Self-organization at the first stage of honeycomb construction: Analysis of an attachment-excavation model

Sub-cell scale features govern the placement of new cells by honeybees during comb construction

Honeybee comb architecture and the manner of its construction have long been the subject of scientific curiosity. Comb is characterised by an even hexagonal layout and the sharing of cell bases and side walls, which provides maximised storage volume while requiring minimal wax. The efficiency of this structure relies on a regular layout and the correct positioning of cells relative to each other, with each new cell placed at the junction of two previously constructed cells. This task is complicated by the incomplete nature of cells at the edge of comb, where new cells are to be built. We presented bees with wax stimuli comprising shallow depressions and protuberances in simulation of features found within partially formed comb, and demonstrated that construction work by honeybee builders was influenced by these stimuli. The building of new cells was aligned to concave stimuli that simulated the clefts that naturally appear between two partially formed cells, revealing how new cells may be aligned to ensure proper tessellation within comb. We also found that bees built cell walls in response to edges formed by our stimuli, suggesting that cell and wall construction was specifically directed towards the locations necessary for continuation of hexagonal comb.

Strong and Flexible Braiding Pattern of Carbon Nanotubes for Composites: Stiff and Robust Structure Active in Composite Materials

Carbon nanotubes (CNTs) exhibit high strength, Young's modulus, and flexibility and serve as an ideal reinforcement for composite materials. Owing to their toughness against bending and/or twisting, they are typically used as fabric composites. The conventional multiaxial braiding method lacks tension and resultant strength in the thickness direction. Some braiding patterns are proposed; however, they may have shortcomings in flexibility. Thus, this study proposed three types of braiding pattern for fabrics based on natural products such as spider net and honeycomb, in accordance with thickness-direction strength. The spider-net-based structure included wefts with spaces in the center with overlapping warps. At both sides, the warps crossed and contacted the wefts to impart solidness to the structure and enhance its strength as well as flexural stability. In addition, box-type wefts were proposed by unifying the weft and warps into boxes, which enhanced the stability and flexibility of the framework. Finally, we proposed a structure based on rectangular and hexagonal shapes mimicking the honeycomb. Moreover, finite element calculations were performed to investigate the mechanisms through which the proposed structures garnered strength and deformation ability. The average stress in fabrics becomes smaller than half (43%) when four edges are restrained and sliding is inserted. Under three-dimensional forces, our proposed structures underwent mechanisms of wrapping, warping, sliding and doubling, and partial locking to demonstrate their enhanced mechanical properties. Furthermore, we proposed a hierarchical structure specialized for CNTs, which could facilitate applications in structural components of satellites, wind turbines, and ships. The hierarchical structure utilizing discontinuity and sliding benefits the usage for practical mechanical systems.

Crystallography of honeycomb formation under geometric frustration

As honeybees build their nests in preexisting tree cavities, they must deal with the presence of geometric constraints, resulting in nonregular hexagons and topological defects in the comb. In this work, we study how bees adapt to their environment in order to regulate the comb structure. Specifically, we identify the irregularities in honeycomb structure in the presence of various geometric frustrations. We 3D-print experimental frames with a variety of constraints imposed on the imprinted foundations. The combs constructed by the bees show clear evidence of recurring patterns in response to specific geometric frustrations on these starter frames. Furthermore, using an experimental-modeling framework, we demonstrate that these patterns can be successfully modeled and replicated through a simulated annealing process, in which the minimized potential is a variation of the Lennard-Jones potential that considers only first-neighbor interactions according to a Delaunay triangulation. Our simulation results not only confirm the connection between honeycomb structures and other crystal systems such as graphene, but also show that irregularities in the honeycomb structure can be explained as the result of analogous interactions between cells and their immediate surroundings, leading to emergent global order. Additionally, our computational model can be used as a first step to describe specific strategies that bees use to effectively solve geometric mismatches while minimizing cost of comb building.

Self-Assembled Micro-Sized Hexagons Built from Short DNA in a Crowded Environment

DNA programmable structures of various morphologies have attracted extensive attention due to their potential for materials science and biomedical applications. Here, we report the formation of micro-sized hexagons via assembly of only one pair of short double-stranded DNA in buffer-salt poly(ethylene glycol) solution. Each DNA strand had complementary bases with a two-base overhang. The procedure of heating and subsequent cooling of blunt-ended double-stranded DNA resulted in different assemblies. These results indicated that end-to-end adhesion at the terminals induced by complementary overhangs were required to construct the hexagonal DNA assemblies. The stable formation of the hexagons was highly dependent on heating temperature. In addition, concentration adjustments of DNA and poly(ethylene glycol) were essential. Circular dichroism spectral measurements and polarization microscopy observations indicated parallel alignment of double-stranded DNA in the hexagonal platelet. Self-assembled micro-sized hexagons composed of simple building blocks may have great potential for future biomedical device development.

Unraveling the Mechanisms of the Apis mellifera Honeycomb Construction by 4D X-ray Microscopy

Honeycomb is one of nature's best engineered structures. Even though it has inspired several modern engineering structures, an understanding of the process by which the hexagonal cells are formed in 3D space is lacking. Previous studies on the structure of the honeycomb are based on either 2D microscopy or by direct visual observations. As a result, several critical features of its microstructure and the precise mechanisms of its growth are not well understood. Using 4D X-ray microscopy, this study shows how individual and groups of honeycomb cells are formed. Cells grow additively from a corrugated central spine in a dynamic manner. The previously undocumented, corrugated spine contributes significantly to the comb's robust mechanical properties in all three dimensions. As cells grow, honey bees create a "coping," which this study shows to be the location where new wax material is deposited behind where compaction and densification take place. This is exemplified by pores in the wax observed at the coping and alternating rear junctions between the comb cells that arise from the additive building technique and the highly efficient cell packing methodology, respectively. Additional mechanisms for growth and formation are discussed and described.

Cell orientation characteristics of the natural combs of honey bee colonies

The cell orientation characteristics of the natural combs of honey bees have received much research attention. Although natural combs have been shown to be composed of cells with three orientations-vertical, intermediate (oblique), and horizontal-the proportion of comb cells in these three orientations varies. Knowledge of the comb-building preferences of honey bees is essential for the installation of wax comb foundations, and clarification of the cell orientation characteristics of natural honey bee combs is important for beekeeping. The purpose of this study was to determine the cell orientation characteristics of natural combs of Eastern honey bees (Apis cerana cerana) and Western honey bees (Apis mellifera ligustica). Newly built combs were used to measure the orientation of hexagonal cells and calculate the proportion of cells in different orientations relative to the total number of cells. The number of eggs laid by queens in the cells of different orientations was also determined. The orientation of cells in the natural combs of Eastern and Western honey bees was determined based on the value of the minimum included angle between the pair of parallel cell walls and a vertical line connecting the top and bottom bars of the movable frame in the geometric plane of the comb: 0°≤θ≤10°, 10°<θ≤20°, and 20°<θ≤30° for vertical, intermediate, and horizontal orientations, respectively. Natural combs were composed of cells with at least one orientation (vertical or horizontal), two orientations (vertical + intermediate (oblique) or vertical + horizontal), or three orientations (vertical + intermediate + horizontal), and the proportions of combs with the three aforementioned configurations differed. Both Eastern honey bees and Western honey bees preferred building combs with cells in a vertical orientation. Queens showed no clear preference for laying eggs in cells of specific orientations. The results of this study provide new insight that could aid the production and cutting of wax comb foundations of Eastern and Western honey bees. Our study highlights the importance of installing wax comb foundations compatible with the comb-building preferences of bees.

Evaluating and Comparing the Natural Cell Structure and Dimensions of Honey Bee Comb Cells of Chinese Bee, Apis cerana cerana (Hymenoptera: Apidae) and Italian Bee, Apis mellifera ligustica (Hymenoptera: Apidae)

The hexagonal structure of the honey bee comb cell has been the source of many studies attempting to understand its structure and function. In the storage area of the comb, only honey is stored and no brood is reared. We predicted that honey bees may construct different hexagonal cells for brood rearing and honey storage. We used quantitative analyses to evaluate the structure and function of the natural comb cell in the Chinese bee, Apis cerana cerana and the Italian bee, A. mellifera ligustica. We made cell molds using a crystal glue solution and measured the structure and inclination of cells. We found that the comb cells of A. c. cerana had both upward-sloping and downward-sloping cells; while the A. m. ligustica cells all tilted upwards. Interestingly, the cells did not conform to the regular hexagonal prism structure and showed irregular diameter sizes. In both species, comb cells also were differentiated into worker, drone and honey cells, differing in their diameter and depth. This study revealed unique differences in the structure and function of comb cells and showed that honey bees design their cells with precise engineering to increase storage capacity, and to create adequate growing room for their brood.

Complex fluids in animal survival strategies

Animals have evolved distinctive survival strategies in response to constant selective pressure. In this review, we highlight how animals exploit flow phenomena by manipulating their habitat (exogenous) or by secreting (endogenous) complex fluids. Ubiquitous endogenous complex fluids such as mucus demonstrate rheological versatility and are therefore involved in many animal behavioral traits ranging from sexual reproduction to protection against predators. Exogenous complex fluids such as sand can be used either for movement or for predation. In all cases, time-dependent rheological properties of complex fluids are decisive for the fate of the biological behavior and vice versa. To exploit these rheological properties, it is essential that the animal is able to sense the rheology of their surrounding complex fluids in a timely fashion. As timing is key in nature, such rheological materials often have clearly defined action windows matching the time frame of their direct biological behavior. As many rheological properties of these biological materials remain poorly studied, we demonstrate with this review that rheology and material science might provide an interesting quantitative approach to study these biological materials in particular in context towards ethology and bio-mimicking material design.