Spike rate vs. <i>N</i>, the average number of vesicles released by the IHC per sound wave cycle for the 3d SNIC model.

<p>The size of the data points shows the standard error in the spike rate, which increases with <i>N</i> (red; <i>gKl</i> = 8, <i>gL</i> = 5, <i>gH</i> = 1). The plot is similar to spike frequency vs. input current and is made linear across approximately a 48 dB range (from <i>N</i>∼1/8 to <i>N</i>∼32) by fast negative feedback from the low threshold potassium conductance <i>gKl</i>. For small input the small standard error allows the <i>N</i> = 0, 1/8, 1/4 excitations to be resolved from each other, while for large inputs the accompanying large standard error limits the ability to resolve intensities above <i>N</i> = 32. Turning off inward leak H current moves dynamic range to higher sound intensities (black; <i>gKl</i> = 8, <i>gL</i> = 5, <i>gH</i> = 0; ∼27 dB range from <i>N</i> = 2 to 46). H was turned off as if it were under the control of cholinergic feedback from the olive. Here the standard error starts out large for the small spike rates just above the bifurcation (<i>N</i> = 2), decreases away from the bifurcation and then increases for large inputs. For comparison we show the loss of dynamic range and nonlinear rise of the spike rate due to turning off the low threshold potassium conductance (green; <i>gKl</i> = 0, <i>gL</i> = 5, <i>gH</i> = 1). This curve was extended to negative <i>N</i> to show the square root shape in the rise of the spike rate above the now 2d SNIC bifurcation. Fluctuations in the size of the standard errors occurred because spike rates and standard errors were calculated over short time intervals, trying to reproduce the approximately one quarter second that the auditory pathway has to resolve the intensities of specific formant frequencies in order to be able to identify a particular vowel sound in real time. At a given frequency that is sensed by a particular IHC small numbers of ANF rapidly and accurately determine the intensity of the tone, each using only a small number of spikes.