Figure S1. Examples of Click Stimuli
The four panels show different examples of stimuli used in our study. Each panel illustrates the computer-generated pulse signal that drives the loud speaker (upper trace) and the resulting air-pressure fluctuations as measured with a high-precision microphone at the site of the animal's ear (lower trace). The computer-generated clicks are triangular with a total width of 20 μs. The stimuli shown are (A) a single click, (B) a double click with a peak-to-peak interval Δt = 50 μs, (C) a double click with Δt = 500 μs, and (D) another double click with Δt = 500 μs whose second click points in the oppositve (“negative”) direction. The measurements of air-pressure fluctuations indicate a slight broadening of the click width and some residual vibrations, but they nevertheless present a good approximation of the sharp original pulses.
Figure S2. Simulation and Analysis of the General Cascade Model in Response to Two-Click Stimuli
The general cascade model, equation 2 in the main text, was used with filters modeled as l(t) = sin(2πft)exp(−t/τdec) and q(t) = exp(−t/τint). The parameters were taken from the first two cells presented in detail in the main text: f = 14.5 kHz, τdec = 100 μs, and τint = 300 μs for Cell 1 (left column) and f = 5.1 kHz, τdec = 154 μs, and τint = 590 μs for Cell 2 (right column).
(A and B) Responses of tympanic vibration. x(t) denotes the signal after application of the linear filter l(t), arbitrary units, for positive second click (solid line) and negative second click (dashed line). Inter-click intervals in these two shown examples were Δt = 80 μs for Cell 1 and Δt = 130 μs for Cell 2.
(C and D) Corresponding responses of J(Δt). The second click was tuned so that the maximum of J(Δt) was equal for positive and negative second clicks. This required click amplitudes of size 1.92 and −2.49 relative to the first click for Cell 1 and 2.09 and −1.27 for Cell 2.
(E–H) Filters L(Δt) and Q(Δt) extracted according to equation 1 in the main text from tuning the maximum of J(Δt) for many different values of Δt (gray dots). The parameters f, τdec, and τint indicated in the plots were obtained by fitting a damped harmonic oscillator and an exponential function to L(Δt) and Q(Δt), respectively (black lines). The initial part of Q(Δt) shows small fluctuations that result from the oscillatory influx of charge following the tympanic vibrations. In (G), a magnified view of the initial section is shown in the inset.
We thank C. D. Brody, M. J. Chacron, G. M. Klump, K. P. Körding, C. K. Machens, I. Segev, M. Stemmler, and H. Wagner for stimulating discussions and J. Benda, C. K. Machens, and H. Schütze for technical assistance with the experiments. This work was supported by Boehringer Ingelheim Fonds (TG) and by the Deutsche Forschungsgemeinschaft through SFB 618 (AH).
Competing interests. The authors have declared that no competing interests exist.
Author contributions. TG and AH conceived and designed the experiments. TG performed the experiments and analyzed the data. TG and AH wrote the paper.