The self-oscillation paradox in the flight motor of Drosophila melanogaster.

Tiny flying insects, such as Drosophila melanogaster, fly by flapping their wings at frequencies faster than their brains are able to process. To do so, they rely on self-oscillation: dynamic instability, leading to emergent oscillation, arising from muscle stretch-activation. Many questions concerning this vital natural instability remain open. Does flight motor self-oscillation necessarily lead to resonance-a state optimal in efficiency and/or performance? If so, what state? And is self-oscillation even guaranteed in a motor driven by stretch-activated muscle, or are there limiting conditions? In this work, we use data-driven models of wingbeat and muscle behaviour to answer these questions. Developing and leveraging novel analysis techniques, including symbolic computation, we establish a fundamental condition for motor self-oscillation common to a wide range of motor models. Remarkably, D. melanogaster flight apparently defies this condition: a paradox of motor operation. We explore potential resolutions to this paradox, and, within its confines, establish that the D. melanogaster flight motor is probably not resonant with respect to exoskeletal elasticity: instead, the muscular elasticity plays a dominant role. Contrary to common supposition, the stiffness of stretch-activated muscle is an obstacle to, rather than an enabler of, the operation of the D. melanogaster flight motor.

A hull reconstruction-reprojection method for pose estimation of free-flying fruit flies.

Understanding the mechanisms of insect flight requires high-quality data of free-flight kinematics, e.g. for comparative studies or genetic screens. Although recent improvements in high-speed videography allow us to acquire large amounts of free-flight data, a significant bottleneck is automatically extracting accurate body and wing kinematics. Here, we present an experimental system and a hull reconstruction-reprojection algorithm for measuring the flight kinematics of fruit flies. The experimental system can automatically record hundreds of flight events per day. Our algorithm resolves a significant portion of the occlusions in this system by a reconstruction-reprojection scheme that integrates information from all cameras. Wing and body kinematics, including wing deformation, are then extracted from the hulls of the wing boundaries and body. This model-free method is fully automatic, accurate and open source, and can be readily adjusted for different camera configurations or insect species.

Solving the thoracic inverse problem in the fruit fly.

In many insect species, the thoracic exoskeletal structure plays a crucial role in enabling flight. In the dipteran indirect flight mechanism, thoracic cuticle acts as a transmission link between the flight muscles and the wings, and is thought to act as an elastic modulator: improving flight motor efficiency thorough linear or nonlinear resonance. But peering closely into the drivetrain of tiny insects is experimentally difficult, and the nature of this elastic modulation is unclear. Here, we present a new inverse-problem methodology to surmount this difficulty. In a data synthesis process, we integrate literature-reported rigid-wing aerodynamic and musculoskeletal data into a planar oscillator model for the fruit flyDrosophila melanogaster, and use this integrated data to identify several surprising properties of the fly's thorax. We find that fruit flies likely have an energetic need for motor resonance: absolute power savings due to motor elasticity range from 0%-30% across literature-reported datasets, averaging 16%. However, in all cases, the intrinsic high effective stiffness of the active asynchronous flight muscles accounts for all elastic energy storage required by the wingbeat. TheD. melanogasterflight motor should be considered as a system in which the wings are resonant with the elastic effects of the motor's asynchronous musculature, and not with the elastic effects of the thoracic exoskeleton. We discover also thatD. melanogasterwingbeat kinematics show subtle adaptions that ensure that wingbeat load requirements match muscular forcing. Together, these newly-identified properties suggest a novel conceptual model of the fruit fly's flight motor: a structure that is resonant due to muscular elasticity, and is thereby intensely concerned with ensuring that the primary flight muscles are operating efficiently. Our inverse-problem methodology sheds new light on the complex behaviour of these tiny flight motors, and provides avenues for further studies in a range of other insect species.

Distinct forms of resonant optimality within insect indirect flight motors.

Insect flight motors are extraordinary natural structures that operate efficiently at high frequencies. Structural resonance is thought to play a role in ensuring efficient motor operation, but the details of this role are elusive. While the efficiency benefits associated with resonance may be significant, a range of counterintuitive behaviours are observed. In particular, the relationship between insect wingbeat frequencies and thoracic natural frequencies is uncertain, with insects showing wingbeat frequency modulation over both short and long time scales. Here, we offer new explanations for this modulation. We show how, in linear and nonlinear models of an indirect flight motor, resonance is not a unitary state at a single frequency, but a complex cluster of distinct and mutually exclusive states, each representing a different form of resonant optimality. Additionally, by characterizing the relationship between resonance and the state of negative work absorption within the motor, we demonstrate how near-perfect resonant energetic optimality can be maintained over significant wingbeat frequency ranges. Our analysis leads to a new conceptual model of flight motor operation: one in which insects are not energetically restricted to a precise wingbeat frequency, but instead are robust to changes in thoracic and environmental properties-an illustration of the extraordinary robustness of these natural motors.