Time course of dynamic range adaptation in the auditory nerve

Abstract

Auditory adaptation to sound-level statistics occurs as early as in the auditory nerve (AN), the first stage of neural auditory processing. In addition to firing rate adaptation characterized by a rate decrement dependent on previous spike activity, AN fibers show dynamic range adaptation, which is characterized by a shift of the rate-level function or dynamic range toward the most frequently occurring levels in a dynamic stimulus, thereby improving the precision of coding of the most common sound levels (Wen B, Wang GI, Dean I, Delgutte B. J Neurosci 29: 13797-13808, 2009). We investigated the time course of dynamic range adaptation by recording from AN fibers with a stimulus in which the sound levels periodically switch from one nonuniform level distribution to another (Dean I, Robinson BL, Harper NS, McAlpine D. J Neurosci 28: 6430-6438, 2008). Dynamic range adaptation occurred rapidly, but its exact time course was difficult to determine directly from the data because of the concomitant firing rate adaptation. To characterize the time course of dynamic range adaptation without the confound of firing rate adaptation, we developed a phenomenological "dual adaptation" model that accounts for both forms of AN adaptation. When fitted to the data, the model predicts that dynamic range adaptation occurs as rapidly as firing rate adaptation, over 100-400 ms, and the time constants of the two forms of adaptation are correlated. These findings suggest that adaptive processing in the auditory periphery in response to changes in mean sound level occurs rapidly enough to have significant impact on the coding of natural sounds.

Fig. 1.

Switching-high-probability-region (HPR) stimuli. A 30-s portion of the switching-HPR stimuli comprising 3 switching cycles (left) is shown in which each dot represents a 50-ms broadband noise burst; in the first half (black dots) of each switching cycle, the sound levels of the stimulus are drawn randomly from a nonuniform level distribution (right) with the HPR centered at 1 level (66 dB SPL), whereas in the second half (gray dots), the HPR is centered at a different level (42 dB SPL). Typically, a total of 60 switching cycles, lasting 10 min, were used for measuring the time course of auditory nerve (AN) adaptation.

Fig. 2.

An AN fiber's firing rate responses to switching-HPR stimuli. A: normalized rate-level functions (RLFs) obtained from steady-state rate responses (the responses in the last 3 s of each half switching cycle) to the stimuli shown in C. The dynamic range shift (L₅₀ shift, the horizontal span between the dashed gray and black lines) is 5.6 dB. B: same as A but in response to the stimuli shown in D. The dynamic range shift is 6.1 dB. C: time course of the averaged sound levels across all 60 switching cycles, with the HPR mean level switching between 66 and 42 dB SPL. D: same as C but with the HPR mean switching between 78 and 45 dB SPL. E: averaged firing rate across all the switching cycles with time in response to the stimuli shown in C. F: averaged firing rate across all the switching cycles with time in response to the stimuli shown in D. This AN fiber's characteristic frequency (CF) is 841 Hz, and its spontaneous firing rate is 61 spikes/s (spk/s).

Fig. 3.

Characteristics of firing rate adaptation to switching-HPR stimuli for AN fiber population. A: time constants (τ) of average firing rate for upward and downward switches. Medians and 25–75% quartiles are 131 and 74–246 ms, respectively, for upward switches and 272 and 170–670 ms, respectively, for downward switches. Dotted line indicates identity (y = x). B: time constants do not show significant dependence on CF (P = 0.10 for upward switches and P = 0.42 for downward switches). C: time constants show a decreasing trend with spontaneous rate (r = −0.38, P = 0.006 for upward switches; r = −0.39, P = 0.004 for downward switches).

Fig. 4.

Time course of dynamic range shift in the AN. The AN fiber shown in A and C has its CF at 4.9 kHz and its spontaneous firing rate at 25.6 spk/s, whereas the fiber shown in B and D has its CF at 592 Hz and its spontaneous firing rate at 8.7 spk/s. A: evolution of RLFs with time for upward switches with HPR changing from 54 to 78 dB SPL in an AN fiber. Fitted data are represented as follows: blue line, steady-state RLF before the switch; red line, steady-state RLF after the switch; dotted blue line, pre-switch steady-state RLF (blue line) normalized to post-switch steady-state RLF (red line). Raw data are represented as follows: green line/dots, averaged HPR-region RLF for the high HPR levels of the first 300-ms epoch after the switch; magenta line/dots, HPR-region RLF of the second 300-ms after the switch; black line/dots, HPR-region RLF of the third 300-ms epoch. Fitted straight lines to the HPR-region RLF are not shown. Thick horizontal bars with filled circles along the x-axis denote the HPRs and their mean levels, respectively. The gray arrow indicates the direction of RLF evolution with time. B: same as in A but for downward switches from 78 to 54 dB SPL in a different AN fiber. C: horizontal shift of the RLF with time from the normalized steady-state RLF before the switch for consecutive 300-ms epochs for upward switches. Dots represent raw data (color-coded circles designate the results for the first three 300-ms epochs); line is fitted single exponential. The time constant is 251 ms. D: same as C but for the downward switch shown in B in which the shift has a negative sign, indicating the shift direction is opposite that for upward switches. The time constant is 671 ms.

Fig. 5.

Schematic of the dual-adaptation model. The model comprises 2 adaptation modules: dynamic range adaptation and firing rate adaptation. The input to the model, L_in(t), is a time sequence of sound levels of switching-HPR stimuli (re. Fig. 1). The output of the dynamic range adaptation module is the effective level, L_eff(t), which is the difference between the original level's L_in(t) and a linearly filtered version (with time constant τ_L and gain g_L) of L_eff(t). As illustrated in the top left block, dynamic range adaptation produces a pure horizontal shift (ΔL) of the RLF. The saturating nonlinearity module, taking the form of the baseline RLF and sandwiched between the 2 adaptation modules, converts the effective levels, L_eff(t), to unadapted firing rates, R_unadp(t). The output of the firing rate adaptation module is the adapted firing rates, R_adp(t), calculated as the difference between R_unadp(t) and a linearly filtered version (with time constant τ_R and gain g_R, g′_R) of R_adp(t). As illustrated in the top right block, firing rate adaptation produces a pure firing rate decrement (ΔR), thus a vertical drop of the RLF. The threshold module half-wave rectifies R_adp(t) and yields the final firing rate output, R_out(t).

Fig. 6.

Fit of the dual-adaptation model to AN fibers' responses to switching-HPR stimuli. Typical switching-HPR stimuli contained 60 switching cycles and lasted 600 s. A: an AN fiber's rate responses during a 20-s epoch (from 300 to 320 s) of the stimuli. This fiber is the same as that shown in Fig. 4, B and D. LH_Diff, the percentage difference in log-likelihood, is 5.6% for this fiber, indicating a good fit. B: the time course of the average firing rates across all 60 cycles in the model matches closely to that of the data. An exponential was fit to the responses of each half switching cycle for extracting the time constants of average rate (fitted lines not shown). C: the steady-state RLFs predicted by the model (lines) compared with those in the AN recordings (dots). For both data and model, lighter colors correspond to lower HPR and darker colors to higher HPR. The L₅₀ shift between the 2 RLFs for both the model and the data are provided. D–F: same content as A–C, respectively, but for another AN fiber. This fiber is the same as that shown in Fig. 4, A and C. G: histogram of LH_Diff for 46 AN recordings, of which the model fit meets the goodness-of-fit criterion for 40 recordings (i.e., LH_Diff ≤ 25%). H: average rate time constants predicted by the model are close to those estimated from neural data for our AN fiber population. I: the normalized L₅₀ shifts in the model are comparable with those in the data.

Fig. 7.

The dual-adaptation AN model predicts the shift time constants with less bias. This fiber is the same as that shown in Fig. 4, A and C. A: evolution of RLFs with time for upward switches from 54 to 78 dB SPL. RLFs of the steady state before (blue) and after (red) the switch and of the first 300-ms epoch (six 50-ms epochs combined) after the switch (green) are plotted for both AN neural data (dots) and the model (lines). The model was first fitted to the fiber's responses to the switching-HPR stimuli, containing 60 switching cycles, and then run for 4,320 switching cycles to allow for extracting the time course of dynamic range adaptation. The gray arrow indicates the direction of the RLF evolution with time. B: normalized model RLFs for the steady state before the switch and the first 300-ms epoch (six 50-ms epochs combined). The RLF shift between the first 300-ms epoch and the pre-switch steady-state RLF is 5.3 dB when calculated from the model responses (measured as the L₅₀ shift between the 2 corresponding complete normalized RLFs) compared with 1.4 dB when directly estimated from the AN data (measured as the horizontal distance between the HPR-region RLFs of the first 300-ms epoch and the steady-state RLF). The gray arrow indicates the direction of the RLF shift with time. C: predicted time course of dynamic range adaptation in the model at time steps of 50 ms. Time course of dynamic range adaptation is characterized by the shift of the L₅₀ of the RLF for each consecutive 50-ms epoch. The time constant of 79 ms, extracted from the fitted exponential curve, is about one-third of the 251 ms directly estimated from neural data (see Fig. 4C).

Fig. 8.

Time constants of dynamic range adaptation estimated by the dual-adaptation AN model. A: the shift time constants of the model compared with those of the data. For upward switches, there are 13 AN fibers with which we were able to estimate the shift time course directly from neural data and the model met the goodness-of-fit criterion. For downward switches, there are 24 such fibers. B: the shift time constants predicted by the model for AN fibers with good model fitting results (n = 40) plotted against the model-predicted average rate time constant. The straight line is the fitted curve in the orthogonal least-squares sense (i.e., type II linear regression for 2 variables both dependent or having errors) for all data points with the outliers excluded (only 1 data point was excluded for which the model average time constant is smaller than 20 ms, which is well below the analysis time bin, 50 ms); the slope of the line is 0.76.