Sensory stimuli are represented in the brain through the activity of large populations of neurons. While this fact has motivated the study of neural population codes for several decades, the bulk of this work has been theoretical, since only recently has it become feasible to record the simultaneous activity of large neuronal ensembles.

Early theoretical studies relied on parametric models of neuronal firing to quantify how the accuracy of a population code depended on factors such as the shape of neural tuning curves, the dimensionality of sensory stimuli or the duration of spike-count windows (Seung and Sompolinsky, 1993; Zhang and Sejnowski, 1999; Bethge et al., 2002). It was recognized that pairwise ‘noise’ correlations between the activity of different neurons had a potentially large impact on the accuracy of a population code, and that the effect of correlated variability depends on the relative orientation of the subspaces where the signal and the noise reside (Abbott and Dayan, 1999; Panzeri et al., 1999; Sompolinsky et al., 2001; Wu et al., 2001; Shamir and Sompolinsky, 2006; Averbeck et al., 2006; Cohen and Kohn, 2011; Ecker et al., 2011; Moreno-Bote et al., 2014). The signal subspace describes the set of trial-averaged network states visited by the population as the sensory stimulus is varied. The noise subspace describes the set of states visited by the population as a result of trial-to-trial variability for any given fixed stimulus. If the signal and noise subspaces are aligned, then a putative decoder will be unable to tease apart the stimulus from the noise, and this will decrease the accuracy of the code. Despite the amount of theoretical work on this topic, the geometry of the signal and noise subspaces in large populations of neurons has not yet been thoroughly characterized.

Here, we conducted such an investigation with an emphasis on understanding how the geometry of the population is affected by the global dynamics of the brain. A salient feature of brain dynamics that becomes immediately apparent when global activity is measured — either in the form of populations of single neurons or in the form of mesoscopic signals such as the LFP or EEG — is the existence of different ‘global dynamical regimes’, or ‘brain states’ (Vanderwolf, 2003; Harris and Thiele, 2011; McCormick et al., 2015). Behavioral context, such as overt motion during wakefulness (Vanderwolf, 1988; Castro-Alamancos, 2004; Gervasoni et al., 2004), whisking (Poulet and Petersen, 2008; Fanselow and Nicolelis, 1999), sleep phase (Steriade et al., 1990; Steriade and McCarley, 2013), or the type of actions that animals are performing (Vanderwolf, 2003; Gervasoni et al., 2004), have a large impact on brain state. Different brain states are also associated to different neuromodulatory systems (Vanderwolf, 2003; Lydic and Baghdoyan, 1998; Lee and Dan, 2012). From a physiological perspective, different brain states can be arranged along a one-dimensional continuum of cortical activation (Berger, 1929; Harris and Thiele, 2011). At one end of the continuum (inactive or synchronized state) the population undergoes global, large-amplitude, low-frequency oscillations leading to alternations between periods of firing and of silence referred to as up and down states (Steriade et al., 1993). These states are typical of slow-wave sleep, the anesthetized brain under most, but not all, anesthetics, and quiet wakefulness (Harris and Thiele, 2011). At the other end of the continuum (active or desynchronized state), firing rates are tonic, and the population-averaged activity of the population shows much weaker fluctuations (Destexhe et al., 2003; Steriade and McCarley, 2013; Renart et al., 2010). Active states are typical of REM sleep, can be observed under urethane anesthesia (Clement et al., 2008) and are associated with locomotion and active sampling of the environment, including attentive wakefulness (Vanderwolf, 2003; Harris and Thiele, 2011). The population can find itself also in intermediate activation states (Curto et al., 2009). Since the magnitude and nature of correlated variability change along the activation continuum, brain state can be expected to have a strong influence on the geometry of sensory population codes. Recent studies generally tend to find that the amount of information about the stimulus in a population code is larger during active than during inactive states (Goard and Dan, 2009; Marguet and Harris, 2011; Pachitariu et al., 2015; Beaman et al., 2017).

We have studied the state-dependence of the geometry of population codes in the rat auditory cortex. Different brain states were evoked through the use of urethane anesthesia (Murakami et al., 2005; Clement et al., 2008; Renart et al., 2010). We recorded population activity in response to binaural noise bursts varying both in inter-aural level difference (ILD: the difference in sound intensity in dB between the two ears) as well as in absolute binaural level (ABL: the arithmetic average of the left and right intensities). Since rodents do not use phase information for sound localization, they rely mainly on ILD to localize sounds in the horizontal plane (Wesolek et al., 2010; Lauer et al., 2011). Neurons in the auditory cortex in several species, including rats, represent ILD in the form of broad tuning curves with maximum slope at near-zero ILDs, that is corresponding to sounds arriving from the front of the animal (Stecker et al., 2005; Campbell et al., 2006; Yao et al., 2013). ABL and ILD are prototypical examples of prothetic and metathetic sensory continua, respectively (Stevens, 1957). Prothetic sensory continua are associated with changes in the total energy carried by the stimulus, whereas along metathetic continua the total amount of energy stays constant and the stimuli differ along some other feature dimensions — in our case in lateralization. Other examples of metathetic continua include sound frequency, or spatial location and stimulus orientation in vision. By systematically varying ABL and ILD, our study allowed us to investigate how these two types of sensory continua are represented at the population level. The state-dependence of the representation of prothetic stimuli is particularly interesting, both because it has not been systematically explored previously, and because global up-down fluctuations in the inactive state are expected to specially interfere with the representation of stimuli varying along a prothetic continuum (ABL).

The simultaneous activity of many well-isolated single units was recorded unilaterally from the auditory cortex of urethane-anesthetized rats using 8-shank, 64-channel silicon probes (Neuronexus Tech.). We obtained data from $n=23$ sessions (after quality control, see Materials and methods), with 104 ± 23 isolated neurons per session (mean ± standard deviation across sessions).

Under urethane anaesthesia, the cortex undergoes spontaneous transitions between states with varying degrees of ‘activation’, also known as ‘desynchronization’ (Clement et al., 2008). Characteristic examples of these states are shown in Figure 1 as raster plots (sorted by firing rate), taken from periods of spontaneous activity. As shown previously (Curto et al., 2009; Renart et al., 2010), during the inactive state, there are globally correlated low-frequency fluctuations in population activity (Figure 1A; also known as the ‘slow oscillation’). In this state, there are brief periods when all neurons are silent (down states) separated by periods of firing (up states). These up-down oscillations induce positive correlations between most pairs of neurons evident as vertical stripes in the population raster (Renart et al., 2010; Ecker et al., 2014). In contrast, during the active state, neurons fire tonically in a globally uncorrelated fashion (Figure 1B), as evident from the lack of vertical stripes in the raster (Renart et al., 2010; Ecker et al., 2010).

Figure 1

Download asset Open asset

Our set of auditory stimuli was designed to probe the representation of ILD (the cue used by rodents to localize sound on the horizontal plane [Wesolek et al., 2010; Lauer et al., 2011]) and its intensity dependence. We varied the ILD of the sounds at constant absolute binaural level (ABL, the arithmetic mean of the level (in dB SPL) across the two ears). We used a headphone-like configuration with two speakers positioned closely (0.5 cm) to each ear in order to replicate the conditions of a behavioral study in our laboratory where we have thoroughly characterized the ILD-discrimination abilities of freely moving rats using custom made headphones (Pardo-Vazquez et al., 2018). Since that study focused on ILD discrimination with respect to the midline, our stimulus set also focused on small-magnitude ILDs (±1.5, ±3, ±4.5, ±6, ±12, ±20 dB), which were presented at three different overall intensities (ABL = 20, 40, 60 dB SPL; see Figure 1C). Sounds consisted of wide-band (5–20 KHz) noise bursts lasting 150 ms separated by ~850 ms silence. Each of the 36 stimuli was presented 100 times.

We quantified the degree of (in)activation in two different ways. First, we computed the coefficient of variation (CV, standard deviation divided by the mean) of the total number of spikes from all single neurons across 20 ms bins (see Materials and methods). This number — the CV of the population rate — varied from around 0.4 to around 2.2. If all neurons are Poisson and statistically independent, then the CV of the population rate will approach zero. Second, we also quantified the degree of inactivation by the fraction of 20 ms windows corresponding to down states, which varied from 0% to over 70% across sessions. Both measures turned out to be strongly correlated ($r=0.98$, Figure 1D), and we will subsequently use the CV of the population rate to quantify the degree of activation. The distribution of either of these measures is unimodal, suggesting that active and inactive states are not clearly distinct bur rather form a continuum (Curto et al., 2009). Thus, we quantify the effect of brain state on different aspects of neural activity using regressions against the value of the CV across sessions. In order to illustrate the state-dependence of various features of interest, we arbitrarily defined all sessions with $\text{𝐶𝑉}<0.6$ as ‘active’ ($n=3$) and all sessions with $\text{𝐶𝑉}>1.2$ as ‘inactive’ ($n=9$), see Figure 1D. This was used only for illustration purposes. In addition, throughout the paper, we will use one example active and one example inactive sessions for illustration purposes.

Mean evoked activity

We begin with analyzing evoked activity averaged across all neurons within a session. Figure 2A shows mean evoked activity for an exemplary inactive session, and Figure 2B shows evoked responses additionally averaged across all inactive sessions. We see that the magnitude of the neural response strongly depends on the presented stimulus: loud stimuli evoke stronger responses than silent stimuli, and contralateral stimuli evoke stronger responses than ipsilateral stimuli. The same responses averaged over the whole 150 ms of stimulus duration are shown in Figure 2C. This ‘tuning curve’ clearly shows contralateral as well as loud preference. The same effect is observed in the ‘onset’ response (20–40 ms, small dots), perhaps even stronger. We observed that an increase in overall stimulus intensity (ABL) leads to the increased slope of the ILD tuning: for ABLs 20, 40, and 60 dB, the absolute value of the slope of firing rate regressed on ILD increased from 0.012 to 0.018 to 0.028 (and from 0.022 to 0.026 to 0.048 for onset responses). This effect of overall stimulus intensity (ABL) as a modulation of the gain of the tuning to ILD is reminiscent of the effect of visual contrast on, for example orientation tuning (Skottun et al., 1987). Note, however, that the effect shown in Figure 2C is at the level of the population-averaged tuning curve. We address gain modulation at the level of single neurons below.

Figure 2 with 2 supplements see all

Download asset Open asset

In the active state the picture is different (Figure 2D–F). Here, the responses are similar and strongly overlap without a pronounced monotonic ILD or ABL tuning. Especially close to the midline, which is the most critical stimulus region where behavioral accuracy is the highest (Heffner and Heffner, 1988; Recanzone et al., 1998; Recanzone and Beckerman, 2004), the tuning curve displays very weak contralateral tuning and is approximately flat, meaning that all stimuli evoke roughly the same neural response (number of spikes) in the auditory cortex of a single hemisphere.

To quantify this effect on a session-by-session basis, we computed the ratio of the mean response (mean across neurons and across 150 ms) evoked by the loudest, most contralateral stimulus (large blue circle in Figure 2C,F) and that evoked by the faintest, most ipsilateral stimulus (small orange circle). This ratio was positively correlated with CV with $r=0.74$ (Figure 2G, $p=0.00005$), being close to one in the most active sessions and reaching almost five in the most inactive one.

In the above analysis, we averaged the responses over all trials with the same stimulus. However, in the inactive state any given stimulus will sometimes occur during a down state and sometimes during an up state. Conditioning the analysis on these two situations showed that responses to stimuli arriving during down-states are more similar to the unconditioned responses shown above. However, the responses to stimuli arriving during up-states are still different from those in the active state, particularly in the early onset response. While onset responses in the active state show no clear ILD tuning (Figure 2F), onset responses to sounds arriving during up-states show a clear preference for contralateral ILDs (Figure 2—figure supplement 1). Given that the difference between responses in the active and inactive states persists when only responses during up-states are considered (see also Pachitariu et al., 2015), we will not be conditioning on the phase of the slow oscillation in subsequent analyses.

Evoked activity of single neurons

The small and unspecific population-averaged responses in the active state could result from a generic lack of tuning of single neurons. Alternatively, single neurons during the active state could be strongly tuned, but with heterogeneous preferences, leading to unspecific population-averaged responses. To distinguish between these two possibilities, we examined the tuning of single cells to ILD and ABL.

As typical in the cortex, the tuning of single neurons was highly diverse. A snapshot of this diversity is shown in Figure 2—figure supplement 2, where we plot the tuning curves for the 50 neurons with highest activity in our exemplary recordings of active and inactive states. To summarize the tuning of each single neuron, we regressed its mean firing rate in each condition (computed in the 150 ms window of stimulus presentation and averaged across trials) on the ABL and ILD values. For each neuron, mean firing rates were $z$-scored before the regression, so that the regression coefficients were not affected by high/low overall firing rate and only quantified the strength of linear tuning (see Figure 3—figure supplement 1 for the same analysis without $z$-scoring). ABL values (possible values: 20, 40, and 60) were centered by subtracting 40. For each neuron, the model takes the following form:

(1) ${\displaystyle z\text{-score}(\text{Mean}\text{firing}\text{rate})={\beta }_0+{\beta }_{\mathrm{I}\mathrm{L}\mathrm{D}}\cdot \mathrm{I}\mathrm{L}\mathrm{D}+{\beta }_{\mathrm{A}\mathrm{B}\mathrm{L}}\cdot (\mathrm{A}\mathrm{B}\mathrm{L}-40)+{\beta }_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}\cdot (\mathrm{A}\mathrm{B}\mathrm{L}-40)\cdot \mathrm{I}\mathrm{L}\mathrm{D}+\epsilon .}$

Approximately linear ILD tuning near the midline is expected given previous characterizations (Stecker et al., 2005; Yao et al., 2013). The interaction term can account for the effects of gain modulation that we described above at the level of the population-averaged response. Note that both ILD and ABL (after subtracting 40) are centered and the $3\times 12$ design is balanced; it follows that all three linear terms in this model are estimated independently (i.e. each of them corresponds to the value that one would obtain using uni-variate linear regression), and the presence of the interaction term does not influence ${\beta }_{\mathrm{ILD}}$ and ${\beta }_{\mathrm{ABL}}$.

Of course, this simple model cannot fully represent the complexity of neural tuning, but it provides a first approximation sufficient to reveal strong differences in tuning between brain states. The quality of the model fit was roughly the same in the inactive and the active states ($R^2=0.36\pm 0.24$ and $0.34\pm 0.22$ correspondingly, mean ± SD across all neurons in all active and all inactive sessions). In both states, around one half of the neurons showed significant linear tuning with overall $p<0.01$ (53.5%, 489/914, in the inactive sessions and 49.5%, 154/311, in the active sessions).

We first focused on the way neurons are separately tuned to ILD and ABL, by examining the distribution of coefficients ${\beta }_{\mathrm{ILD}}$ and ${\beta }_{\mathrm{ABL}}$ across the population. Figure 3A shows these coefficients for each neuron in an exemplary inactive session, with ${\beta }_{\mathrm{ILD}}$ on the horizontal and ${\beta }_{\mathrm{ABL}}$ on the vertical axis. Only neurons with significant ($p<0.01$) tuning are shown here; Figure 3—figure supplement 2 presents the same analysis with all neurons. Most neurons are located in the upper-left quadrant with negative ${\beta }_{\mathrm{ILD}}$ and positive ${\beta }_{\mathrm{ABL}}$, meaning that they are tuned to the loud contralateral sounds. Figure 3B pools neurons from nine inactive sessions and Figure 3C shows the corresponding angular histogram, both supporting the same conclusion. This is consistent with previous work showing a preference for contralateral sounds in the auditory cortex (Stecker et al., 2005; Campbell et al., 2006; Yao et al., 2013).

Figure 3 with 5 supplements see all

Download asset Open asset

In the active state the situation is again different (Figure 3D–F). The distribution of linear coefficients is roughly symmetric with respect to the horizontal and the vertical axes. As we go around the clock in Figure 3D, we see neurons preferring loud, then ipsilateral, then faint, then contralateral sounds (insets show tuning curves of eight exemplary neurons using the same format as in Figure 2C,F). Separate analysis of the onset (0–50 ms) and the late (100–150 ms) responses revealed that this strong tuning heterogeneity was already present in the onset responses (Figure 3—figure supplement 3), even though there was some contralateral and loud bias in the early responses. Interestingly, in the active state more neurons were significantly tuned in the late response compared to the early response (41.8% vs. 23.1%, Figure 3—figure supplement 3).

This tuning heterogeneity was not explained by the physical location of the neurons in the tissue: it persisted within individual shanks of our recording probes (8 shanks spaced 200 μm apart; Figure 3—figure supplement 4). Also, the surprising preference for ipsilateral and faint sounds was not explained by the inhibitory contralateral responses: many ipsilateral neurons had evoked responses well above their baseline (insets in Figure 3D, see also Figure 2—figure supplement 2).

These observations provide an explanation for the population PSTHs in Figure 2. In the inactive state, most neurons are similarly tuned, leading to the loud contralateral preference of the average. In the active state, the neural tuning is diverse and, when averaging across neurons, individual differences get averaged out. Across sessions, the fraction of significantly tuned neurons with contralateral preference is positively correlated with CV ($r=0.70$, $p=0.0002$, Figure 3G), and so is the fraction of neurons with loud preference ($r=0.71$, $p=0.0002$, Figure 3H).

Inspection of the regression coefficients ${\beta }_{\text{𝑖𝑛𝑡𝑒𝑟}}$ of the $\text{𝐼𝐿𝐷}\cdot \text{𝐴𝐵𝐿}$ interaction term revealed that the degree of gain modulation across the population is also state-dependent (Figure 3—figure supplement 5). One might expect that loud sounds should make ipsilateral cells more ipisilateral, and contralateral cells more contralateral, which would imply a positive correlation between the coefficients ${\beta }_{\text{𝐼𝐿𝐷}}$ and ${\beta }_{\text{𝑖𝑛𝑡𝑒𝑟}}$. Scatter plots of these two coefficients across cells show a much stronger correlation in the inactive than in the active state. Figure 3I shows the fraction of significantly tuned neurons in the first and third quadrants of this scatter plot as a function of CV. This fraction is positively correlated with CV ($r=0.66$, $p=0.0006$, Figure 3I). Thus, in the inactive state ABL increases the gain of the tuning of single neurons to ILD, consistent with Figure 2C. In the active state, on the other hand, the fraction is approximately 0.5, consistent with an idiosyncratic effect of ABL on ILD tuning. This means that, while ABL might change the tuning to ILD for single neurons, the nature of this change is, across neurons, not consistent with the standard notion of gain modulation.

Signal and noise correlation matrices

We now turn to the structure and state-dependence of the evoked activity at the population level, which is the main focus of this study.

The regions in firing rate space spanned by the sensory stimuli and those occupied by trial-to-trial variability can be estimated through the eigendecomposition of the signal and noise correlation matrices, respectively (Figure 4). In each session, both matrices are of size $p\times p$ where $p$ is the number of recorded neurons. A signal correlation matrix contains correlations between ‘tuning curves’ of all pairs of neurons (i.e. correlations are computed across trial-averaged responses for $n=36$ stimuli). An element $(i,j)$ of this matrix is the similarity between the tuning of neurons $i$ and $j$. A noise correlation matrix contains correlations between trial-to-trial fluctuations for all pairs of neurons (here we pool the trials from all stimuli and compute correlations across all $n=36\cdot 100$ single trial responses after subtraction of the corresponding mean responses). An element $(i,j)$ of this matrix is the similarity between trial-to-trial fluctuations between neurons $i$ and $j$.

Figure 4

Download asset Open asset

Consider the signal correlation matrices for one exemplary inactive and one exemplary active session shown in Figure 4A–B. The neurons are sorted (from up/left to bottom/right) according to the value of ${\beta }_{\mathrm{ILD}}$ from Figure 3A,D. In the inactive state, there is a group of similar neurons with contralateral preference, and the remaining neurons do not seem to show any similarity. On the other hand, in the active state there are neurons with similar contralateral preference but also neurons with similar ipsilateral preference. The tuning of these two sets of neurons is anti-correlated.

For the signal correlation matrix in each session, we can compute: (a) the mean correlation, (b) the fraction of variance explained by the first principal component (i.e. ${\lambda }_{\text{𝑚𝑎𝑥}}/p$, where ${\lambda }_{\text{𝑚𝑎𝑥}}$ is the largest eigenvalue), and (c) the dimensionality. Here, ‘dimensionality’ refers to the number of significant principal components (out of the total number of 36 PCs). We estimated the dimensionality using Monte Carlo permutations to obtain the distribution of eigenvalues under the assumption of uncorrelated neurons (see Materials and methods). We found that all these three measures were correlated with CV: the more inactive the cortical state, the larger the signal correlations, the larger the first eigenvalue, and the smaller the dimensionality (Figure 4C–E). All these effects point to the same underlying phenomenon: as the state progresses from active to inactive, signal correlation matrix ‘simplifies’ as all neurons become similarly tuned. An alternative analysis using unbiased estimates of the signal correlation matrices yielded the same conclusions (see Materials and methods).

The same analysis for the noise correlation matrices is shown in Figure 4F–J. Consistent with previous reports (Goard and Dan, 2009; Renart et al., 2010; Ecker et al., 2010; Pachitariu et al., 2015; Beaman et al., 2017), we found that the mean pairwise correlation in the active state was around zero (Figure 4F) but reached $\sim \mathrm{\hspace{0.17em}0.1}$ in the most inactive sessions. The reason for this is well understood (Renart et al., 2010; Ecker et al., 2014; Okun et al., 2015): up-down fluctuations in the inactive state (Figure 1A) induce positive correlations between most neurons. Going beyond pairwise analysis, we again see that, with increasing CV, the dimensionality of the noise subspace decreases, while the first eigenvalue of the correlation matrix increases (Figure 4I–J). In the active state, the fraction of variance explained by the first PC was not much bigger than $1/p$ (Figure 4I), suggesting that the shape of the noise subspace in the active state was approximately (although not perfectly) spherical. Nonetheless, the number of trials in our dataset provided us with enough power to find a large number of significant noise PCs even during the most active states (Figure 4J).

Geometry of the population activity

We saw that both the signal and the noise correlation matrices get similarly re-structured when CV is increasing. To explore how these two processes influence the overall population geometry, we consider $p$-dimensional space where each recorded neuron corresponds to one dimension (Figure 5A). The state when all neurons are silent corresponds to the origin of coordinates. Evoked activity in every single trial can be thought of as one point in this space. For each stimulus, there is a ‘cloud’ of 100 points centered at the mean response. Overall, we have 36 such clouds.

Figure 5 with 1 supplement see all

Download asset Open asset

We use principal component analysis (PCA) to define a two-dimensional signal plane that approximately goes through the 36 mean stimulus responses (cloud centers). To do this, we compute an ILD axis as the PC1 direction of the 12 mean stimulus responses after averaging over ABL, and similarly compute an ABL axis as the PC1 direction of the three mean stimulus responses after averaging over ILD. These two axes span a plane, which we define as the signal plane. In our data, this plane is usually very close to the plane spanned by PC1 and PC2 of all 36 mean stimulus responses, but we prefer to use the ILD axis and the ABL axis because it gives an opportunity to explore the relationship between the two.

Figure 5B shows the projection of all single trials onto the signal plane in the exemplary inactive session. The loud contralateral stimulus is prominently removed from the rest, corresponding to the single neuron tuning we saw above. At the same time, not much of the ipsilateral tuning can be seen. The same plot for the example active session is shown in Figure 5C and is strikingly different. Here, the stimuli locations closely resemble the grid structure of the used stimuli (cf. Figure 1C). The ABL and the ILD axes are nearly orthogonal, unlike in Figure 5B.

We systematically assessed how the organization of the code changes as a function of state by computing the angle between several salient axes in firing rate space and by evaluating the dependence of these angles on CV. When interpreting these results, one should keep in mind that, because of the large dimensionality of the space (equal to the number of neurons in a particular recording), random vectors will be close to orthogonal. Angles of approximately 90° should thus be expected if all axes were randomly oriented. Using this approach, we found that, across all sessions, the angle between the ILD and the ABL axes is negatively correlated with CV ($r=-0.57$, $p=0.004$; Figure 5D).

Another important axis in the population representation is the dominant noise axis, which we define as the direction in which the clouds are most stretched (Figure 5A). We find it by doing PCA on the pooled noise data (i.e. on all 3600 single-trial points after subtracting the corresponding stimulus means). The orientation of the noise axis relative to the signal plane can show how much the noise interferes with the stimulus representation. Across sessions, the angle between the noise axis and the signal plane is negatively correlated with CV ($r=-0.46$, $p=0.03$; Figure 5E), reflecting a significant overlap between the signal and noise subspaces in the inactive, but not in the active, state. If we analyze the angles between the noise axis and the ILD and ABL axes separately, both are negatively correlated with CV ($r=-0.42$ and $-0.39$). Given that the noise subspace is approximately spherical in the active state (Figure 4I), the direction of the principal noise axis is expected to be effectively random in this state, and thus close to orthogonal to the signal plane, as we observe.

We also explored the relationship between the signal and noise subspaces and the ‘global’ direction, which we define as going from the center of coordinates to the grand mean of all single-trial responses (Figure 5A). This is approximately the direction along which the population fluctuates during up-down transitions. The angle between the noise axis and the global axis is also negatively correlated with CV ($r=-0.64$, $p=0.001$; Figure 5F). In the active state, they are close to orthogonal, but in the inactive state up-down fluctuations become the dominant mode of the noise in the evoked responses. The angle between the signal plane and the global axis is negatively correlated with CV as well ($r=-0.67$, $p=0.0005$; Figure 5G), and this remains true for ILD and ABL axes separately ($r=-0.61$ and $-0.61$). This shows that, in the active state, different stimuli evoke approximately the same number of spikes from the population as a whole, whereas in the inactive state different stimuli evoke different numbers of spikes from the population.

We get very similar results if instead of PCA we use demixed PCA (dPCA) that we have previously developed (Kobak et al., 2016) to define ABL and ILD axes (with dPCA, the four correlation coefficients in Figure 5D–G differed at most by 0.01; see Materials and methods). For the main analysis, we chose PCA for the reason of simplicity. Also, repeating the analysis shown in Figure 5D–G using only the early onset responses (0–50 ms instead of 0–150 ms) led to similar conclusions (Figure 5—figure supplement 1) with only ABL/ILD angle becoming somewhat less correlated with the CV.

In summary, we saw that the evoked activity in the rat auditory cortex in the inactive state is squeezed along the global axis. However, in the active state all relevant subspaces become close to orthogonal to each other: ABL encoding is nearly orthogonal to the ILD encoding, both of them are nearly orthogonal to the global axis (due to the diversity in tuning across neurons), and the noise axis (as expected from the approximately spherical shape of the noise subspace) is nearly orthogonal to ILD, ABL and global axis. We can see this more directly using a 3D animation (Video 1), where the shown three-dimensional subspace is spanned by the signal plane and the global axis. Note that the dominant noise dimension cannot be fully shown because there is only space for three axes in a 3D animation.

Video 1

Download asset

Decoding analysis

How do the state-dependent changes of the population geometry described above influence the amount of information about the stimulus carried by the evoked activity? We can use the decoding of stimulus identity from the population activity to answer this question.

For each session, we trained a binary classifier (decoder) to predict the sign of ILD from neural activity. We chose ILD sign because this allows us to compare the performance of the classifier with the behavioral performance of animals classifying sounds according to ILD (Pardo-Vazquez et al., 2018). Furthermore, behavioral studies suggest that ILD discrimination with respect to the midline is more relevant than the estimation of arbitrary ILDs (Heffner and Heffner, 1988; Recanzone et al., 1998; Recanzone and Beckerman, 2004), consistent with the observation that tuning with respect to ILD generally displays a high slope, rather than a peak, at the midline (Stecker et al., 2005; Yao et al., 2013). We used logistic regression regularized with elastic net and employed nested cross-validation to compute all performance estimates (see Materials and methods). The classifier was trained on trials pooled across all ABLs.

Figure 6B shows ‘population neurometric curves’: classifier performance for each ABL and ILD, averaged over inactive sessions. Individual sessions often yielded noisy curves, but the averages can be very accurately fit with logistic functions. The performance clearly decreases and becomes biased (asymmetric) with decreasing ABL. Because neurons in the inactive state prefer loud contralateral sounds, the overall number of spikes evoked by the population increases with increasing ABL for negative (contralateral) ILDs. The decoder classifies trials with many spikes as contralateral, and so its performance for negative ILDs degrades with decreasing ABL. For positive (ipsilateral) ILDs, there are almost no spikes, which the decoder reliably and correctly classifies as ipsilateral for all ABLs.

Figure 6 with 2 supplements see all

Download asset Open asset

Each logistic curve can be conveniently summarized with a ‘just noticeable difference’ (JND): horizontal distance between points with 75% performance on each side. JND was equal to 9.1 for ABL = 20 dB, to 8.5 for ABL = 40 dB, and to 5.5 for ABL = 60 dB.

Figure 6B shows the same analysis for the active sessions. Here, the neurometric curves for three ABLs strongly overlap, are approximately symmetric, and display little bias. JND ranges from 2.5 to 3.4 which is similar to behavioral values measured in other species (Scott et al., 2007; Keating et al., 2013). We have recently studied ILD discrimination in rats using a subset of stimuli used here with ILDs between ±6 dB (Pardo-Vazquez et al., 2018). The average JND of rats was 2.2 dB, thus just slightly smaller than the decoded JND in the active state. Comparisons between behavioral discrimination accuracy and the discrimination accuracy of a decoder from a neural population, however, should be interpreted carefully, as the latter quantity can depend on the number of recorded neurons or time window of analysis. Indeed, we found that the classification accuracy increased with the number of neurons and did not saturate when using all available neurons, either in the active or inactive state (Figure 6—figure supplement 1). We also found that the accuracy increased with the length of the spike count window and did not saturate at 150 ms in the active state. In the inactive state, it did tend to saturate at ~50 ms, converging to an ABL-dependent value (Figure 6—figure supplement 1).

To quantify classifier performance across ILDs in each session and for each ABL, we computed the average (integral) classification accuracy for all ILDs from −20 to +20 according to the logistic fit (see Materials and methods). Figure 6C–E shows these average accuracies for every session and for every ABL. For each ABL, the average accuracy dropped with increasing CV. We summarized the average accuracies using a simple linear model

(2) $\text{𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦}=\left(a+b\cdot \text{𝐴𝐵𝐿}\right)+\left(c+d\cdot \text{𝐴𝐵𝐿}\right)\cdot \text{𝐶𝑉}+\epsilon ,$

which was preferred by both AIC and BIC over three independent regressions, one for each ABL (BIC = −327 vs. −320). Linear fits for three ABLs intersected at $\text{𝐶𝑉}\approx 0.3$, indicating that in the active state there was no difference in performance between ABLs. In recordings of the inactive state, on the other hand, the difference between ABLs was pronounced, in agreement with Figure 6A–B.

In the above analysis, we used one common classifier for all ABLs in a given session. If instead we train three separate classifiers per session, then the performance increases but only slightly: Figure 6F shows the comparison of linear fits for the ‘common’ and ‘ABL-specialized’ classifiers. The difference is absent in the active state, meaning that the sign of ILD can be classified with an ABL-invariant decoder. In the inactive state, the difference was 0.019 ± 0.023 (mean ± SD across nine inactive sessions and 3 ABLs), a small but statistically significant difference ($p=0.0004$, Wilcoxon sign-rank test).

In the previous sections, we saw that the inactive state is characterized by different neural tuning and by different noise structure. How much of the classification performance decrease can be attributed to each of these two factors? To address this question, we employed a previously suggested shuffling approach (Averbeck et al., 2006). We randomly permuted all the trials within each stimulus, separately for each neuron; this procedure effectively sets all noise correlations to zero while preserving the mean responses. After that we ran the same decoding analysis as above (with a single, common decoder for all ABLs), and averaged the results across random shuffles. Figure 6G shows the comparison of linear fits for the shuffled and non-shuffled cases. The difference was absent in the active state, while performance increased after shuffling in the inactive state (0.025 ± 0.028, $p=0.0004$). In other words, the noise correlations in the inactive state impair the accuracy of the code, consistent with our observations above that the noise subspace is aligned with the stimulus subspace in the inactive state.

This finding does not necessarily imply that the presence of noise correlations affects the optimal decoding strategy, as has been pointed out before (Averbeck et al., 2006). To check this, we performed trial shuffling only on the training sets, while preserving the testing sets intact (Averbeck et al., 2006). Figure 6H shows the comparison of linear fits for the shuffled and non-shuffled cases. Once more, the difference was absent in the active state, but performance noticeably decreased in the inactive state (−0.050 ± 0.047, $p=0.0003$). These analyses suggest that, while the signal and noise subspaces display a significant degree of collinearity in the inactive state, they are still not fully aligned.

Decoding performance in the inactive state after shuffling remains clearly worse than performance in the active state (Figure 6G), suggesting that tuning curve reorganization also contributes strongly to the state-dependence of ILD discrimination. The fact that many neurons in the active state, but not in the inactive state, are tuned to ipsilateral ILDs, raises the question of whether this increased discrimination ability is simply due to an ability to represent ipsilateral sounds in the active state. To address this question, we assessed the accuracy of ILD estimation (as opposed to discrimination with respect to the midline) separately for ipsi- and contralateral sounds across states. This analysis revealed that estimation accuracy still degrades with increasing CV for both ipsi- as well as contralateral ILDs, even when they are considered separately (Figure 6—figure supplement 2).

We have described the state-dependence of population activity in the rat auditory cortex at three different levels: the average population response, the responses of single neurons, and the geometrical structure of the high-dimensional population responses. Our stimulus set was two-dimensional, with one dimension, ABL, varying along a prothetic continuum (different stimulus intensity), and the other, ILD, varying along a metathetic one (different lateralization at constant intensity). One can expect that the intensity of the neural population response reflects the intensity of the stimulus; at the same time, the intensity of population activity is strongly affected by the brain state, with inactive states causing global up-down fluctuations of this intensity. Thus, our stimulus set is particularly useful to explore the state-dependence of the representation of intensity, and of the effect of intensity on other tuning dimensions (typically described as changes in gain). Both these issues have so far remained largely unexplored. That said, our stimulus set is still low-dimensional, preventing us from studying the state-dependence of the geometrical structure of high-dimensional stimulus spaces such as natural images or sounds (Stringer et al., 2018). Nevertheless, Pachitariu et al. (2015) also found more accurate representations of natural sounds in the desynchronized state.

The full MATLAB code for the analysis is located at https://github.com/dkobak/a1geometry (copy archived at https://github.com/elifesciences-publications/a1geometry). We made the spike count data (spike counts for each neuron for each stimulus presentation from −50 ms to 150 ms in 50 ms bins) available in the same repository. This allows most of our figures to be reproduced. The complete dataset that was collected, including spike time data not analysed here, is available upon reasonable request to the corresponding author.

1. 1. Abbott LF
   2. Dayan P

   (1999) The effect of correlated variability on the accuracy of a population code

   Neural Computation 11:91–101.

   https://doi.org/10.1162/089976699300016827

   • PubMed
   • Google Scholar
2. 1. Aitkin L

   (1991) Rate-level functions of neurons in the inferior colliculus of cats measured with the use of free-field sound stimuli

   Journal of Neurophysiology 65:383–392.

   https://doi.org/10.1152/jn.1991.65.2.383

   • PubMed
   • Google Scholar
3. 1. Averbeck BB
   2. Latham PE
   3. Pouget A

   (2006) Neural correlations, population coding and computation

   Nature Reviews Neuroscience 7:358–366.

   https://doi.org/10.1038/nrn1888

   • PubMed
   • Google Scholar
4. 1. Battaglia FP
   2. Sutherland GR
   3. McNaughton BL

   (2004) Hippocampal sharp wave bursts coincide with neocortical "up-state" transitions

   Learning & Memory 11:697–704.

   https://doi.org/10.1101/lm.73504

   • Google Scholar
5. 1. Bazhenov M
   2. Timofeev I
   3. Steriade M
   4. Sejnowski TJ

   (2002) Model of thalamocortical slow-wave sleep oscillations and transitions to activated states

   The Journal of Neuroscience 22:8691–8704.

   https://doi.org/10.1523/JNEUROSCI.22-19-08691.2002

   • PubMed
   • Google Scholar
6. 1. Beaman CB
   2. Eagleman SL
   3. Dragoi V

   (2017) Sensory coding accuracy and perceptual performance are improved during the desynchronized cortical state

   Nature Communications 8:.

   https://doi.org/10.1038/s41467-017-01030-4

   • PubMed
   • Google Scholar
7. 1. Berger H

   (1929) Über das elektrenkephalogramm des menschen

   Archiv Für Psychiatrie Und Nervenkrankheiten 87:527–570.

   https://doi.org/10.1007/BF01797193

   • Google Scholar
8. 1. Bethge M
   2. Rotermund D
   3. Pawelzik K

   (2002) Optimal short-term population coding: when Fisher information fails

   Neural Computation 14:2317–2351.

   https://doi.org/10.1162/08997660260293247

   • PubMed
   • Google Scholar
9. 1. Brunton BW
   2. Botvinick MM
   3. Brody CD

   (2013) Rats and humans can optimally accumulate evidence for decision-making

   Science 340:95–98.

   https://doi.org/10.1126/science.1233912

   • PubMed
   • Google Scholar
10. 1. Campbell RA
    2. Schnupp JW
    3. Shial A
    4. King AJ

    (2006) Binaural-level functions in ferret auditory cortex: evidence for a continuous distribution of response properties

    Journal of Neurophysiology 95:3742–3755.

    https://doi.org/10.1152/jn.01155.2005

    • PubMed
    • Google Scholar
11. 1. Castro-Alamancos MA

    (2004) Absence of rapid sensory adaptation in neocortex during information processing states

    Neuron 41:455–464.

    https://doi.org/10.1016/S0896-6273(03)00853-5

    • PubMed
    • Google Scholar
12. 1. Chen N
    2. Sugihara H
    3. Sur M

    (2015) An acetylcholine-activated microcircuit drives temporal dynamics of cortical activity

    Nature Neuroscience 18:892–902.

    https://doi.org/10.1038/nn.4002

    • PubMed
    • Google Scholar
13. 1. Clement EA
    2. Richard A
    3. Thwaites M
    4. Ailon J
    5. Peters S
    6. Dickson CT

    (2008) Cyclic and sleep-like spontaneous alternations of brain state under urethane anaesthesia

    PLOS ONE 3:e2004.

    https://doi.org/10.1371/journal.pone.0002004

    • PubMed
    • Google Scholar
14. 1. Cohen MR
    2. Kohn A

    (2011) Measuring and interpreting neuronal correlations

    Nature Neuroscience 14:811–819.

    https://doi.org/10.1038/nn.2842

    • Google Scholar
15. 1. Cohen MR
    2. Maunsell JH

    (2009) Attention improves performance primarily by reducing interneuronal correlations

    Nature Neuroscience 12:1594–1600.

    https://doi.org/10.1038/nn.2439

    • PubMed
    • Google Scholar
16. 1. Compte A
    2. Sanchez-Vives MV
    3. McCormick DA
    4. Wang XJ

    (2003) Cellular and network mechanisms of slow oscillatory activity (<1 hz) and wave propagations in a cortical network model

    Journal of Neurophysiology 89:2707–2725.

    https://doi.org/10.1152/jn.00845.2002

    • PubMed
    • Google Scholar
17. 1. Constantinople CM
    2. Bruno RM

    (2011) Effects and mechanisms of wakefulness on local cortical networks

    Neuron 69:1061–1068.

    https://doi.org/10.1016/j.neuron.2011.02.040

    • PubMed
    • Google Scholar
18. 1. Curto C
    2. Sakata S
    3. Marguet S
    4. Itskov V
    5. Harris KD

    (2009) A simple model of cortical dynamics explains variability and state dependence of sensory responses in urethane-anesthetized auditory cortex

    Journal of Neuroscience 29:10600–10612.

    https://doi.org/10.1523/JNEUROSCI.2053-09.2009

    • PubMed
    • Google Scholar
19. 1. Davis KA
    2. Ding J
    3. Benson TE
    4. Voigt HF

    (1996) Response properties of units in the dorsal cochlear nucleus of unanesthetized decerebrate gerbil

    Journal of Neurophysiology 75:1411–1431.

    https://doi.org/10.1152/jn.1996.75.4.1411

    • PubMed
    • Google Scholar
20. 1. Destexhe A
    2. Rudolph M
    3. Paré D

    (2003) The high-conductance state of neocortical neurons in vivo

    Nature Reviews. Neuroscience 4:.

    https://doi.org/10.1038/nrn1198

    • PubMed
    • Google Scholar
21. 1. DiCarlo JJ
    2. Cox DD

    (2007) Untangling invariant object recognition

    Trends in Cognitive Sciences 11:333–341.

    https://doi.org/10.1016/j.tics.2007.06.010

    • PubMed
    • Google Scholar
22. 1. Ecker AS
    2. Berens P
    3. Keliris GA
    4. Bethge M
    5. Logothetis NK
    6. Tolias AS

    (2010) Decorrelated neuronal firing in cortical microcircuits

    Science 327:584–587.

    https://doi.org/10.1126/science.1179867

    • PubMed
    • Google Scholar
23. 1. Ecker AS
    2. Berens P
    3. Tolias AS
    4. Bethge M

    (2011) The effect of noise correlations in populations of diversely tuned neurons

    Journal of Neuroscience 31:14272–14283.

    https://doi.org/10.1523/JNEUROSCI.2539-11.2011

    • PubMed
    • Google Scholar
24. 1. Ecker AS
    2. Berens P
    3. Cotton RJ
    4. Subramaniyan M
    5. Denfield GH
    6. Cadwell CR
    7. Smirnakis SM
    8. Bethge M
    9. Tolias AS

    (2014) State dependence of noise correlations in macaque primary visual cortex

    Neuron 82:235–248.

    https://doi.org/10.1016/j.neuron.2014.02.006

    • PubMed
    • Google Scholar
25. 1. Evans EF
    2. Whitfield IC

    (1964) Classification of unit responses in the auditory cortex of the unanaesthetized and unrestrained cat

    The Journal of Physiology 171:476–493.

    https://doi.org/10.1113/jphysiol.1964.sp007391

    • PubMed
    • Google Scholar
26. 1. Fanselow EE
    2. Nicolelis MA

    (1999) Behavioral modulation of tactile responses in the rat somatosensory system

    The Journal of Neuroscience 19:7603–7616.

    https://doi.org/10.1523/JNEUROSCI.19-17-07603.1999

    • PubMed
    • Google Scholar
27. 1. Friedman J
    2. Hastie T
    3. Tibshirani R

    (2010) Regularization paths for generalized linear models via coordinate descent

    Journal of Statistical Software 33:.

    https://doi.org/10.18637/jss.v033.i01

    • PubMed
    • Google Scholar
28. 1. Fu Y
    2. Tucciarone JM
    3. Espinosa JS
    4. Sheng N
    5. Darcy DP
    6. Nicoll RA
    7. Huang ZJ
    8. Stryker MP

    (2014) A cortical circuit for gain control by behavioral state

    Cell 156:1139–1152.

    https://doi.org/10.1016/j.cell.2014.01.050

    • PubMed
    • Google Scholar
29. 1. Gervasoni D
    2. Lin SC
    3. Ribeiro S
    4. Soares ES
    5. Pantoja J
    6. Nicolelis MA

    (2004) Global forebrain dynamics predict rat behavioral states and their transitions

    Journal of Neuroscience 24:11137–11147.

    https://doi.org/10.1523/JNEUROSCI.3524-04.2004

    • PubMed
    • Google Scholar
30. 1. Goard M
    2. Dan Y

    (2009) Basal forebrain activation enhances cortical coding of natural scenes

    Nature Neuroscience 12:1444–1449.

    https://doi.org/10.1038/nn.2402

    • PubMed
    • Google Scholar
31. 1. Gold JI
    2. Shadlen MN

    (2002)

    Banburismus and the brain: decoding the relationship between sensory stimuli, decisions, and reward

    Neuron 36:.

    • PubMed
    • Google Scholar
32. 1. Greenwood DD
    2. Maruyama N

    (1965) Excitatory and inhibitory response areas of auditory neurons in the cochlear nucleus

    Journal of Neurophysiology 28:863–892.

    https://doi.org/10.1152/jn.1965.28.5.863

    • PubMed
    • Google Scholar
33. 1. Harris KD
    2. Thiele A

    (2011) Cortical state and attention

    Nature Reviews Neuroscience 12:509–523.

    https://doi.org/10.1038/nrn3084

    • PubMed
    • Google Scholar
34. 1. Heffner RS
    2. Heffner HE

    (1988) Sound localization acuity in the cat: effect of azimuth, signal duration, and test procedure

    Hearing Research 36:221–232.

    https://doi.org/10.1016/0378-5955(88)90064-0

    • PubMed
    • Google Scholar
35. 1. Kanashiro T
    2. Ocker GK
    3. Cohen MR
    4. Doiron B

    (2017) Attentional modulation of neuronal variability in circuit models of cortex

    eLife 6:e23978.

    https://doi.org/10.7554/eLife.23978

    • PubMed
    • Google Scholar
36. 1. Keating P
    2. Nodal FR
    3. Gananandan K
    4. Schulz AL
    5. King AJ

    (2013) Behavioral sensitivity to broadband binaural localization cues in the ferret

    Journal of the Association for Research in Otolaryngology 14:561–572.

    https://doi.org/10.1007/s10162-013-0390-3

    • PubMed
    • Google Scholar
37. 1. Keating P
    2. Dahmen JC
    3. King AJ

    (2015) Complementary adaptive processes contribute to the developmental plasticity of spatial hearing

    Nature Neuroscience 18:185–187.

    https://doi.org/10.1038/nn.3914

    • PubMed
    • Google Scholar
38. 1. Kobak D
    2. Brendel W
    3. Constantinidis C
    4. Feierstein CE
    5. Kepecs A
    6. Mainen ZF
    7. Qi XL
    8. Romo R
    9. Uchida N
    10. Machens CK

    (2016) Demixed principal component analysis of neural population data

    eLife 5:e10989.

    https://doi.org/10.7554/eLife.10989

    • PubMed
    • Google Scholar
39. Software

    1. Kobak D

    (2019) Analysis code for 'State-dependent geometry of population activity in rat auditory cortex', version bcaa4a5

    GitHub.

    https://github.com/dkobak/a1geometry
40. 1. Kyweriga M
    2. Stewart W
    3. Wehr M

    (2014) Neuronal interaural level difference response shifts are level-dependent in the rat auditory cortex

    Journal of Neurophysiology 111:930–938.

    https://doi.org/10.1152/jn.00648.2013

    • PubMed
    • Google Scholar
41. 1. Latham PE
    2. Richmond BJ
    3. Nelson PG
    4. Nirenberg S

    (2000) Intrinsic dynamics in neuronal networks. I. theory

    Journal of Neurophysiology 83:808–827.

    https://doi.org/10.1152/jn.2000.83.2.808

    • PubMed
    • Google Scholar
42. 1. Lauer AM
    2. Slee SJ
    3. May BJ

    (2011) Acoustic basis of directional acuity in laboratory mice

    Journal of the Association for Research in Otolaryngology 12:633–645.

    https://doi.org/10.1007/s10162-011-0279-y

    • PubMed
    • Google Scholar
43. 1. Lee SH
    2. Dan Y

    (2012) Neuromodulation of brain states

    Neuron 76:209–222.

    https://doi.org/10.1016/j.neuron.2012.09.012

    • PubMed
    • Google Scholar
44. 1. Lui LL
    2. Mokri Y
    3. Reser DH
    4. Rosa MG
    5. Rajan R

    (2015) Responses of neurons in the marmoset primary auditory cortex to interaural level differences: comparison of pure tones and vocalizations

    Frontiers in Neuroscience 9:.

    https://doi.org/10.3389/fnins.2015.00132

    • PubMed
    • Google Scholar
45. Book

    1. Lydic R
    2. Baghdoyan HA

    (1998)

    Handbook of Behavioral State Control: Cellular and Molecular Mechanisms

    CRC Press.

    • Google Scholar
46. 1. Machens CK
    2. Romo R
    3. Brody CD

    (2005) Flexible control of mutual inhibition: a neural model of two-interval discrimination

    Science 307:1121–1124.

    https://doi.org/10.1126/science.1104171

    • PubMed
    • Google Scholar
47. 1. Malhotra S
    2. Stecker GC
    3. Middlebrooks JC
    4. Lomber SG

    (2008) Sound localization deficits during reversible deactivation of primary auditory cortex and/or the dorsal zone

    Journal of Neurophysiology 99:1628–1642.

    https://doi.org/10.1152/jn.01228.2007

    • PubMed
    • Google Scholar
48. 1. Malhotra S
    2. Lomber SG

    (2007) Sound localization during homotopic and heterotopic bilateral cooling deactivation of primary and nonprimary auditory cortical areas in the cat

    Journal of Neurophysiology 97:26–43.

    https://doi.org/10.1152/jn.00720.2006

    • PubMed
    • Google Scholar
49. 1. Marguet SL
    2. Harris KD

    (2011) State-dependent representation of amplitude-modulated noise stimuli in rat auditory cortex

    Journal of Neuroscience 31:6414–6420.

    https://doi.org/10.1523/JNEUROSCI.5773-10.2011

    • PubMed
    • Google Scholar
50. 1. McCormick DA
    2. McGinley MJ
    3. Salkoff DB

    (2015) Brain state dependent activity in the cortex and thalamus

    Current Opinion in Neurobiology 31:133–140.

    https://doi.org/10.1016/j.conb.2014.10.003

    • Google Scholar
51. 1. McGinley MJ
    2. David SV
    3. McCormick DA

    (2015a) Cortical membrane potential signature of optimal states for sensory signal detection

    Neuron 87:179–192.

    https://doi.org/10.1016/j.neuron.2015.05.038

    • PubMed
    • Google Scholar
52. 1. McGinley MJ
    2. Vinck M
    3. Reimer J
    4. Batista-Brito R
    5. Zagha E
    6. Cadwell CR
    7. Tolias AS
    8. Cardin JA
    9. McCormick DA

    (2015b) Waking state: rapid variations modulate neural and behavioral responses

    Neuron 87:1143–1161.

    https://doi.org/10.1016/j.neuron.2015.09.012

    • PubMed
    • Google Scholar
53. 1. Mochol G
    2. Hermoso-Mendizabal A
    3. Sakata S
    4. Harris KD
    5. de la Rocha J

    (2015) Stochastic transitions into silence cause noise correlations in cortical circuits

    PNAS 112:3529–3534.

    https://doi.org/10.1073/pnas.1410509112

    • PubMed
    • Google Scholar
54. 1. Montijn JS
    2. Meijer GT
    3. Lansink CS
    4. Pennartz CM

    (2016) Population-Level neural codes are robust to Single-Neuron variability from a multidimensional coding perspective

    Cell Reports 16:2486–2498.

    https://doi.org/10.1016/j.celrep.2016.07.065

    • PubMed
    • Google Scholar
55. Book

    1. Moore DR
    2. Fuchs PA
    3. Rees A
    4. Palmer A
    5. Plack CJ

    (2010)

    The Oxford Handbook of Auditory Science: The Auditory Brain

    Oxford University Press.

    • Google Scholar
56. 1. Moreno-Bote R
    2. Beck J
    3. Kanitscheider I
    4. Pitkow X
    5. Latham P
    6. Pouget A

    (2014) Information-limiting correlations

    Nature Neuroscience 17:1410–1417.

    https://doi.org/10.1038/nn.3807

    • PubMed
    • Google Scholar
57. 1. Murakami M
    2. Kashiwadani H
    3. Kirino Y
    4. Mori K

    (2005) State-dependent sensory gating in olfactory cortex

    Neuron 46:285–296.

    https://doi.org/10.1016/j.neuron.2005.02.025

    • PubMed
    • Google Scholar
58. 1. Nodal FR
    2. Bajo VM
    3. Parsons CH
    4. Schnupp JW
    5. King AJ

    (2008) Sound localization behavior in ferrets: comparison of acoustic orientation and approach-to-target responses

    Neuroscience 154:397–408.

    https://doi.org/10.1016/j.neuroscience.2007.12.022

    • PubMed
    • Google Scholar
59. 1. Ogawa T
    2. Riera J
    3. Goto T
    4. Sumiyoshi A
    5. Nonaka H
    6. Jerbi K
    7. Bertrand O
    8. Kawashima R

    (2011) Large-scale heterogeneous representation of sound attributes in rat primary auditory cortex: from unit activity to population dynamics

    Journal of Neuroscience 31:14639–14653.

    https://doi.org/10.1523/JNEUROSCI.0086-11.2011

    • PubMed
    • Google Scholar
60. 1. Okun M
    2. Steinmetz N
    3. Cossell L
    4. Iacaruso MF
    5. Ko H
    6. Barthó P
    7. Moore T
    8. Hofer SB
    9. Mrsic-Flogel TD
    10. Carandini M
    11. Harris KD

    (2015) Diverse coupling of neurons to populations in sensory cortex

    Nature 521:511–515.

    https://doi.org/10.1038/nature14273

    • PubMed
    • Google Scholar
61. 1. Pachitariu M
    2. Lyamzin DR
    3. Sahani M
    4. Lesica NA

    (2015) State-dependent population coding in primary auditory cortex

    Journal of Neuroscience 35:2058–2073.

    https://doi.org/10.1523/JNEUROSCI.3318-14.2015

    • PubMed
    • Google Scholar
62. 1. Pagan M
    2. Urban LS
    3. Wohl MP
    4. Rust NC

    (2013) Signals in inferotemporal and perirhinal cortex suggest an untangling of visual target information

    Nature Neuroscience 16:1132–1139.

    https://doi.org/10.1038/nn.3433

    • PubMed
    • Google Scholar
63. 1. Panzeri S
    2. Schultz SR
    3. Treves A
    4. Rolls ET

    (1999) Correlations and the encoding of information in the nervous system

    Proceedings of the Royal Society of London. Series B: Biological Sciences 266:1001–1012.

    https://doi.org/10.1098/rspb.1999.0736

    • Google Scholar
64. Preprint

    1. Pardo-Vazquez JL
    2. Castineiras J
    3. Valente M
    4. Costa T
    5. Renart A

    (2018) Weber’s law is the result of exact temporal accumulation of evidence

    bioRxiv.

    https://doi.org/10.1101/333559

    • Google Scholar
65. 1. Parga N
    2. Abbott LF

    (2007) Network model of spontaneous activity exhibiting synchronous transitions between up and down states

    Frontiers in Neuroscience 1:57–66.

    https://doi.org/10.3389/neuro.01.1.1.004.2007

    • PubMed
    • Google Scholar
66. 1. Park TJ
    2. Klug A
    3. Holinstat M
    4. Grothe B

    (2004) Interaural level difference processing in the lateral superior olive and the inferior colliculus

    Journal of Neurophysiology 92:289–301.

    https://doi.org/10.1152/jn.00961.2003

    • PubMed
    • Google Scholar
67. 1. Pfingst BE
    2. O'Connor TA

    (1981) Characteristics of neurons in auditory cortex of monkeys performing a simple auditory task

    Journal of Neurophysiology 45:16–34.

    https://doi.org/10.1152/jn.1981.45.1.16

    • PubMed
    • Google Scholar
68. 1. Polack P-O
    2. Friedman J
    3. Golshani P

    (2013) Cellular mechanisms of brain state–dependent gain modulation in visual cortex

    Nature Neuroscience 16:1331–1339.

    https://doi.org/10.1038/nn.3464

    • Google Scholar
69. 1. Poulet JF
    2. Fernandez LM
    3. Crochet S
    4. Petersen CC

    (2012) Thalamic control of cortical states

    Nature Neuroscience 15:370–372.

    https://doi.org/10.1038/nn.3035

    • PubMed
    • Google Scholar
70. 1. Poulet JF
    2. Petersen CC

    (2008) Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice

    Nature 454:881–885.

    https://doi.org/10.1038/nature07150

    • PubMed
    • Google Scholar
71. 1. Recanzone GH
    2. Makhamra SD
    3. Guard DC

    (1998) Comparison of relative and absolute sound localization ability in humans

    The Journal of the Acoustical Society of America 103:1085–1097.

    https://doi.org/10.1121/1.421222

    • PubMed
    • Google Scholar
72. 1. Recanzone GH
    2. Beckerman NS

    (2004) Effects of intensity and location on sound location discrimination in macaque monkeys

    Hearing Research 198:116–124.

    https://doi.org/10.1016/j.heares.2004.07.017

    • PubMed
    • Google Scholar
73. 1. Renart A
    2. de la Rocha J
    3. Bartho P
    4. Hollender L
    5. Parga N
    6. Reyes A
    7. Harris KD

    (2010) The asynchronous state in cortical circuits

    Science 327:587–590.

    https://doi.org/10.1126/science.1179850

    • PubMed
    • Google Scholar
74. 1. Rossant C
    2. Kadir SN
    3. Goodman DFM
    4. Schulman J
    5. Hunter MLD
    6. Saleem AB
    7. Grosmark A
    8. Belluscio M
    9. Denfield GH
    10. Ecker AS
    11. Tolias AS
    12. Solomon S
    13. Buzsaki G
    14. Carandini M
    15. Harris KD

    (2016) Spike sorting for large, dense electrode arrays

    Nature Neuroscience 19:634–641.

    https://doi.org/10.1038/nn.4268

    • PubMed
    • Google Scholar
75. Book

    1. Rust NC

    (2014)

    Population-Based Representations: From Implicit to Explicit

    In: Gazzaniga MS, Mangun GR, Blakemore SJ, Preuss TM, Baillargeon R, editors. The Cognitive Neurosciences. MIT Press. pp. 337–348.

    • Google Scholar
76. 1. Sadagopan S
    2. Wang X

    (2008) Level invariant representation of sounds by populations of neurons in primary auditory cortex

    Journal of Neuroscience 28:3415–3426.

    https://doi.org/10.1523/JNEUROSCI.2743-07.2008

    • PubMed
    • Google Scholar
77. 1. Sakata S
    2. Harris KD

    (2012) Laminar-dependent effects of cortical state on auditory cortical spontaneous activity

    Frontiers in Neural Circuits 6:.

    https://doi.org/10.3389/fncir.2012.00109

    • PubMed
    • Google Scholar
78. Conference

    1. Sanchez-Vives M
    2. Perez-Zabalza M
    3. Manrique J
    4. Reig R
    5. Winograd M
    6. Parga N

    (2010)

    Gabab modulation of emergent cortical rhythms: an experimental and computational study

    Annual Meeting of the Society for Neuroscience.

    • Google Scholar
79. 1. Sanchez-Vives MV
    2. McCormick DA

    (2000) Cellular and network mechanisms of rhythmic recurrent activity in neocortex

    Nature Neuroscience 3:1027–1034.

    https://doi.org/10.1038/79848

    • PubMed
    • Google Scholar
80. Book

    1. Schnupp J
    2. Nelken I
    3. King A

    (2011) Auditory Neuroscience: Making Sense of Sound

    MIT press.

    https://doi.org/10.7551/mitpress/7942.001.0001

    • Google Scholar
81. 1. Scott BH
    2. Malone BJ
    3. Semple MN

    (2007) Effect of behavioral context on representation of a spatial cue in core auditory cortex of awake macaques

    Journal of Neuroscience 27:6489–6499.

    https://doi.org/10.1523/JNEUROSCI.0016-07.2007

    • PubMed
    • Google Scholar
82. 1. Seung HS
    2. Sompolinsky H

    (1993) Simple models for reading neuronal population codes

    PNAS 90:10749–10753.

    https://doi.org/10.1073/pnas.90.22.10749

    • PubMed
    • Google Scholar
83. 1. Shamir M
    2. Sompolinsky H

    (2006) Implications of neuronal diversity on population coding

    Neural Computation 18:1951–1986.

    https://doi.org/10.1162/neco.2006.18.8.1951

    • PubMed
    • Google Scholar
84. 1. Skottun BC
    2. Bradley A
    3. Sclar G
    4. Ohzawa I
    5. Freeman RD

    (1987) The effects of contrast on visual orientation and spatial frequency discrimination: a comparison of single cells and behavior

    Journal of Neurophysiology 57:773–786.

    https://doi.org/10.1152/jn.1987.57.3.773

    • PubMed
    • Google Scholar
85. 1. Sompolinsky H
    2. Yoon H
    3. Kang K
    4. Shamir M

    (2001) Population coding in neuronal systems with correlated noise

    Physical Review E 64:.

    https://doi.org/10.1103/PhysRevE.64.051904

    • Google Scholar
86. 1. Stecker GC
    2. Harrington IA
    3. Middlebrooks JC

    (2005) Location coding by opponent neural populations in the auditory cortex

    PLOS Biology 3:e78.

    https://doi.org/10.1371/journal.pbio.0030078

    • PubMed
    • Google Scholar
87. 1. Stellmack MA
    2. Viemeister NF
    3. Byrne AJ

    (2004) Monaural and interaural intensity discrimination: level effects and the "binaural advantage"

    The Journal of the Acoustical Society of America 116:1149–1159.

    https://doi.org/10.1121/1.1763971

    • PubMed
    • Google Scholar
88. 1. Steriade M
    2. Gloor P
    3. Llinás RR
    4. Lopes da Silva FH
    5. Mesulam M-M

    (1990) Basic mechanisms of cerebral rhythmic activities

    Electroencephalography and Clinical Neurophysiology 76:481–508.

    https://doi.org/10.1016/0013-4694(90)90001-Z

    • Google Scholar
89. 1. Steriade M
    2. Nuñez A
    3. Amzica F

    (1993) A novel slow (< 1 hz) oscillation of neocortical neurons in vivo: depolarizing and hyperpolarizing components

    The Journal of Neuroscience 13:3252–3265.

    https://doi.org/10.1523/jneurosci.13-08-03252.1993

    • PubMed
    • Google Scholar
90. Book

    1. Steriade MM
    2. McCarley RW

    (2013)

    Brainstem Control of Wakefulness and Sleep

    Springer Science & Business Media.

    • Google Scholar
91. 1. Stevens SS

    (1957) On the psychophysical law

    Psychological Review 64:153–181.

    https://doi.org/10.1037/h0046162

    • PubMed
    • Google Scholar
92. 1. Stringer C
    2. Pachitariu M
    3. Steinmetz NA
    4. Okun M
    5. Bartho P
    6. Harris KD
    7. Sahani M
    8. Lesica NA

    (2016) Inhibitory control of correlated intrinsic variability in cortical networks

    eLife 5:e19695.

    https://doi.org/10.7554/eLife.19695

    • PubMed
    • Google Scholar
93. Preprint

    1. Stringer C
    2. Pachitariu M
    3. Steinmetz N
    4. Carandini M
    5. Harris KD

    (2018) High-dimensional geometry of population responses in visual cortex

    bioRxiv.

    https://doi.org/10.1101/374090

    • Google Scholar
94. 1. Thiele A
    2. Bellgrove MA

    (2018) Neuromodulation of attention

    Neuron 97:769–785.

    https://doi.org/10.1016/j.neuron.2018.01.008

    • PubMed
    • Google Scholar
95. 1. Tsai JJ
    2. Koka K
    3. Tollin DJ

    (2010) Varying overall sound intensity to the two ears impacts interaural level difference discrimination thresholds by single neurons in the lateral superior olive

    Journal of Neurophysiology 103:.

    https://doi.org/10.1152/jn.00911.2009

    • PubMed
    • Google Scholar
96. 1. Vanderwolf CH

    (1988) Cerebral activity and behavior: control by central cholinergic and serotonergic systems

    International Review of Neurobiology 30:225–340.

    https://doi.org/10.1016/s0074-7742(08)60050-1

    • PubMed
    • Google Scholar
97. Book

    1. Vanderwolf CH

    (2003)

    An Odyssey Through the Brain, Behavior and the Mind

    Springer Science & Business Media.

    • Google Scholar
98. 1. Wesolek CM
    2. Koay G
    3. Heffner RS
    4. Heffner HE

    (2010) Laboratory rats (Rattus norvegicus) do not use binaural phase differences to localize sound

    Hearing Research 265:54–62.

    https://doi.org/10.1016/j.heares.2010.02.011

    • PubMed
    • Google Scholar
99. 1. Wu S
    2. Nakahara H
    3. Amari S

    (2001) Population coding with correlation and an unfaithful model

    Neural Computation 13:775–797.

    https://doi.org/10.1162/089976601300014349

    • PubMed
    • Google Scholar
100. 1. Wu GK
     2. Li P
     3. Tao HW
     4. Zhang LI

     (2006) Nonmonotonic synaptic excitation and imbalanced inhibition underlying cortical intensity tuning

     Neuron 52:705–715.

     https://doi.org/10.1016/j.neuron.2006.10.009

     • PubMed
     • Google Scholar
101. 1. Yao JD
     2. Bremen P
     3. Middlebrooks JC

     (2013) Rat primary auditory cortex is tuned exclusively to the contralateral hemifield

     Journal of Neurophysiology 110:2140–2151.

     https://doi.org/10.1152/jn.00219.2013

     • PubMed
     • Google Scholar
102. 1. Young ED
     2. Brownell WE

     (1976) Responses to tones and noise of single cells in dorsal cochlear nucleus of unanesthetized cats

     Journal of Neurophysiology 39:282–300.

     https://doi.org/10.1152/jn.1976.39.2.282

     • Google Scholar
103. 1. Zagha E
     2. McCormick DA

     (2014) Neural control of brain state

     Current Opinion in Neurobiology 29:178–186.

     https://doi.org/10.1016/j.conb.2014.09.010

     • PubMed
     • Google Scholar
104. 1. Zhang K
     2. Sejnowski TJ

     (1999) Neuronal tuning: to sharpen or broaden?

     Neural Computation 11:75–84.

     https://doi.org/10.1162/089976699300016809

     • PubMed
     • Google Scholar

Author details

1. Dmitry Kobak

   1. Champalimaud Center for the Unknown, Lisbon, Portugal
   2. Institute for Ophthalmic Research, University of Tübingen, Tübingen, Germany

   Contribution

   Writing—original draft, Writing—review and editing, Designed and performed the data analysis

   Contributed equally with

   Jose L Pardo-Vazquez

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-5639-7209

2. Jose L Pardo-Vazquez

   1. Champalimaud Center for the Unknown, Lisbon, Portugal
   2. Neuroscience and Motor Control Group, University of A Coruña, Coruña, Spain

   Contribution

   Conceptualization, Writing—review and editing, Performed experiments

   Contributed equally with

   Dmitry Kobak

   For correspondence

   jose.pardovazquez@neuro.fchampalimaud.org

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-4623-2440

3. Mafalda Valente

   Champalimaud Center for the Unknown, Lisbon, Portugal

   Contribution

   Performed experiments

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1824-0462

4. Christian K Machens

   Champalimaud Center for the Unknown, Lisbon, Portugal

   Contribution

   Supervision, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1717-1562

5. Alfonso Renart

   Champalimaud Center for the Unknown, Lisbon, Portugal

   Contribution

   Conceptualization, Supervision, Writing—original draft, Writing—review and editing

   For correspondence

   alfonso.renart@neuro.fchampalimaud.org

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-7916-9930

• 2,706

  views

• 382

  downloads

• 15

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.