A new computational growth model for sea urchin skeletons

Hexagonal Voronoi pattern detected in the microstructural design of the echinoid skeleton

Repeated polygonal patterns are pervasive in natural forms and structures. These patterns provide inherent structural stability while optimizing strength-per-weight and minimizing construction costs. In echinoids (sea urchins), a visible regularity can be found in the endoskeleton, consisting of a lightweight and resistant micro-trabecular meshwork (stereom). This foam-like structure follows an intrinsic geometrical pattern that has never been investigated. This study aims to analyse and describe it by focusing on the boss of tubercles—spine attachment sites subject to strong mechanical stresses—in the common sea urchin Paracentrotus lividus. The boss microstructure was identified as a Voronoi construction characterized by 82% concordance to the computed Voronoi models, a prevalence of hexagonal polygons, and a regularly organized seed distribution. This pattern is interpreted as an evolutionary solution for the construction of the echinoid skeleton using a lightweight microstructural design that optimizes the trabecular arrangement, maximizes the structural strength and minimizes the metabolic costs of secreting calcitic stereom. Hence, this identification is particularly valuable to improve the understanding of the mechanical function of the stereom as well as to effectively model and reconstruct similar structures in view of future applications in biomimetic technologies and designs.

Population Characteristics of the Upper Infralittoral Sea Urchin Arbacia lixula (Linnaeus, 1758) in Eastern Mediterranean (Central Greece): An Indicator Species for Coastal Water Quality

The black sea urchin (Arbacia lixula, Linnaeus, 1758) is a non-edible marine echinoderm of high ecological importance with the potential to affect marine ecological communities. A. lixula were sampled monthly for one year from the supralittoral fringe at two locations in the Pagasitikos Gulf, in the north-western Aegean Sea. Morphometric characteristics exhibited significant spatiotemporal variation. The population in closer proximity to treated sewage effluent outflow exhibited significantly higher biometric relationships resulting in possible improved physiological conditions. Spatial distribution exhibited a clumped pattern of dispersion, consisting of predominantly six age classes. The dominant cohort was the four-year age class, comprising 31.2% of the total population. Significant negative allometric relationships were exhibited between all morphometric characteristics. The maximum approximate age of the total A. lixula population was estimated at 15.27 years. The von Bertalanffy growth equation for the entire population was estimated as: test diameter = 62.881×1−e−0.196×Age+1.147. The gonadosomatic index indicated a seasonal cycle with a peak in late spring. The approximate age of sexual maturity was estimated at 4.45 years. We observed a significantly higher number of females than expected at the site in closer proximity to the treated sewage effluents (32% of total female number).

Constructional design of echinoid endoskeleton: main structural components and their potential for biomimetic applications

The endoskeleton of echinoderms (Deuterostomia: Echinodermata) is of mesodermal origin and consists of cells, organic components, as well as an inorganic mineral matrix. The echinoderm skeleton forms a complex lattice-system, which represents a model structure for naturally inspired engineering in terms of construction, mechanical behaviour and functional design. The sea urchin (Echinodermata: Echinoidea) endoskeleton consists of three main structural components: test, dental apparatus and accessory appendages. Although, all parts of the echinoid skeleton consist of the same basic material, their microstructure displays a great potential in meeting several mechanical needs according to a direct and clear structure-function relationship. This versatility has allowed the echinoid skeleton to adapt to different activities such as structural support, defence, feeding, burrowing and cleaning. Although, constrained by energy and resource efficiency, many of the structures found in the echinoid skeleton are optimized in terms of functional performances. Therefore, these structures can be used as role models for bio-inspired solutions in various industrial sectors such as building constructions, robotics, biomedical and material engineering. The present review provides an overview of previous mechanical and biomimetic research on the echinoid endoskeleton, describing the current state of knowledge and providing a reference for future studies.

Sea urchin growth dynamics at microstructural length scale revealed by Mn-labeling and cathodoluminescence imaging

Background

Fluorochrome staining is among the most widely used techniques to study growth dynamics of echinoderms. However, it fails to detect fine-scale increments because produced marks are commonly diffusely distributed within the skeleton. In this paper we investigated the potential of trace element (manganese) labeling and subsequent cathodoluminescence (CL) imaging in fine-scale growth studies of echinoderms.

Results

Three species of sea urchins (Paracentrotus lividus, Echinometra sp. and Prionocidaris baculosa) were incubated for different periods of time in seawater enriched in different Mn²⁺ concentrations (1 mg/L; 3 mg/L; 61.6 mg/L). Labeling with low Mn²⁺ concentrations (at 1 mg/L and 3 mg/L) had no effect on behavior, growth and survival of sea urchins in contrast to the high Mn²⁺ dosage (at 61.6 mg/L) that resulted in lack of skeleton growth. Under CL, manganese produced clearly visible luminescent growth fronts in these specimens (observed in sectioned skeletal parts), which allowed for a determination of the average extension rates and provided direct insights into the morphogenesis of different types of ossicles. The three species tend to follow the same patterns of growth. Spine growth starts with the formation of microspines which are simultaneously becoming reinforced by addition of thickening layers. Spine septa develop via deposition of porous stereom that is rapidly (within less than 2 days) filled by secondary calcite. Development of the inner cortex in cidaroids begins with the formation of microspines which grow at ~3.5 μm/day. Later on, deposition of the outer polycrystalline cortex with spinules and protuberances proceeds at ~12 μm/day. The growth of tooth can be rapid (up to ~1.8 mm/day) and starts with the formation of primary plates (pp) in plumula. Later on, during the further growth of pp in aboral and lateral directions, secondary extensions develop inside (in chronological order: lamellae, needles, secondary plate, prisms and carinar processes), which are increasingly being solidified towards the incisal end. Interradial growth in the ambital interambulacral test plates exceeds meridional growth and inner thickening.

Conclusions

Mn²⁺ labeling coupled with CL imaging is a promising, low-cost and easily applicable method to study growth dynamics of echinoderms at the micro-length scale. The method allowed us to evaluate and refine models of echinoid skeleton morphogenesis.

Micromechanics of Sea Urchin spines

The endoskeletal structure of the Sea Urchin, Centrostephanus rodgersii, has numerous long spines whose known functions include locomotion, sensing, and protection against predators. These spines have a remarkable internal microstructure and are made of single-crystal calcite. A finite-element model of the spine’s unique porous structure, based on micro-computed tomography (microCT) and incorporating anisotropic material properties, was developed to study its response to mechanical loading. Simulations show that high stress concentrations occur at certain points in the spine’s architecture; brittle cracking would likely initiate in these regions. These analyses demonstrate that the organization of single-crystal calcite in the unique, intricate morphology of the sea urchin spine results in a strong, stiff and lightweight structure that enhances its strength despite the brittleness of its constituent material.

Holotestoid: a computational model for testing hypotheses about echinoid skeleton form and growth

Regular echinoid skeletons, or tests, comprise plate patterns and overall shapes that have proven challenging to analyse solely on the basis of any one approach or process. Herein, we present a computational model, Holotestoid, that emulates four macrostructural ontogenic processes involved in test growth (plate growth, plate addition, plate interaction, and plate gapping). We devise a geometric representation for analysing tests and describe how we use analogies (bubble interactions and close-packing) to emulate the processes. In the computational model, the emulated processes are used to determine the plate size and plate shape and combined to simulate a growth zone. We simulated growth zones for Arbacia punctulata and for Strongylocentrotus franciscanus by changing the value for one parameter, the ambulacral column angle. We quantitatively compared morphological features for simulated forms to those for real specimens to test the computational model. Additionally, we simulated growth zones for A. punctulata, S. franciscanus, Eucidaris thouarsii, and Mellita quinquiesperforata by changing three parameters, ambulacral column angle, peristome radius to apical system radius ratio, and apical system radius to column length ratio. Holotestoid can be used to explain morphological disparity among echinoid tests.

Substratum cavities affect growth-plasticity, allometry, movement and feeding rates in the sea urchinStrongylocentrotus purpuratus

We assessed the influence of rock cavities, or pits, on the growth dynamics and behavior of the purple sea urchin, Strongylocentrotus purpuratus. In a paired-designed, laboratory experiment, sea urchins were assigned to sandstone blocks that were either ‘Flat’ or had a ‘Pit’ drilled into the center. At the start, both groups were approximately the same shape and size. In just 2 months, the shapes of the tests were significantly different between the two treatments, with the Pit urchins having an increased height:diameter profile. This result demonstrates the plastic nature of the sea urchin test and that, despite its apparent rigidity, it is capable of deforming during growth. In addition, the presence of pits modified behavior and food consumption as well as allometric growth of the test and Aristotle's lantern. Sea urchins on Pit sandstone blocks tended to stay in the cavities and not move about the flat areas, whereas individuals on Flat blocks changed position. Sea urchins in the Pit treatment consumed less food and had relatively larger demipyramids (the ‘jaw’ ossicle in Aristotle's lantern). These morphological and allometric changes occurred over a short time-period (8–20 weeks). We conclude that microhabitat is an important factor in controlling the behavior and growth dynamics of the bioeroding sea urchin S. purpuratus.