A generalization of the van-der-Pol oscillator underlies active signal amplification in Drosophila hearing

Abstract

The antennal hearing organs of the fruit fly Drosophila melanogaster boost their sensitivity by an active mechanical process that, analogous to the cochlear amplifier of vertebrates, resides in the motility of mechanosensory cells. This process nonlinearly improves the sensitivity of hearing and occasionally gives rise to self-sustained oscillations in the absence of sound. Time series analysis of self-sustained oscillations now unveils that the underlying dynamical system is well described by a generalization of the van-der-Pol oscillator. From the dynamic equations, the underlying amplification dynamics can explicitly be derived. According to the model, oscillations emerge from a combination of negative damping, which reflects active amplification, and a nonlinear restoring force that dictates the amplitude of the oscillations. Hence, active amplification in fly hearing seems to rely on the negative damping mechanism initially proposed for the cochlear amplifier of vertebrates.

Signal-Coupled Subthreshold Hopf-Type Systems Show a Sharpened Collective Response

“…This was already known 30 years ago, then termed "small-signal amplification" [3][4][5]. Its important role as the working principle of biological sensors was recognized much later [6,7]; in particular, the mechanism was shown to play a decisive role in insect hearing [8,9]. Regarding mammalian hearing [1,[10][11][12], this principle still is fighting its way against classical engineering hearing solutions.…”

Frequency locking in auditory hair cells: Distinguishing between additive and parametric forcing

“…We note that the Bonhoeffer-van der Pol type equations have already been employed in modeling the dynamics of the auditory system [67,68]. The trivial solution to the unforced equation (12) crosses the Hopf instability at = c = a −1 and a critical frequency ω c = √ c − 1.…”

Principles and Typical Computational Limitations of Sparse Speaker Separation Based on Deterministic Speech Features

“…In simple auditory environments, binaural hearing plays a prominent role in this task by providing sound directionality and associated time difference information. Evolution could have equipped us with more than two hearing sensors for more complex tasks, as is generally the case with insects (Göpfert & Robert, 2002;Stoop et al, 2006). For mammalians, this seems unnecessary, provided that two sensors work properly.…”

“…We propose that one purpose of the auditory nuclei and the ascending auditory pathway is to activate filters within the cochlea, as well as on the signals emerging from it. A primitive, hardware hardwired example of such a strategy is the Drosophila hearing sensor, which is tuned to the signal generated by the female wingbeat (Göpfert & Robert, 2002;Stoop et al, 2006). We will show how the source separation problem can be solved by using characteristic signal properties (=features) of specific objects and will suggest that this, in addition to the sound source localization information, is at the origin of the mammalian's excellence in the source separation and noise cleaning tasks.…”