Olaf Ellers

A mechanical model of growth in regular sea urchins: predictions of shape and a developmental morphospace

The shapes of several urchins are correctly predicted by a model that uses only measured height and diameter as fitted variables. The predicted shape is based on the engineering theory of thin shells, which is conventionally used to calculate the shapes of a fluid droplet on a horizontal plane, and of ‘buckle-free’ engineered domes. The magnitudes of forces theoretically required to generate urchin shapes at realistic sizes are similar to forces typically exerted on the skeleton by self-weight, podia and coelomic pressure. An urchin’s shape, despite complex details of plate growth, is thus determined by a force balance at each point in the skeleton. Despite the skeleton’s apparent rigidity, over developmental time it must deform in a manner similar to a stretchy balloon. This membrane model of morphogenesis specifies two developmental shape parameters: (i) the apical curvature; and (ii) a ratio of the mimicked vertical gradient of pressure (podial forces, etc.) to the internal coelomic pressure. An ontogenetic series of urchins is represented as a curved line in a two-dimensional, developmental morphospace. This morphospace, which is useful for studying developmental constraints and macroevolutionary dynamics, explains observed patterns of allometry in height and diameter in urchins.

Behavioral Control of Swash-Riding in the Clam Donax variabilis

Clams of the species Donax variabilis migrate shoreward during rising tides and seaward during falling tides. These clams spend most of the time in the sand, emerging several times per tidal cycle to ride waves. Migration is not merely a passive result of waves eroding clams out of the sand; rather clams actively jump out of the sand and ride specific waves. Such active migration is experimentally demonstrated during a falling tide by comparing the motion of dead and live clams; live clams emerge from the sand and move seaward even when dead ones do not. As low tide approaches, live clams become progressively less active. They cease migrating for 2 hours around low tide and resume jumping to migrate shoreward after the tide has turned. During the rising tide, far from being passive, the clams jump out to ride only the largest 20% of waves. Specifically, they choose swash that have the largest excursion, i.e., those swash that move furthest on the beach.

Structural Strengthening of Urchin Skeletons by Collagenous Sutural Ligaments

Sea urchin skeletons are strengthened by flexible collagenous ligaments that bind together rigid calcite plates at sutures. Whole skeletons without ligaments (removed by bleaching) broke at lower apically applied forces than did intact, fresh skeletons. In addition, in three-point bending tests on excised plate combinations, sutural ligaments strengthened sutures but not plates. The degree of sutural strengthening by ligaments depended on sutural position; in tensile tests, ambital and adapical sutures were strengthened more than adoral sutures. Adapical sutures, which grow fastest, were also the loosest, suggesting that strengthening by ligaments is associated with growth. In fed, growing urchins, sutures overall were looser than in unfed urchins. Looseness was demonstrated visually and by vibration analysis: bleached skeletons of unfed urchins rang at characteristic frequencies, indicating that sound traveled across tightly fitting sutures; skeletons of fed urchins damped vibrations, indicating loss of vibrational energy across looser sutures. Furthermore, bleached skeletons of fed urchins broke at lower apically applied forces than bleached skeletons of unfed urchins, indicating that the sutures of fed urchins had been held together relatively loosely by sutural ligaments. Thus, the apparently rigid dome-like skeleton of urchins sometimes transforms into a flexible, jointed membrane as sutures loosen and become flexible during growth.

Discrimination Among Wave-Generated Sounds by a Swash-Riding Clam.

Clams, Donax variabilis, responded to sound stimuli presented to them in a laboratory aquarium by jumping out of the sand, lying on the sand for several seconds, and digging in again. On a beach, clams jump out of the sand and ride waves, migrating shoreward with the rising tide and seaward with the falling tide. Parallels between clam behavior on a beach and that elicited in the laboratory suggest that clams cue on wave sounds to jump out of the sand. Three aspects of the response to sound were parallel. (i) Clams were most responsive to low-frequency sounds similar to those produced on a beach by waves rolling onto shore. (ii) Clams were also more responsive to louder sounds; on a beach, clams jump preferentially for the largest (loudest) 20% of waves, (iii) Responsiveness in the laboratory had an endogenous tidal rhythm, with highest activity occurring at high tide and no activity occurring at low tide; this rhythm corresponds to the activity of clams on the beach from which they were collected. By using sounds to identify large waves, clams can ride selected waves and continuously maintain position at the seas edge as the tide floods and ebbs.

Causes and Consequences of Fluctuating Coelomic Pressure in Sea Urchins

We measured coelomic pressure in sea urchins to determine whether it was high enough to support a pneu hypothesis of growth. In Strongylocentrotus purpuratus the pressure was found to fluctuate rhythmically about a mean of -8 Pa, and was negative for 70% of the time. This is at variance with the theoretically required positive pressures of the pneu hypothesis. Furthermore, there were no sustained significant differences between the pressure patterns of fed and starved urchins, presumed to be growing and not growing, respectively. The rhythmical fluctuations in pressure were caused by movements of the lantern which changed the curvature and tension of the peristomial membrane. We developed a mathematical and morphological model relating lantern movements, membrane tension, and pressure, that correctly predicts the magnitude of the fluctuations. Pressures predicted by the model depend also on coelomic volume changes. In Lytechinus variegatus simultaneous retraction of the podia, which causes expansion of the ampullae, resulted in an 8.8 Pa increase in coelomic pressure, relative to the pressure during simultaneous podial protraction.

A NEW MODEL OF PODIAL DEPOSIT FEEDING IN THE SAND DOLLAR, MELLITA QUINQUJESPERFORATA (LESKE): THE SIEVE HYPOTHESIS CHALLENGED

The feeding mechanism of Mellita quinquiesperforata (Leske) has been examined in detail. This sand dollar is a deposit feeder, ingesting particles mostly in the range of 100-250 µm. The particles are picked out of the substrate individually by specialized long barrel-tipped podia, which form a narrow palisade surrounding the geniculate spine fields on the oral surface. Selected food items are passed to short barrel-tipped podia, thence from podium to podium until they reach the food grooves where they are finally aggregated into mucus cords. The cords are passed to the mouth by the activity of food groove podia. At the peristome, the cord is passed between the circumoral spines by large food groove podia and steered into the mouth by five pairs of buccal podia. The lantern is powerfully muscled and has hardened teeth which crush diatoms and fracture many sand grains. For this reason, there is an apparent accumulation of fine particles (<50 µm) in the gut. Analysis of size frequencies of the material in the mucus cords and substrate indicates that no selection of fine particles occurs and, in fact, that they are virtually absent from the native sediment. An account of spine and podial morphology and distribution is included with descriptions and measurements of surface ciliary currents. It is shown that the formerly accepted sieve hypothesis of feeding cannot be entirely rejected on theoretical grounds. However, during feeding there was no evidence of the operation of any of the elements of the supposed sieve mechanism. Furthermore, the ciliary currents are not fast enough to account for the movement of most ingested material. Patterns of ciliary flow on the oral surface are not simply centripetal, but are much more complex than previously supposed.

Sutural loosening and skeletal flexibility during growth: determination of drop-like shapes in sea urchins.

The shape of sea urchins may be determined mechanically by patterns of force analogous to those that determine the shape of a water droplet. This mechanical analogy implies skeletal flexibility at the time of growth. Although comprised of many rigid calcite plates, sutural collagenous ligaments could confer such flexibility if the sutures between plates loosened and acted as joints at the time of growth. We present experimental evidence of such flexibility associated with weight gain and growth. Over 13–, 4–, and 2–week periods, fed urchins (Strongylocentrotus droebachiensis) gained weight and developed looser sutures than unfed urchins that maintained or lost weight. Further, skeletons of fed urchins force–relaxed more than did those of unfed urchins and urchins with loose sutures force–relaxed more than those with tight sutures. Urchins (Strongylocentrotus franciscanus) fed for two and a half weeks, gained weight, also had looser skeletons and deposited calcite at sutural margins, whereas unfed ones did not. In field populations of S. droebachiensis the percentage having loose sutures varied with urchin diameter and reflected their size–specific growth rate. The association between feeding, weight gain, calcite deposition, force relaxation and sutural looseness supports the hypothesis that urchins deform flexibly while growing, thus determining their drop-like shapes.

Form and Motion of Donax variabilis in Flow

The coquina clam, Donax variabilis, rides flow from waves, migrating shoreward during rising tides and seaward during falling tides. This method of locomotion, swash-riding, is controlled not only behaviorally but also morphologically. The shape of this clam causes it to orient passively; a clam rotates in flow, usually in backwash, until its anterior end is upstream. Rotation is about a vertical axis through a pivotal point where the shell touches the sand. The density, weight distribution, and wedge-like shape are all important in effecting orientation. Such orientation is significant because it contributes to stability of motion. On an unoriented clam, upward lift can be higher than its underwater weight--a circumstance that results in uncontrollable tumbling. In contrast, once oriented with its anterior end upstream, a clam experiences downward lift that contributes to its stability while sliding in backwash. Furthermore, when the anterior end is upstream, drag is reduced relative to when the ventral, dorsal, or posterior ends are upstream. Since orientation occurs only above a minimum velocity, it has the effect of slowing a clams motion over the substratum in rapid flows. Stability, drag, and speed reduction enhance a clams ability to gain a foothold and dig in after a swashride, before wave flows can wash it off the beach and out to sea.

COLLECTION OF FOOD BY ORAL SURFACE PODIA IN THE SAND DOLLAR, ECHINARACHNIUS PARMA (LAMARCK)

In Echinarachnius parma all spine types have cilia arranged in two bands along the shaft. Ciliary currents flow perpendicular to these bands and reversals were not observed. On the aboral surface the bands of cilia were oriented perpendicular to lines radiating from the apex. Flow visualization using dyes and particles showed that aboral currents flow radially towards the ambitus. In contrast, on the oral surface, currents flow from anterior to posterior and the bands of cilia are arranged at right angles to this axis. Oral surface ciliary currents do not carry particles to the mouth nor to the food grooves. At least 80% of the particles carried over the aboral surface are lost at the ambitus. Only particles < 20 µm, if any, pass around the ambitus and these were not seen to enter the food grooves.Light microscope observations showed that oral surface and ambital podia continuously probe the substrate and draw particles towards the test. Particles are passed from podium to podium, to the food grooves, and...

Advancement Mechanics of Growing Teeth in Sand Dollars (Echinodermata, Echinoidea): A Role for Mutable Collagenous Tissue

Regulation of growth involves the integration of several body systems including nerves, muscles and connective tissues. We demonstrate how changes in material properties of a connective tissue permit advancement of the continuously growing teeth of sand dollars. During growth, each tooth advances in a tooth slide. During chewing, however, teeth are rigidly attached by collagenous dental ligaments. We found that there was a natural, bimodal variation in tooth looseness where some sand dollars had teeth so loosely attached that they could not crush sand particles without detaching their teeth. We also found that soaking these dental ligaments in divalent cation-free artificial seawater caused more rapid force-relaxation than control artificial seawater. These results suggest that the dental ligaments are a special mutable collagenous tissue (MCT), found in echinoderms, and that sand dollars periodically loosen their teeth via changes in the MCT to allow the teeth to advance. This process could be under nervous control, as material properties of MCT can be altered via nervous control. Thus mutable collagenous tissue in echinoderms is used not only for many skeletal functions, but also for regulation of tooth growth.