To test the state-dependence of auditory cortical representation of continuous stimuli, we recorded neural populations using multisite silicon electrodes in auditory cortex of urethane-anesthetized rats. Acoustic stimuli consisted of a repeatedly presented 50 s frozen amplitude-modulated noise stimulus, whose amplitude envelope had power in the range 1–100 Hz.
An example of data collected with this method can be seen in . LFPs during the synchronized state were dominated by a low-frequency (<10 Hz) pattern, whereas the desynchronized state LFPs exhibited greatly reduced low-frequency power (). The smaller narrowband oscillation at 3–4 Hz seen in the desynchronized state likely corresponds to volume-conducted hippocampal theta (which has a lower frequency than in awake rats, and occurs together with cortical desynchronization (Sirota et al., 2008
AM noise presentation in synchronized and desynchronized states
Presentation of the stimulus did not change these low-frequency patterns, but it did cause an increase in higher frequency power, which was more prominent in the desynchronized state. Rasters of population activity () show that the synchronized state consists of alternations between periods of generalized spiking activity (“up states”) accompanied by negative LFP deflections, and periods of very little spiking (“down states”), accompanied by positive LFP deflections; stimulus presentation did little to change this pattern. In the desynchronized state, such global oscillations were not seen, but instead cells fired more continuously during both AM Noise stimulation and silence.
The use of a repeatedly-presented frozen-noise stimulus allowed us to examine the reliability with which the cortex responded to the stimulus. In are overlaid evoked LFPs from two presentations of the stimulus (synchronized: blue, cyan; desynchronized: red, magenta); below each pair of traces are a raster representation of a single neuron’s response to multiple stimulus repetitions. It can be seen that the response in the desynchronized state is highly reliable from trial to trial. In the synchronized state, cortical activity is modulated by the stimulus in a less reliable way. This reliability of LFP responses was quantified using the coherence of the evoked LFP with the stimulus envelope (). In all cases, the LFP showed greater coherence to the stimulus envelope in the desynchronized state. To quantify the reliability of spiking responses across multiple stimulus repetitions, we computed Fano factors for each cell in the two states (; see Methods). In the synchronized state, Fano factors were typically above 1 (p<.001, one-sample t-test; mean±SD:1.19±.36), indicating that spiking was more variable than expected from a (inhomogeneous) Poisson process, whereas in the desynchronized state Fano factors were typically below 1 (p<.001, one-sample t-test; mean±SD:.84±.25), indicating spiking was less variable than Poisson. A significant difference was also found between states (p<.001, paired t-test).
Reliability of cortical responses varies with brain state
We next set out to quantify the degree to which individual neurons were reliably entrained by the AM Noise stimuli. To do this, we used a “spike train prediction” method, in which the stimulus envelope was used to generate a predicted firing rate, which was then compared to the spike train actually observed. To avoid over-fitting we used cross-validation: parameters of the prediction function were estimated from one part of the data (the “training set”) and evaluated on another (the “test set”). Prediction was assessed by log-likelihood ratio compared to the prediction of constant mean firing rate, and normalized by the number of spikes, resulting in a measurement in bits/spike (see Methods).
Two methods were used to predict spike firing probability from the amplitude envelope. The first was based on convolution with a linear filter followed by a static nonlinearity (see Methods). To ensure results were not dependent on this specific prediction method, we also applied a second technique we termed the “2D STA,” simplified from the method of Sharpee et al. (Sharpee et al., 2006
; Atencio et al., 2008
). In this approach, firing probability was predicted as a nonlinear function of the amplitude and slope of the envelope at a fixed time lag in the past (). illustrates how both the shape of the 2D STA and quality of the prediction vary as a function of the time-lag. When quantifying predictions using this method, the value of time-lag giving optimal performance was used.
Three examples of this prediction can be seen in . In the desynchronized state, the first neuron () showed a preference for high amplitudes ~16 ms prior to spiking, visible as sharp peaks in the linear STA, and near the top of the 2D STA plot, with predictability of ~1.1–1.4 bits/spike for both methods. In the synchronized state, however, this predictability was completely abolished, with a flat linear STA and unstructured 2D STA plot. For the second neuron (), the desynchronized linear STA showed a broad peak spanning -40 to -20 ms, yielding predictability of ~1.3 bits/spike. The 2D STA showed a diffuse peak in the upper half, with poorer predictability reflecting the inability of the amplitude and derivative at any single time point to accurately capture the lower-frequency amplitude modulations that drove this neuron. As with the first example, however, predictability according to both measures was abolished in the synchronized state. The third example cell () showed a complex receptive field structure in the desynchronized state, with a biphasic linear STA, and a sharp peak at the right side of the 2D STA plot indicating preference for the rising phase with a lag of ~16 ms. Unlike the other examples, this neuron did show some predictability in the synchronized state, but its 2D STA moved from a sharp peak to a more diffuse ring, indicating that loud sounds would make it fire, but with unreliable timing. Consistent with this picture, the linear STA in the synchronized state was broad but provided no information about spiking. These examples suggest that the two prediction methods give similar though not always identical results, but that with either method, predictions from stimulus envelope are worse in the synchronized state.
Cortical activity is not simply a deterministic function of sensory input, and cortical circuits can exhibit autonomous activity independent of external stimuli. Thus, even if a cell is poorly predicted from sensory stimuli, it is possible that its activity is strongly related to internally generated activity patterns. To determine whether this was the case, we applied the same methods to predict neural activity from the LFP signal (averaged over neighbouring recording shanks to avoid contamination by the neuron’s own waveform). The results of this analysis are seen in for the same three example cells as before. Prediction from LFPs was typically better with the nonlinear method. The optimal time-lag near 0 indicated that the instantaneous LFP amplitude and derivative was a good predictor of spiking. 2D STAs showed peaks to the left or below the origin, consistent with references to fire on the descending phase or trough of LFP oscillations. In contrast to prediction from stimulus, prediction from LFP was often better in the synchronized state, likely as a result of the strong modulation of population activity by up states and down states.
The intuition suggested by the above examples is confirmed by group-level analysis. The two STA methods produce highly correlated predictions (), with a slight advantage to the linear method when predicting from stimulus envelopes in the desynchronized state (; synchronized: p=0.051, desynchronized: p<0.001, paired t-test), and to the nonlinear method when predicting from LFPs in both states (; p<0.001, paired t-test). For further analyses, we therefore used the best method in each case (linear for AM noise envelope, 2D for LFP). Prediction from the AM noise envelope was better by a large margin in the desynchronized state (; p<0.001, paired t-test), while prediction from the LFP was generally better in the synchronized state (; p<0.001, paired t-test). Comparing prediction from LFP to prediction from the stimulus, we found that LFP prediction outperformed the poor AM Noise prediction by large margins in synchronized states (; p<0.001, paired t-test), and that in desynchronized states the LFP was also generally a better predictor of neural activity than the stimulus envelope (; p<0.005, paired t-test) when using the optimal method in each case.
Summary of predictability results