Navigating the Depths of Hydrozoan and Bryozoan Physical Design Solutions

Keywords: Skeletons, locomotion, medusoid jet propulsion, hydrodynamics, feeding mechanisms, nematocytes.

Abstract

The phylum Bryozoa and the class Hydrozoa are easily confused due to having similar appearances in many specimens. Even if there exists an abundance of scientific literature allowing us to distinguish their physiology, behavior and anatomy, there remains a gap in comparing their respective physical adaptations. Thus, this paper aims to compare how these superorganisms overcame similar environmental pressures through the connecting lens of physics. In the context of skeletal design, hydrozoans uniquely bear a hydrostatic skeleton whereas calcified exoskeletons are a shared feature among hydrozoans and bryozoans. Secondly, while bryozoans lack a medusoid stage altogether, hydrozoans have adapted through different means of locomotion during the latter stage for enhanced mobility and better prey capture success. Finally, many distinctions were found between hydrozoan feeding mechanisms such as how they utilize current flow and engage their tentacles, obvious in their medusoid stage, but very surprising in their polyp stage when compared to bryozoan polyps.

Introduction

Hydrozoa

Known as “the stinging creatures,” phylum Cnidaria, spanning over 11,000 species, includes the hydrozoan class. Composed of approximately 3,500 species of its own, Hydrozoa shares common ancestry with other polypoid and medusoid marine organisms, such as sea anemones and jellyfish, and is a sister to other medusozoan classes such as Staurozoa, Scyphozoa and Cubozoa (Figure 1) (Leclère et al., 2016).

Hydrozoa differs from the rest of the cnidarian classes when it comes to its reproduction and life cycles, particularly with respect to its morphologies across each stage. While historically challenging, differentiation of species within Hydrozoa today is also based on their life cycles, which greatly vary in their polyp, colony and medusa morphologies, as well as the total absence of the polyp or medusa stage in some species (Figure 1) (Cartwright & Nawrocki, 2010).

Fig. 1. Hydrozoan phylogeny and life cycle diversity and evolution. Red, orange, and blue dots indicate planula, polyp, or medusa stages in the life cycles of their last common ancestor. White and black diamonds respectively indicate loss or gain of forms. (c) Various species (i, ii, iii, iv) are shown to illustrate these varying morphologies. (Leclère et al., 2016).

Hydrozoans reproduce by means of sexual and asexual reproduction. Budding is the main method of asexual conception of polyps among colonies and medusae (LaDouceur, 2021; Shikina & Chang, 2018). In some species, medusae can reproduce by fission or budding as well (e.g., Cladonema sp.).

Generally, the life cycles of many hydrozoans start with a free-swimming planula larva that can swim or crawl using cilia and eventually attach to a substrate (LaDouceur, 2021). Planulae afterwards transform into primary polyps, from which other genetically identical polyps bud to form the benthic colony. Once it reaches reproductive maturity, the colony develops gonophores, specialized reproductive zooids, that release pelagic, free-swimming medusae, which in turn carry out sexual reproduction by releasing gametes in the water column (Cartwright & Nawrocki, 2010; LaDouceur, 2021). Although it is descriptive of many species, this lifecycle framework however does not apply unconditionally to all species as many of them exhibit variability in their morphologies or the complete lack altogether of certain stages.

Hydrozoans exist in both benthic and pelagic environments depending on their stages and their species. Due to their relatively small size and shape, medusae in Hydrozoa are vulnerable to damage due to wave action, currents and predators (LaDouceur, 2021).

Bryozoa

Bryozoans (phylum Bryozoa), or “moss animals” are small (less than 1 mm in diameter) colonial filter feeding invertebrates living in a broad spectrum of aquatic environments (Smith, 2020). There are more than 6,500 recent species and over 15,000 fossil species, divided into three classes: Phylactolaemata, Stenolaemata and Gymnolaemata. The former is composed entirely of freshwater species lacking a calcified skeleton, while the latter two consist of mostly marine and entirely marine species, respectively. Moreover, the majority have mineralized skeletal components (Schwaha, 2021b; Smith, 2020).

While colony structure varies significantly and polymorphism creates highly specialized zooids, the general morphology of autozooids (feeding zooids) is consistent across the phylum (Figure 2).

Fig. 2. The general body plan of autozooidal bryozoans. On the left, the polypide is protruded. The right shows the retracted form. The axes (anal, oral, distal, and proximal) refer to the orientation of a single zooid. Abbreviations: a – anus, at – atrium, bw – body wall, cae – caecum, cg – cerebral ganglion, db – duplicature band, f – funiculus, int – intestine, l – lophophore, lb – lophophoral base, o – orifice, rm – retractor muscle, ts – tentacle sheath, v – vestibulum, vm – vestibular muscles, vw – vestibular wall. (Schwaha, 2021b).

Each zooid is divided into two main sections: the cystid and the polypide. The latter consists of the soft tissues of the zooid, such as the lophophore (feeding tube), digestive tract, and musculature. Meanwhile, the cystid comprises the cellular body wall (the endocyst) and the cuticle (the ectocyst). The ectocyst also refers to mineralized skeletal elements in classes having a calcified skeleton (Schwaha, 2021b).

A point of contention in scientific community is the phylogenetic classification of bryozoans. Initially, bryozoans were classified as “zoophytes”, due to the plant-like appearance of some colonies (Winston & Migotto, 2021). Currently, bryozoans are a part of the clade Lophophorata, which unites them with phoronids and brachiopods (Figure 3), based upon the similarities of the tentacle crown (lophophore) present in these phyla. However, despite morphological similarities, molecular phylogenetic tests do not yield the same results. As such, the phylogenetic placement of bryozoans is an active area of research in bryozoology (Schwaha, 2021a).

Fig. 3. On the left, the phylogenetic position of Bryozoa as a part of Lophophorata (shown by the red box). On the right, the bryozoan classes, where Ctenostomata 1 refers to the predecessor to the modern gymnolaemate orders. (Smith, 2020).

Colonies are hermaphroditic, meaning zooids produce both male and female gametes, and participate in sexual and asexual reproduction. Sexually reproduced zygotes are either released into the water column or incubated within the colony. Once released, individual zygotes are free to establish new colonies (the zygote is then called the ancestrula). All subsequent zooids making up the colony are produced via asexual budding from the ancestrula (Ostrovsky, 2021).

Skeletal systems in Hydrozoa and Bryozoa

Skeletons provide essential structural support, protection, and allow movement. While the word “skeleton” generally refers to an internal calcium carbonate skeleton (endoskeleton), there are two additional skeletal systems. First is a hydrostatic skeleton, which is generally found in soft-bodied animals, including hydrozoans, such as Physalia physalis (Clark, 2018; Munro et al., 2019). The second is the exoskeleton, an external, rigid skeleton composed of various materials found in both bryozoans and certain hydrozoans. For instance, phenolactolaemates have gelatinous or chitinous exoskeletons, while stenolaemates, gymnolaemates, and members of family Milleporidae (Hydrozoa: Anthoathecata) have calcified exoskeletons (Lewis, 2006; Schwaha, 2021b). The relationship between skeletal systems and environment will be explored in greater detail in this section, through the hydrozoans P. physalis and Milleporidae, as well as stenolaemate bryozoans.

Hydrostatic skeletons

In hydrostatic skeletons, the force of muscle contraction is transmitted by the internal pressure of an enclosed fluid and the deformation of the body. Interestingly, animals or structures that rely on hydrostatic skeletons tend to be approximately cylindrical in shape, with musculature arranged to be able to control the diameter and length of the cylinder (Kier, 2012). There are three muscle arrangements responsible for controlling the diameter, which are perpendicular to the longitudinal axis (circular, radial, and transverse fibers), and one arrangement parallel to the longitudinal axis (longitudinal fibers) that governs changes in length (Kier, 2012). The working principle of hydrostatic skeletons involve the bulk modulus of the enclosed fluid, which is a measure of resistance to compression. Thus, a high bulk modulus corresponds to low compressibility, such as in fluids. In the context of hydrostatic skeletons, the contraction of the circular, radial or transverse muscle fibers causes a decrease in the diameter. As a result, the internal pressure is increased, which would usually result in a change in volume. However, as no major change in volume can occur, the length of the cylinder increases. An inverse process, wherein the longitudinal fibers contract, decreasing the length and expanding the diameter of the cylinder, reverses the deformation. Hydrostatic skeletons lack a fulcrum, which provides a mechanical advantage in rigid skeletons. Instead, they amplify force through the relationship between cylinder diameter and length (Figure 4). This relationship can also be represented by the equation for the volume, V, of a cylinder of length, l, and radius, r, (Kier, 2012):

Assuming constant volume and rearranging Eqn. 1, the derivative of the radius with respect to length gives (Kier, 2012):

Since diameter and length are not linearly proportional, a small decrease in the diameter will result in a far larger increase in the length.

Fig. 4. A graphical representation of the relationship between diameter and length of a constant volume cylinder. The positions on the graph of cylinders A-D (drawn to scale) are indicated. Note that a small decrease in diameter from shape B to D causes a significant increase in length. (Kier, 2012).

There are many hydrozoans with a hydrostatic skeleton, such as P. physalis (Siphonophorae). This species is a member of the pleuston, a group of marine organisms living at the surface of the ocean (Munro et al., 2019). A unique characteristic of this species is the pneumatophore, a layered structure composed of the codon (containing muscle fibers); the pneumatosaccus, which acts a gas-filled sac; and a gas gland. Muscle contractions of the codon erect the pneumatophore like a sail, allowing P. physalis to drift on the water (Munro et al., 2019). The pneumatophore is an example of a hydrostatic skeleton that utilizes a gas instead of liquid. A hydrostatic skeletal system allows P. physalis to control the pneumatophore’s inflation to combat desiccation caused by sunlight exposure, and avoid “breaking” due to the rough conditions at the surface of the ocean, which may occur with a rigid skeleton (Munro et al., 2019).

Calcified exoskeletons

Calcium carbonate skeletons may be composed of two different crystallite polymorphs, calcite, or aragonite. In general, skeletal substructures are composed of layers of one or both crystallites with thin layers of elastic biopolymers between them. Calcite and aragonite can form blocks, laths, plates, fibres, or granules, which are arranged into layers. These can give rise to various microstructures with unique mechanical properties (Figure 5) (Negrini et al., 2022).

Fig. 5. Pplanar spherulitic crystallite fabrics found in stenolaemates. A) Crisia signoidea; strips of planar spherulitic fabric in exterior frontal wall with slit-like pseudopores at strip boundaries. B) Tubulipora elegans; new terminal diaohragm growing from interior wall with transverse fibrous fabric (left). C)-D) rhombic semi-nacreous crystallite fabric in skeletal walls of Heteropora magna. Wall surfaces consist of rhombic tablets with frequent screw dislocations and scatttered small, newly formed crystallites. (Scale bars: 12 μm in A); 15 μm in B); 5 μm in C) and 7.5 μm in D)) (Taylor & Weedon, 2000).

Millepora is the only genus within the family Milleporidae of hydrocorals, which are found at depths of 1 to 40 m in coral reefs worldwide. Commonly known as “fire corals” or “stinging corals” due to the defensive polyps found within the colony, millepores secrete a branching or encrusting calcareous skeleton. Many colony morphotypes (see Figure 6) are common within species as colony morphology varies as environmental conditions change (Lewis, 2006).

Fig. 6. Three possible growth forms of Millepora alcicornis colonies. (A) Coarse branching. (B) Bushy branching. (C) Fine branching. (Lewis, 2006). It has been suggested that colonial growth morphologies, particularly the type of branching, are related to the environment in which a colony lives.

In a study conducted on Millepora complanata, colonies with a specific morphology were transported to different depths and locations on reefs. As a result, the branching morphology of the colonies changed in response to their environment (Lewis, 2006). Thus, the external stresses within the environment have a direct impact on the physical structure of millepores. It is possible that with the change in morphotype of the colonies, an accompanying change in the skeletal substructure occurred as well, although further research and imaging of samples is required to confirm this. The skeletal surface of millepore hydrocorals is described as consisting of bundles of crystalline needles (Lewis, 2006). Meanwhile, the main portion of the exoskeleton is made up of small rods (trabeculae) of dense calcium carbonate crystal fibres (Lewis, 2006) arranged in thin layers (lamellae), with the fibres crossing each other at all angles (Figure 7).

Fig. 7. A) The fasciculate skeletal surface of Millepora dichotoma. The surface of each fasciculus is nodular, and each nodule is a conglomerate of individual crystals. B) Fractured fasciculi of M. dichotoma showing the arrangement of individual crystals into linear series forming needles. Note the rounded shape of individual crystals. FS = fasciculus. (Le Tissier, 1991).

Significantly, chemical analysis of the exoskeleton suggests that the composition is not markedly different from other hard corals, such as scleractinian corals (Lewis, 2006). Therefore, it is possible to conclude that millepore hydrocorals may share a similar skeletal substructure with scleractinian corals, which secrete aragonite skeletons (Hendricks, 2019), as they occupy similar environments.

Similarly, stenolaemates, represented uniquely by the order Cyclostomata, secrete a calcareous skeleton. However, in the case of stenolaemate bryozoans, the epithelial cells secrete calcite exoskeletons (Ernst, 2021). A study by Negrini et al (2022) compared the crystallographic properties of Hornera currieae and Hornera robusta, which both develop low-Mg calcite laminated walls (Negrini et al., 2022). H. currieae is found at depths of about 1000 m, with minimal currents but immense hydrostatic pressure. In contrast, H. robusta is found at depths between 50 and 400 m, where it is exposed to currents and storms. The study explores the relationship between water depth, aquatic environment, and physical properties, such as the Young’s modulus, of the skeleton.

Did you know? The National Oceanic and Atmospheric Administration (NOAA) estimates that for every 10 m below the surface, the pressure increases by 1 atm (NOAA, 2024). At 1000 m deep, the pressure increases by 100 atm, or about 1×10⁷ Pa! Thus, H. currieae experiences 2.5-20 times more pressure than H. robusta.

While H. currieae and H. robusta have a similar ultrastructure, the crystallite orientations vary slightly. Generally, the crystallites are oriented with their c-axes (0001) perpendicular to the skeleton wall, and the a-(11-20) and m-(10-10) axes oriented randomly around the c-axes (Figure 8) (Negrini et al., 2022).

Fig. 8. Electron Backscatter Diffraction (EBSD) analysis of crystallite orientations. (A) EBSD orientation map of crystallites in H. currieae, with the location of the map shown in the upper right corner. (B) EBSD orientation map of crystallites in H. robusta, with the location of the map shown in the lower right corner. Crystallites with their c-axis pointing out of plane are red in both maps, with pole figures showing the orientation of the c-(0001), a-(11-20), and m-(10-10) axes. Note the difference in colorations of the maps, corresponding to a difference in the number of c-axes oriented out of plane. (Negrini et al., 2022).

In H. currieae, the c-axes show strong crystal preferred orientation (CPO) (Figure 8A), whereas in H. robusta, the c-axes show more variation, resulting in a lower CPO (Figure 8B). Crystallite mechanical properties are orientation-dependent, as individual calcite crystals are elastically anisotropic; their elasticity varies with the direction it is measured in (Negrini et al., 2022). Calculation of the Young’s modulus of the samples (Figure 9) demonstrates that the strong CPO of H. currieae leads to a direction of lower stiffness perpendicular to the skeleton walls and a plane of higher stiffness parallel to the skeleton walls. The plane is isotropic, which maximizes the stiffness coefficient in all directions within the plane. In comparison, the weaker CPO caused by scattered c-axes in H. robusta leads to a direction of lower stiffness parallel to the c-axis (approximately perpendicular to the skeleton wall), and a slightly anisotropic plane of higher stiffness perpendicular to the c-axis. The plane has a stiffer direction parallel to the growth direction, with the less stiff direction perpendicular to it (Negrini et al., 2022).

Fig. 9. Young’s modulus calculations and distributions in (A)-(B) H. currieae and (C)-(D) H. robusta. (A) and (C) are calculated Young’s modulus values in the plane. (B) and (D) are Young’s modulus distribution maps in three different orientations calculated using the EBSD data in Fig. 6 above. The map orientations from left to right are parallel to the growth direction, normal to the growth direction and normal to the skeleton wall. (Negrini et al., 2022).

Overall, the Young’s modulus anisotropy in H. currieae is 45.9% compared to 20.2% in H. robusta. The disparity in anisotropy can be related to the environment each species lives in. For instance, H. currieae experiences high hydrostatic pressure in its environment, and the anisotropy of its skeleton helps to concentrate stiffness in the direction of the pressure. In contrast, H. robusta lives in an environment with external stresses coming from many directions. The isotropic nature of its skeleton allows it to better resist multidirectional forces (Negrini et al., 2022).

In brief, the skeletal system and structure found in hydrozoans and bryozoans is a direct result of their adaptations to their environment. A hydrostatic skeleton, as found in P. physalis, allows the species to face harsh surface conditions without damage. Similarly, millepore corals and H. robusta are both subject to variable currents and storms, and thus have adapted sturdier branching morphologies and skeletal substructures, respectively. Finally, H. currieae experiences significant hydrostatic pressure in its environment, but comparatively little currents, and thus concentrates the stiffness of its skeleton in the direction of greatest pressure. The variety of skeletal structures found in hydrozoans and bryozoans contributes to the clades’ ability to live in virtually any marine habitat.

Modelling Jet Propulsion in Medusoid Organisms

Based on the methods developed by Colin and Costello (2002), instantaneous acceleration in jetting medusae can be modelled as follows:

Where jet thrust (T), drag (D), weight (W) and effective mass (E) are considered, and the subscript “i” denotes instantaneous measurements. The weight (W) can be neglected since medusae are neutrally buoyant in water. Thrust is described as the product of the change in mass of an object per unit time (dm/dt) and fluid velocity (j), both due to fluid jetted from the medusa (Colin & Costello, 2002). Change in mass per unit time is estimated by the following:

where ρ is the density of sea water at 25°C (ρ=1.024g·cm^-3) and V­_s,i is the instantaneous volume in the medusa umbrella. We may assume an ideal hemi-ellipsoid to approximate the form of an oblate, jetting medusa using the following equation:

Where l is the height of the subumbrellar cavity and d is the bell diameter. Jet velocity can be estimated as follows:

where A_v is the orifice area through which fluid jets outwards or refills the bell, which is of variable geometry depending on the species.

As opposed to rowing medusae that only partially contract their bell, a jetting medusa fully contracts its bell, thus propelling itself with relatively high acceleration rates (Weston et al., 2009; Yang et al., 2018).

Design Solutions of Physonect Siphonophores

Siphonophores are an order within Hydrozoa that describes highly polymorphic, pelagic, colonial organisms (Dunn & Wagner, 2006; LaDouceur, 2021). Specialized medusoid and polypoid zooids enable a whole colony to carry out biological activities, such as digestion and reproduction (Mackie et al., 1988). These are organized along the linear nectosome, which gives the colony its overall shape (Figure 10).

The physonect suborder of siphonophores has the most complex modular architecture among colonial organisms. In these species, medusoid zooids, referred to as nectophores, are clustered at the front of the nectosome, where they enable colony locomotion (Figure 8) (Du Clos et al., 2022). They produce pulsed, high-velocity jets that allow for swimming, reverse swimming, and turning of the whole superorganism (Mackie, 1964). Besides salps, siphonophores are the only known marine organisms who swim using multiple jets, whereas all other jetting organisms make use of a single jet (Du Clos et al., 2022).

Fig. 10. Schematic overview of physonect siphonophore architecture by Dunn and Wagner (2006). At the apex of the colony, the gas-filled pneumatophore provides buoyancy. The nectosome carries two rows of nectophores which originate at the anterior, while the siphosome holds the reproductive and digestive units, the gonodendrons and gastrozooids, respectively.

This unique architecture enables them to benefit from several advantages in terms of locomotion unavailable to most organisms. Most apparently, multiple jetting units along the nectosome allow for redundancy: in the event of failure of one or more propulsive units, effective movement of the colony would still be ensured as opposed to that of single-jet organisms like cnidarian medusae (Du Clos et al., 2022).

In the case of Nanomia bijuga, newly budded nectophores at the apex of the colony are responsible for steering, whereas older, larger ones located further down provide most of the straight swimming thrust. The former generates jets directed at greater angles away from the nectosome compared to the latter whose jets are directed downward, parallel to the nectosome (Sutherland et al., 2019). These differences in the distribution of nectophores nonetheless enable both steering and forward thrust of the colony. In fact, despite the weaker forces they exert, steering is executed by the younger nectophores since they are positioned such that their lever arm length and the angle of the jetting force maximize generated torque and consequently angular velocity (Du Clos et al., 2022; Sutherland et al., 2019) as described by the following equation:

Additionally, whereas most other jet-propelled swimmers display asymmetric jetting, which refers to a ratio of jetting versus refilling times of less than one, nectophores in N. bijuga exhibit a comparatively large ratio of up to 0.95:1 (Sutherland et al., 2019). In most other single-jet marine organisms, longer refilling times relative to jetting time are necessary to produce more forward thrust than rearward relaxation flow. As a result of shorter jetting contraction times, higher fluid velocities are generated during jetting compared to refilling, which serve to decrease rearward thrust produced by refilling velocities. Although a greater ratio would hinder forward motion in most jetting marine organisms, N. bijuga avoids this limitation. Its multiple nectophores contract in coordination, allowing ratios closer to 1. This coordination maintains fast, linear motion and enables the colony to travel long distances (Sutherland et al., 2019).

Feeding mechanisms within Hydromedusae

Hydrozoan medusae are important planktivorous predators often dominating pelagic ecosystems. Though, due to their small size and the vicious forces in the fluid flow of their environment, these species have adapted into using specialized feeding mechanisms for higher prey capture success. One of them being the filter-feeding/feeding-current mechanism. Filter-feeders are characterized as cruising and foraging species with low fineness ratios (height/width) that use swimming and jet propulsion as their means to capture prey. This style of feeding is highly influenced by the hydrodynamics surrounding the medusae, tentacle kinematics and distinct nematocyst distribution (Sutherland et al., 2016).

Filter-Feeding Hydrodynamics of Obelia sp.

To illustrate the mechanics of filter-feeding by small hydromedusae, a study by Sutherland et al. (2016) was conducted on individual Obelia sp. hydromedusae by which they measured the tentacle and bell velocities velocities at different time intervals. Equations on the swimming kinematics, which are featured on this paper, were developed to describe its filter-feeding hydrodynamics. This species swims and feeds in viscous regimes and is characterized by thick boundary layers around its body and tentacles. Reynolds number is a dimensionless quantity that is used to measure the ratio of inertial forces to viscous forces in the fluid flow of their environement. The whole body Reynolds number can be calculated using the following equation:

Where (l_b) is relaxed bell diameter, (U_b) is bell velocity, and (v) is kinematic viscosity of seawater at 12°C. The tentacle Reynolds number (Re_t) and the boundary layer thickness (δ) were calculated at three locations along the tentacle based on the respective length scales and velocities using the following equation:

where (l_t) is tentacle diameter and, (U_t) is tentacle velocity (Sutherland et al., 2016). The boundary layer thickness (δ) around the bell was approximated around a flat plate as follows:

The boundary layer around a tentacle was approximated as (δ) around a cylinder in laminar flow as follows:

(Sumer and Fredsoe 2006).

Tentacle Kinematics of Filter-Feeders

In the study by Sutherland et al. (2016), Reynolds number peaked midway through the contraction of a medusoid bell pulse cycle. At this point, kinematic data showed that the tentacles accelerated to their maximum speed. This thinned the boundary layers around the tips of the tentacles and increased the likelyhood of prey contact (Figure 11).

Fig. 11. Bell and tentacle kinematics through three full bell pulsation cycles. (a) whole-body velocity and Re, (b) tentacle tip velocity and Re and (c) boundary layer around the tentacle tip. Maximum velocity and Re and minimum boundary layer thickness occur midway through a contraction. Horizontal grey line in (c) indicates the mean size of prey captured during feeding experiments (70 µm) (Sutherland et al., 2016).

With each bell contraction and relaxation, filter-feeding predators create start and stopping vortices that allow for fluids to circulate in between tentacle (Costello & Colin, 2002) . The starting vortex entrains fluid adjacent to the bell and transports it throught the tentacles. This continues during bell expansion as the stopping vortex moves fluid up into the subumbrellar cavity (Figure 12) (Katija et al., 2011; Shadden et al., 2006). When the body motion stops, the surrounding fluid also ceases moving. During contraction, fluid flow is orthogonal to the tentacles’ velocity and vorticity is highest at the tentacle tips (Sutherland et al., 2016). This behavior determines the lower limit in size of the prey captured since the boundary layer thickness corresponds closely to the mean size of prey captured.

Fig. 12. Flow field (black vector arrows) and vorticity (s^-1, colored contours) around swimming Obelia over one full pulsation cycle. Bell is relaxed at 24 ms and fully contracted at 72 ms. The recovery stroke begins at 96 ms and ends at 144 ms. Velocity through the tentacles is at a maximum midway through the contraction (48 ms). Vector scale arrow in the first panel represents 20 mm s^-1; size scale bar is 1 mm (Sutherland et al., 2016).

During a contraction cycle, medusae swiming in intertial regimes recapture energy and continue moving forward. At lower Reynolds number, the body moves backwards during the relaxation phase (Figure 13). This requires more pulses per cycle and more time to capture its prey. At an intermediate Reynolds number, there is an increase in prey encounter since the interial and viscous forces allow for streamline compression around the cylinder, thus increasing prey movement near the capture zone (Sutherland et al., 2016).

Fig. 13. Obelia x, y position through three full bell pulsation cycles showing forward motion during contraction and reverse motion during relaxation (Sutherland et al., 2016).

Polyp Feeding through Mouth-Opening Dynamics

When it comes to the mouth opening mechanism of polyps, a study on Hydra demonstrated that this mechanism occurred through change in cell shape, contractile processes, neural signaling and the elastic force present in the myonemes (the circular and radial contractile muscles of the mouth). The hydra head is composed of a dome-shaped hypostome surrounded by a ring of tentacles. A mouth at the center can be triggered to open by osmotic regulation and myoneme influence (Figure 14) (Carter et al., 2016).

Fig. 14. Adapted diagrams of the Hydra mouth. (A) Schematic showing the apical region of Hydra in cross section, including ectodermal and endodermal epithelia and mesoglea. (Dashed line) Position of head amputation before imaging. (B) Top view and (C) side view showing orientation of myonemes in the two epithelial layers. (Carter et al., 2016).

Mouth opening and Myonemes

Mouth opening is achieved by active contraction of the ectodermal radial myonemes in response to signals generated by the ectodermal nerves since nerve-free Hydra are unable to open their mouths even under osmotic regulation or part of a feeding response (Carter et al., 2016). In a study to evaluate this, these polyps were mounted in magnesium chloride, a chemical relaxant. In response to this exposure, myoneme contraction was inhibited and mouth opening mechanisms were prevented (Figure 15).

Fig. 15. (A–D) Still images showing the reduced glutathione-induced opening of the ectodermal epithelial layer. The head is mounted in Hydra medium and exposed to the stimulant as it is flushed onto the slide. (I–L) Still images showing the ectodermal epithelial layer of a Hydra head mounted in 2.5% (wt/vol) magnesium chloride in Hydra medium. The tentacles appear relaxed, and the mouth does not open when the animal is exposed to 0.2 mM reduced glutathione. (Carter et al., 2016).

Forces governing mouth opening.

For mouth opening to occur in a Hydra polyp, the opening forces must overcome the forces holding both the ectoderm, (sealing of septate junctions), and endoderm (septate junctions and circularly oriented myonemes) closed (Carter et al., 2016). The endoderm and ectoderm both have elastic properties that can be quantified using Young’s Elastic modulus, telling us to which degree of ease the material in these tissue layers can stretch and deform. The equation of this modulus is as follows:

Where r is the original radius of the tissue sphere before compression, F_EI is the elastic force, and R is the radius of the contact between the tissue sphere and the compression plate (Carter et al., 2016).

The force needed to septate junctions is unknown, but it can be approximated using the force required to separate sealed tight junctions, which is a few nanonewtons (Vedula et al., 2009). At the point of rupture, mouth opening begins when the net force is equal to the sum of the force exerted by the radial and circular myonemes, where maximum velocity is attained at the inflection point. After that, the mouth opening becomes a damped spring system with a constant opening force. The increase in cell deformation will lead to an elastic restoring force to oppose further compression. Mouth opening reaches it’s maximum when the net forces acting on the tissue are in equilibrium. By equating the tissue elastic modulus (E) to that of single cells, while using the change in aspect ratio of single cells, we can approximate the required force for maximal opening as follows:

Where F_El the elastic force, A the area, Δl the change in radial length, and L the original radial length. This gives a force of ~1–2 nanonewtons, which is of similar magnitude as breaking septate junctions (Carter et al., 2016).

Relationship between Nematocyst and Predation

Being by far the most diverse group of cnidocytes in the cnidarian phylum, nematocytes are the cells hydrozoan species use for prey capture, defense, and locomotion. These cells are designed to withstand extreme mechanical stresses by combining high resistance and flexibility, and vary in type, density and distribution depending the chosen predation mechanism (Özbek et al., 2009). Indeed, feeding-current medusae can capture most of their prey closer to their bell because their nematocytes are concentrated in higher density. They are distributed either uniformly along the tentacles, or along the first half, thus enabling better grabbing closer to the bell. Filter-feeding predators will have a higher concentration of mastigophore, a type of nematocyte that use a whiplash motion to provide locomotion and allow them to eat softer smaller prey (Corrales-Ugalde et al., 2017).

Discharge Kinetics in Nematocysts

Stenoteles are a type of nematocyte found predominantly in ambush predator hydromedusae used to adhere to or penetrate prey. Though, the process of tubular discharge remains similar across all nematocysts. Before discharge of toxins, the nematocytes sensory receptors (cnidocil) will generate an action potential upon mechanical stimulation by prey, with a delay of ~1ms (Figure 16A). During this lag phase, there is minimal delay of 330–450 ms and 230–350 ms between depolarizing and large hyperpolarizing stimuli depending on the presence of Ca²⁺ in the capsule. Then, the nematocyst vesicle fuses with the nematocyte membrane to begin nematocyte discharge. When the lid opens, a dart-like stylet is ejected from the tubule with an average velocity (v) of 18.6 m/s. This initial speed is produced by the internal osmotic pressure built-up in the capsule, suggesting that nematocytes comprise a powerful molecular spring mechanism able to release energy stored in capsular walls within nanoseconds. Assuming a constant acceleration of 5,413,000 times Earth’s gravity, the resulting force explains how such a small mass can generate the 7.7 GPa of pressure required for the stylet to penetrate a prey’s solid cuticle. Following the ejection is a phase of temporal arrest when the stylet creates an opening to release its tubule into the prey’s body (Figure 16D). The long tubule (500 µm) will evaginate at a velocity of 0.27 ± 0.21 m/s and finally release its toxins (Figure 16E) (Özbek et al., 2009).

Did you know? According to Nüchter et al. (2006), stylet ejection could be as short as 700ns, making it one of the fastest known processes generated in animal systems (Nüchter et al., 2006).

Fig. 16. Morphodynamics of nematocyst discharge. Discharge of a stenotele is depicted schematically, recorded with a Hamamatsu C4187 high-speed camera in the framing mode at 1,430,000 frames per second (Özbek et al., 2009). (A) The nematocyte vesicle fuses with the nematocyte membrane. (B) The lid opens, ejecting the stylet from the nematocyte capsule. (C) The stylet hits the membrane of another organism. (D) Creation of a mechanical opening for the tubule to be released. (E) Release of the tubule into the prey’s body.

Feeding mechanisms and solutions in Bryozoa

Bryozoans feed on minute planktonic particles with the help of their lophophore, a circular or U-shaped structure fringed by tentacles surrounding a mouth and supported by the distal part of the polypide (Tamberg & Shunatova, 2016). Each tentacle is composed of three types of ciliary bands: frontal, latero-frontal, and lateral bands. The introvert, a component of the polypide, supports the lophophore when everted and shelters the tentacles when it is retracted. With their lateral cilia, Bryozoans generate water currents from above the lophophore and capture particles between their tentacles, most of them being directed to either the mouth or the oral side (Figure 17). Some particles may be manually transported by tentacles or tentacle cilia (particles 2,3, 4). On the inner face of the tentacles, shorter cilia drag food particles toward the mouth without using mucus. From there, food is sucked into the pharynx.

Fig. 17. General plan of particle capture and water currents around phylactolaemate lophophore. Currents are represented by wide grey arrows while the trajectories of particles are illustrated by black arrows. Particle 1 travels within the main current with a tentacle flick. A tentacle flick returns particle 2 to the main current. Particles 3 and 4 move along the ciliary band. (Tamberg & Shunatova, 2016).

Exhalant chimneys

Filtered water is directed below lophophores, which lie above the colonial surface. At the scale of individual zooids, water is very viscous and needs to be removed from the colony to avoid diluting food-carrying currents to other zooids. To remedy this, Bryozoans developed ‘exhalant chimneys,’ regular spaces enlarged by the divergent posture of surrounding lophophores into which exhalant water enters and exits well above the colony (Figure 18).

Fig. 18. Velocity distribution above chimney illustrating exhalant jets and inflows adjacent to lophophores, diagram adapted by Larsen and Riisgård (2001).

Pump characteristics

The local feeding rate of zooids depends on the local base pressure in the substratum which is determined by the pump characteristics of zooids (Larsen & Riisgård, 2001). The pump characteristic of a single zooid can be expressed in a linear relation with dimensionless terms as follows:

Where P denotes the base pressure (more than the ambient pressure) and W denotes the feeding rate which refers to volume flow per unit area, or the average velocity of water entering zooids. Maximal values of P_max and W_max, correspond to zero flow and zero pressure, respectively.

From a precise view, the pump system is formed by the lateral surfaces along the tentacles of a zooid itself. We thus consider a backpressure characteristic where the base pressure is equal to the back pressure. This includes the internal system’s resistance to flow within the lophophore and tentacles. Both the pump and resistances are expected to obey a linear pattern, as the flow operates at a low Reynolds number. Hence, the functional characteristic of the zooid are expected to follow a linear relationship.

Governing equations

The conservation of mass for steady, incompressible, radial flow with mean velocity V_in the of assumed uniform height h may be written as follows (Larsen & Riisgård, 2001):

Where (r) represents the radial coordinate. Ignoring inertia, the viscous flow in the 'neck space' is nearly fully developed and is therefore governed by the balance between pressure and viscous forces, hence:

where μ denotes the dynamic viscosity.

The Stokes equations

Calculating the flow around the tentacles with active cilia is derived from the extension of the theory (Brennan and Winet, 1977; Lighthill, 1975) of flow around slender bodies at low Reynolds number around an arbitrary array of cylinders. The theory allows to evaluate forces and flow fields resulting from a slender cylinder with no slip boundary conditions.

It is assumed that the fluid around the bryozoan colony obeys the stokes equations for incompressible flow at very low Reynolds numbers.

The velocity u of a simple fluid such as water is governed by the Navier–Stokes equations where boldface denotes a vector quantity,

Here is p pressure, μ is dynamic velocity, u is velocity, and f is external force. Boldface denotes vector quantity.

The stokes equation can be non-dimensionalized with a length, L, and a speed, V, which characterize the structure around which flow occurs. The Reynolds number associated with such a structure is given by:

Where μ is the dynamic viscosity of water and u is the flow speed.

The ciliary flow near a single zooid shows specific patterns in velocity observed in both horizontal and vertical directions (Figure 19). These patterns describe how water moves above the zooid and around the tips of its tentacles (Grünbaum, 1995). The model used to describe ciliary action, along with a simplified shape of the lophophore, crates a smooth and understandable flow pattern, even near the tentacles where changes might be expected. However, in the excurrent flow, there is a noticeable change in velocity both above and below, indicating strong resistance to the ciliary flow. This means that the water movement is significantly influenced by the surrounding fluid, especially in areas with high resistance.

Fig. 19. Velocity profiles of ciliary feeding currents adjacent to an isolated model (Grünbaum, 1995). x₁ and x_3-coordinates are as indicated; velocities are measured off the axis of symmetry, at x₂=0.15. Horizontal velocities (x₁ component) are indicated by circles vertical velocities (x₃-component) by squares. (a) Profiles along a horizontal section immediately above the lophophore (x₃=1.25) show that cilia induce a strong, converging current into the lophophore. (b) After passing through the lophophore, fluid is expelled laterally, shown in a vertical transect just outside the tentacle tips (x₁=0.55).

The feeding currents around a single, isolated zooid can be seen by the paths of particles, both with and without any external flow and with a linear sublayer wall flow (Figure 20). Particles were introduced at various positions x₁ and x₃, and slightly off the symmetry axis (x₂=0.05). Particle paths are logical, even as they pass between tentacles. Without external flow, particle paths reveal an increased recirculation around the zooid. Orbital size is directly proportional to time taken for a loop around a zooid.

Fig. 20. Particle trajectories near an isolated model zooid (Grünbaum, 1995). (a) significant recirculation is produced by the cilia-induced currents, as particles passing near the lophophore are pulled back into the flow. (b) when a moderately strong external velocity is present (U=0.3x₃), recirculation is much weaker; particles coming from above are pulled back into the flow and are redirected before going downstream.

Zooid flow rate is obtained by subdividing the quadrangle defined by corresponding area on neighboring tentacles into twelve smaller quadrangles and adding the product of the normal velocity and projected area for each of these. The flow rate of an isolated standard zooid is 0.549. The ideal value of the flow rate is 1.314. This is when the unit normal velocity everywhere on the cone described by the lophophore is ideal. The difference between of these two values of flow rate indicates that there is a viscous resistance due to the substrate and blockage caused by the tentacles.

Conclusion

In this paper, adaptations developed by Hydrozoa and Bryozoa are discussed from a physics perspective and related to the challenges they meet in their environments. Despite being distantly related, it is shown that they evolved both similar and unique solutions by the fact of many of them being colonial organisms. These design solutions are discussed in three steps. Firstly, the paper explores hydrostatic and calcified skeletons developed by these creatures and the environmental challenges they aim to solve, either immense hydrostatic pressures or strong surrounding currents. Secondly, locomotion solutions are discussed, particularly in the case of physonect siphonophores that exist as long, linear colonies. We show that the linear arrangement of nectophores enables them to reap many benefits, such as redundancy, faster refilling times, and efficient steering. Lastly, a discussion is given of the feeding mechanisms developed by both clades. Hydrozoan medusae leverage currents to capture prey and use nematocytes to poison, while polyps have evolved the ability to extend their oral apertures to capture food, compensating for their lack of mobility. In contrast, bryozoans increase passive food acquisition by generating currents with their tentacles and organize their colony to maintain concentrated, food-rich flow.