Interaural level difference discrimination thresholds for single neurons in the lateral superior olive

Abstract

The lateral superior olive (LSO) is one of the earliest sites in the auditory pathway that is involved in processing acoustical cues to sound location. Here, we tested the hypothesis that LSO neurons can signal small changes in interaural level differences (ILDs), a cue to horizontal sound location, of pure tones based on discharge rate consistent with psychophysical performance in the discrimination of ILDs. Neural thresholds for ILD discrimination were determined from the discharge rates and associated response variability of single units in response to 300 ms tones in the LSO of barbiturate-anesthetized cats using detection theory. Neural response variability was well described by a power function of the mean rate, both in individual neurons and collectively; LSO neurons were less variable than expected from a Poisson process. Compared with psychophysical data, the best-threshold ILDs of single LSO neurons were comparable with or better than behavior over the full range of frequencies (0.3-35 kHz) and pedestal ILDs (+/-25 dB) explored in this study. With a pedestal ILD of 0 dB, ILD increments of 1 dB could be discriminated by some neurons, with a median of 4.35 dB across neurons. For pedestal ILDs away from 0 dB, the best-threshold ILDs were as low as 0.5 dB, with a median of 2.3 dB. These findings support the hypothesis that the LSO plays a role in the extraction of ILD, and that the representation of ILD by LSO neurons may set a lower bound on the behavioral sensitivity to ILDs.

Figure 1.

Determination of ILD discrimination threshold of an LSO neuron (unit 110–24). A, Mean discharge rate (•) and SD (○) of an LSO neuron to variations in the ILD of a 300 ms duration CF (16 kHz) tone. The black line shows the best-fitting sigmoid to the rate and the gray line shows the SD computed from the fitted power function of the rate (inset). The inset shows the variance of the rate as a function of the rate on double-log coordinates along with the best-fitting power function (dashed line). B, Example of computing threshold ILD via standard separation metric, D (see definition in Materials and Methods), as a function of increment ILD from the pedestal. The threshold for discrimination was defined as the smallest increment ILD that results in D of 1. C, ILD thresholds as a function of pedestal ILD for the neuron in A. D, A magnified view of C, which delineates three points of interest: the best threshold, corresponding to the minimum of the function, the pedestal ILD at the best threshold, and the threshold at midline, corresponding to pedestal ILD of 0 dB.

Figure 2.

The variance of the responses of LSO neurons to repeated presentations of CF tones is well described by a power function of mean response when plotted on double-log coordinates. A, Variance of discharge rate as a function of the mean discharge rate (○). The line (solid) shows the best-fitting power function (for details of the goodness of the fit, see Results). n is the number of variance-rate pairs from 36 neurons. For all neurons, the stimuli were 300 ms duration tones at the CF. B, Variance of spike count over the 300 ms duration of the stimuli as a function of the mean spike count (○). The line (solid) shows the best-fitting power function. C, The Fano factor (ratio of the variance to the mean spike count) decreases as a function of mean spike count. The solid line shows the Fano factor computed from the power function in B. In both B and C, the results expected for a Poisson process (variance equal to the mean, and FF equals 1) is also shown (dashed line).

Figure 3.

ROC analysis and standard separation metric yield similar estimates of neuronal threshold ILDs. A, Mean rate (•), SD of rate (○), and model function fits (lines) as functions of ILD for one neuron (CF, 31.1 kHz). Mean and SD of rate are based on 100 presentations of the 300 ms stimulus at each ILD. Symbols and lines are as in Figure 1A. B, ILD thresholds computed by three different methods are shown for the neuron in A. Results from ROC analysis (•) using the response distributions, the standard separation metric (□) using the computed mean and SDs of the response distributions measured at 1 dB intervals of pedestal ILD, and the standard separation metric using mean and variance obtained from the best-fitting functions (line) are shown. Threshold was defined as either the ILD increment or decrement that results in an area under the ROC curve of 0.75 or 0.25, respectively, or a standard separation of 1. C, Thresholds of five neurons at pedestal ILDs from ±5 to 6 dB in 1 dB intervals are shown as a scatter plot (n = 65). Thresholds calculated by the standard separation metric, directly using the empirical distributions (×) or via the function-based approach (○), are plotted against thresholds from ROC analysis. The dashed line is the line of equality.

Figure 4.

Threshold ILDs of individual LSO neurons are comparable with psychophysical thresholds. Best threshold (▵) and threshold at midline (0 dB pedestal ILD) (▿) as a function of the CF of the neuron (n = 42). For comparison, the shaded region depicts the range of ILD discrimination thresholds (∼0.5–4 dB) in human, monkey, and cat psychophysical data (see Results). Three data points with values >12 dB are not shown for the sake of clarity. Data from low-CF (<3 kHz) and high-CF (>3 kHz) neurons are separated by the dashed line.

Figure 5.

A, Best-threshold ILDs (•, high CF; □, low CF) of individual neurons as a function of the pedestal ILD at which they occurred. The minimum of the threshold-ILD functions of the population (line), the lower envelope, is relatively invariant with pedestal ILD. The invariance of threshold as a function of pedestal ILD increases from the midline is consistent with human psychophysical data (see Results). B, Distribution of pedestal ILDs corresponding to best-threshold ILDs. Across the population of neurons, the best thresholds tended to occur near the midline. C, Threshold ILDs at midline as a function of the best-threshold ILDs (○, high CF; □, low CF). Best thresholds of LSO neurons are not always found at midline (pedestal ILD of 0 dB). The dashed line is the line of equality.

Figure 6.

The neural determinants of the best ILD thresholds. A, The contribution of response variability to threshold ILD was examined by comparing best-threshold ILD as a function of the SD of the discharge rate at the pedestal ILD of best threshold (○, high CF; □, low CF). If response variability was a major determinant of the threshold ILD, then a positive correlation would be expected. Rather, a significant negative correlation was observed (the two obvious outliers were not included in the regression). B, Contribution of the rate of change of the discharge rate with changes in ILD (slope) was examined by comparing best-threshold ILD as a function of the reciprocal of the slope at the pedestal ILD of best threshold (○, high CF; □, low CF). If the slope of the rate was a major determinant of the threshold ILD, then a positive correlation would be expected because a larger change in mean discharge rate (i.e., smaller reciprocal of the slope) results in better discrimination (smaller threshold). A significant positive correlation was observed.

Figure 7.

The best ILD thresholds do not occur where the rate-ILD curve is the steepest. The function relating the pedestal ILD at the best-threshold ILD as a function of the pedestal ILD corresponding to the maximum slope of the rate-ILD function exhibits a consistent offset (○, high CF; □, low CF). The pedestal ILD at best threshold for all neurons was always larger than the pedestal ILD of maximal slope of the rate-ILD function, suggesting that the best threshold does not depend exclusively on the maximum rate of change in response. The dashed line is the line of equality.

Figure 8.

Relationship between the mean and SD of the neuronal discharge rate reveals why best threshold does not occur at the steepest slope. A, Mean rates, SDs, and model fits as functions of ILD for one neuron (CF, 16 kHz). Symbols and lines are as in Figure 1A. B, The slope of the rate, the SD, the ratio of the slope and SD, and the threshold ILD as functions of pedestal ILD for the neuron in A. Note that the ILD axis for this neuron has been slightly adjusted so that the rate slope maximum occurs at 0 dB ILD. The maximum ratio of slope and SD and thus, the best-threshold ILD, does not occur where the slope is maximal (point C in A), but at a point slightly contralateral (positive ILDs between B and C in A).

Figure 9.

Neuronal thresholds obtained by using the generalized description of response variance computed from the population of LSO neurons (e.g., Fig. 2A) are plotted against those obtained by using each neuron's own variance–mean relationship: the best threshold (○, high CF; □, low CF) and threshold at midline (•, high CF; ■, low CF; n = 42). For clarity, four data points with values >14 dB were not plotted (these data were included in the regression analysis). Regression of the data revealed a significant positive correlation (r = 0.97; p < 0.0001; n = 84).