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Mathematical modelling of the active hearing process in mosquitoes

Avitabile, D. and Homer, M. and Champneys, A. R. and Jackson, J. C. and Robert, D. (2010) Mathematical modelling of the active hearing process in mosquitoes. Interface, 7 (42). pp. 105-122. ISSN 1742-5689

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Abstract

Insects have evolved diverse and delicate morphological structures in order to capture the inherently low energy of a propagating sound wave. In mosquitoes, the capture of acoustic energy and its transduction into neuronal signals are assisted by the active mechanical participation of the scolopidia. We propose a simple microscopic mechanistic model of the active amplification in the mosquito species Toxorhynchites brevipalpis. The model is based on the description of the antenna as a forced-damped oscillator coupled to a set of active threads (ensembles of scolopidia) that provide an impulsive force when they twitch. This twitching is in turn controlled by channels that are opened and closed if the antennal oscillation reaches a critical amplitude. The model matches both qualitatively and quantitatively with recent experiments: spontaneous oscillations, nonlinear amplification, hysteresis, 2 : 1 resonances, frequency response and gain loss owing to hypoxia. The numerical simulations presented here also generate new hypotheses. In particular, the model seems to indicate that scolopidia located towards the tip of Johnston's organ are responsible for the entrainment of the other scolopidia and that they give the largest contribution to the mechanical amplification.