Solving the thoracic inverse problem in the fruit fly

Abstract

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 fly Drosophila 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. The D. melanogaster flight 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 that D. melanogaster wingbeat 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.

The self-oscillation paradox in the flight motor ofDrosophila melanogaster

“…assumption-the treatment of a 1 d.f. drivetrain pathway between a reference muscular strain and a wingbeat kinematic variable [12,15]. The presence of series elasticity-between the muscles and each wing-may technically extend the model to 2 d.f.…”

“…Making the 1 d.f. assumption typically involves the assumption of a rigid wing [12], though these assumptions are properly distinct. There is no preclusion of the use of wing deformation for aerodynamic modelling in a 1 d.f.…”

“…Second, the planar assumption-the analysis of the wingbeat stroke angle as the primary d.f. for muscular forcing [12,15]. The planar assumption also does not preclude the use of non-planar wingbeat kinematics for aerodynamic modelling.…”

“…The landmark experiments of Machin and Pringle [4], on asynchronous muscles attached to a lightly-damped load system, demonstrated characteristics of the self-oscillatory response that would suggest alignment with the system natural and/or resonant frequency [6]. Subsequently, self-oscillation and resonance have become blended terms in the literature [7][8][9], and the dipteran flight motor is widely depicted as resonant [10][11][12]. However, a remarkable feature of the results of Machin and Pringle [4] is now seldom noted: in a general system, there is no particular reason why self-oscillation and resonance should align [13].…”

“…Is self-oscillation still resonant under in vivo heavy damping conditions? [12] If so, resonant in what sense? [6] And what, indeed, is the quantitative mechanism by which motor self-oscillation arises from stretch-activation?…”