Context dependence of excitatory and inhibitory conductances. A: the population average of the variance of excitatory conductance over contexts (black; 29 probes tested in 14 cells; Eq. 30 in context dependence at synaptic input level in methods). The data were well fit by the sum of 2 exponentials (gray; α₁ = 0.28, τ₁ = 0.14 s, α₂ = 0.08, and τ₂ = 1.22 s with α = 0.02 in Eq. 44). B: the population average of the variance of inhibitory conductance over contexts (black; 29 probes tested in 14 cells). The data were well fit by the sum of 2 exponentials (gray; α₁ = 0.48, τ₁ = 0.13 s, α₂ = 0.14, and τ₂ = 2.50 s with α = 0.10 in Eq. 44).

Context dependence induced by frequency changes. A: typical mean subthreshold responses of a rat A1 neuron to part of a sound sequence, in which a natural sound stimulus probe was preceded by 3 different synthetic conditioning stimuli with different bandwidths [red, blue, and green lines for contexts with 0.625–2.5 kHz (top spectrogram), 10–40 kHz (bottom spectrogram), and 2.5–10 kHz (see Supplemental Fig. S9), respectively; time 0 indicates the transition from conditioning to probe stimuli]. Spikes were clipped by a median filter (window length, 10 ms). Significant context dependence was observed for >4 s (gray bands; see B for details). B: black line represents P values and gray bands show the time points where the context dependence was statistically significant under the criterion: P < 0.01 for ≥5 ms (in the same format as Fig. 2D). C: the response power estimate that depends on the context (black line; in the same format as that in Fig. 2E). The population average of this quantity normalized by the average predictable power is shown in Fig. 8B (the 2nd panel from the top).

Rapid decay of context dependence in auditory thalamus. A: typical suprathreshold responses of a neuron in rat auditory thalamus to part of a natural sound sequence (spectrogram; the same example in Fig. 2) over 10 repeats. Rasters in red indicate spike occurrences on individual trials. B: the poststimulus time histogram (PSTH); red line for the one shown in A, blue line for the one in response to the same probe stimulus following “silence” period, and green line for the one in response to the same probe stimulus but preceded by a different conditioning stimulus (see also Supplemental Fig. S10). Substantially different responses were observed only in the first bin after the onset of the probe stimulus (0 < t ≤ 100 ms). C: we assessed the context dependence at the spike level by computing the SD of PSTHs to the probe stimulus over all different contexts (black). D: average SD of the PSTHs—as in C—over the population (93 probes in 14 cells, black; Eq. 42). Context dependence in auditory thalamus lasted only a short period of time. The decay size and constant are: α₁ = 15.0, τ₁ = 80 ms with α = 2.0 spike/s (gray; Eq. 44).

Excitatory and inhibitory conductances showed different context dependence patterns. A: spectrogram of part of a natural sound sequence presented to a rat A1 neuron. Time zero indicates the transition from conditioning to probe stimuli. B: example of the mean sound-evoked synaptic currents at 3 different holding potentials. The raw traces are shown in Supplemental Fig. S3B. Spikes were blocked pharmacologically. C: estimated total synaptic conductance (g_syn in Eqs. 26 and 27 in context dependence at synaptic input level in methods) and its excitatory and inhibitory components (g_exc and g_inh from Eqs. 28 and 29, respectively) evoked by natural sounds shown in A. See also Supplemental Fig. S3C. Note that both evoked excitatory and inhibitory conductances typically decayed within about 100 ms. D and F: estimated excitatory and inhibitory conductances in response to the probe stimulus in 6 different contexts (D and F, respectively). Estimates for different contexts are represented by different colors (red lines for those shown in C; see also C in Supplemental Figs. S3–S8) and estimated excitatory and inhibitory conductances are shown in light and dark colors, respectively. E and G: estimated variance of excitatory and inhibitory conductances over the 6 contexts for the probe period (E and G, respectively; Eq. 30 without population average). In this example, context dependence in inhibitory conductance was longer than that in excitatory conductance.

Context dependence of response predictability. Using responses to natural sound probe stimuli in different natural sound contexts (305 probe stimuli in 39 cells), we computed the ratio between the context-independent fraction of the response power and the stimulus-related response power in A1 neurons (thick black; Eq. 43 in response predictability). The stimulus-related fraction is given by the mean response over trials in each context—or the best response estimate under additive noise assumption—whereas the context-independent fraction is given by the mean over all contexts or the best estimate of the responses to a probe stimulus without any knowledge on the conditioning stimulus. Therefore the ratio (at time t after probe onset) represents the upper bound of the response prediction performance for a given window length t, which asymptotically approached the true upper limit (black broken line; unit model performance) by extending the window length—or available stimulus history—on the timescale of seconds (thick gray; α₁ = −0.49 and τ₁ = 1.04 s for exponential curve fit as in Eq. 44 with α = 1). In contrast, the performance (Eq. 53; 20 cells from Machens et al. 2004) of linear encoding models (spectrotemporal receptive field [STRF], thin gray; Eq. 46) was low for any window length up to about 4 s, even with static nonlinearities (LN, thin black; Eq. 51). Crosses and open circles, respectively, show the average model performance on the validation and training data sets, corresponding to the lower and upper estimates of the performance. Here we varied the bin sizes in a pseudologarithmic manner for changing the window length of the STRF models while fixing the model complexity (for details, see neural encoding models in methods).

Long-lasting context dependence in auditory cortex. A: significance measure. Top: each raster shows periods during which the significance measure exceeds threshold (P < 0.01 for ≥5 ms; see context dependence at subthreshold voltage level in methods) for a particular probe–stimulus combination in a given neuron (an example is shown as gray bands in Fig. 2). The rasters are sorted according to the longest-lasting effect, so successive rasters may correspond to different neurons. Significant context dependence was observed in about two thirds of probe stimuli (204 of 305 probes in 39 neurons). Bottom: the thick black curve shows the proportion—or the probability—of observing the significant context dependence and the thin gray curve shows the noise floor computed by resampling methods. The probability curve is well fit by the sum of 2 exponentials (thick gray; α₁ = 0.17, τ₁ = 0.20 s, α₂ = 0.09, and τ₂ = 0.90 s for Eq. 44 with the mean noise floor over time α = 2.8 × 10⁻³). Around a quarter of the context-dependent events occurred at ≥1 s from the onset of probe stimuli (thin black; cumulative probability corrected for the noise floor and normalized at its peak t = 4.72 s; broken part indicates the events at the noise level). B: fractional power measure. Top: from the same population data, we computed the stimulus-related response power (thin black; ̂[μ(t) + ν_i(t)] in Eq. 17; gray, its moving average over the data in [0, 2t] at time t) and the fraction that depends on stimulus history and its context (thick black; ̂[ν_i(t)] in Eq. 19). The context-dependent fraction corresponds well to the significance measure as shown in A (bottom). See also Fig. 1A. Bottom: the ratio of the context-dependent power to the stimulus-related power represents well the contribution of stimulus history to the response dynamics (black; Eq. 20). The decay size and constant are: α₁ = 0.49, τ₁ = 1.04 s with α = 0 (gray).

Relation between context dependence and sound properties. Using synthetic sounds, we examined the effects of the changes in a particular sound property of interest on the responses to following probe stimuli. Top to bottom: the population analysis for the changes in amplitude (95 probes in 31 cells), frequency (110 probes in 35 cells), AM rates and depths (96 probes in 27 cells), FM rates and depths (82 probes in 25 cells), and higher-order properties (137 probes in 27 cells). The thick gray curves show the exponential curve fit as in Eq. 44, with the constant α equal to the mean noise floor over time for A (thin gray) and with α = 0 for B (broken). A: significance measure. Shown is the population analysis based on the probability of observing context dependence, in the same format as that in Fig. 3A, but overlaid. Top to bottom: the parameters for the exponential model were [α₁, τ₁, α] = [0.23, 0.25, 2.8 × 10⁻³], [0.19, 0.27, 2.3 × 10⁻³], [0.13, 0.17, 2.3 × 10⁻³], [0.07, 0.15, 2.1 × 10⁻³], and [0.04, 0.13, 3.6 × 10⁻³], respectively. B: fractional power measure. Shown in the population analysis, indicating the contribution of context dependence to the response dynamics, in the same format as that in Fig. 3B. Top to bottom: the parameters for the exponential curves (all with α = 0) were [α₁, τ₁] = [0.57, 0.66], [0.54, 0.97], [0.86, 0.11], [0.64, 0.15], and [0.52, 0.20], respectively. C: relative context-dependence effects. We computed the area under the curve (Eq. 21; from 0 to 4 s) of the normalized context-dependent power examined with various synthetic stimulus ensembles (black lines in B) and normalized it by the corresponding area examined with natural sound ensembles (Fig. 3B, bottom). For details, see context dependence at subthreshold voltage level in methods. The area itself represents well the total effects induced by ignoring the conditioning stimuli and the normalized area shows the relative context-dependence effects for each of the following stimulus properties (from left to right, with the 95% confidence intervals computed by resampling methods): natural sounds (bar height of one), amplitude, frequency, AM, FM, and higher-order acoustic property.

Experimental design and auditory stimuli. A: experimental design for analyzing context dependence. During the recording, we presented well-designed N sequences of a given set of N sound fragments with no interstimulus interval in a randomly interleaved manner (shown is an example for N = 4; intersequence interval, ∼6 s). For the analysis, we aligned the recording data to examine the variability in the responses to a given sound fragment (probe; S₁ in this example) due to the presence of different preceding stimuli (context; “silence,” S₁, S₂, S₃, and S₄). The choice of conditioning stimuli depends on the goal of the analysis (for details, see Stimulus design in methods). Here we assumed that the response power (broken line; [r_ij(t)] from Eq. 11) to a probe stimulus at time t from probe onset can be divided into noise power ([ε_ij(t)]) and stimulus-related power (thin black; [μ(t) + ν_i(t)] in Eq. 17) that can be further decomposed into a context-independent fraction ([μ(t)] in Eq. 18) and a context-dependent fraction (gray; [ν_i(t)] in Eq. 19). For details, see Analysis in methods. B: natural sounds and synthetic sounds. Natural sound fragments (S_NS1 and S_NS2; 4.11 s long; sound pressure waveforms, spectrograms, and temporal and spectral marginal distributions) differ substantially in their spectrotemporal components, which causes a large and long context dependence in A1 when they are used as conditioning stimuli (Figs. 2 and 3). On the other hand, the temporal and spectral patterns in the marginal distributions between modulated colored noise S_MCN1 and the corresponding natural sound S_NS1 are nearly identical, resulting in a small and short context dependence (Fig. 8). Synthetic sounds such as modulated harmonic tones (sound pressure waveform and corresponding spectrograms; 1 s long) can be used to assess the effects of the changes in sound properties in more detail. Compared with S_MHT, for example, S_ΔAMP has 30 dB less power, S_ΔFREQ has the frequency components up-shifted by 1.5 octaves, S_ΔAM has slower AM rates by 4 Hz on average, and S_ΔFM has half the SD for the frequency-modulated (FM) depth. For details, see synthetic sounds in methods.

Context dependence can persist for several seconds. A: typical subthreshold responses of a rat A1 neuron to part of a natural sound sequence (spectrogram; time 0 indicates the transition from conditioning to probe stimuli) over 6 repeats (red lines). Spikes were clipped by a median filter (window length, 10 ms; see also Supplemental Fig. S2). The neuron showed high trial-to-trial reliability (correlation coefficients across trials to this particular probe stimulus, 0.74 ± 0.08; and across trials across all natural sound stimuli examined in this cell, 0.61 ± 0.07; mean ± SD). B: the mean responses to the probe stimulus in 3 different contexts: red line for the one shown in A and blue and green lines for the one in response to the same probe stimulus but preceded by “silence” and another conditioning stimulus, respectively. Significant dependence on the stimulus history was observed for >4 s (gray bands; see D for details), whereas the responses between 2 and 4 s after the onset of the probe stimulus were not affected by the differences in conditioning stimuli. C: the recorded cell in this example was histologically identified as a layer II–III pyramidal neuron (scale bar: 100 μm). D: we performed a pointwise statistical (Kruskal–Wallis) test for equal medians between the responses to the probe stimulus in all different contexts (black line; P values) and the gray bands show the time points where the context dependence was statistically significant under the criterion: P < 0.01 for ≥5 ms. E: the response power estimate that depends on the context [black line; 〈ν̂_i²(t)〉_i from Eqs. 17–19 without population average] well represents the magnitude of the context dependence. (Note that the estimated power can be negative; see context dependence at subthreshold voltage level in methods for details.) The population average of this quantity with and without normalization by the average predictable power is shown in Fig. 3B (thick black curves in the bottom and top panels, respectively).