The self-oscillation paradox in the flight motor of <i>Drosophila melanogaster</i>.

Abstract

Tiny flying insects, such as <i>Drosophila melanogaster</i>, 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, <i>D. melanogaster</i> flight apparently defies this condition: a paradox of motor operation. We explore potential resolutions to this paradox, and, within its confines, establish that the <i>D. melanogaster</i> 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 <i>D. melanogaster</i> flight motor.