Level-Tuned Neurons in Primary Auditory Cortex Adapt Differently to Loud versus Soft Sounds

The responses of auditory neurons tuned to stimulus intensity (i.e., nonmonotonic rate-level responders) have typically been analyzed with stimulus paradigms that eliminate neuronal adaptation to recent stimulus statistics. This procedure is usually accomplished by presenting individual sounds with long silent periods between them. Studies using such paradigms have led to hypotheses that nonmonotonic neurons may play a role in amplitude spectrum coding or level-invariant representations of complex spectral shapes. We have previously proposed an alternate hypothesis that level-tuned neurons may represent specialized coders of low sound levels because they preserve their sensitivity to low levels even when average sound level is relatively high. Here we demonstrate that nonmonotonic neurons in awake marmoset primary auditory cortex accomplish this feat by adapting their upper dynamic range to encode sounds with high mean level, leaving the lower dynamic range available for encoding relatively rare low-level sounds. This adaptive behavior manifests in nonmonotonic relative to monotonic neurons as 1) a lesser amount of overall shifting of rate-level response thresholds and (2) a nonmonotonic gain adjustment with increasing mean stimulus level.


Introduction
Many neurons in the auditory system utilize a nonmonotonic level coding scheme whereby the neuron responds most robustly to a particular best sound level, and the response drops off at both higher and lower sound levels. This response property is often referred to as intensity tuning or sound-level tuning. Nonmonotonic level responses have been reported in the cochlear nucleus (Rose et al. 1959;Young and Brownell 1976), in the inferior colliculus (Rose et al. 1963; Rees and Palmer 1988;Aitkin 1991;Ramachandran et al. 1999), in the medial geniculate body (Galambos 1952), and in auditory cortex of non-bat species (Erulkar et al. 1956;Pfingst and O'Connor 1981;Phillips and Irvine 1981;Phillips et al. 1985Phillips et al. , 1995Shamma and Symmes 1985;Sutter and Schreiner 1995;Sadagopan and Wang 2008) as well as echolocating bats (Suga 1977;Suga and Manabe 1982). No level-tuned responses have been reported in the auditory nerve, however (Galambos and Davis 1943;Kiang et al. 1965;Sachs and Abbas 1974); therefore, level-tuned responses must be created centrally by neural circuits. Direct evidence of this phenomenon has also been reported (Faingold et al. 1991;Sivaramakrishnan et al. 2004;Wu et al. 2006;Tan et al. 2007). The active creation and maintenance of level tuning by the nervous system implies that this response feature is potentially important for encoding of stimulus intensity or a related stimulus property. Some studies report that a substantial percentage of neurons in primary auditory cortex (A1) are tuned to level: 60--80% in awake monkey A1, for example (Sadagopan and Wang 2008;Watkins and Barbour 2008), and 20--30% in anesthetized cat A1 (Phillips and Irvine 1981;Sutter and Schreiner 1995). The prevalence of level tuning in the auditory system implies that this phenomenon has a particular relevance for auditory processing. In particular, animals trained in level discrimination tasks show an increased proportion of level-tuned neurons over control animals (Polley et al. 2004(Polley et al. , 2006, implying that nonmonotonic level encoding also plays an important behaviorally relevant role. Audition in humans and other mammalian species encompasses a wide dynamic range of sound level to which these species are behaviorally sensitive. In particular, the human auditory system is capable of maintaining a level discriminability of 2 dB or less across the entirety of the approximately 120-dB dynamic range of hearing (Rabinowitz et al. 1976). This remarkable preservation of level sensitivity over a large dynamic range may be due in part to many neurons altering their response properties on short time scales as a function of the recent history of stimulus attributes-a characteristic typically referred to as adaptation. Neurons in the inferior colliculus appear to adapt their response properties to be better suited for encoding the most probable sound levels in the environment, thereby resulting in improved coding accuracy (Kvale and Schreiner 2004;Dean et al. 2005). Until recently, adaptation of nonmonotonic level responders in response to dynamic-level stimuli had not been characterized.
We have previously hypothesized that one role of nonmonotonic level encoding is to preserve sensitivity to low sound levels even when much of the neuronal population is adapted to high sound levels (Watkins and Barbour 2008). Here we extend these results to demonstrate how the inhibition shaping the responses of these neurons at high intensities and near their characteristic frequencies enables them to preserve their sensitivity. In other words, we show that inhibition at the characteristic frequency (CF) of level-tuned neurons is directly involved in their ability to preferentially encode low sound levels. We find that nonmonotonic neurons achieve this unique dynamic behavior because they encode and adapt to sound level with both of their dynamic ranges, that is, both slopes of their rate-level responses. We find that monotonic neurons as a population show greater shifting of their dynamic ranges in the direction of the more probable levels than do nonmonotonic neurons. When their upper and lower dynamic ranges are considered separately, however, nonmonotonic neurons demonstrate a shift in coding accuracy individually similar to that of monotonic neurons. Coding accuracy is quantified with Fisher information (FI), a measure of the upper limit of sound-level discriminability possible by decoding neurons' rate-level responses. FI is used in the present context to compare the behavior of monotonic and nonmonotonic neurons rather than to make specific predictions regarding how this information is actually decoded in the brain. When the most probable sound levels fall below their best level (BL), nonmonotonic neurons tend to adapt their lower dynamic range; when the most probable sound levels fall above their BL, however, they tend to adapt their upper dynamic range. This behavior explains how nonmonotonic neurons still maintain overall coding accuracy similar to that of monotonic neurons although they shift their input--output functions less. Furthermore, because nonmonotonic neurons use their upper dynamic range for sound encoding during periods of high mean sound level, their lower dynamic range remains available under these conditions for encoding occasional sounds of lower level.

Electrophysiology
All animal procedures were approved by the Washington University in St Louis Animal Studies Committee. A head cap consisting of stainless steel screws, titanium head posts, and dental acrylic was affixed to the skull of each marmoset monkey (Callithrix jacchus) under isoflurane anesthesia and with aseptic procedures. Immediately following temporalis muscle removal during surgery, the vasculature running within the lateral sulcus became visible through the skull and its location was marked on the skull. This landmark allows later microcraniotomies ( <1 mm diameter) to be drilled through the skull with a custom drill directly over auditory cortex (just inferior to lateral sulcus). Following surgery, the animals were allowed to recover sufficiently prior to beginning experiments. During experimentation, the animals were awake and sat upright in a custom, minimally restraining primate chair inside a double-walled sound-attenuation booth (IAC 120a-3) with their heads fixed in place by the head posts. The location of primary auditory cortex was identified anatomically using lateral sulcus and bregma landmarks and then confirmed physiologically by high driven rates (up to 50--100 spikes/s), short latencies (10--15 ms), robust responses to tones, and a cochleotopic frequency map oriented from low frequencies to high frequencies in the rostral to caudal direction along lateral sulcus.
High-impedance tungsten-epoxy electrodes (~5 MX at 1 kHz; FHC) were advanced perpendicularly to the cortical surface within the microcraniotomies. Microelectrode signals were amplified using an AC differential amplifier (AM Systems 1800) with the differential lead attached to a grounding screw. Single-unit action potentials were sorted online using manual template-based spike-sorting hardware and software (Alpha Omega). When a template match occurred, the spike-sorting hardware relayed a 5-volt trigger pulse to a DSP system (TDT RX6) that temporally aligned recorded spike times (2.5 ls accuracy) with stimulus delivery. Raw waveforms were also band-pass filtered at 300--5000 Hz and digitally sampled at 25 kilosamples/s (TDT RX6 24-bit ADC) for offline analysis. Both spike times and digitized raw waveforms were saved to hard disk on a PC running Microsoft Windows XP.
Acoustic stimuli were synthesized digitally online at 100 kilosamples/ s with custom MatLab software (MathWorks). The stimuli were then passed through a digital-to-analog converter (TDT RX6 24-bit DAC), amplified (Crown 40W D75A), and delivered to a loudspeaker (B&W 601S3) located 1 m directly in front of the animal's head. Speaker output was calibrated so that the maximum sound level delivered was approximately 105 dB SPL with a flat frequency response (±5 dB) from 60 Hz to 32 kHz (B&K 4191 Microphone with 2669 Preamplifier).

Acoustic Stimuli
Each single unit was analyzed with tones delivered at its CF, estimated as the frequency eliciting the greatest response from the neuron at a sound level no more than 10 dB above absolute threshold. A small number of neurons (4/47) were found to respond poorly to pure tones. These neurons were therefore probed for further experiments with band-pass noise centered at CF and with the narrowest bandwidths eliciting substantial spiking responses. ''Static'' rate-level functions were measured by delivering 100-ms CF tones (or CF narrowband noise) of different amplitudes, typically 12 amplitudes spaced 10 dB apart from -15 to 95 dB SPL, separated by at least 1 s of silence. Static ratelevel functions essentially represent input--output functions of the neurons when adapted to silence; hence, we also refer to this condition as ''silence adapted.'' Each stimulus amplitude was presented in pseudorandom order 10 times, and the mean rate over these repetitions was used for construction of the static rate-level function.
Dynamic-level stimuli were created using up to 6 different level distributions to probe adaptation effects in auditory cortical neurons (Fig. 1). These distributions were probability mass functions with probabilities given discretely for each 1 dB. One stimulus consisted of all sound levels represented uniformly over the full 120-dB range tested. The remaining distributions each had nonoverlapping 20-dB-level subranges (probability plateaus) that were more likely to occur than any of the other levels. Using such distributions allowed the sound levels from which stimulus amplitudes were drawn most commonly to be easily parameterized by the plateau midpoint or center (Dean et al. 2005). An example of one such probability distribution can be seen in Figure 1A. Initial experiments used a ''full set'' of levels drawn from the full 120-dB range (-15 to 105 dB SPL) with 20-dB-wide probability plateaus centered at 5, 25, 45, 65, and 85 dB SPL (Fig. 1B). In the full set, plateau levels were 10 times more likely to be drawn during any particular time interval than were levels outside the plateau. After a few experiments, however, it became clear that our awake animals poorly tolerated stimuli at the highest plateau, most likely because of the relatively high level of these stimuli. We then modified the stimulus paradigm into a ''reduced set'' of distributions that spanned a 100-dB range (-15 to 85 dB SPL) and omitted the highest level plateau at 85 dB SPL. In the reduced set, plateau levels were 15 times more likely to occur within any particular time interval than were levels outside the plateau. This alteration allowed the adaptation effects to be more clearly observed. The full set was run for 12 out of a total of 47 neurons, so the 85-dB SPL plateau is only represented by 9 nonmonotonic and 3 monotonic neurons. Because of the smaller number of neurons recorded at the highest probability plateau, regression analyses exclude these data points, although the points themselves are included for visual comparison in the relevant figures.
At every 100-ms time interval of a dynamic stimulus, a new level was drawn pseudorandomly from the same distribution and used to set the amplitude of a pure tone whose frequency matched the CF of the neuron under study. An example of the time-varying amplitude during a portion of one 2-min-long dynamic stimulus can be seen in Figure 1C. Amplitudes in the dynamic stimuli were linearly transitioned from one time interval to the next with 10-ms ramps to reduce acoustic transients (i.e., clicks). No transients were detected in any of the stimuli by 3 human listeners, and we used relatively long intervals in the dynamic stimuli (100 ms) to ensure that transient events did not dominate our responses.
For the full stimulus set, dynamic stimuli were delivered for 3 repetitions of 2 min each. For the reduced stimulus set, dynamic stimuli were delivered for 2 repetitions of 3 min each. All neurons for which a complete dynamic protocol was collected were included in the current analysis.

Data Analysis
Dynamic rate-level functions were determined by averaging the rate response to the stimulus in each 100-ms temporal interval of a particular dynamic stimulus and across all level bins (see below) and repetitions. The latency for each neuron in response to the staticlevel stimuli was estimated from the peristimulus time histogram, and rates were calculated for the static rate-level function from a time window beginning at this latency and ending 100 ms later. These latencies were then used to attribute spikes to a particular temporal interval of the dynamic stimuli. For example, if the response latency for a neuron when stimulated by the static stimuli was 15 ms, then spikes occurring within the first 15 ms of each 100-ms temporal interval were assigned to the previous temporal interval of the dynamic stimuli. Because the levels for each time interval were selected randomly and independently, spikes potentially associated with any offset response from a preceding time interval would therefore be distributed across the entire dynamic rate-level function and would not contribute systematically to any individual data point. Adaptation trends were also measured using only spikes from the final 50 ms of every temporal interval, during which onset effects arising from the current time interval and offset effects from the previous interval would be diminished. This alternate analysis resulted in adaptation trends similar to those measured using the entire interval. Additionally, dynamic ratelevel functions using spikes confined strictly to the stimulus interval (i.e., with a latency estimate of 0) were similar to dynamic rate-level functions that accounted for response latency. Rates were averaged over all repetitions of temporal intervals with levels falling within a particular 10-dB bin. These level bins were centered from -10 to 100 dB SPL (12 bins) for the full set and -10 to 80 dB SPL (10 bins) for the reduced set. This averaging was necessary to reduce noise and to enable the determination of adaptation trends for individual neurons with the limited amount of dynamic data that could be collected. Population trends observed by averaging across 1-dB bins were similar to those observed with 10-dB bins.
Rate-level functions were fit with a 6-parameter, 2-tailed split Gaussian function to evaluate response characteristics (Fig. 2). This model allowed the upper and lower dynamic ranges of nonmonotonic neurons to fit separately but could still fit monotonic functions easily by ignoring the upper dynamic range parameters. The sum squared error between the data and model was minimized using nonlinear optimization (fmincon medium scale algorithm in MatLab). Because the model contained a discontinuity where the 2 Gaussians joined, model values falling between the fit data points could be considerably different from interpolated values. For this reason, the visually depicted model values were linearly interpolated from the fit data points. The result is an overfitted representation of the original data, but one that eliminated spurious rate values quite successfully. This completely automated denoising procedure was particularly effective at providing quantitative estimates of threshold and saturation values that matched visual estimates better than any other technique we employed.
Threshold and saturation points were measured at 20% and 80%, respectively, of the maximum driven firing rate (i.e., discharge rate minus spontaneous rate) of the model functions linearly interpolated to the nearest dB. Spontaneous firing rate was averaged in the silenceadapted state from time intervals when no audible stimulus was presented. Threshold and saturation were also measured for the upper dynamic range of nonmonotonic neurons, but the 20% and 80% points in these cases were calculated relative to the response to the most intense sound presented (105 dB SPL for the full set and 85 dB SPL for the reduced set). BL was also taken from the model-fitted and linearly interpolated curves as the sound level eliciting the maximum firing rate. For the purpose of calculating mean firing rates across the population, rate-level functions were first normalized between zero and one to create a percentage of maximum rate-level function. The minimum and maximum rates over all the rate-level functions collected with both the static and dynamic paradigms were used to perform the normalization, so that adaptation of the response gain (i.e., the scaling of the rate-level function) could be compared between neurons directly.
Monotonicity index (MI) refers to the degree of reduced spiking at higher stimulus levels (de la Rocha et al. 2008;Sadagopan and Wang 2008) and was calculated from the fitted rate-level responses as: where rate is the fitted rate-level function, rate max_level is the rate in response to the most intense sound presented, and rate spontaneous is the spontaneous rate measured as above. Neurons were classified as nonmonotonic if the mean MI for all dynamic and static fitted rate-level functions was less than or equal to 0.5 and were classified as monotonic otherwise.
To evaluate coding accuracy in response to each dynamic stimulus distribution, we used an information theoretic measure called the FI. FI provides an estimate of the upper bound on encoding accuracy or discriminability that can be conveyed by an independent coding element to an unbiased estimator (Dayan and Abbott 2001). If neuronal response variance is constant as a function of response, then a steeper slope in the rate-level function would allow greater discrimination of stimulus level. Rate variability may be a function of mean rate, however, in which case an improved estimate of discriminability would be the slope of the mean rate-level function divided by the variance. The FI estimate is conceptually similar.
We calculated FI by estimating response probabilities directly: where f i (s) is the FI of the ith neuron to stimulus s and P i [rjs] is the probability that stimulus s elicited r spikes from the ith neuron. In our Figure 2. Six-parameter, 2-tailed split Gaussian model used for fitting all rate-level functions. The model function has separate parameters (variance and offset) for the upper and lower dynamic ranges being fit. The remaining parameters (amplitude and mean) are the same for both dynamic ranges. case, s indexes stimulus level in dB SPL, grouped into 10-dB bins as described above. The conditional probability was calculated by measuring a 2D histogram of the number of times r number of spikes occurred during each 10-dB bin (over all time bins and repetitions). This histogram was then smoothed with a 2D Gaussian kernel having standard deviations of 8 dB and 0.5 spikes, then normalized into a probability distribution (i.e., the spike probabilities sum to one for each 10-dB bin). Differentiation was performed with a 5-point numerical method, disregarding 2 points on either end of the ratelevel functions (FI for these points set to zero). Overall coding accuracy across each of the 2 neuronal subpopulations was assessed by averaging the individual neuronal FIs: where n represents the number of neurons in each subpopulation. A mean FI function was then computed for each of the 2 neuronal subpopulations and each of the dynamic stimuli. Mean FI for nonmonotonic populations was for some analyses computed by evaluating the mean of partial FI curves on only one side of the BL. For this manipulation, the portion of the FI curve on the side of BL nearest the stimulus-level distribution's plateau center was averaged. Because nonmonotonic neurons have 2 dynamic ranges, this analysis provided a clearer estimation how FI curves for these neurons differed between dynamic stimuli by only analyzing the portion of the FI that was most involved in encoding the most probable levels.

Results
We investigated the responses of 47 primary auditory cortex neurons from 7 hemispheres of 6 awake marmoset monkeys (C. jacchus) for their adaptive coding properties in response to dynamic auditory stimuli.

Static Rate-Level Responses
Static rate-level functions for 2 example neurons reflect the extremes of rate-level shapes (Fig. 3). Very monotonic neurons saturate at higher levels ( Fig. 3A,B), whereas very nonmonotonic neurons do not respond at higher levels ( Fig. 3C,D). For dynamic range and monotonicity analyses, rate-level functions were fitted with a 6-parameter, 2-tailed, split Gaussian model, which typically resulted in a very good fit (r 2 > 0.95), and are presented as solid black lines in Figure 3B,D. Threshold and saturation levels were determined from the model fits at 20% and 80% of maximum firing rate above spontaneous. The dynamic range for monotonic neurons was measured between saturation and threshold (Fig. 3B, blue lines). For nonmonotonic neurons, a lower dynamic range was measured in the same manner as for monotonic neurons (Fig. 3D, red lines). An upper dynamic range for nonmonotonic neurons was measured from 80% to 20% of maximum firing rate above the response to the greatest level presented (Fig. 3D, green lines). The same calculations were performed to determine threshold, saturation, and MI for the dynamic rate-level functions. Neurons were classified as monotonic if the average MI for the static and dynamic rate-level functions was greater than 0.5 and as nonmonotonic if this value was less than or equal to 0.5.

Single-Neuron Adaptation to Dynamic-Level Stimuli
Although a few neurons showed little adaptation in response to dynamic-level stimuli, most neurons adapted their rate-level functions with a combination of response gain adaptation (i.e., a scaling of the rate response) and dynamic range shifting (i.e., a shifting in level of the response curve). Individual neurons, however, exhibited a variety of adaptive changes in their rate-level responses. Example rate-level responses and FI curves calculated in response to dynamic stimuli (those depicted in Fig. 1B or Fig. 1C) are shown for representative neurons in Figure 4. Each curve is color coded to match the colored bars on the abscissa, which indicate the location of the probability plateau for the dynamic stimulus that elicited the response curve. Solid black lines indicate responses to the uniformly distributed dynamic stimulus, and the dashed black lines are the static rate-level responses.
All neurons demonstrated adaptation in their maximum firing rate (i.e., gain adaptation) for dynamic stimuli. These gain changes typically reduce the slope of the corresponding ratelevel functions. Lower response rates usually brought about lower response variance, however, so measures of coding accuracy might not be expected to decrease in this situation. In actuality, FI curves were mostly unaffected by gain changes. The most variety in individual neuronal adaptation was exhibited in the amount of rate-level response shifting in the direction of the dynamic stimuli probability plateaus. Monotonic neurons could demonstrate a large amount of shifting (Fig. 4A,B) or a small amount of shifting (Fig. 4C,D); similarly, nonmonotonic neurons could demonstrate a large (Fig. 4E,F) or small amount of shifting (Fig. 4G,H). Nonmonotonic neurons could also exhibit adaptation (causing both gain and shift changes) predominantly in their lower dynamic

Population Adaptation to Dynamic-Level Stimuli
Previously, we reported that nonmonotonic neurons may be specialized for encoding low-intensity sounds because such neurons maintained coding accuracy for low levels, as measured by a low-intensity peak in the FI, even when they were adapted to dynamic stimuli of high mean level (Watkins and Barbour 2008). This finding led us to hypothesize that the reason nonmonotonic neurons are able to maintain coding accuracy at low levels is because on average they adapt primarily their upper dynamic range for encoding of high levels, leaving the lower dynamic range available for encoding the occasional low-intensity sound. Mean rate-level functions for monotonic neurons (Fig. 5A) show that their overall dynamic ranges shift in the direction of the most probable levels in the dynamic stimuli, consistent with the FI curves reported previously for subcortical neurons. Nonmonotonic neurons, on the other hand, appear to shift either their upper or lower dynamic ranges depending upon the value of the most probable stimulus levels (Fig. 5B). Adaptation in the nonmonotonic neurons is most apparent for the 5-and 85-dB SPL plateau stimuli and is less pronounced for the other dynamic stimuli, whose most probable levels are relatively near the mean BL of the nonmonotonic population. For the 5-dB SPL dynamic stimuli, nonmonotonic neurons appear to predominantly adapt their lower dynamic range, although substantial gain adaptation is apparent in the upper dynamic range as well.
To further quantify population averages of neuronal adaptation to dynamic stimuli, we calculated the mean dynamic ranges elicited by each dynamic stimulus (Fig. 6). For monotonic neurons, this measure consisted of a single contiguous dynamic range (depicted in blue in Fig. 6A) from threshold to saturation. For nonmonotonic neurons, this measure consisted of both lower (depicted in red in Fig. 6A) and upper (depicted in green in Fig. 6A) contiguous dynamic ranges corresponding to the 2 slopes of nonmonotonic rate-level responses. For both neuron types, the average dynamic ranges adapted toward the probability plateaus (i.e., a shifting of the rate-level responses), although the amount of this change between any 2 dynamic stimuli was less than the corresponding difference between the probability plateau centers (indicated by the diagonal line of unity slope). On average, monotonic neurons adapted their dynamic ranges more than nonmonotonic neurons (i.e., steeper slope of the blue curve in Fig. 6A). Average dynamic ranges collected with static rate-level functions were consistently lower in both threshold and saturation than for any dynamic stimulus, as expected to be the case under silence-adapted conditions. For both monotonic and nonmonotonic neurons, the average dynamic ranges elicited by the uniformly distributed dynamic stimulus were closest to that elicited by the dynamic stimuli with probability plateau of 45 dB SPL.
We calculated the mean range of firing rates for each stimulus condition in order to quantify the other effect of adaptation: a change in the overall firing rate as a function of plateau center, termed response gain adaptation. Rate-level responses were normalized for each neuron over all dynamic and static stimuli, and the mean was taken over these normalized values for each stimulus type. Although trends in the gain are visible in the average rates from Figure 5, gain adaptation is presented separately in Figure 6B to quantify these trends. Monotonic neurons on average showed monotonically decreasing response gain with increasing plateau center (blue curve), whereas nonmonotonic neurons showed a nonmonotonic trend in response gain (red curve). In the latter case, the response gain increased for the 65-and 85-dB plateau stimuli, coincident with the probability plateau being closer to the population mean upper dynamic range of these neurons' rate-level functions than to the population mean lower dynamic range. This result provides more evidence that more than one adaptation process is occurring for nonmonotonic neurons. Collectively, this entire neuronal population exhibited a nearly consistent mean rate for dynamic stimuli when the most common sounds were at or above intermediate sound levels (purple curve).
In order to quantify the previously observed adaptation effects as a function of MI and under different stimulus conditions, we compiled dynamic range midpoints (midpoints of both lower and upper dynamic ranges for nonmonotonic neurons) as a simple summary of the relevant coding regions. Lower dynamic range midpoints of nonmonotonic neurons were systematically lower than dynamic range midpoints of monotonic neurons (Fig. 7A--E), reflecting a lower average threshold and corresponding encoding of lower levels for nonmonotonic neurons (Watkins and Barbour 2008). For all dynamic stimuli, a significant correlation between MI and the midpoint of the dynamic range existed. Four neurons out of 47 with a combination of low maximum firing rates and substantial inhibition below spontaneous spiking rates in response to the  . Average adapted dynamic ranges as a function of dynamic stimulus probability plateau center. (A) Monotonic dynamic ranges are indicated in blue, nonmonotonic lower dynamic ranges in red, and nonmonotonic upper dynamic ranges in green. Thresholds and saturations are indicated with vertical lines representing standard error of the mean. Dynamic ranges for the silence-adapted (static) rate-level functions and for the uniformly distributed dynamic stimulus are presented to the left for comparison. Changes in dynamic ranges with plateau center reflect adaptive threshold shifts. Adaptation that perfectly maximized coding accuracy based on stimulus statistics would follow a line with a slope of 1. (B) Changes in mean response amplitude with plateau center reflect gain adaptation, which is monotonically decreasing with plateau center for the monotonic population (blue), nonmonotonic for the nonmonotonic population (red), and asymptotic for the population as a whole (purple).
Cerebral Cortex January 2011, V 21 N 1 183 highest levels yielded large negative MIs because the denominator of the MI calculation was near 0. The resulting illconditioned data points were omitted from this particular analysis because they exerted a disproportionate influence on the regression. A linear regression between MI and dynamic range midpoint for the remaining 43 neurons (all with an MI > -1) gave a slope of 21 dB SPL and intercept of 22 dB SPL (r 2 = 0.35; P = 3.4 3 10 -5 , regression F test) for the 5-dB plateau, a slope of 23 dB SPL and intercept of 28 dB SPL (r 2 = 0.49; P = 2.1 3 10 -7 , regression F test) for the 25-dB plateau, a slope of 29 dB SPL and intercept of 29 dB SPL (r 2 = 0.56; P = 6.5 3 10 -9 , regression F test) for the 45-dB plateau, and a slope of 31 dB SPL and intercept of 32 dB SPL (r 2 = 0.52; P = 5.9310 -8 , regression F test) for the 65-dB plateau. The regression intercepts become progressively larger with increasing plateau center, indicating that over the population, neurons adapted in the direction of the plateau center. The regression slopes also increased with increasing plateau center, indicating that monotonic neurons were adapting more in response to dynamic stimuli containing more high-intensity sounds than were nonmonotonic neurons. Comparing the regression lines directly (Fig. 7F) reveals graphically that higher intensity probability plateaus induce upward shifts and increasing regression slopes. Therefore, cortical neurons adapt to stimulus-level statistics across all MI values, but population adaptation increases with degree of monotonicity.
By subdividing the neuronal population based upon MI and analyzing dynamic range midpoint trends as a function of plateau center, the monotonic neurons can be seen to shift their dynamic range toward each plateau center more than nonmonotonic neurons shift their lower dynamic range (Fig. 8). Note that data from the highest level plateau (9 nonmonotonic and 3 monotonic neurons) were not included in this regression analysis, although the regression line was extended (dotted line) toward the highest level plateau to demonstrate qualitatively that these data are consistent with the trends from the other 4 plateaus. Neurons were segregated based upon their MI into 4 groups: ''very monotonic'' (1 > MI > 0.9), ''mostly monotonic'' (0.9 > MI > 0.5), ''mostly nonmonotonic'' (0.5 > MI > 0.1), and ''very nonmonotonic'' (MI < 0.1). The very nonmonotonic category included the 4 neurons with MI < -1 that were excluded from the regression analysis of Figure 7. Very monotonic neurons showed the most correlation based upon a linear regression between plateau center and dynamic range midpoint (slope = 0.35, intercept = 45; r 2 = 0.35; P = 1.5 3 10 -4 , regression F test), followed by mostly monotonic neurons (slope = 0.27, intercept = 33; r 2 = 0.22; P = 0.0014, regression F test), then mostly nonmonotonic neurons (slope = 0.23; intercept = 27; r 2 = 0.20; P = 0.010, regression F test), and finally very nonmonotonic neurons (slope = 0.12; intercept = 19; r 2 = 0.036; P = 0.10, regression F test). Again, lower dynamic range midpoints were used for nonmonotonic neurons in this particular analysis.
The very nonmonotonic neurons did not show significant adaptation of their lower dynamic range as a function of plateau center, as shown in Figure 8D, but they did for their upper dynamic range. Very nonmonotonic neurons had a larger slope and better linear fit between upper dynamic range midpoint and dynamic stimuli plateau center (slope = 0.17, intercept = 46; r 2 = 0.065; P = 0.026, regression F test) than did mostly nonmonotonic neurons, for which the fit was not significant (slope = 0.073, intercept = 60; r 2 = 0.035; P = 0.30, We investigated other criteria for segregating the nonmonotonic population besides MI as a way to evaluate whether adaptation primarily in the upper dynamic range of very nonmonotonic neurons was truly due to their high degree of nonmonotonicity or whether additional factors were better predictors. We found that segregating nonmonotonic responses in half according to population median BL of the static rate-level functions (Fig. 9A,B) revealed a better correlation between upper dynamic range midpoint and plateau center for neurons with BL < 25 dB (slope = 0.19; intercept = 44; r 2 = 0.13; P = 0.0023, regression F test). Neurons with BL > 25 dB did not show a significant correlation (slope = 0.061; intercept = 61; r 2 = 0.0087; P = 0.57, regression F test).
Nonmonotonic neurons were also analyzed for shifting of BL instead of upper dynamic range midpoint. When classified by MI (as was done in Fig. 8), neither mostly nonmonotonic nor very nonmonotonic neurons demonstrated a significant change in BL as a function of plateau center (P > 0.10, regression F test). When classified by BL (as was done in Fig. 9), the trend for BL as a function of plateau center was consistent with that of the upper dynamic range midpoint. Neurons with BL < 25 dB showed a significant trend (slope = 0.13; intercept = 30; r 2 = 0.059; P = 0.046, regression F test), whereas neurons with BL > 25 dB did not (slope = 0.11; intercept = 46; r 2 = 0.022; P = 0.36, regression F test).
We next performed an analogous segregation by BL for each nonmonotonic neuron's contribution to population FI curves. The purpose of this particular analysis was not to assess limits of decoding accuracy but to infer from adaptive properties of the upper and lower dynamic ranges for nonmonotonic neurons which stimulus features these neurons considered "important" enough to preserve through adaptation. Indeed, output neurons would not be capable of discerning from any individual nonmonotonic neuron which portion of its dynamic range was being excited. Most previous work, however, has largely disregarded the encoding properties of the upper dynamic range (e.g., Rees and Palmer 1988;Semple and Kitzes 1985;Phillips 1990;Aitkin 1991;Heil et al. 1994).
FI was separated into upper and lower dynamic ranges for each nonmonotonic neuron, and FI values from the dynamic range closer to the probability plateau of each neuron were averaged (see Materials and Methods). These mean FI curves showed peaks aligned near the 5-, 25-, and 45-dB plateaus for the lower dynamic ranges (Fig. 9C) and near the 25-, 45-, 65-, and 85-dB plateaus for the upper dynamic ranges (Fig. 9D). By using an analysis that segregates the upper and lower dynamic ranges, therefore, the adaptive nature of nonmonotonic neurons to dynamic-level stimuli in a manner that improves coding accuracy can be readily discerned. The converse analysis, collecting FI values of the dynamic ranges on the opposite side of BL from the stimulus plateau, can be seen in Figure 9E,F. This method revealed how encoding accuracy changed for the dynamic range not actively involved in encoding the most probable sound levels in the dynamic stimulus. The peak FI for the lower dynamic range remained at relatively low sound levels in response to the high-level dynamic stimuli (Fig. 9E), confirming that the lower dynamic range remained sensitive to low sound levels even when nonmonotonic neurons were adapted to high sound levels. The peak FI for the upper dynamic range of nonmonotonic neurons did exhibit some shifting in the direction of the low-level stimulus plateaus (Fig. 9F), however, even when these sound levels were most accurately encoded by the lower dynamic range. This result implies that the neurons on average are shifting their BLs as well as their thresholds as they adapt to the lower level dynamic stimuli, thereby inducing the shift in the upper dynamic range. This combined population shift of BL, lower, and upper dynamic ranges fades when more intense sounds become more common, however. As probability plateau centers increase past BL, both dynamic ranges ''snap back,'' leaving the lower dynamic range relatively fixed at the lowest sound levels while the upper dynamic range begins adapting again, this time aligning more closely with the plateau center.
Taken together, the results of these experiments reveal that the population of nonmonotonic neurons in primary auditory cortex evaluated in this study: 1) preferentially aligned either their lower or upper dynamic ranges with the most probable stimulus levels, depending upon the center level of the stimulus probability plateau; 2) as a population shifted their dynamic ranges less than monotonic neurons; 3) showed significant shifting of their upper dynamic ranges only for the neurons with low BLs; and 4) maintained population encoding accuracy for the most probable stimulus levels, a response feature most clearly discerned when the upper and lower dynamic ranges were analyzed separately.

Discussion
We have previously reported that even in response to stimuli with high mean sound level, level-tuned or nonmonotonic neurons in primary auditory cortex maintain sensitivity to lower sound levels (Watkins and Barbour 2008). Monotonic neurons, on the other hand, tend to shift their dynamic ranges toward the most probable sound levels in a stimulus, consistent with findings in inferior colliculus (Dean et al. 2005) and auditory nerve (Wen et al. 2009). Consequently, monotonic neurons as a population do not retain much of their sensitivity to lower sound levels when high levels are common. Assuming that the inhibition at high sound levels in nonmonotonic neurons (either in the cortical neurons themselves or in their inputs) contributes to this unique adaptation, inhibition could be ''shielding'' the neurons from sensory inputs that might otherwise induce adaptation or it may be ''capturing'' the adaptive process such that the inhibition itself adapts to soundlevel statistics, thereby reducing the amount of adaptation of the excitatory process at lower sound levels. Results of the current study indicate that when loud sounds are common, nonmonotonic neurons tend to adapt their upper dynamic ranges toward the loud sounds, lending support to for the adaptation capture hypothesis. By this mechanism, nonmonotonic neurons are able to remain sensitive to softer sounds with their lower dynamic range even while encoding louder sounds with their upper dynamic range.
Collectively, monotonic neurons shift their dynamic ranges more than nonmonotonic neurons, and nonmonotonic neurons appear to exhibit 2 regimes of adaptation depending upon the ratio of high levels to low levels present in the stimulus at short time scales. A schematic summary of these findings based upon population averages can be seen in Figure 10. The monotonic population exhibits a decreasing response gain with increasing plateau center, whereas response gain for nonmonotonic neurons decreases with increasing plateau center up to about 45 dB, beyond which gain actually increases. This gain increase at high dynamic levels, coupled with decreases in response threshold, provides a mechanism for nonmonotonic neurons to encode low levels more accurately than monotonic neurons under dynamic conditions with frequent intense sounds. Note that the average nonmonotonic BL, where less information is available from the nonmonotonic population, always falls within the average dynamic range of the monotonic population. When information from both populations is considered collectively, therefore, this complementary encoding scheme enables high encoding accuracy over a larger dynamic range than either subpopulation is able to provide on its own.
One result of such a scheme is that the normalized responses over the entire population (Fig. 6B, labeled ''All'') do indeed show a relatively flatter gain response independent of the most probable sound levels. With this information, we would speculate that population response rates at many frequencies may be relatively constant across a wide range of sound levels (Sadagopan and Wang 2008). This speculation would need to be verified with the appropriate experiments that include background noise or off-CF responses, however.

Dynamic Range and Sound Level Encoding
In order to distinguish unique encoding properties of leveltuned neurons, we utilized the technique of subdividing each neuron's response into its upper and lower dynamic range-regions of negative and positive slope in the rate-level function, respectively. These regions are separated by the In this case, the lower dynamic range (E) does not shift much at all, whereas the upper dynamic range (F) does shift somewhat in a direction consistent with improving coding accuracy. This result is likely due to some shift in BL in addition to threshold as the lower dynamic range adapts to lower level dynamic stimuli. Collectively, these results indicate that nonmonotonic neurons preferentially adapt some portion of their dynamic ranges closer to the most common stimulus levels.
neuron's BL. In terms of sound-level discriminability, the sloped portions of an input--output function convey the most information. Under noisy conditions, other aspects of the ratelevel response, particularly BL, may be more useful for encoding (Butts and Goldman 2006). We do not consider this situation here for 2 reasons. First, in the current study, we confined the stimuli employed in our investigation to pure tones in isolation as a first step toward characterizing the dynamic behavior of these neurons, about which little was known previously. Second, we intended to make inferences regarding the usefulness of nonmonotonic neurons for encoding by comparing with monotonic neurons, which do not necessarily have a particular BL. We exploited adaptation in order to discern how these neurons are likely to be encoding sounds at their CFs under dynamic conditions. Inferences about encoding follow from the assumption that the sloped portions of an input--output function (the most useful for level discriminability) adapt as the stimulus context is altered slightly. Because the slope at the maximum response (i.e., BL) is necessarily 0 and therefore conveys minimal information regarding sound-level discrimination, it represents a logical point at which to separate the neuron into 2 functional dynamic ranges. It is, however, flanked by 2 portions of the rate-level response useful for discriminability, indicated by positive FI values (e.g., see Fig. 4F,H,J,L). Additionally, because we were interested in testing the hypothesis that on-CF inhibition of level-tuned (i.e., nonmonotonic) neurons is directly involved in the ability of level-tuned neurons to preferentially encode low sound levels, BL also represents a logical point to split the neuron into predominantly excitatory and predominantly inhibitory regimes of the ratelevel function. These 2 regimes might very well be expected to exhibit different adaptation (and therefore different encoding) behavior, and the observed results were consistent with this hypothesis.
The current results and those we reported previously (Fig. 2, Watkins and Barbour 2008) are consistent with studies of adaptation in cortical and subcortical levels of the auditory system, indicating that preceding spiking rate alone is an incomplete predictor of the amount of observed adaptation (Malone and Semple 2001;Bartlett and Wang 2005;Dean et al. 2005;Nelson et al. 2009). Therefore, it seems likely that additional processes, possibly inhibitory in nature, participate in creating the observed responses. Adaptation similar to that of the monotonic neurons in the present study have also been observed in inferior colliculus (Dean et al. 2005), implying that this type of adaptation emerges subcortically, as well. Examples of adapting neurons with nonmonotonic rate-level functions have been reported subcortically (Wen et al. 2009), but such examples in the current study would have been classified as monotonic (MI > 0.5). Because nonmonotonic neurons have not been analyzed as a population subcortically, a cortical origin or refinement of complementary level-tuned adaptation cannot presently be ruled out. The overall amount of adaptation observed by mean population rate alone in cortical neuron populations is insufficient to fully adjust neural coding for the stimuli used (best visualized in Fig. 6A). Given that FI measures do reveal adaptation matched well to stimulus statistics for both monotonic (Fig. 1, Watkins and Barbour 2008) and nonmonotonic neurons (Fig. 9C,D), the neural code is likely to include spiking properties beyond simply mean rate. The overall variety in dynamic range location for dynamic stimuli evident in Figure 7 reflects a distributed code under dynamic conditions so that even though the population adapts to maintain coding accuracy for high-probability events, enough variability in individual responses remains to encode lower probability events.

Relation to Previous Studies
Several hypotheses have been put forward to explain the encoding role of level-tuned neurons. The best-intensity model (Shamma 2003) proposes that nonmonotonic neurons represent a place code for intensity as sounds are transformed along spectral and intensity dimensions. In this model, frequency and intensity are encoded over a population of neurons that are narrowly tuned to both stimulus parameters. Studies in the auditory cortex of bats have found evidence for this model, which has been termed an amplitude spectrum representation (Suga 1977;Suga and Manabe 1982). These studies also raised the possibility that level-tuned neurons create a ''level-tolerant'' representation of sounds generally. Later investigation in awake marmoset monkeys suggested that a major function of nonmonotonic neurons is to create a level-invariant representation for complex sounds (Sadagopan and Wang 2008). Furthermore, nonmonotonic neurons have been hypothesized to play a role in the detection of tones in noise (Rees and Palmer 1988), be responsible for detecting head-related transfer function spectral notches used in sound source localization (Davis et al. 2003) and may contribute to stimulus-level discrimination (Polley et al. 2004(Polley et al. , 2006. The conclusion we draw from the current experiments, that nonmonotonic neurons may be specialized for encoding low-intensity dynamic stimuli, does not directly address the issue of coding sound information across frequency but does imply that monotonic and nonmonotonic neurons encode intensity for different purposes. Nonmonotonic neurons, for example, would be particularly useful for encoding softer sounds immediately following louder sounds, leaving the coding of monotonic neurons to be optimized over longer time scales of adaptation (from milliseconds upward).
The mechanism by which nonmonotonicity is created in higher levels of the auditory system remains the subject of investigation. Nonmonotonicity in primary auditory cortex can be inherited from input Wehr and Zador 2003) or it can be refined or even created locally by combinations of unbalanced excitation and inhibition (Faingold et al. 1991;Sivaramakrishnan et al. 2004;Wu et al. 2006;Tan et al. 2007). These findings are consistent with a general trend of increasing percentages of nonmonotonic responses at higher auditory centers. Given that this transformation in the neural code appears to occur gradually across multiple auditory stations, level-tuned neurons in auditory cortex seem unlikely to exhibit properties fundamentally different from analogous neurons in subcortical auditory areas. In fact, we would anticipate that subcortical level-tuned neurons would exhibit adaptive behavior similar to that reported here for cortex. We speculate that locally created nonmonotonic neurons in both subcortical and primary cortical areas may inherit excitatory inputs from particular auditory nerve fibers. This role is likely filled by a subpopulation of high spontaneous rate, lowthreshold fibers that saturate at relatively low sound levels, and show no or very little adaptation to higher levels. In this mechanistic model, nonmonotonic neurons would also receive inhibitory inputs from local highly adaptive monotonic neurons. These inputs together would explain that when high sound levels are present, nonmonotonic neurons would demonstrate adaptation in the upper dynamic range, corresponding to inhibition by the adapting monotonic neurons, and demonstrate little or no adaptation in the lower dynamic range, corresponding to the saturated and nonadapting highly sensitive auditory nerve fiber inputs whose pathways are preserved throughout multiple levels of the auditory system. Nonmonotonic neurons at higher auditory centers may inherit much of their nonmonotonic behavior from ascending inputs and, therefore, not require such a mechanism locally.
Adaptive processes have been of considerable interest as a potential mechanism to help explain well-studied psychophysical phenomena such as forward masking. In classic forward masking, the detection of a brief tone is degraded by the occurrence of a preceding tone at the same frequency, and all other factors being equal, the amount of masking is proportional to the level of the masker (Lu¨scher and Zwislocki 1949;Jesteadt et al. 1982). Auditory nerve studies reveal that while adaptation in the periphery is evident under these stimulus conditions, it alone cannot fully account for this masking phenomenon (Harris and Dallos 1979;Relkin and Turner 1988;Turner et al. 1994). Subcortical excitatory and inhibitory circuits, on the other hand, appear to contribute substantially to forward masking (Nelson et al. 2009). While similar to masking protocols, the sound sequences used in the current experiments were sufficiently different to make direct comparisons with forward masking studies challenging. In particular, we were largely examining the suprathreshold behavior of cortical neurons, which does not necessarily mirror the behavior at threshold even for classic forward masking (Zeng et al. 1991). Nevertheless, the adaptation of level-tuned neurons to maintain coding accuracy for soft sounds when loud sounds are common appears to run counter to the type of adaptation underlying psychophysical forward masking. In masking paradigms, gain adaptation of nonmonotonic neurons has been shown in some cases to be a nonmonotonic function of masker level, although not systematically so (Calford and Semple 1995;Brosch and Schreiner 1997;Bartlett and Wang 2005). The nonmonotonic gain adaptation for nonmonotonic neurons apparent in Figure 6B could be a reflection of a similar process.
The stimuli in this study were designed to enable analysis predominantly of rate-level changes depending upon the central tendency of dynamic sound-level distributions. A change in the mean of the particular distributions used also resulted in a change in the variance. This effect was small, however, because of the relatively low probability of choosing any level outside a plateau. We did not systematically investigate the effect of changing the width of the probability plateaus (fixed at 20 dB) that would have been required to thoroughly investigate adaptation to variance (Kvale and Schreiner 2004;Nagel and Doupe 2006), except in the case of the uniformly distributed dynamic stimulus. Our uniformly distributed stimulus, which has much higher level variance than the high-probability plateau stimuli, always resulted in a gain decrease relative to silence-adapted conditions (see Fig. 5, solid black lines), consistent with results in songbirds (Nagel and Doupe 2006). Additionally, although the design of the dynamic stimuli used here is inherently time varying, it is difficult to compare with studies of amplitude modulation or those that consider linear temporal receptive fields because each time interval of the dynamic stimulus is composed of a stationary signal (typically a pure tone at CF). These 100-ms time intervals are relatively short when compared with typical best modulation frequencies of cortical neurons in response to AM stimuli (Liang et al. 2002;Bartlett and Wang 2005) and relatively long when compared with the duration of a typical cortical linear temporal receptive field (Depireux et al. 2001).
In conclusion, we have found that the level-dependent differences between excitation and inhibition (either local or inherited from subcortical inputs) that contribute to leveltuned cortical neurons appear to drive neuronal adaptation when high intensities occur commonly in dynamic stimuli. Unlike classically studied neurons whose input--output functions increase or saturate at high levels, adaptation of leveltuned neurons does not appear simply to optimize overall coding accuracy. The nature of their adaptation implies that they purposefully remain sensitive to rare, faint sounds even when louder sounds are much more common. If sensory neurons with tuned input-output functions are truly specialized for encoding low input values and maintain this sensitivity even when the most common input values are high, we speculate that the high prevalence of such neurons in the auditory system relative to other sensory systems implies that behaviorally relevant sound processing uniquely requires the ability to preserve sensitivity over a wide dynamic range.

Funding
The Wallace H. Coulter Foundation; The McDonnell Foundation for Higher Brain Function; the National Institutes of Health (DC008880 and DC009215).