the tentacles (A to M). Particle indicated by arrow; 0.02 s between video graphic prints.
25% down the lophophore (Fig. 5, upper left). The inactivity of the laterofrontal cilia filter in the narcotised case apparently changes the variation of the pump flow per unit length of tentacles from root to tip because this variation affects the velocity distribution in the lophophore as appears from the section on cilia pumping below.
Fig. 6 shows the flow pattern and velocity distribution in the lophophore of Electra pilosa. In the periphery of the lophophore inlet, incoming particles are captured by a close interaction between the sensory laterofrontal ciliary filter (which cannot be seen on the video film) and tentacle flicks, as indicated on the figure by abrupt, inward changes of particle paths.
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Fig. 4. Bowerbankia imbricata. Drawings: Examples of particle trajectories in lophophore. Particles captured on the distal part of a tentacle may trigger a tentacle flick (I, II and III indicated by dotted tentacles). Flow lines and velocities (mm s 1) based on a time interval of 0.02 s between subsequent video frames of particles. Plot, right bottom: Velocity profile at different depths in lophophore. Highest velocity occurs about 25% down.
Only particles in the stagnant central current are captured without making contact with the tentacles. 3.2. Ciliary sieving 3.2.1. Particle retention The distance between the stiff laterofrontal cilia, which act as a sieve, determines the lower size of particles that can be retained by the ciliary filter-
feeding bryozoans. The particle retention efficiency of the laterofrontal filter has previously been measured in two other bryozoans and it was found that particles >5 Am in diameter are retained with near 100% efficiency in both Celleporella hyalina (Riisga˚rd and Manrı´quez, 1997) and Electra crustulenta (Riisga˚rd and Goldson, 1997). This shows that the spacing between the stiff 0.2 Am diameter laterofrontal cilia (Llfc f 15 to 20 Am long) may be about 5.5
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Fig. 5. Flustrellidra hispida. Upper left: Particle trajectories in lophophore of intact animal. Highest velocity occurs about 20 to 25% down. Flow lines and velocities (mm s 1) based on a time interval of 0.02 s between subsequent video frames of particles. Upper right: Particle trajectories in ‘leaky’ lophophore dissected out and narcotised with MgCl2 to prevent tentacle flicking. Lower: Velocity profile at different depths in narcotised lophophore. Highest velocity occurs at inlet, 0% down.
Am in these bryozoans. But the spacing seems to vary between groups and species: in cyclostome bryozoans the spacing varies between 2.5 and 4 Am (Nielsen and Riisga˚rd, 1998). The spacing observed on SEM pictures presented by Nielsen (2002) is about 2 Am in F.
hispida and about 3 Am in Alcyonidium gelatinosum. The fact that particles are still seen to escape between tentacles in the outer (distal) region (Fig. 4) is due to the increased spacing between tentacles in this region where the opposing laterofrontal cilia do not meet.
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For an approximate estimate of the pressure drop across the laterofrontal filter in bryozoans a screen of parallel cylinders with a mean diameter of d and spacing b may be a usable model. For a flat screen consisting of parallel cylinders forming a mesh of infinite extent, the pressure drop (DH in mm H2O) is given by the equation of Tamada and Fujikawa (1957), see also Riisga˚rd and Larsen (1995, their Eq.(16)) DH ¼ Kvul =gd
ð3Þ
where K = 8H /(1 – 2lnH + H 2 /6), H = k(d/b), u l = velocity of upstream flow, g = acceleration of gravity (9.807 m s 2), and v = kinematic viscosity of water (1.1 10 6 m2 s 1). Assuming d = 0.2 Am, b = 3.5 Am, and ul c um = 0.5 mm s 1 the pressure drop across the laterofrontal ciliary filter is DH = 0.09 mm H2O, or Dp = UgDH f 0.9 Pa. In the case of spacing b = 5.5 Am the pressure drop is estimated at DH = 0.05 mm H2O, or Dp f 0.5 Pa.
Fig. 6. Electra pilosa. Flow lines and velocities (mm s 1) based on a time interval of 0.02 s between subsequent video frames of particles. Highest velocity occurs close to inlet.
3.2.2. Pressure drop across laterofrontal ciliary filter The pressure drop across the laterofrontal filter cannot be determined in a simple way because of its geometry and because the water is not leaking through the ciliary filter array with the same velocity along the length of the cilia, from tip to base. For an estimate, however, we assume a uniform mean velocity (um) determined from a simple analysis of the lateral cilia pump (Riisga˚rd et al., 2000), um ¼ 0:5 utip ðTa =T Þ
ð1Þ
where T is the full period of beat and Ta is the period of active beat of lateral cilia of length L through angle u (degrees), giving the tip velocity utip ¼ ðu=360Þ2pL=Ta
3.2.3. Drag force and deflection of laterofrontal cilia We now evaluate how much the drag of a food particle captured by the laterofrontal cilia may deflect the about 20 Am long, but only 0.2 Am thick ‘filter’ cilia, as well as the force and moment exerted locally on the tentacle (see Fig. 7). A similar analysis for cilia spaced far apart was given by Riisga˚rd et al. (2000). The force of friction ( F = ‘drag force’) on a stationary
ð2Þ
Using L = 15 Am, 1/T = 25 Hz, Ta = 0.2 T, and u = 150j, gives utip = 4.9 mm s 1 and um = 0.5 mm s 1.
Fig. 7. Ciliary sieving. (Upper) Cross section of three tentacles of a lophophore with frontal cilia (fc), water pumping lateral cilia (lc), stiff laterofrontal cilia (lfc) acting as a mechanical sieve, and a stopped particle subject to downward water velocity u. (Lower) Laterofrontal cilium subject to load from (A) drag on particle and (B) ‘background’ drag on cilium from water velocity, increasing linearly from root to tip, both giving rise to force F, bending moment M at point of fixation to tentacle, and deflection of cilium tip X.
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sphere of diameter (D) placed in a fluid with undisturbed velocity (u) may be calculated according to Stokes’ law for creeping flow, F ¼ 3pDAu
ð4Þ
where A is the dynamic viscosity (1.1 10 3 N s m 2). The predicted deflection (X) of a cilium at the point of loading at a certain distance (l) from the base of the cilium is given by (Strathmann and McEdward, 1986), X ¼ Fc l 3 =3S
ð5Þ
where Fc is the force acting on one cilium and S is the flexural stiffness of the cilium (found to be about 2 10 19 N m2; Baba, 1972). At the point of fixation to the tentacle will act the force Fc and a bending moment of Mp = Fcl. For a realistic case example consider a 6 Am diameter particle that has been stopped by two laterofrontal cilia which ensures that the drag force on the particle is distributed on both cilia. Due to the actively beating lateral cilia the water flow past the particle may vary from u f 1 mm s 1 near the tip to 0 near the base of the laterofrontal ciliary filter, and further the loading point may vary between 0 and 20 Am. For an estimate of the maximum possible drag force, bending moment, and deflection caused by a stopped particle (at u = 1 mm s 1, l = 20 Am, S = 2 10 19 N m2) it is found that Fc = F/2 = 3 10 11 N, Mp = 6 10 16 N m, and X = 0.4 Am. The 0.4 Am deflection of the cilium tip due to drag on the stopped particle is negligible and indicates that the laterofrontal ciliary array has a sufficient stiffness to act as a sieve (‘mechanical filter’). 3.2.4. Trigger mechanism of tentacle flicking Each stiff laterofrontal cilium is situated in a depression surrounded by a collar of microvilli, which suggests that they are sensory (Lutaud, 1973; Mukai et al., 1997; Nielsen and Riisga˚rd, 1998), i.e. they may be able to trigger a tentacle flicking when a particle is retained by the ciliary filter. Further, according to Gordon (1974) the stiff laterofrontal cilia, observed in a single tentacle of a live Cryptosula pallasiana using a negative-field phase-contrast microscope, ‘‘are not rigid, but capable of occasional flicking movements’’.
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The exact mechanism that triggers such a flick is unknown, but it is reasonable to suggest that a certain extra drag force, besides the ‘background’ force exerted on the laterofrontal cilia due to the moving water, may be a prerequisite for triggering a tentacle flick. This is illustrated by the following considerations. An estimate of the ciliary-root moment (Mf) from the loading due to viscous flow (see Fig. 7) may be obtained from the pressure drop of Dp = 0.5 Pa across the laterofrontal filter (see previous section), which implies a force on each laterofrontal cilium of Fc = DpbL, where b = 3.5 Am is the centre distance between two cilia, and L = 20 Am is the length of laterofrontal cilia. Considering each cilium to be a lever arm the bending moment is estimated to be Mf = 2FcL/3 = 2DpbL2/3 = 4 10 16 N m, which is about identical to the above bending moment Mp due to a captured particle. This shows that the drag force of a captured particle is likely to be sufficiently strong to transfer a perceptible force and moment via the clamped root of the laterofrontal cilia affixed to the tentacle, i.e. the laterofrontal cilia may have a sensory function. If this is actually the case it implies that particles too small to be retained by the laterofrontal ciliary filter should not be able to trigger the flick mechanism. So far, however, this assumption has not been supported by experimental evidence. The dynamics of the trigger event should also be considered. As a tentacle is triggered it moves quickly a distance towards the centre of the lophophore with an estimated velocity of Vflick f 2.4 mm s 1 in B. imbricata and 10.7 mm s 1 in Flustrellidra hispida (Riisga˚rd and Manrı´quez, 1997, Table 3). Being retained by the stiff laterofrontal cilia the particle necessarily follows this motion and the fluid velocity relative to the particle may therefore increase from the value u f 1 mm s 1 (see above) to a value of u + Vflick. Since linear in approach velocity, all loads calculated previously will increase by a factor of 1 + Vflick/u f 3.4 to 11.7. Apparently, the laterofrontal cilia can handle such increased loads. Subsequently the tentacle moves back from the region of increased downward flow in a recovery stroke, which lasts 2.3 to 7.7 times longer than the active stroke (Riisga˚rd and Manrı´quez, 1997). During this event the fluid velocity relative to the particle, due to both pump action and tentacle motion, is probably negative or
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close to zero, which may explain why the particle is released to the core flow.
coordinate along the tentacle, ttip being the length of tentacles (Fig. 8), Eq.(6) becomes
3.3. Ciliary pumping
dðg2 sinbVm Þ=dg ¼ 4gVn
3.3.1. Pumping rate along tentacle The observed velocity distributions in the lophophore may be related to the pumping rate along tentacles by a simple mass balance. Plots in Figs. 4 and 5 show that radial distributions of downward velocity in the lophophore may be approximated by parabolas, hence the mean velocity equals one-half the maximum at the centreline, 1/2 Vm. Using this and equating the change in downward flow to loss between tentacles, the steady, one-dimensional form of conservation of mass for incompressible flow yields
According to this relation, a constant pumping rate along tentacles, V n f constant, would lead to Vm f constant, which is not observed (recall Figs. 4 and 5) so Vn must vary along tentacles. The velocity distribution in the lophophore, with the highest velocity at the centreline, Vm, is easily understood because the laminar streamlines for downward flow in the lophophore are being compressed along the centreline according to the apex angle. Thus, the maximum centreline velocity tends to be higher in a lophophore with long tentacles and a small apex angle than in a lophophore with short tentacles and a wide apex angle. Less obvious is the depth at which the maximum centreline velocity appears in a lophophore of a certain morphometry. To complete a general description of water flow and velocity distribution in a specific lophophore, the consequences of variable space between adjacent tentacles must also be taken into account. The form of the lophophore is constrained within certain limits: the number of tentacles may vary from 8 to 31, the length of tentacles may vary from 0.124 to 0.929 mm, the lophophore diameter from 0.187 to 1.226 mm, and the distance between the tips of the tentacles from 0.077 to 0.142 mm (Ryland, 1975, 1976; Winston, 1978; Gordon et al., 1987), and further, the distance between the tentacle tips determines the axillary angle which may vary between 10.5j and 30.8j (Ryland, 1976, Fig. 18 therein). The axillary angle is of great significance for the intertentacular gap and thus the distance between the water pumping lateral cilia on the opposing sides of the tentacles. The width of the intertentacular gap determines the velocity profile driven by the lateral cilia, and as the intertentacular gap vanishes downward the lateral cilia get more and more close, eventually impeding their pump efficiency. The intertentacular gap and the length of the lateral cilia have been measured in F. hispida by Markham and Ryland (1991). It was found that the lengths of the lateral cilia decrease proximally toward the mouth from a sub-distal maximum of about 23 Am to only 14 Am near the mouth so that the cilia completely span the gap for 25% of its length.
dðprt2 1=2Vm Þ ¼ 2prt Vn dz=cosb
ð6Þ
where rt denotes the radius of the lophophore at any location z, Vn the mean velocity normal to tentacles over the full circumference, and h the apex half-angle (see Fig. 8). Changing variables to D = t/ttip, noting dz = cosh dt, rt = t sinh where t is a convenient local
Fig. 8. Radial section of axisymmetric lophophore of apex halfangle h (schematic), showing velocity profile in lophophore with maximum Vm at axis, and variation of pumping rate, Vn, along tentacle having local coordinates (t,n).
ð7Þ
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Therefore, the mean velocity referred to area between tentacles may vary along tentacles. Since this value is greater than Vn in Eq.(6) by a factor 2krt /(2krt-ntdt) where nt denotes the number of tentacles and dt their diameter (or width), it is clear that the velocity normal to the tentacles may vary along the tentacle and possibly influence the depth at which the maximum centreline velocity appears in the lophophore. In order to examine how different variations Vn affect the variation of maximum downward velocity in the lophophore, consider two possible variations along tentacles of the pumping rate: linearly increasing, and parabolic with vanishing pumping rate at root and tip, i.e. Vn(D)/Vn(1) = D and D(1 D), respectively. Using (7) for these cases gives the results Vm(D)/ Vm(1) = D and D(4– 3D), respectively. In Fig. 9 the two cases are compared to experimental observations (from Figs. 4 –6). Data for B. imbricata (Vm(1) f 4 mm s 1), the untreated F. hispida (Vm(1) f 2.5 mm s 1), and E. pilosa (Vm(1) f 3.4 mm s 1) appear to follow a parabolic variation with a maximal value near 20 to 25% into the lophophore, while those of the narcotised F. hispida (Vm(1) f 4 mm s 1) show a nearly linear variation.
Fig. 9. Normalised centreline velocity Vm(D)/Vm(1) in lophophore versus position in terms of % from inlet, 100(1 D). Experiment: Bowerbankia imbricata (+); Flustrellidra hispida (o) narcotised and ( ) untreated; Electra pilosa (D). Approximate theory assuming the distribution of pumping rate along tentacle to be linear, D ( – – – ), and parabolic, D(1 D) (- - - -). Two-dimensional model, case D(1 D), h = 17.5j of Fig. 10 (——).
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To evaluate the approximate one-dimensional model of (6)-(7) a numerical solution has been made to the equations governing low-Reynolds number creeping flow in a two-dimensional axisymmetric model of a single, isolated lophophore with prescribed pumping rate Vn along tentacles (recall Fig. 8). Fig. 10 (upper) shows the computational domain in the r,z-plane, which extends to r = 10L and z = 10L, where L denotes the height of both lophophore and stem. For the cases of h = 17.5j and 30j, and Vn f D(1 D), Fig. 10 (lower) shows the resulting streamlines of the recirculating flow in the proximity of the lophophore set up by the pumps, which gives an idea of the extent of the flow. Given the streamline solution, the radial and vertical components of velocity are known, particularly the downward velocity in the lophophore. The computed maximal velocity, Vm, along the centreline of the lophophore is shown in Fig. 9 for the cases of h = 17.5j to illustrate the differences between the approximate one-dimensional model and a twodimensional numerical model. Although the normalized distribution of Vm is similar for the two models their magnitudes are different, in part because the former does not account for viscous effects. Once captured by the lophophore, the particles accumulate above the open, circular mouth where the muscular pharynx acts as a suction pump (Atkins, 1932). Occasional and rapid pharyngeal dilation, which is not included into the model, results in ingestion of the particles. For B. imbricata in the present work, it has been estimated that during ingestion a water volume of about 4 10 4 mm3 is sucked into the pharynx through the open mouth (diameter 50 Am) within 0.02 s resulting in a suction speed of 10 mm s 1 through the mouth. As the pharynx ‘slowly’ (during the following about 0.8 s) returns to its relaxed state, surplus water is drained back through the mouth while the particles remain in the pharynx and eventually are swallowed through the esophagus into the stomach. Particles entering the lophophore along the centreline may be carried directly to the mouth; but ingestion seems to be dependent on action of the pharynx suction pump. Particle capture in the central water current is a normal part of the feeding process in all bryozoans, but the quantitative importance for food uptake seems to be insignificant, only about 5% (Nielsen and Riisga˚rd, 1998).
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Fig. 10. Upper: Axisymmetric computational domain for model of single, isolated bryozoan with cone-shaped lophophore of height L formed by a large number of tentacles, each forming apex half-angle h with axis. Lower: Computed streamlines showing the recirculating flow driven by specified pumping rate, Vn f D(1 D), h = 17.5j and 30j. (Only part of the computational domain near lophophore is shown).
3.3.2. Energy cost of pumping Hunter et al. (1996) measured the oxygen uptake in Celleporella hyalina to be 2.2 F 1.5 10 6 cm3 O2 h 1 zooid 1 (after correction of a printing error; R.N. Hughes pers. comm., 1997). The oxygen uptake in Schizoporella bifrons and Membranipora hyadesi was measured by Moyano et al. (1974) to be 6.15 and 3.45 10 6 cm3 O2 h 1 zooid 1, respectively, and in Bugula turrita Magnum and Schopf (1967) measured the respiration to be 4.25 10 6 cm3 O2 h 1 zooid 1. For the present purpose, a mean respiration rate of 4 10 6 cm3 O2 h 1 zooid 1 may be applied, and using a conversion factor (Elliott and Davison, 1975) 1 cm3 O2 h 1 = 20 J h 1 = 5555 AW, the metabolic power for a ‘standard’ zooid is estimated at R = 0.02 AW.
The present measurements for an isolated B. imbricata showed a mean velocity of w0 f 2.0 mm s 1 at the entrance to the lophophore of diameter di f 0.5 mm (Fig. 4), hence the volume flow through a zooid is about Q = Ai w0=(k/4)di2 w0 f 0.39 mm3 s 1. Using the estimated pump pressure of Dp f 0.5 Pa, the pumping power supplied to the water is PP = Q Dp f 0.0002 AW, which is 1% of the above metabolic power of the ‘standard’ zooid. The corresponding values for F. hispida are w 0 f 1.9 mm s 1 , di f 1.1 mm (Fig. 5) and Dp f 0.5 Pa, yielding Q f 1.8 mm3 s 1 and PP f 0.0009 AW, which is 4.5% of the metabolic power of the ‘standard’ zooid. These results may be compared to those presented by Larsen and Riisga˚rd (2001) in modelling the chimney spacing in encrusting bryozoan colonies of
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Membranipora membranacea. Here the backpressure characteristic was modelled as Dp ¼ pmax ð1 w=wmax Þ
ð8Þ 1
inferred with pmax f 2.2 Pa and wmax f 3 mm s from the model of Gru¨nbaum (1995). Using Eq.(8) and noting that the volume flow per zooid is Q = Ai w0, the pumping power may be expressed as PP ¼ QDp ¼ wmax Ai pmax w=wmax ð1 w=wmax Þ
ð9Þ
The experimental observations of isolated zooids by Larsen and Riisga˚rd (2001, Fig. 2 therein) gave the values w f 1.2 – 1.3 mm s 1, di f 0.6– 0.7 mm, hence Dp = 1.28 Pa and PP f 0.00043 AW or about 2% of the metabolic power of the ‘standard’ zooid, which is in reasonable agreement with the present results. 3.4. Functional integration and hydromechanical aspects The present work is primarily based on observations and modelling of individual bryozoan zooids feeding in stagnant water. Although such simple, standardised laboratory conditions may be profitable for revealing basic functions and flow patterns, it is clear that the feeding success of the individual zooid is dependent on external water flow and mixing to supply food particles and to prevent recirculation of once filtered water. Although all bryozoans are colonial, the individual feeding zooids may be arranged in such a way that the hydrodynamic influence of the neighbouring zooids is rather insignificant, as may be the case in colonies forming erect slender branches of zooids (e.g. Crisia sp.), or colonies with more or less solitary zooids along a stolon (e.g. Bowerbankia sp.). However, in other colonies, such as Membranipora membranacea, forming extensive encrusting sheets of close-set zooids, the water currents generated by the individuals is indistinct, but co-ordinated to create benefits for the whole colony. Crowding of individuals reduces the feeding flow to individuals in the interior of the colony (Gru¨nbaum, 1995) and could mean a scarcity of food, but linked together in a colony zooids form a structurally and physiologically integrated compound organism with new properties. Colony morphology may thus have profound consequences for feeding. Thus, closely packed zooids in encrusting bryozoan colonies pump water against
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friction in the canopy region below the lophophores in order to drive the filtered water to either the rim of the colony or to so-called chimneys (areas without lophophores) for exhalant water from a larger number of zooids. The chimneys are arranged at regular intervals and appear to develop in a given area when the feeding rate of the zooids becomes less than a certain minimum value (Larsen and Riisga˚rd, 2001). Strong exhalant jets may prevent recirculation (Lidgard, 1981), and closely packed lophophores may be an advantage in the benthic boundary layer in which flow speeds increase with height above the surface. Fig. 11 shows the flow pattern and velocity distribution in the region above two neighbouring lophophores of E. pilosa. It is seen that the combined feeding currents produced by the two lophophores are faster and more vertically directed than the bending ‘recirculating’ currents of the isolated lophophore (cf. streamlines in Fig. 10). This is in agreement with the assumption that colonies with tightly packed lophophores develop
Fig. 11. Electra pilosa. Flow pattern and velocity distribution in the region above two neighbouring lophophores. Flow lines and velocities of particles (mm s 1) based on a time interval of either 0.02 s between subsequent video frames (crosses) or 0.1 s (dots).
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cylindrical feeding zones which divert water into the lophophore from a greater height than widely spaced lophophores (Eckman and Okamura, 1998; Okamura et al., 2001). Thus, colonies with tightly packed lophophores and exhalant chimney jets may have a higher feeding rate than colonies with more scattered lophophores. 4. Conclusion Over the years, the objective of many experimental and morphological studies has been to understand the method by which suspended particles are being captured by bryozoans. The present work, based on new insight provided during recent years’ research, has in detail described the particle capture mechanism and aspects of water flow related to the morphology of the bryozoan lophophore. The physical conditions related to the capture process have been examined, and the pump-design analysed by modelling. It has been found that water flow and velocity distribution in the lophophore is a consequence of the morphometry of variable space between adjacent tentacles and that the low energy pump is a necessary requisite for the ciliary sieving mechanism to operate in bryozoans. The bryozoan lophophore is a highly integrated pump- and filter system in which the particle-capture mechanism is based on a close and sophisticated interplay between a sensory ciliary filter that triggers an inward tentacle flick, which brings the arrested particle closer to the axis of the lophophore, and a centrally focused, downward stagnating current caused by the special pump design. Acknowledgements H.U.R. was supported by a grant from the Danish Natural Research Council (no. 28– 808). Thanks are due to the reviewers, who waived anonymity (Dr. Frank K. McKinney and Dr. Judith E. Winston). References Atkins, D., 1932. The ciliary feeding mechanism of the entoproct Polyzoa, and a comparison with that of the ectoproct Polyzoa. Q. J. Microsc. Sci. 75, 393 – 423.
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Riisga˚rd, H.U., Nielsen, C., Larsen, P.S., 2000. Downstream collecting in ciliary suspension feeders: the catch-up principle. Mar. Ecol. Prog. Ser. 207, 33 – 51. Ryland, J.S., 1975. Parameters of the lophophore in relation to population structure in a bryozoan community. In: Barnes, H. (Ed.), Proc. 9th EMBS. Aberdeen University Press, Aberdeen, pp. 363 – 393. Ryland, J.S., 1976. Physiology and ecology of marine bryozoans. Adv. Mar. Biol. 14, 285 – 443. Shunatova, N.N., Ostrovsky, A.N., 2001. Individual autozooidal behaviour and feeding in marine bryozoans. Sarsia 86, 113 – 142. Strathmann, R.R., 1982. Cinefilms of particle capture by an induced local change of beat of lateral cilia of a bryozoan. J. Exp. Mar. Biol. Ecol. 62, 225 – 236. Strathmann, R.R., McEdward, L.R., 1986. Cyphonautes’ ciliary sieve breaks a biological rule of inference. Biol. Bull. 171, 694 – 700. Tamada, K., Fujikawa, H., 1957. The steady two-dimensional flow of viscous fluid at low Reynolds numbers passing through an infinite row of equal parallel circular cylinders. Q. J. Mech. Appl. Math. 10, 426 – 432. Winston, J.E., 1977. Feeding in marine bryozoans. In: Woollacott, R.M., Zimmer, R.L. (Eds.), Biology of Bryozoans. Academic Press, New York, pp. 233 – 271. Winston, J.E., 1978. Polypide morphology and feeding behavior in marine ectoprocts. Bull. Mar. Sci. 28, 1 – 31.