Author response: State-dependent geometry of population activity in rat auditory cortex
2019-04-01

Article Figures and data Abstract Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract The accuracy of the neural code depends on the relative embedding of signal and noise in the activity of neural populations. Despite a wealth of theoretical work on population codes, there are few empirical characterizations of the high-dimensional signal and noise subspaces. We studied the geometry of population codes in the rat auditory cortex across brain states along the activation-inactivation continuum, using sounds varying in difference and mean level across the ears. As the cortex becomes more activated, single-hemisphere populations go from preferring contralateral loud sounds to a symmetric preference across lateralizations and intensities, gain-modulation effectively disappears, and the signal and noise subspaces become approximately orthogonal to each other and to the direction corresponding to global activity modulations. Level-invariant decoding of sound lateralization also becomes possible in the active state. Our results provide an empirical foundation for the geometry and state-dependence of cortical population codes. https://doi.org/10.7554/eLife.44526.001 Introduction 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). Results 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 Population activity in rat auditory cortex during inactive and active states. (A) Exemplary raster plot of 20 s of spontaneous activity in an inactive state (N=141 neurons, sorted by firing rate). (B) Exemplary raster plot of 20 s of spontaneous activity in an active state (N=114 neurons, sorted by firing rate). (C) Stimulus set. The auditory stimuli used throughout this study consisted of brief broad-band (5–20 KHz) noise bursts. The colors represent ILD and the dot sizes represent ABL. This color/size code is maintained throughout our study. (D) Relationship between coefficient of variation (CV) of the total spike count and the fraction of down states across all recorded sessions. Green/orange dots correspond to sessions that we will use as ‘active sessions’ and ‘inactive sessions’ (as the two extremes of the activation-inactivation continuum) but state-dependence will always be assessed using all recordings by regressing various quantities of interest against CV. Black circles show two sessions used for raster plots in (A), (B). https://doi.org/10.7554/eLife.44526.002 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 CV<0.6 as ‘active’ (n=3) and all sessions with 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 Evoked activity in inactive and active states, averaged across neurons. (A) Exemplary inactive session. Each line is a population PSTH (peri-stimulus time histogram) corresponding to one stimulus (color coded as in Figure 1, line thickness corresponds to ABL). Population PSTHs were computed by averaging the Gaussian-smoothed (σ=5 ms) PSTHs of N=141 single neurons. (B) Mean of the population PSTHs across nine inactive sessions. (C) Average firing rate over 150 ms of stimulus duration for each stimulus, corresponding to panel B. Dots show the early response, defined as the average over 20–40 ms window. (D–F) The same for one exemplary and three overall active sessions. (G) The ratio of the evoked responses for the loudest, most contralateral stimuli and the most silent, most ipsilateral stimuli, computed for each session. Green dots are active sessions, orange dots are inactive sessions, black circles mark the two exemplary sessions used in (A) and (D). https://doi.org/10.7554/eLife.44526.003 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) z-score(Meanfiringrate)=β0+βILD⋅ILD+βABL⋅(ABL−40)+βinter⋅(ABL−40)⋅ILD+ε. 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 3×12 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 βILD and βABL. Of course, this model represent the of neural but it a to strong in tuning between brain states. The quality of the model was roughly the same in the inactive and the active states and mean ± across all neurons in all active and all inactive sessions). In both states, around one of the neurons showed linear tuning with overall in the inactive sessions and in the active sessions). We focused on the neurons are to ILD and by the distribution of coefficients βILD and across the Figure shows these coefficients for each in an exemplary inactive session, with βILD on the horizontal and on the vertical neurons with tuning are shown Figure 3—figure supplement 2 the same analysis with all neurons. neurons are in the with βILD and positive meaning that they are to the loud contralateral Figure neurons from nine inactive sessions and Figure shows the corresponding both the same This is with previous work a preference for contralateral sounds in the auditory cortex (Stecker et al., 2005; Campbell et al., 2006; Yao et al., 2013). Figure with supplements see all Download asset Open asset curves in inactive and active states. (A) neurons from one exemplary inactive session. The tuning of each was characterized with a linear model (see horizontal shows ILD coefficient and vertical shows ABL neurons with tuning are (B) neurons neurons with tuning out of from nine inactive sessions. values correspond to the average ± standard deviation across the neurons. (C) distribution of the neurons from panel (B). (D) neurons from one exemplary active session. show tuning curves of exemplary neurons. neurons neurons with tuning out of from three active sessions. distribution of the neurons from panel (G) of neurons with contralateral preference to the left of the in (A) and across sessions. Green dots are active sessions, orange dots are inactive sessions, black circles mark the two exemplary sessions used in (A) and (D). The same for the fraction of neurons with loud preference above the The same for the fraction of neurons with positive gain modulation (see In the active state the is different (Figure The distribution of linear coefficients is roughly symmetric with respect to the horizontal and the vertical As we go around the in Figure we see neurons preferring then then then contralateral sounds show tuning curves of exemplary neurons using the same as in Figure analysis of the onset ms) and the ms) responses that this strong tuning was in the onset responses (Figure 3—figure supplement even there was some contralateral and loud in the early responses. in the active state more neurons were in the response to the early response Figure 3—figure supplement This tuning was not by the location of the neurons in the it within of our probes Figure 3—figure supplement the preference for ipsilateral and sounds was not by the contralateral many ipsilateral neurons had evoked responses well above in Figure see also Figure 2—figure supplement These provide an for the population PSTHs in Figure In the inactive state, most neurons are tuned, leading to the loud contralateral preference of the In the active state, the neural tuning is when averaging across neurons, averaged sessions, the fraction of neurons with contralateral preference is positively correlated with CV Figure and so is the fraction of neurons with loud preference Figure of the regression coefficients of the interaction term that the degree of gain modulation across the population is also (Figure 3—figure supplement that loud sounds ipsilateral cells more and contralateral cells more which would a positive between the coefficients and plots of these two coefficients across cells show a much stronger in the inactive than in the active state. Figure shows the fraction of neurons in the and of this plot as a of CV. This fraction is positively correlated with CV Figure Thus, in the inactive state ABL the gain of the tuning of single neurons to ILD, with Figure 2C. In the active state, on the other the fraction is approximately with an effect of ABL on ILD tuning. This ABL change the tuning to ILD for single neurons, the nature of this change across neurons, not with the standard of gain and noise We to the and state-dependence of the evoked activity at the population which is the of this study. The in firing rate by the sensory stimuli and those by trial-to-trial variability can be estimated through the of the signal and noise respectively (Figure In each session, both are of where is the number of recorded neurons. A signal correlations between ‘tuning of all pairs of neurons (i.e. correlations are computed across trial-averaged responses for of this is the between the tuning of neurons and A noise correlations between trial-to-trial fluctuations for all pairs of neurons we the trials from all stimuli and correlations across all single responses of the corresponding mean responses). of this is the between trial-to-trial fluctuations between neurons and Figure Download asset Open asset and noise correlations in inactive and active states. (A) in an exemplary inactive session. Neurons are by ILD tuning from contralateral to ipsilateral (B) in an exemplary active session. Neurons are in the same (C) Average signal as a of CV. and in the other dots are active sessions, dots are inactive sessions, black circles mark the two exemplary sessions. (D) of by the of the signal as a of CV. dimensionality of the signal as a of CV. The same for noise Note that the in (G) is different from (A), (B). the signal for one exemplary inactive and one exemplary active session shown in Figure The neurons are sorted to to the value of βILD from Figure In the inactive state, there is a of similar neurons with contralateral and the neurons do not to show any the other in the active state there are neurons with similar contralateral preference but also neurons with similar ipsilateral preference. The tuning of these two of neurons is For the signal in each session, we can the mean the fraction of by the (i.e. where is the and the Here, to the number of of the total number of 36 We estimated the dimensionality using to obtain the distribution of under the of uncorrelated neurons (see Materials and methods). We that all these three measures were correlated with the more inactive the cortical state, the larger the signal the larger the and the the dimensionality (Figure these effects to the same as the state from active to signal as all neurons become analysis using of the signal the same (see Materials and methods). The same analysis for the noise is shown in Figure with previous (Goard and Dan, 2009; Renart et al., 2010; Ecker et al., 2010; Pachitariu et al., 2015; Beaman et al., we that the mean pairwise in the active state