The bee Tetragonula builds its comb like a crystal

Selectively advantageous instability in biotic and pre-biotic systems and implications for evolution and aging

Rules of biology typically involve conservation of resources. For example, common patterns such as hexagons and logarithmic spirals require minimal materials, and scaling laws involve conservation of energy. Here a relationship with the opposite theme is discussed, which is the selectively advantageous instability (SAI) of one or more components of a replicating system, such as the cell. By increasing the complexity of the system, SAI can have benefits in addition to the generation of energy or the mobilization of building blocks. SAI involves a potential cost to the replicating system for the materials and/or energy required to create the unstable component, and in some cases, the energy required for its active degradation. SAI is well-studied in cells. Short-lived transcription and signaling factors enable a rapid response to a changing environment, and turnover is critical for replacement of damaged macromolecules. The minimal gene set for a viable cell includes proteases and a nuclease, suggesting SAI is essential for life. SAI promotes genetic diversity in several ways. Toxin/antitoxin systems promote maintenance of genes, and SAI of mitochondria facilitates uniparental transmission. By creating two distinct states, subject to different selective pressures, SAI can maintain genetic diversity. SAI of components of synthetic replicators favors replicator cycling, promoting emergence of replicators with increased complexity. Both classical and recent computer modeling of replicators reveals SAI. SAI may be involved at additional levels of biological organization. In summary, SAI promotes replicator genetic diversity and reproductive fitness, and may promote aging through loss of resources and maintenance of deleterious alleles.

The inheritance of alternative nest architectural traditions in stingless bees

The transmission of complex behavior and culture in humans has long been attributed to advanced forms of social learning,1,2 which play a crucial role in our technological advancement.3 While similar phenomena of behavioral traditions and cultural inheritance have been observed in animals,1,2,4,5,6 including in primates,7 whales,8 birds,9 and even insects,10 the underlying mechanisms enabling the persistence of such animal traditions, particularly in insects, are less well understood. This study introduces pioneering evidence of enduring architectural traditions in the stingless bee Scaptotrigona depilis, which are maintained without any evidence for social learning. We demonstrate that S. depilis exhibits two distinct nest architectures, comprising either helicoidal or flat, stacked horizontal combs, which are transmitted across generations through stigmergy11,12,13,14,15,16,17-an environmental feedback mechanism whereby the presence of the existing comb structures guides subsequent construction behaviors-thereby leading to a form of environmental inheritance.18,19,20 Cross-fostering experiments further show that genetic factors or prior experience does not drive the observed variation in nest architecture. Moreover, the experimental introduction of corkscrew dislocations within the combs prompted helicoidal building, confirming the use of stigmergic building rules. At a theoretical level, we establish that the long-term equilibrium of building in the helicoidal pattern fits with the expectations of a two-state Markov chain model. Overall, our findings provide compelling evidence for the persistence of behavioral traditions in an insect, based on a simple mechanism of environmental inheritance and stigmergic interactions, without requiring any sophisticated learning mechanism, thereby expanding our understanding of how traditions can be maintained in non-human species.

Collective behaviour: Stingless bees are self-organised nest builders

A new study compiles compelling evidence that stingless bees construct their brood combs in a self-organised manner in which local modification of a structure stimulates further modifications, a process known as stigmergy.

Chiral spiral cyclic twins. II. A two-parameter family of cyclic twins composed of discrete circle involute spirals

A mathematical toy model of chiral spiral cyclic twins is presented, describing a family of deterministically generated aperiodic point sets. Its individual members depend solely on a chosen pair of integer parameters, a modulus m and a multiplier μ. By means of their specific parameterization they comprise local features of both periodic and aperiodic crystals. In particular, chiral spiral cyclic twins are composed of discrete variants of continuous curves known as circle involutes, each discrete spiral being generated from an integer inclination sequence. The geometry of circle involutes does not only provide for a constant orthogonal separation distance between adjacent spiral branches but also yields an approximate delineation of the intrinsically periodic twin domains as well as a single aperiodic core domain interconnecting them. Apart from its mathematical description and analysis, e.g. concerning its circle packing densities, the toy model is studied in association with the crystallography and crystal chemistry of α-uranium and CrB-type crystal structures.

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.

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.

Archimedean Spirals Form at Low Flow Rates in Confined Chemical Gardens

We describe and study the formation of confined chemical garden patterns. At low flow rates of injection of cobalt chloride solution into a Hele-Shaw cell filled with sodium silicate, the precipitate forms with a thin filament wrapping around an expanding "candy floss" structure. The result is the formation of an Archimedean spiral structure. We model the growth of the structure mathematically. We estimate the effective density of the precipitate and calculate the membrane permeability. We set the results within the context of recent experimental and modeling work on confined chemical garden filaments.

A damage-tolerant, dual-scale, single-crystalline microlattice in the knobby starfish, Protoreaster nodosus

Cellular solids (e.g., foams and honeycombs) are widely found in natural and engineering systems because of their high mechanical efficiency and tailorable properties. While these materials are often based on polycrystalline or amorphous constituents, here we report an unusual dual-scale, single-crystalline microlattice found in the biomineralized skeleton of the knobby starfish, Protoreaster nodosus. This structure has a diamond-triply periodic minimal surface geometry (lattice constant, approximately 30 micrometers), the [111] direction of which is aligned with the c-axis of the constituent calcite at the atomic scale. This dual-scale crystallographically coaligned microlattice, which exhibits lattice-level structural gradients and dislocations, combined with the atomic-level conchoidal fracture behavior of biogenic calcite, substantially enhances the damage tolerance of this hierarchical biological microlattice, thus providing important insights for designing synthetic architected cellular solids.