A simple developmental model recapitulates complex insect wing venation patterns

Allometric Scaling Reveals Evolutionary Constraint on Odonata Wing Cellularity via Critical Crack Length

Scaling in insect wings is a complex phenomenon that seems pivotal in maintaining wing functionality. In this study, the relationship between wing size and the size, location, and shape of wing cells in dragonflies and damselflies (Odonata) is investigated, aiming to address the question of how these factors are interconnected. To this end, WingGram, the recently developed computer-vision-based software, is used to extract the geometric features of wing cells of 389 dragonflies and damselfly wings from 197 species and 16 families. It has been found that the cell length of the wings does not depend on the wing size. Despite the wide variation in wing length (8.42 to 56.5 mm) and cell length (0.1 to 8.5 mm), over 80% of the cells had a length ranging from 0.5 to 1.5 mm, which was previously identified as the critical crack length of the membrane of locust wings. An isometric scaling of cells is also observed with maximum size in each wing, which increased as the size increased. Smaller cells tended to be more circular than larger cells. The results have implications for bio-mimetics, inspiring new materials and designs for artificial wings with potential applications in aerospace engineering and robotics.

Vein-Membrane Interaction in Cambering of Flapping Insect Wings

It is still unclear how elastic deformation of flapping insect wings caused by the aerodynamic pressure results in their significant cambering. In this study, we present that a vein-membrane interaction (VMI) can clarify this mechanical process. In order to investigate the VMI, we propose a numerical method that consists of (a) a shape simplification model wing that consists of a few beams and a rectangular shell structure as the structural essence of flapping insect wings for the VMI, and (b) a monolithic solution procedure for strongly coupled beam and shell structures with large deformation and large rotation to analyze the shape simplification model wing. We incorporate data from actual insects into the proposed numerical method for the VMI. In the numerical analysis, we demonstrate that the model wing can generate a camber equivalent to that of the actual insects. Hence, the VMI will be a mechanical basis of the cambering of flapping insect wings. Furthermore, we present the mechanical roles of the veins in cambering. The intermediate veins increase the out-of-plane deflection of the wing membrane due to the aerodynamic pressure in the central area of the wing, while they decrease it in the vicinity of the trailing edge. As a result, these veins create the significant camber. The torsional flexibility of the leading-edge veins increases the magnitude of cambering.

Dragonfly-Inspired Wing Design Enabled by Machine Learning and Maxwell's Reciprocal Diagrams

This research is taking the first steps toward applying a 2D dragonfly wing skeleton in the design of an airplane wing using artificial intelligence. The work relates the 2D morphology of the structural network of dragonfly veins to a secondary graph that is topologically dual and geometrically perpendicular to the initial network. This secondary network is referred as the reciprocal diagram proposed by Maxwell that can represent the static equilibrium of forces in the initial graph. Surprisingly, the secondary graph shows a direct relationship between the thickness of the structural members of a dragonfly wing and their in-plane static equilibrium of forces that gives the location of the primary and secondary veins in the network. The initial and the reciprocal graph of the wing are used to train an integrated and comprehensive machine-learning model that can generate similar graphs with both primary and secondary veins for a given boundary geometry. The result shows that the proposed algorithm can generate similar vein networks for an arbitrary boundary geometry with no prior topological information or the primary veins' location. The structural performance of the dragonfly wing in nature also motivated the authors to test this research's real-world application for designing the cellular structures for the core of airplane wings as cantilever porous beams. The boundary geometry of various airplane wings is used as an input for the design proccedure. The internal structure is generated using the training model of the dragonfly veins and their reciprocal graphs. One application of this method is experimentally and numerically examined for designing the cellular core, 3D printed by fused deposition modeling, of the airfoil wing; the results suggest up to 25% improvements in the out-of-plane stiffness. The findings demonstrate that the proposed machine-learning-assisted approach can facilitate the generation of multiscale architectural patterns inspired by nature to form lightweight load-bearable elements with superior structural properties.

Golden ratio in venation patterns of dragonfly wings

The vein pattern in insect wings allows this lightweight structure to carry multiple biological functions. Here, an investigation of the angular distribution of the vein struts in dragonfly wings revealed that the golden angle or golden ratio dominates the venation patterns. We find that the golden angle dominates the intervein angles in regions where thin veins and membranes demand strength reinforcement. A golden ratio partition method has thus been developed that explains a set of preferred intervein angles in distorted polygon-shaped venation cells throughout the venation pattern in dragonfly wings. These observations provide new evidence that the wing structure is spatially optimized, by the golden rule in nature, for supporting biomechanical functions of dragonfly wings.

Investigation of chordwise functionally graded flexural rigidity in flapping wings using a two-dimensional pitch-plunge model

Insect wings are heterogeneous structures, with flexural rigidity varying one to two orders of magnitude over the wing surface. This heterogeneity influences the deformation the flapping wing experiences during flight. However, it is not well understood how this flexural rigidity gradient affects wing performance. Here, we develop a simplified 2D model of a flapping wing as a pitching, plunging airfoil using the assumed mode method and unsteady vortex lattice method to model the structural and fluid dynamics, respectively. We conduct parameter studies to explore how variable flexural rigidity affects mean lift production, power consumption and the forces required to flap the wing. We find that there is an optimal flexural rigidity distribution that maximizes lift production; this distribution generally corresponds to a 3:1 ratio between the wing's flapping and natural frequencies, though the ratio is sensitive to flapping kinematics. For hovering flight, the optimized flexible wing produces 20% more lift and requires 15% less power compared to a rigid wing but needs 20% higher forces to flap. Even when flapping kinematics deviate from those observed during hover, the flexible wing outperforms the rigid wing in terms of aerodynamic force generation and power across a wide range of flexural rigidity gradients. Peak force requirements and power consumption are inversely proportional with respect to flexural rigidity gradient, which may present a trade-off between insect muscle size and energy storage requirements. The model developed in this work can be used to efficiently investigate other spatially variant morphological or material wing features moving forward.

An image based application in Matlab for automated modelling and morphological analysis of insect wings

Despite extensive research on the biomechanics of insect wings over the past years, direct mechanical measurements on sensitive wing specimens remain very challenging. This is especially true for examining delicate museum specimens. This has made the finite element method popular in studies of wing biomechanics. Considering the complexities of insect wings, developing a wing model is usually error-prone and time-consuming. Hence, numerical studies in this area have often accompanied oversimplified models. Here we address this challenge by developing a new tool for fast, precise modelling of insect wings. This application, called WingGram, uses computer vision to detect the boundaries of wings and wing cells from a 2D image. The app can be used to develop wing models that include complex venations, corrugations and camber. WingGram can extract geometric features of the wings, including dimensions of the wing domain and subdomains and the location of vein junctions. Allowing researchers to simply model wings with a variety of forms, shapes and sizes, our application can facilitate studies of insect wing morphology and biomechanics. Being an open-access resource, WingGram has a unique application to expand how scientists, educators, and industry professionals analyse insect wings and similar shell structures in other fields, such as aerospace.

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.

Insect wing 3D printing

Insects have acquired various types of wings over their course of evolution and have become the most successful terrestrial animals. Consequently, the essence of their excellent environmental adaptability and locomotive ability should be clarified; a simple and versatile method to artificially reproduce the complex structure and various functions of these innumerable types of wings is necessary. This study presents a simple integral forming method for an insect-wing-type composite structure by 3D printing wing frames directly onto thin films. The artificial venation generation algorithm based on the centroidal Voronoi diagram, which can be observed in the wings of dragonflies, was used to design the complex mechanical properties of artificial wings. Furthermore, we implemented two representative functions found in actual insect wings: folding and coupling. The proposed crease pattern design software developed based on a beetle hindwing enables the 3D printing of foldable wings of any shape. In coupling-type wings, the forewing and hindwing are connected to form a single large wing during flight; these wings can be stored compactly by disconnecting and stacking them like cicada wings.

The wing venation of a new fossil species, reconstructed using geometric morphometrics, adds to the rare fossil record of Triassic Gondwanian Odonata

Probably the most common rock-imprint fossil-insect remain is an incomplete isolated wing. This pitfall has been traditionally addressed by manually reconstructing missing parts, which is not ideal to comprehend long-term evolutionary trends in the group, in particular for morphological diversity (i.e., disparity) approaches. Herein we describe a new Triassic relative of dragon- and damselflies (Odonata), Moltenophlebia lindae gen. et sp. nov., from the Molteno Formation (Karoo Basin, South Africa), on the basis of three incomplete, isolated wings. In order to provide a reconstruction of the complete wing venation of the species, we formalized and applied a repeatable method aiming at inferring the missing parts of a given specimen. It is based on homologous veins automatically identified thanks to a standardized color-coding. The dedicated script can be applied broadly to the fossil record of insect wings. The species is identified as a member of the Zygophlebiida, within the Triadophlebiomorpha. This discovery, therefore, represents the first ascertained occurrence of the latter group in Gondwana, an area where the fossil record of Odonata is depauperate.

Computer Vision, Machine Learning, and the Promise of Phenomics in Ecology and Evolutionary Biology

For centuries, ecologists and evolutionary biologists have used images such as drawings, paintings and photographs to record and quantify the shapes and patterns of life. With the advent of digital imaging, biologists continue to collect image data at an ever-increasing rate. This immense body of data provides insight into a wide range of biological phenomena, including phenotypic diversity, population dynamics, mechanisms of divergence and adaptation, and evolutionary change. However, the rate of image acquisition frequently outpaces our capacity to manually extract meaningful information from images. Moreover, manual image analysis is low-throughput, difficult to reproduce, and typically measures only a few traits at a time. This has proven to be an impediment to the growing field of phenomics – the study of many phenotypic dimensions together. Computer vision (CV), the automated extraction and processing of information from digital images, provides the opportunity to alleviate this longstanding analytical bottleneck. In this review, we illustrate the capabilities of CV as an efficient and comprehensive method to collect phenomic data in ecological and evolutionary research. First, we briefly review phenomics, arguing that ecologists and evolutionary biologists can effectively capture phenomic-level data by taking pictures and analyzing them using CV. Next we describe the primary types of image-based data, review CV approaches for extracting them (including techniques that entail machine learning and others that do not), and identify the most common hurdles and pitfalls. Finally, we highlight recent successful implementations and promising future applications of CV in the study of phenotypes. In anticipation that CV will become a basic component of the biologist’s toolkit, our review is intended as an entry point for ecologists and evolutionary biologists that are interested in extracting phenotypic information from digital images.

Circulation in Insect Wings

Insect wings are living, flexible structures composed of tubular veins and thin wing membrane. Wing veins can contain hemolymph (insect blood), tracheae, and nerves. Continuous flow of hemolymph within insect wings ensures that sensory hairs, structural elements such as resilin, and other living tissue within the wings remain functional. While it is well known that hemolymph circulates through insect wings, the extent of wing circulation (e.g., whether flow is present in every vein, and whether it is confined to the veins alone) is not well understood, especially for wings with complex wing venation. Over the last 100 years, scientists have developed experimental methods including microscopy, fluorescence, and thermography to observe flow in the wings. Recognizing and evaluating the importance of hemolymph movement in insect wings is critical in evaluating how the wings function both as flight appendages, as active sensors, and as thermoregulatory organs. In this review, we discuss the history of circulation in wings, past and present experimental techniques for measuring hemolymph, and broad implications for the field of hemodynamics in insect wings.

Shaping Organs: Shared Structural Principles Across Kingdoms

Development encapsulates the morphogenesis of an organism from a single fertilized cell to a functional adult. A critical part of development is the specification of organ forms. Beyond the molecular control of morphogenesis, shape in essence entails structural constraints and thus mechanics. Revisiting recent results in biophysics and development, and comparing animal and plant model systems, we derive key overarching principles behind the formation of organs across kingdoms. In particular, we highlight how growing organs are active rather than passive systems and how such behavior plays a role in shaping the organ. We discuss the importance of considering different scales in understanding how organs form. Such an integrative view of organ development generates new questions while calling for more cross-fertilization between scientific fields and model system communities.

DE-cadherin and Myosin II balance regulates furrow length for onset of polygon shape in syncytial Drosophila embryos

Cell shape morphogenesis, from spherical to polygonal, occurs in epithelial cell formation in metazoan embryogenesis. In syncytial Drosophila embryos, the plasma membrane incompletely surrounds each nucleus and is organized as a polygonal epithelial-like array. Each cortical syncytial division cycle shows a circular to polygonal plasma membrane transition along with furrow extension between adjacent nuclei from interphase to metaphase. In this study, we assess the relative contribution of DE-cadherin (also known as Shotgun) and Myosin II (comprising Zipper and Spaghetti squash in flies) at the furrow to polygonal shape transition. We show that polygonality initiates during each cortical syncytial division cycle when the furrow extends from 4.75 to 5.75 μm. Polygon plasma membrane organization correlates with increased junctional tension, increased DE-cadherin and decreased Myosin II mobility. DE-cadherin regulates furrow length and polygonality. Decreased Myosin II activity allows for polygonality to occur at a lower length than controls. Increased Myosin II activity leads to loss of lateral furrow formation and complete disruption of the polygonal shape transition. Our studies show that DE-cadherin-Myosin II balance regulates an optimal lateral membrane length during each syncytial cycle for polygonal shape transition.This article has an associated First Person interview with the first author of the paper.

A DNA polymerization-independent role for mitochondrial DNA polymerase I-like protein C in African trypanosomes

Mitochondrial DNA of Trypanosoma brucei and related parasites is a catenated network containing thousands of minicircles and tens of maxicircles, called kinetoplast DNA (kDNA). Replication of a single nucleoid requires at least three DNA polymerase I-like proteins (i.e. POLIB, POLIC and POLID), each showing discrete localizations near the kDNA during S phase. POLIB and POLID have roles in minicircle replication but the specific role of POLIC in kDNA maintenance is less clear. Here, we use an RNA interference (RNAi)-complementation system to dissect the functions of two distinct POLIC regions, i.e. the conserved family A DNA polymerase (POLA) domain and the uncharacterized N-terminal region (UCR). While RNAi complementation with wild-type POLIC restored kDNA content and cell cycle localization of kDNA, active site point mutations in the POLA domain impaired minicircle replication similar to that of POLIB and POLID depletions. Complementation with POLA domain alone abolished the formation of POLIC foci and partially rescued the RNAi phenotype. Furthermore, we provide evidence that the UCR is crucial in cell cycle-dependent protein localization and facilitates proper distribution of progeny networks. This is the first report of a DNA polymerase that impacts on mitochondrial nucleoid distribution.This article has an associated First Person interview with the first author of the paper.

Molecular mechanisms underlying simplification of venation patterns in holometabolous insects

How mechanisms of pattern formation evolve has remained a central research theme in the field of evolutionary and developmental biology. The mechanism of wing vein differentiation in Drosophila is a classic text-book example of pattern formation using a system of positional-information, yet very little is known about how species with a different number of veins pattern their wings, and how insect venation patterns evolved. Here, we examine the expression pattern of genes previously implicated in vein differentiation in Drosophila in two butterfly species with more complex venation Bicyclus anynana and Pieris canidia. We also test the function of some of these genes in B. anynana. We identify both conserved as well as new domains of decapentaplegic, engrailed, invected, spalt, optix, wingless, armadillo, blistered, and rhomboid gene expression in butterflies, and propose how the simplified venation in Drosophila might have evolved via loss of decapentaplegic, spalt and optix gene expression domains, silencing of vein inducing programs at Spalt-expression boundaries, and changes in gene expression of vein maintenance genes.

Computational analysis of size, shape and structure of insect wings

The size, shape and structure of insect wings are intimately linked to their ability to fly. However, there are few systematic studies of the variability of the natural patterns in wing morphology across insects. We have assembled a dataset of 789 insect wings with representatives from 25 families and performed a comprehensive computational analysis of their morphology using topological and geometric notions in terms of (i) wing size and contour shape, (ii) vein topology, and (iii) shape and distribution of wing membrane domains. These morphospaces are complementary to existing methods for quantitatively characterizing wing morphology and are likely to be useful for investigating wing function and evolution. This Methods and Techniques paper is accompanied by a set of computational tools for open use.

This article has an associated First Person interview with the first author of the paper.

Summary: We provide a set of simple quantitative measures to compare morphological variation in size, shape, and structure of insect wings across species, families and orders.