Submaximal power output from the dorsolongitudinal flight muscles of the hawkmothManduca sexta

Moth resonant mechanics are tuned to wingbeat frequency and energetic demands

An insect's wingbeat frequency is a critical determinant of its flight performance and varies by multiple orders of magnitude across Insecta. Despite potential energetic benefits for an insect that matches its wingbeat frequency to its resonant frequency, recent work has shown that moths may operate off their resonant peak. We hypothesized that across species, wingbeat frequency scales with resonance frequency to maintain favourable energetics, but with an offset in species that use frequency modulation as a means of flight control. The moth superfamily Bombycoidea is ideal for testing this hypothesis because their wingbeat frequencies vary across species by an order of magnitude, despite similar morphology and actuation. We used materials testing, high-speed videography and a model of resonant aerodynamics to determine how components of an insect's flight apparatus (stiffness, wing inertia, muscle strain and aerodynamics) vary with wingbeat frequency. We find that the resonant frequency of a moth correlates with wingbeat frequency, but resonance curve shape (described by the Weis-Fogh number) and peak location vary within the clade in a way that corresponds to frequency-dependent biomechanical demands. Our results demonstrate that a suite of adaptations in muscle, exoskeleton and wing drive variation in resonant mechanics, reflecting potential constraints on matching wingbeat and resonant frequencies.

Bridging two insect flight modes in evolution, physiology and robophysics

Since taking flight, insects have undergone repeated evolutionary transitions between two seemingly distinct flight modes1-3. Some insects neurally activate their muscles synchronously with each wingstroke. However, many insects have achieved wingbeat frequencies beyond the speed limit of typical neuromuscular systems by evolving flight muscles that are asynchronous with neural activation and activate in response to mechanical stretch2-8. These modes reflect the two fundamental ways of generating rhythmic movement: time-periodic forcing versus emergent oscillations from self-excitation8-10. How repeated evolutionary transitions have occurred and what governs the switching between these distinct modes remain unknown. Here we find that, despite widespread asynchronous actuation in insects across the phylogeny3,6, asynchrony probably evolved only once at the order level, with many reversions to the ancestral, synchronous mode. A synchronous moth species, evolved from an asynchronous ancestor, still preserves the stretch-activated muscle physiology. Numerical and robophysical analyses of a unified biophysical framework reveal that rather than a dichotomy, these two modes are two regimes of the same dynamics. Insects can transition between flight modes across a bridge in physiological parameter space. Finally, we integrate these two actuation modes into an insect-scale robot11-13 that enables transitions between modes and unlocks a new self-excited wingstroke strategy for engineered flight. Together, this framework accounts for repeated transitions in insect flight evolution and shows how flight modes can flip with changes in physiological parameters.

Single-cell type analysis of wing premotor circuits in the ventral nerve cord of Drosophila melanogaster

To perform most behaviors, animals must send commands from higher-order processing centers in the brain to premotor circuits that reside in ganglia distinct from the brain, such as the mammalian spinal cord or insect ventral nerve cord. How these circuits are functionally organized to generate the great diversity of animal behavior remains unclear. An important first step in unraveling the organization of premotor circuits is to identify their constituent cell types and create tools to monitor and manipulate these with high specificity to assess their function. This is possible in the tractable ventral nerve cord of the fly. To generate such a toolkit, we used a combinatorial genetic technique (split-GAL4) to create 195 sparse driver lines targeting 198 individual cell types in the ventral nerve cord. These included wing and haltere motoneurons, modulatory neurons, and interneurons. Using a combination of behavioral, developmental, and anatomical analyses, we systematically characterized the cell types targeted in our collection. Taken together, the resources and results presented here form a powerful toolkit for future investigations of neural circuits and connectivity of premotor circuits while linking them to behavioral outputs.

An information theoretic method to resolve millisecond-scale spike timing precision in a comprehensive motor program

Sensory inputs in nervous systems are often encoded at the millisecond scale in a precise spike timing code. There is now growing evidence in behaviors ranging from slow breathing to rapid flight for the prevalence of precise timing encoding in motor systems. Despite this, we largely do not know at what scale timing matters in these circuits due to the difficulty of recording a complete set of spike-resolved motor signals and assessing spike timing precision for encoding continuous motor signals. We also do not know if the precision scale varies depending on the functional role of different motor units. We introduce a method to estimate spike timing precision in motor circuits using continuous MI estimation at increasing levels of added uniform noise. This method can assess spike timing precision at fine scales for encoding rich motor output variation. We demonstrate the advantages of this approach compared to a previously established discrete information theoretic method of assessing spike timing precision. We use this method to analyze the precision in a nearly complete, spike resolved recording of the 10 primary wing muscles control flight in an agile hawk moth, Manduca sexta. Tethered moths visually tracked a robotic flower producing a range of turning (yaw) torques. We know that all 10 muscles in this motor program encode the majority of information about yaw torque in spike timings, but we do not know whether individual muscles encode motor information at different levels of precision. We demonstrate that the scale of temporal precision in all motor units in this insect flight circuit is at the sub-millisecond or millisecond-scale, with variation in precision scale present between muscle types. This method can be applied broadly to estimate spike timing precision in sensory and motor circuits in both invertebrates and vertebrates.

Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations

Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.

Experimental studies suggest differences in the distribution of thorax elasticity between insects with synchronous and asynchronous musculature

Insects have developed diverse flight actuation mechanisms, including synchronous and asynchronous musculature. Indirect actuation, used by insects with both synchronous and asynchronous musculature, transforms thorax exoskeletal deformation into wing rotation. Though thorax deformation is often attributed exclusively to muscle tension, the inertial and aerodynamic forces generated by the flapping wings may also contribute. In this study, a tethered flight experiment was used to simultaneously measure thorax deformation and the inertial/aerodynamic forces acting on the thorax generated by the flapping wing. Compared to insects with synchronous musculature, insects with asynchronous muscle deformed their thorax 60% less relative to their thorax diameter and their wings generated 2.8 times greater forces relative to their body weight. In a second experiment, dorsalventral thorax stiffness was measured across species. Accounting for weight and size, the asynchronous thorax was on average 3.8 times stiffer than the synchronous thorax in the dorsalventral direction. Differences in thorax stiffness and forces acting at the wing hinge led us to hypothesize about differing roles of series and parallel elasticity in the thoraxes of insects with synchronous and asynchronous musculature. Specifically, wing hinge elasticity may contribute more to wing motion in insects with asynchronous musculature than in those with synchronous musculature.

A biomechanical model for the relation between bite force and mandibular opening angle in arthropods

Bite forces play a key role in animal ecology: they affect mating behaviour, fighting success, and the ability to feed. Although feeding habits of arthropods have a significant ecological and economical impact, we lack fundamental knowledge on how the morphology and physiology of their bite apparatus controls bite performance, and its variation with mandible gape. To address this gap, we derived a biomechanical model that characterizes the relationship between bite force and mandibular opening angle from first principles. We validate this model by comparing its geometric predictions with morphological measurements on the muscoloskeletal bite apparatus of Atta cephalotes leaf-cutter ants, using computed tomography (CT) scans obtained at different mandible opening angles. We then demonstrate its deductive and inductive utility with three examplary use cases: Firstly, we extract the physiological properties of the leaf-cutter ant mandible closer muscle from in vivo bite force measurements. Secondly, we show that leaf-cutter ants are specialized to generate extraordinarily large bite forces, equivalent to about 2600 times their body weight. Thirdly, we discuss the relative importance of morphology and physiology in determining the magnitude and variation of bite force. We hope that a more detailed quantitative understanding of the link between morphology, physiology, and bite performance will facilitate future comparative studies on the insect bite apparatus, and help to advance our knowledge of the behaviour, ecology and evolution of arthropods.

Musculoskeletal wing-actuation model of hummingbirds predicts diverse effects of primary flight muscles in hovering flight

Hummingbirds have evolved to hover and manoeuvre with exceptional flight control. This is enabled by their musculoskeletal system that successfully exploits the agile motion of flapping wings. Here, we synthesize existing empirical and modelling data to generate novel hypotheses for principles of hummingbird wing actuation. These may help guide future experimental work and provide insights into the evolution and robotic emulation of hummingbird flight. We develop a functional model of the hummingbird musculoskeletal system, which predicts instantaneous, three-dimensional torque produced by primary (pectoralis and supracoracoideus) and combined secondary muscles. The model also predicts primary muscle contractile behaviour, including stress, strain, elasticity and work. Results suggest that the primary muscles (i.e. the flight 'engine') function as diverse effectors, as they do not simply power the stroke, but also actively deviate and pitch the wing with comparable actuation torque. The results also suggest that the secondary muscles produce controlled-tightening effects by acting against primary muscles in deviation and pitching. The diverse effects of the pectoralis are associated with the evolution of a comparatively enormous bicipital crest on the humerus.

Modeling the musculoskeletal system of an insect thorax for flapping flight

Indirect actuation of the wings via thoracic deformation is a unique mechanism widely observed in flying insect species. The physical properties of the thorax have been intensively studied in terms of their ability to efficiently generate wingbeats. The basic mechanism of indirect wing actuation is generally explained as a lever model on a cross-sectional plane, where the dorsoventral movement of the mesonotum (dorsal exoskeleton of the mesothorax) generated by contractions of indirect muscles actuates the wing. However, the model considers the mesonotum as an ideal flat plane, whereas the mesonotum is hemispherical and becomes locally deformed during flight. Furthermore, the conventional model is two-dimensional; therefore, three-dimensional wing kinematics by indirect muscles have not been studied to date. In this study, we develop structural models of the mesonotum and mesothorax of the hawkmothAgrius convolvuli, reconstructed from serial cross-sectional images. External forces are applied to the models to mimic muscle contraction, and mesonotum deformation and wing trajectories are analyzed using finite element analysis. We find that applying longitudinal strain to the mesonotum to mimic strain by depressor muscle contraction reproduces local deformation comparable to that of the thorax during flight. Furthermore, the phase difference of the forces applied to the depressor and elevator muscles changes the wing trajectory from a figure eight to a circle, which is qualitatively consistent with the tethered flight experiment. These results indicate that the local deformation of the mesonotum due to its morphology and the thoracic deformation via indirect power muscles can modulate three-dimensional wing trajectories.

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.

The hawkmoth wingbeat is not at resonance

Flying insects have elastic materials within their exoskeletons that could reduce the energetic cost of flight if their wingbeat frequency is matched to a mechanical resonance frequency. Flapping at resonance may be essential across flying insects because of the power demands of small-scale flapping flight. However, building up large-amplitude resonant wingbeats over many wingstrokes may be detrimental for control if the total mechanical energy in the spring-wing system exceeds the per-cycle work capacity of the flight musculature. While the mechanics of the insect flight apparatus can behave as a resonant system, the question of whether insects flap their wings at their resonant frequency remains unanswered. Using previous measurements of body stiffness in the hawkmoth, Manduca sexta, we develop a mechanical model of spring-wing resonance with aerodynamic damping and characterize the hawkmoth's resonant frequency. We find that the hawkmoth's wingbeat frequency is approximately 80% above resonance and remains so when accounting for uncertainty in model parameters. In this regime, hawkmoths may still benefit from elastic energy exchange while enabling control of aerodynamic forces via frequency modulation. We conclude that, while insects use resonant mechanics, tuning wingbeats to a simple resonance peak is not a necessary feature for all centimetre-scale flapping flyers.

Liquid-amplified zipping actuators for micro-air vehicles with transmission-free flapping

Flapping micro-air vehicles (MAVs) can access a wide range of locations, including confined spaces such as the inside of industrial plants and collapsed buildings, and offer high maneuverability and tolerance to disturbances. However, current flapping MAVs require transmission systems between their actuators and wings, which introduce energetic losses and additional mass, hindering performance. Here, we introduce a high-performance electrostatic flapping actuation system, the liquid-amplified zipping actuator (LAZA), which induces wing movement by direct application of liquid-amplified electrostatic forces at the wing root, eliminating the requirement of any transmission system and their associated downsides. The LAZA allows for accurate control of flapping frequency and amplitude, exhibits no variation in performance over more than 1 million actuation cycles, and delivers peak and average specific powers of 200 and 124 watts per kilogram, respectively, exceeding mammalian and insect flight muscle and on par with modern flapping MAV actuation systems. The inclusion of 50-millimeter-long passively pitching wings in a dragonfly-sized LAZA flapping system allowed the rectification of net directional thrust up to 5.73 millinewtons. This thrust was achieved while consuming only 243 milliwatts of electrical power, implying a thrust-to-power ratio of 23.6 newtons per kilowatt, similar to state-of-the-art flapping MAVs, helicopter rotors, and commercial drone motors. Last, a horizontally moving LAZA flapping system supported by a taut nylon wire was able to accelerate from at-rest and travel at speeds up to 0.71 meters per second. The LAZA enables lightweight, high-performance transmission-free flapping MAVs for long-term remote exploration and search-and-rescue missions.

A mechanism for sarcomere breathing: volume change and advective flow within the myofilament lattice

During muscle contraction, myosin motors anchored to thick filaments bind to and slide actin thin filaments. These motors rely on energy derived from ATP, supplied, in part, by diffusion from the sarcoplasm to the interior of the lattice of actin and myosin filaments. The radial spacing of filaments in this lattice may change or remain constant during contraction. If the lattice is isovolumetric, it must expand when the muscle shortens. If, however, the spacing is constant or has a different pattern of axial and radial motion, then the lattice changes volume during contraction, driving fluid motion and assisting in the transport of molecules between the contractile lattice and the surrounding intracellular space. We first create an advective-diffusive-reaction flow model and show that the flow into and out of the sarcomere lattice would be significant in the absence of lattice expansion. Advective transport coupled to diffusion has the potential to substantially enhance metabolite exchange within the crowded sarcomere. Using time-resolved x-ray diffraction of contracting muscle, we next show that the contractile lattice is neither isovolumetric nor constant in spacing. Instead, lattice spacing is time varying, depends on activation, and can manifest as an effective time-varying Poisson ratio. The resulting fluid flow in the sarcomere lattice of synchronous insect flight muscles is even greater than expected for constant lattice spacing conditions. Lattice spacing depends on a variety of factors that produce radial force, including cross-bridges, titin-like molecules, and other structural proteins. Volume change and advective transport varies with the phase of muscle stimulation during periodic contraction but remains significant at all conditions. Although varying in magnitude, advective transport will occur in all cases in which the sarcomere is not isovolumetric. Akin to "breathing," advective-diffusive transport in sarcomeres is sufficient to promote metabolite exchange and may play a role in the regulation of contraction itself.

Rapid frequency modulation in a resonant system: aerial perturbation recovery in hawkmoths

Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.

Timing precision in fly flight control: integrating mechanosensory input with muscle physiology

Animals rapidly collect and act on incoming information to navigate complex environments, making the precise timing of sensory feedback critical in the context of neural circuit function. Moreover, the timing of sensory input determines the biomechanical properties of muscles that undergo cyclic length changes, as during locomotion. Both of these issues come to a head in the case of flying insects, as these animals execute steering manoeuvres at timescales approaching the upper limits of performance for neuromechanical systems. Among insects, flies stand out as especially adept given their ability to execute manoeuvres that require sub-millisecond control of steering muscles. Although vision is critical, here I review the role of rapid, wingbeat-synchronous mechanosensory feedback from the wings and structures unique to flies, the halteres. The visual system and descending interneurons of the brain employ a spike rate coding scheme to relay commands to the wing steering system. By contrast, mechanosensory feedback operates at faster timescales and in the language of motor neurons, i.e. spike timing, allowing wing and haltere input to dynamically structure the output of the wing steering system. Although the halteres have been long known to provide essential input to the wing steering system as gyroscopic sensors, recent evidence suggests that the feedback from these vestigial hindwings is under active control. Thus, flies may accomplish manoeuvres through a conserved hindwing circuit, regulating the firing phase-and thus, the mechanical power output-of the wing steering muscles.

In vitro virtual reality: an anatomically explicit musculoskeletal simulation powered by in vitro muscle using closed-loop tissue-software interaction

Muscle force-length dynamics are governed by intrinsic contractile properties, motor stimulation and mechanical load. Although intrinsic properties are well characterised, physiologists lack in vitro instrumentation to account for combined effects of limb inertia, musculoskeletal architecture and contractile dynamics. We introduce in vitro virtual reality (in vitro-VR) which enables in vitro muscle tissue to drive a musculoskeletal jumping simulation. In hardware, muscle force from a frog plantaris was transmitted to a software model where joint torques, inertia and ground reaction forces were computed to advance the simulation at 1 kHz. To close the loop, simulated muscle strain was returned to update in vitro length. We manipulated (1) stimulation timing and (2) the virtual muscle's anatomical origin. This influenced interactions among muscular, inertial, gravitational and contact forces dictating limb kinematics and jump performance. We propose that in vitro-VR can be used to illustrate how neuromuscular control and musculoskeletal anatomy influence muscle dynamics and biomechanical performance.

Indirect actuation reduces flight power requirements in Manduca sexta via elastic energy exchange

In many insects, wing movements are generated indirectly via exoskeletal deformations. Measurements of inertial and aerodynamic power suggest that elastic recovery of energy between wingstrokes might reduce power requirements of flight. We tested three questions. (1) Can the thorax itself provide significant energy return? (2) Does a simple damped elastic model describe the bulk mechanical behaviour? (3) Are different regions of the thorax specialized for elastic energy exchange? We measured deformation mechanics of the hawkmoth Manduca sexta thorax by recording the force required to sinusoidally deform the thorax over a wide frequency range. Elastic energy storage in the thorax is sufficient to minimize power requirements. However, we find that a structural (frequency-independent) damping model, not a viscoelastic model, best describes the thorax's mechanical properties. We next performed complementary experiments on a structurally damped homogeneous hemisphere. In contrast to the hemispherical shell, we find that mechanical coupling between different regions of the thorax improves energy exchange performance and that local mechanical properties depend on global strain patterns. Specifically, the scutum region provides energy recovery with low dissipation, while the majority of energy loss occurred in the wing hinge region, highlighting the specificity of thorax regions for flight energetics.

Wing flexibility reduces the energetic requirements of insect flight

Flapping insect wings deform under aerodynamic as well as inertial-elastic forces. This deformation is thought to improve power economy and reduce the energetic costs of flight. However, many flapping wing models employ rigid body simplifications or demand excessive computational power, and are consequently unable to identify the influence of flexibility on flight energetics. Here, we derive a reduced-order model capable of estimating the driving torques and corresponding power of flapping, flexible insect wings. We validate this model by actuating a tobacco hornworm hawkmoth Manduca sexta (L.) forewing with a custom single-degree-of-freedom mechanical flapper. Our model predicts measured torques and instantaneous power with reasonable accuracy. Moreover, the flexible wing model predicts experimental trends that rigid body models cannot, which suggests compliance should not be neglected when considering flight dynamics at this scale. Next, we use our model to investigate flight energetics with realistic flapping kinematics. We find that when the natural frequency of the wing is roughly three times that of the flapping frequency, flexibility can reduce energy expenditures by almost 25% compared to a rigid wing if negative work is stored as potential energy and subsequently released to do positive work. The wing itself can store about 30% of the 1200 [Formula: see text]J of total energy required over a wingbeat. Peak potential energy storage occurs immediately before stroke reversal. We estimate that for a moth weighing 1.5-2.5 g, the peak instantaneous power required for flight is 75-125 W kg^-1. However, these peak values are likely lower in natural insect flight, where the wing is able to exchange strain energy with the compliant thorax. Our findings highlight the importance of flexibility in flapping wing micro aerial vehicle design and suggest tuned flexibility can greatly improve vehicle efficiency.

Toward a Dielectric Elastomer Resonator Driven Flapping Wing Micro Air Vehicle

In the last two decades, insect-inspired flapping wing micro air vehicles (MAVs) have attracted great attention for their potential for highly agile flight. Insects flap their wings at the resonant frequencies of their flapping mechanisms. Resonant actuation is highly advantageous as it amplifies the flapping amplitude and reduces the inertial power demand. Emerging soft actuators, such as dielectric elastomer actuators (DEAs) have large actuation strains and thanks to their inherent elasticity, DEAs have been shown a promising candidate for resonant actuation. In this work a double cone DEA configuration is presented, a mathematic model is developed to characterize its quasi-static and dynamic performance. We compare the high frequency performance of two most common dielectric elastomers: silicone elastomer and polyacrylate tape VHB. The mechanical power output of the DEA is experimentally analyzed as a DEA-mass oscillator. Then a flapping wing mechanism actuated by this elastic actuator is demonstrated, this design is able to provide a peak flapping amplitude of 63° at the frequency of 18 Hz.

Flight motor modulation with speed in the hawkmoth Manduca sexta

The theoretical underpinnings for flight, including animal flight with flapping wings, predict a curvilinear U-shaped or J-shaped relationship between flight speed and the power required to maintain that speed. Experimental data have confirmed this relationship for a variety of bird and bat species but not insects, possibly due to differences in aerodynamics and physiology or experimental difficulties. Here we quantify modulation of the main flight motor muscles (the dorsolongitudinal and dorsoventral) via electromyography in hawkmoths (Manduca sexta) flying freely over a range of speeds in a wind tunnel and show that these insects exhibit a U-shaped speed-power relationship, with a minimum power speed of 2ms^-1, indicating that at least large flying insects achieve sufficiently high flight speeds that drag and power become limiting factors.

Recent developments in the study of insect flight

Here we review recent contributions to the study of insect flight, in particular those brought about by advances in experimental techniques. We focus particularly on the following areas: wing flexibility and deformation, the physiology and biophysics of asynchronous insect flight muscle, the aerodynamics of flight, and stability and maneuverability. This recent research reveals the importance of wing flexibility to insect flight, provides a detailed model of how asynchronous flight muscle functions and how it may have evolved, synthesizes many recent studies of insect flight aerodynamics into a broad-reaching summary of unsteady flight aerodynamics, and highlights new insights into the sources of flight stability in insects. The focus on experimental techniques and recently developed apparatus shows how these advancements have occurred and point the way towards future experiments.

Myofilament proteins in the synchronous flight muscles of Manduca sexta show both similarities and differences to Drosophila melanogaster

Insect flight muscles have been classified as either synchronous or asynchronous based on the coupling between excitation and contraction. In the moth Manduca sexta, the flight muscles are synchronous and do not display stretch activation, which is a property of asynchronous muscles. We annotated the M. sexta genes encoding the major myofibrillar proteins and analyzed their isoform pattern and expression. Comparison with the homologous genes in Drosophila melanogaster indicates both difference and similarities. For proteins such as myosin heavy chain, tropomyosin, and troponin I the availability and number of potential variants generated by alternative spicing is mostly conserved between the two insects. The exon usage associated with flight muscles indicates that some exon sets are similarly used in the two insects, whereas others diverge. For actin the number of individual genes is different and there is no evidence for a flight muscle specific isoform. In contrast for troponin C, the number of genes is similar, as well as the isoform composition in flight muscles despite the different calcium regulation. Both troponin I and tropomyosin can include COOH-terminal hydrophobic extensions similar to tropomyosinH and troponinH found in D. melanogaster and the honeybee respectively.

Dual dimensionality reduction reveals independent encoding of motor features in a muscle synergy for insect flight control

What are the features of movement encoded by changing motor commands? Do motor commands encode movement independently or can they be represented in a reduced set of signals (i.e. synergies)? Motor encoding poses a computational and practical challenge because many muscles typically drive movement, and simultaneous electrophysiology recordings of all motor commands are typically not available. Moreover, during a single locomotor period (a stride or wingstroke) the variation in movement may have high dimensionality, even if only a few discrete signals activate the muscles. Here, we apply the method of partial least squares (PLS) to extract the encoded features of movement based on the cross-covariance of motor signals and movement. PLS simultaneously decomposes both datasets and identifies only the variation in movement that relates to the specific muscles of interest. We use this approach to explore how the main downstroke flight muscles of an insect, the hawkmoth Manduca sexta, encode torque during yaw turns. We simultaneously record muscle activity and turning torque in tethered flying moths experiencing wide-field visual stimuli. We ask whether this pair of muscles acts as a muscle synergy (a single linear combination of activity) consistent with their hypothesized function of producing a left-right power differential. Alternatively, each muscle might individually encode variation in movement. We show that PLS feature analysis produces an efficient reduction of dimensionality in torque variation within a wingstroke. At first, the two muscles appear to behave as a synergy when we consider only their wingstroke-averaged torque. However, when we consider the PLS features, the muscles reveal independent encoding of torque. Using these features we can predictably reconstruct the variation in torque corresponding to changes in muscle activation. PLS-based feature analysis provides a general two-sided dimensionality reduction that reveals encoding in high dimensional sensory or motor transformations.

Understanding movement control is challenging because the brains of nearly all animals send motor command signals to many muscles, and these signals produce complex movements. In studying animal movement, one cannot always record all the motor commands an animal uses or know all the ways in which movement varies in response. A combined approach is necessary to find the relevant patterns: the changes in movement that correspond to changes in the recorded motor commands. Techniques exist to identify simple patterns in either the motor commands or the movements, but in this paper we develop an approach that identifies patterns in both simultaneously. We use this technique to understand how agile flying insects control aerial turns. The two main downstroke muscles of moths are thought to produce turns by creating a power difference between the left and right wings. The moth’s brain may only need to specify the difference in activation between the two muscles. We discover that moth’s brain actually has independent control over each muscle, and this separate control increases the moth’s ability to adjust turning within a single wingstroke. Our computational approach reveals sophisticated patterns of movement processing even in the small nervous systems of insects.

The length-tension curve in muscle depends on lattice spacing

Classic interpretations of the striated muscle length-tension curve focus on how force varies with overlap of thin (actin) and thick (myosin) filaments. New models of sarcomere geometry and experiments with skinned synchronous insect flight muscle suggest that changes in the radial distance between the actin and myosin filaments, the filament lattice spacing, are responsible for between 20% and 50% of the change in force seen between sarcomere lengths of 1.4 and 3.4 µm. Thus, lattice spacing is a significant force regulator, increasing the slope of muscle's force-length dependence.

Built for rowing: frog muscle is tuned to limb morphology to power swimming

Rowing is demanding, in part, because drag on the oars increases as the square of their speed. Hence, as muscles shorten faster, their force capacity falls, whereas drag rises. How do frogs resolve this dilemma to swim rapidly? We predicted that shortening velocity cannot exceed a terminal velocity where muscle and fluid torques balance. This terminal velocity, which is below Vmax, depends on gear ratio (GR = outlever/inlever) and webbed foot area. Perhaps such properties of swimmers are 'tuned', enabling shortening speeds of approximately 0.3Vmax for maximal power. Predictions were tested using a 'musculo-robotic' Xenopus laevis foot driven either by a living in vitro or computational in silico plantaris longus muscle. Experiments verified predictions. Our principle finding is that GR ranges from 11.5 to 20 near the predicted optimum for rowing (GR ≈ 11). However, gearing influences muscle power more strongly than foot area. No single morphology is optimal for producing muscle power. Rather, the 'optimal' GR decreases with foot size, implying that rowing ability need not compromise jumping (and vice versa). Thus, despite our neglect of additional forces (e.g. added mass), our model predicts pairings of physiological and morphological properties to confer effective rowing. Beyond frogs, the model may apply across a range of size and complexity from aquatic insects to human-powered rowing.

Abdicating power for control: a precision timing strategy to modulate function of flight power muscles

Muscles driving rhythmic locomotion typically show strong dependence of power on the timing or phase of activation. This is particularly true in insects' main flight muscles, canonical examples of muscles thought to have a dedicated power function. However, in the moth (Manduca sexta), these muscles normally activate at a phase where the instantaneous slope of the power-phase curve is steep and well below maximum power. We provide four lines of evidence demonstrating that, contrary to the current paradigm, the moth's nervous system establishes significant control authority in these muscles through precise timing modulation: (i) left-right pairs of flight muscles normally fire precisely, within 0.5-0.6 ms of each other; (ii) during a yawing optomotor response, left-right muscle timing differences shift throughout a wider 8 ms timing window, enabling at least a 50 per cent left-right power differential; (iii) timing differences correlate with turning torque; and (iv) the downstroke power muscles alone causally account for 47 per cent of turning torque. To establish (iv), we altered muscle activation during intact behaviour by stimulating individual muscle potentials to impose left-right timing differences. Because many organisms also have muscles operating with high power-phase gains (Δ(power)/Δ(phase)), this motor control strategy may be ubiquitous in locomotor systems.

Neuromuscular control of free-flight yaw turns in the hawkmoth Manduca sexta

The biomechanical properties of an animal's locomotor structures profoundly influence the relationship between neuromuscular inputs and body movements. In particular, passive stability properties are of interest as they may offer a non-neural mechanism for simplifying control of locomotion. Here, we hypothesized that a passive stability property of animal flight, flapping counter-torque (FCT), allows hawkmoths to control planar yaw turns in a damping-dominated framework that makes rotational velocity directly proportional to neuromuscular activity. This contrasts with a more familiar inertia-dominated framework where acceleration is proportional to force and neuromuscular activity. To test our hypothesis, we collected flight muscle activation timing, yaw velocity and acceleration data from freely flying hawkmoths engaged in planar yaw turns. Statistical models built from these data then allowed us to infer the degree to which the moths inhabit either damping- or inertia-dominated control domains. Contrary to our hypothesis, a combined model corresponding to inertia-dominated control of yaw but including substantial damping effects best linked the neuromuscular and kinematic data. This result shows the importance of including passive stability properties in neuromechanical models of flight control and reveals possible trade-offs between manoeuvrability and stability derived from damping.

Abdicating power for control: a precision timing strategy to modulate function of flight power muscles

Muscles driving rhythmic locomotion typically show strong dependence of power on the timing or phase of activation. This is particularly true in insects' main flight muscles, canonical examples of muscles thought to have a dedicated power function. However, in the moth (Manduca sexta), these muscles normally activate at a phase where the instantaneous slope of the power-phase curve is steep and well below maximum power. We provide four lines of evidence demonstrating that, contrary to the current paradigm, the moth's nervous system establishes significant control authority in these muscles through precise timing modulation: (i) left-right pairs of flight muscles normally fire precisely, within 0.5-0.6 ms of each other; (ii) during a yawing optomotor response, left-right muscle timing differences shift throughout a wider 8 ms timing window, enabling at least a 50 per cent left-right power differential; (iii) timing differences correlate with turning torque; and (iv) the downstroke power muscles alone causally account for 47 per cent of turning torque. To establish (iv), we altered muscle activation during intact behaviour by stimulating individual muscle potentials to impose left-right timing differences. Because many organisms also have muscles operating with high power-phase gains (Δ(power)/Δ(phase)), this motor control strategy may be ubiquitous in locomotor systems.

Temperature gradients drive mechanical energy gradients in the flight muscle of Manduca sexta

A temperature gradient throughout the dominant flight muscle (dorsolongitudinal muscle, DLM(1)) of the hawkmoth Manduca sexta, together with temperature-dependent muscle contractile rates, demonstrates that significant spatial variation in power production is possible within a single muscle. Using in situ work-loop analyses under varying muscle temperatures and phases of activation, we show that regional differences in muscle temperature will induce a spatial gradient in the mechanical power output throughout the DLM(1). Indeed, we note that this power gradient spans from positive to negative values across the predicted temperature range. Warm ventral subunits produce positive power at their in vivo operating temperatures, and therefore act as motors. Concurrently, as muscle temperature decreases dorsally, the subunits produce approximately zero mechanical power output, acting as an elastic energy storage source, and negative power output, behaving as a damper. Adjusting the phase of activation further influences the temperature sensitivity of power output, significantly affecting the mechanical power output gradient that is expressed. Additionally, the separate subregions of the DLM(1) did not appear to employ significant physiological compensation for the temperature-induced differences in power output. Thus, although the components of a muscle are commonly thought to operate uniformly, a significant within-muscle temperature gradient has the potential to induce a mechanical power gradient, whereby subunits within a muscle operate with separate and distinct functional roles.

Temperature gradients in the flight muscles of Manduca sexta imply a spatial gradient in muscle force and energy output

There is a significant dorso-ventral temperature gradient in the dominant flight muscles [dorsolongitudinal muscles (DLM(1))] of the hawkmoth Manduca sexta during tethered flight. The mean temperature difference was 5.6°C (range=3.8-6.9°C) between the warmer, ventral-most subunits and the cooler, dorsal-most subunits. As force generation in muscle depends on temperature, the mechanical energy output of more dorsal subunits will differ from that of deeper and warmer muscle subunits. To test this hypothesis, we isolated the dorsal subunits and the ventral subunits and recorded both single and 25 Hz (wingbeat frequency) isometric contractions at a range of temperatures. Our data show that the contractile dynamics of the various regions of the DLM(1) are similarly affected by temperature, with higher temperatures leading to reduced contraction times. Furthermore, using standard electromyography, we showed that the different regions are activated nearly simultaneously (mean time difference=0.22 ms). These observations suggest that the existence of a temperature gradient will necessarily produce a mechanical energy gradient in the DLM(1) in M. sexta.

Shifts in a single muscle's control potential of body dynamics are determined by mechanical feedback

Muscles are multi-functional structures that interface neural and mechanical systems. Muscle work depends on a large multi-dimensional space of stimulus (neural) and strain (mechanical) parameters. In our companion paper, we rewrote activation to individual muscles in intact, behaving cockroaches (Blaberus discoidalis L.), revealing a specific muscle's potential to control body dynamics in different behaviours. Here, we use those results to provide the biologically relevant parameters for in situ work measurements. We test four hypotheses about how muscle function changes to provide mechanisms for the observed control responses. Under isometric conditions, a graded increase in muscle stress underlies its linear actuation during standing behaviours. Despite typically absorbing energy, this muscle can recruit two separate periods of positive work when controlling running. This functional change arises from mechanical feedback filtering a linear increase in neural activation into nonlinear work output. Changing activation phase again led to positive work recruitment, but at different times, consistent with the muscle's ability to also produce a turn. Changes in muscle work required considering the natural sequence of strides and separating swing and stance contributions of work. Both in vivo control potentials and in situ work loops were necessary to discover the neuromechanical coupling enabling control.

Developmental changes in dendritic shape and synapse location tune single-neuron computations to changing behavioral functions

During nervous system development, different classes of neurons obtain different dendritic architectures, each of which receives a large number of input synapses. However, it is not clear whether synaptic inputs are targeted to specific regions within a dendritic tree and whether dendritic tree geometry and subdendritic synapse distributions might be optimized to support proper neuronal input-output computations. This study uses an insect model where structure and function of an individually identifiable neuron, motoneuron 5 (MN5), are changed while it develops from a slow larval crawling into a fast adult flight motoneuron during metamorphosis. This allows for relating postembryonic dendritic remodeling of an individual motoneuron to developmental changes in behavioral function. Dendritic architecture of MN5 is analyzed by three-dimensional geometric reconstructions and quantitative co-localization analysis to address the distribution of synaptic terminals. Postembryonic development of MN5 comprises distinct changes in dendritic shape and in the subdendritic distribution of GABAergic input synapses onto MN5. Subdendritic synapse targeting is not a consequence of neuropil structure but must rely on specific subdendritic recognition mechanisms. Passive multicompartment simulations indicate that postembryonic changes in dendritic architecture and in subdendritic input synapse distributions may tune the passive computational properties of MN5 toward stage-specific behavioral requirements.

Differential effects of octopamine and tyramine on the central pattern generator for Manduca flight

The biogenic amine, octopamine, modulates a variety of aspects of insect motor behavior, including direct action on the flight central pattern generator. A number of recent studies demonstrate that tyramine, the biological precursor of octopamine, also affects invertebrate locomotor behaviors, including insect flight. However, it is not clear whether the central pattern generating networks are directly affected by both amines, octopamine and tyramine. In this study, we tested whether tyramine affected the central pattern generator for flight in the moth, Manduca sexta. Fictive flight was induced in an isolated ventral nerve cord preparation by bath application of the octopamine agonist, chlordimeform, to test potential effects of tyramine on the flight central pattern generator by pharmacological manipulations. The results demonstrate that octopamine but not tyramine is sufficient to induce fictive flight in the isolated ventral nerve cord. During chlordimeform induced fictive flight, bath application of tyramine selectively increases synaptic drive to depressor motoneurons, increases the number of depressor spikes during each cycle and decreases the depressor phase. Conversely, blocking tyramine receptors selectively reduces depressor motoneuron activity, but does not affect cycle by cycle elevator motoneuron spiking. Therefore, octopamine and tyramine exert distinct effects on the flight central pattern generating network.

Active control of free flight manoeuvres in a hawkmoth, Agrius convolvuli

By combining optical triangulation with the comb-fringe technique and dual-channel telemetry, wing kinematics and body attitudes accompanying muscle activities of free-flying male hawkmoths were recorded synchronously when they performed flight manoeuvres elicited by a female sex pheromone. The results indicate that the wing leading edge angular position at the ventral stroke reversal, which can be decomposed by two orthogonal angular parameters (a flapping angle and a deviation angle), is well controllable. Two specific flight muscles, the dorsal-ventral muscle (DVM, indirect muscle, a wing elevator) and the third axillary muscle (3AXM, direct muscle, a wing retractor), can modulate the flapping angle and the deviation angle, respectively, by means of regulating the firing timing of muscle activities. The firing timing can be expressed by the firing latency absolutely, which is just before the timing of ventral stroke reversal. The results illustrate that lengthening the firing latency of the DVM and of the 3AXM can increase the flapping angle and the deviation angle, respectively, which both strengthen the downstroke at the ventral stroke reversal. The relationship of bilateral asymmetry shows that the bilateral differences in the firing latency of the DVM and of the 3AXM will cause bilateral differences in the wing position, which accompany the variations of yaw and roll angles in time course. This implies the contribution of the two muscles to active steering controls during turning or banking, though the DVM being an indirect muscle was generally treated as a power generator. Finally, the relationship between the pitch angle and the 3AXM latency, deduced from the relationships between the pitch angle and the deviation angle and between the deviation angle and the 3AXM latency, shows that lengthening the 3AXM latency can increase the pitch angle at the ventral stroke reversal by moving the wing tip far away from the centre of gravity of the body, which indicates a functional role of the 3AXM in active pitching control.

A spatially explicit model of muscle contraction explains a relationship between activation phase, power and ATP utilization in insect flight

Using spatially explicit, stochastically kinetic, molecular models of muscle force generation, we examined the relationship between mechanical power output and energy utilization under differing patterns of length change and activation. A simulated work loop method was used to understand prior observations of sub-maximal power output in the dominant flight musculature of the hawkmoth Manduca sexta L. Here we show that mechanical work output and energy consumption (via ATP) vary with the phase of activation, although they do so with different phase sensitivities. The phase relationship for contraction efficiency (the ratio of power output to power input) differs from the phase relationships of energy consumption and power output. To our knowledge, this is the first report to suggest that ATP utilization by myosin cross-bridges varies strongly with the phase of activation in muscle undergoing cyclic length changes.

The effect of decoupling olfactory and visual stimuli on the foraging behavior of Manduca sexta

Within an appetitive context, Manduca sexta, a nectivorous nocturnal hawkmoth, can be attracted by a range of stimuli including floral volatiles and visual display, carbon dioxide and water vapor. Several studies on this and other flower-visiting insects have shown how olfactory and visual stimulation play (or do not play) a role in attraction and feeding. Nevertheless, these studies have consistently manipulated stimuli in a 'presence-absence' manner. Here, we experimentally decoupled the presentation of both stimuli spatially and temporally in a wind tunnel, rather than entirely eliminating either one, and found that the decision-making process based on these stimuli is more flexible and complex than previously asserted. Manduca sexta was most responsive when both cues were present and emanated from the same source. When stimuli were spatially separated, responsiveness levels were comparable to those elicited by a single stimulus. However, transient olfactory stimulation either before or after visually guided approach (temporal decoupling) enhanced responsiveness to an odorless visual target. Additionally, searching times were increased by either a transient olfactory stimulation before take-off or by having the flower model spatially separated from the odor source tracked by the moths. Finally, in a dual-choice experiment, moths showed a strong bias for the visual display over the odor plume, suggesting the former to be the ultimate indicator of a nectar source. Our manipulation of floral cues shows that the feeding behavior of M. sexta, and probably of other nectivorous insects, is based not only on the sensory stimulation per se but also on the temporal and spatial pattern in which these stimuli are perceived.