Article Figures & Data
Figures
- Figure 1.
Schematic of four different model architectures for sound encoding by neurons in auditory cortex. A, Single neuron activity was recorded from A1 of awake, passively listening ferrets during presentation of a large set of natural sound stimuli. The trial-averaged response to each sound was calculated as the instantaneous firing rate using 10-ms bins. Sound waveforms were transformed into 18-channel spectrograms with log-spaced frequencies for input to the models. B, Linear nonlinear (LN) model: stimulus spectrogram is convolved with a linear spectro-temporal filter followed by nonlinear rectification. C, Short-term plasticity (STP) model: simulated synapses depress or facilitate spectral stimulus channels before temporal convolution. D, Gain control (GC) model: the coefficient of variation (contrast) of the stimulus spectrogram within a rolling window is summed across frequencies. Parameters for the nonlinear rectifier are scaled by time-varying contrast. E, Model performance is measured by the correlation coefficient (Pearson’s R) between the trial-averaged response and the model prediction. The four architectures were defined as follows: LN, B only; STP, B and C; GC, B and D; GC+STP, B–D.
- Figure 2.
Comparison of model prediction accuracy. A, Median prediction correlation for each model (n = 468 neurons). Differences between LN and GC (*p = 7.54 × 10−30), GC and STP (*p = 5.00 × 10−4), and STP and GC+STP (*p = 2.02 × 10−27) models were all significant (two-sided Wilcoxon signed-rank test). B, Scatter plot compares prediction correlation by the LN model and combined GC+STP model for each neuron. Color indicates whether the combined model showed a significant improvement (red, p < 0.05, permutation test) or not (gray).
- Figure 3.
Example model fits and predictions. A, Results from a neuron for which the STP and GC model predictions were not significantly better than the LN model prediction. Top left subpanel, Spectrogram from one natural sound in the validation set. Top right panel, Spectro-temporal filter from the LN model fit (right). Bottom panel, Actual PSTH response (light gray, filled) overlaid with predictions by the LN (dark gray), STP (blue), GC (green), and GC+STP (purple, dashed) models. Values at the bottom right of each panel indicate the prediction correlations for each model in the corresponding color. Below this list is the cell’s equivalence score (black, see Fig. 4B). The actual response was smoothed using a 30-ms boxcar filter for visualization. B, Comparison for a neuron for which the STP model performed significantly better than the LN and GC models, plotted as in A. Arrows indicate times for which the STP model successfully reproduced an increase in firing rate while the other models did not. The combined model prediction closely follows the STP model prediction. C, Comparison for a neuron for which the GC model performed significantly better than the LN and STP models. Right-most arrow indicates a time when the GC model successfully predicted an increase in firing rate while the LN and STP models did not, while the combined model closely followed the GC model. Middle arrow indicates a time when the STP model incorrectly predicted an increase in firing rate, and the combined model nearly matched the STP model. Left-most arrow shows a time when the combined model prediction differed from both the STP and GC model predictions to more closely match a strong onset response.
- Figure 4.
Equivalence of model predictions. A, Difference in prediction correlation between the GC (horizontal axis) or STP (vertical axis) model and the LN model for each neuron (r = 0.18, *p = 6.42 × 10−5). Red points indicate neurons with a significant improvement for the GC+STP model over the LN model (p < 0.05, permutation test); gray points indicate neurons that were not improved. B, Histogram of model equivalence for each unit, measured as the partial correlation between time-varying response predicted by the STP and GC models relative to the LN model prediction. Median equivalence for improved cells (0.29, bottom, red) was significantly greater than for non-improved cells (0.17, top, gray; Mann–Whitney U test, *p = 1.72 × 10−8). Arrows indicate median partial correlation for the GC model (0.43, left) and the STP model (0.68, right) when compared within-model, adjusted for differences in estimation data. C, Scatter plot compares equivalence (vertical axis) versus effect size (horizontal axis), i.e., the average change in prediction correlation for the STP and GC models relative to the LN model, for improved cells. Only a weak relationship between equivalence and effect size was observed (r = 0.22, *p = 0.0103). D, Prediction correlations for the combined GC+STP model (vertical axis) and the maximum of the GC and STP models (horizontal axis) for improved cells. Median prediction correlation was significantly higher for the combined model (0.6568) than for the greater of the individual models (0.6319; Wilcoxon signed-rank test, p = 1.41 × 10−14).
- Figure 5.
Within-model equivalence ordered by response reliability. A, Scatter plot compares within-model equivalence scores for the STP model compared with response reliability (n = 237 neurons recorded with the larger stimulus set). Dashed line indicates median reliability. Within-model equivalence was significantly higher for neurons with above-median reliability (median high reliability: 0.61, low reliability: 0.36, Mann–Whitney U test, *p = 6.01 × 10−12). B, Within-model equivalence scores for the GC model versus reliability, plotted as in A. Again, within-model equivalence was significantly higher for neurons with above-median reliability (median high reliability: 0.42, low reliability: 0.25, *p = 3.91 × 10−5).
- Figure 6.
Model performance for simulated data. A, Simulation based on the fitted LN model from Figure 3A. Simulated PSTH response to one stimulus (spectrogram at top) based on an LN model is plotted in gray shading. Predicted PSTHs for each model (LN, STP, or GC) are overlaid, and model prediction correlation is indicated at right (LN: dark gray, STP: blue, GC: green). For this linear neuron, all three models perform nearly identically. The linear filter fit using the LN model is shown at the top right. B, Model fits for simulation based on the STP model from Figure 3B, plotted as in A. C, Model fits for simulation based on the GC model from Figure 3C.
- Figure 7.
Parameter fit values for the STP model. A, Distribution of τ, representing the time constant for the recovery of synaptic vesicles, Top panel shows data for non-improved neurons (gray) and bottom panel for improved neurons (red). Median values for non-improved (0.0533 s) and improved (0.0833 s) neurons were significantly different (p = 3.53 × 10−6, two-sided Mann–Whitney U test, * p < 0.05), indicating a longer time constant for the improved cells. B, Distribution of u values, representing release probability (i.e., the fraction change in gain per unit of stimulus amplitude). Medians for non-improved (0.0128) and improved (0.0641) neurons were significantly different (p = 2.92 × 10−13), showing higher release probability for neurons with improved performance over the LN model.
- Figure 8.
Parameter fit values for the GC model. A, Histogram of effect of contrast on k, representing the slope of the output nonlinearity, plotted for non-improved neurons (gray, top) and improved neurons (red, bottom) as in Figure 7. The negative median value for improved (−0.14) cells indicates a decrease in slope during high-contrast conditions. This median was significantly more negative than for non-improved neurons (−0.042, p = 1.22 × 10−4, two-sided Mann–Whitney U test). Asterisk indicates p < 0.05. B, Histogram of contrast effect on a (saturation level), plotted as in A. Median values for non-improved (0.0031) and improved (−0.0156) neurons were significantly different, indicating a decreased response amplitude in high contrast conditions (p = 8.01 × 10−6). C, Histograms of contrast effect on b (baseline of the output nonlinearity). Medians for non-improved (0.0005) and improved (0.0058) neurons were significantly different, indicating an increase in baseline for high contrast (p = 5.90 × 10−7). D, Distribution of contrast effect on s (input offset). There was no significant difference between medians for non-improved (0.0088) and improved (0.0082) neurons (p = 0.85).
- Figure 9.
Mean evoked and spontaneous firing rates grouped by nonlinear model performance. A, Histograms of mean evoked firing rate for four mutually exclusive groups of neurons: no significant improvement in prediction accuracy for the nonlinear models (gray, top), significant improvement for the STP model relative to the LN model (blue, middle-top), significant improvement for the GC model relative to the LN model (green, middle-bottom), or significant improvement for both the STP and GC models or the GC+STP model (purple, bottom). Median evoked firing rate was significantly higher for the STP (11.7 spikes/s) and Both (12.7 spikes/s) groups than for the None group (7.31 spikes/s, Mann–Whitney U test, *p = 1.68 × 10−3 and *p = 2.67 × 10−3, respectively, adjusted for multiple comparisons). All other comparisons were not statistically significant (p > 0.05). B, Histograms of spontaneous firing rate for each model, plotted as in A. None of the groups was significantly different from the others (p > 0.05).
- Figure 10.
Comparison of natural sound and clean/noisy vocalization properties. A, Top to bottom, stimulus spectrogram (blue), contrast (red), and frequency-summed contrast (black) for a sequence of three natural sound samples. B, Same as in A, but for vocalizations. The vocalization set contained interleaved trials of ferret vocalizations with and without additive noise. Black bar indicates segment with noise added.
- Figure 11.
Comparison of contrast properties between stimulus sets. A, Scatter plot of SD and mean level (dB SPL) for each natural sound spectrogram. The distribution indicates a smooth variation in contrast level. B, Comparison of SD and mean for clean/noisy vocalizations. There is a clear grouping of noisy (low-contrast) and clean (high-contrast) stimuli.
- Figure 12.
Comparison of model performance for data including clean and noisy vocalizations. A, Median prediction correlation (n = 141) for each model. Statistical significance of median differences was determined via two-sided Wilcoxon signed-rank tests (*p < 0.05). Unlike the natural sound data (Figure 2), performance was not significantly different between the GC and STP models. B, Change in prediction correlation for the GC (horizontal axis) and STP (vertical axis) models relative to the LN model for each neuron (r = 0.18, p = 3.45 × 10−2). C, Prediction correlations for the LN model compared with the combined model for each neuron, grouped by whether the combined model showed a significant improvement (red, n = 12, p < 0.05, permutation test) or not (gray, n = 129). D, Histogram of equivalence for non-improved (top, gray) and improved neurons (bottom, red). Median equivalence for improved cells (0.30) was significantly greater than for non-improved cells (0.16, Mann–Whitney U test, *p = 0.0449).
Tables
- Table 1
Statistical tests reported in the Results, labeled in the text by the letters in the left-hand column
Distribution Test Statistic p value Sample size animals a Non-parametric Permutation test N/A p < 0.05, 468 sig. n = 540 n = 7 b Non-parametric Wilcoxon signed-rank T = 2.17 × 104 p = 7.54 × 10−30 n = 468 n = 7 c Non-parametric Wilcoxon signed-rank 
n = 468 n = 7 d Non-parametric Wilcoxon signed-rank
n = 468 n = 7 e Non-parametric Wilcoxon signed-rank
n = 468 n = 7 f Non-parametric Wilcoxon signed-rank
n = 468 n = 7 g Non-parametric Jackknife t test T (varies) p < 0.05, 132 sig. n = 468 n = 7 h Normal (residuals) Pearson’s correlation r = 0.18
n = 468 n = 7 i Normal (residuals) Pearson’s correlation r = 0.31
n = 237 n = 2 j Normal (residuals) Pearson’s correlation r = 0.50
n = 237 n = 2 k Non-parametric Mann–Whitney U
n = 132, 336 n = 7 l Normal (residuals) Pearson’s correlation r = 0.22 p = 0.0103 n = 132 n = 7 m Non-parametric Wilcoxon signed-rank
n = 132 n = 7 n Non-parametric Mann–Whitney U
n = 119, 118 n = 2 o Non-parametric Mann–Whitney U
n = 119, 118 n = 2 p Non-parametric Mann–Whitney U
n = 93, 141 n = 7 q Normal (residuals) Pearson’s correlation r = 0.34
n = 234 n = 7 r Normal (residuals) Pearson’s correlation r = 0.66
n = 122 n = 2 s Normal (residuals) Pearson’s correlation r = 0.41
n = 122 n = 2 t Non-parametric Mann–Whitney U
n = 132, 336 n = 7 u Non-parametric Mann–Whitney U
n = 132, 336 n = 7 v Non-parametric Mann–Whitney U
n = 132, 336 n = 7 w Non-parametric Mann–Whitney U
n = 132, 336 n = 7 x Non-parametric Mann–Whitney U
n = 132, 336 n = 7 y Non-parametric Mann–Whitney U
n = 132, 336 n = 7 z Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 aa Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 bb Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 cc Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 dd Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 ee Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 ff Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 gg Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 hh Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 ii Non-parametric Mann–Whitney U
p* = 1.00 n = 132, 336 n = 7 jj Non-parametric Mann–Whitney U
n = 132, 336 n = 7 kk Non-parametric Mann–Whitney U
n = 132, 336 n = 7 ll Non-parametric Wilcoxon signed-rank
n = 141 n = 6 mm Non-parametric Wilcoxon signed-rank
n = 141 n = 6 nn Non-parametric Wilcoxon signed-rank
n = 141 n = 6 oo Non-parametric Wilcoxon signed-rank
n = 141 n = 6 pp Non-parametric Wilcoxon signed-rank
p = 0.105 n = 141 n = 6 qq Normal (residuals) Pearson’s Correlation r = 0.18 p = 0.0345 n = 141 n = 6 rr Non-parametric Mann–Whitney U U = 5.02 × 102 p = 0.0449 n = 12, 129 n = 6 p* indicates Bonferroni-adjusted p values for 12 multiple comparisons.
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