Maximizing Sensory Dynamic Range by Tuning the Cortical State to Criticality.

Modulation of interactions among neurons can manifest as dramatic changes in the state of population dynamics in cerebral cortex. How such transitions in cortical state impact the information processing performed by cortical circuits is not clear. Here we performed experiments and computational modeling to determine how somatosensory dynamic range depends on cortical state. We used microelectrode arrays to record ongoing and whisker stimulus-evoked population spiking activity in somatosensory cortex of urethane anesthetized rats. We observed a continuum of different cortical states; at one extreme population activity exhibited small scale variability and was weakly correlated, the other extreme had large scale fluctuations and strong correlations. In experiments, shifts along the continuum often occurred naturally, without direct manipulation. In addition, in both the experiment and the model we directly tuned the cortical state by manipulating inhibitory synaptic interactions. Our principal finding was that somatosensory dynamic range was maximized in a specific cortical state, called criticality, near the tipping point midway between the ends of the continuum. The optimal cortical state was uniquely characterized by scale-free ongoing population dynamics and moderate correlations, in line with theoretical predictions about criticality. However, to reproduce our experimental findings, we found that existing theory required modifications which account for activity-dependent depression. In conclusion, our experiments indicate that in vivo sensory dynamic range is maximized near criticality and our model revealed an unanticipated role for activity-dependent depression in this basic principle of cortical function

The cortical state is a tunable continuum.

<p><b>(a)</b> Example MUA spike count time series during ongoing activity for unaltered inhibition (black), enhanced inhibition (blue), reduced inhibition (red). Green dashed line indicates threshold for defining avalanches. Shaded gray area indicates the size (total spike count) of one example avalanche. <b>(b)</b> Avalanche size distributions reveal that enhancing inhibition leads to a cortical state with predominantly small-scale activity (blue). Reducing inhibition leads to prominent large-scale activity (red). Unaltered inhibition results in diverse spatiotemporal scales (black), often distributed similar to a power law with -1.5 exponent (dashed). The parameter κ measures deviation from the power law. <b>(c)</b> Increasing inhibition tends to decrease κ and decreasing inhibition tends to increase κ, but κ varied widely across experiments with fixed drug condition. Color indicates drug condition: 20 μM muscimol (blue), no drug (black), 40 μM bicuculline (pink), 20 μM bicuculline (red). Filled boxes indicate drug condition. Open boxes indicate post-drug wash condition. Box delineates quartiles, line marks median, and whiskers span range of data. <b>(d)</b> Example distributions illustrating the continuum of cortical states, parameterized by κ (color). Vertical axis is logarithmic as in (b) with the scale bar spanning 5 orders of magnitude. Curves are shifted vertically for clarity. The dashed line is a reference power law with exponent -1.5; it is placed near the distributions with κ nearest 1. Some of these examples are from experiments with drugs applied, some from experiments with no drug. <b>(e)</b> The average spatial area (number of electrodes) of avalanches undergoes a sigmoidal rise as κ increases (green). The average size of avalanches increases sharply as κ increases beyond κ = 1 (brown). The rise in size versus κ lags the rise in spatial area, because size also depends on the avalanche duration. To illustrate these trends, we present median (line) and quartiles (shaded areas) across all experiments with similar κ. <b>(f)</b> Time series from the model at criticality (black, inhibitory modulation at 1), in the subcritical regime (blue, inhibitory modulation at 3) and in the supercritical regime (red, inhibitory modulation at 0). <b>(g)</b> Example distributions illustrating continuum of different model states, parameterized by inhibitory modulation (color). Vertical axis is logarithmic as in (b) with the scale bar spanning 5 decades. Note that power law avalanche size distributions only occur when the model operates at criticality (yellow, inhibitory modulation at 1). The dashed line is a reference power law with exponent -1.5; it is placed near the distributions with κ nearest 1. <b>(h)</b> We measured κ based on model distributions. Inhibitory modulation (color) was inversely and monotonically related to κ.</p

Continuum spans transition from weakly to strongly correlated cortical state.

<p><b>(a,b)</b> Zero-lag Pearson correlation coefficients were computed for all electrode pairs (n = 496) during ongoing activity. Shown are example distributions of all pairwise correlations for unaltered inhibition (black), increased inhibition (blue), and decreased inhibition (red). Broader distributions for unaltered inhibition indicate that correlations are more diverse than for either increased or decreased inhibition. Data in (a) are from one rat; data in (b) is from another rat. <b>(c)</b> Mean pairwise correlations undergo a sigmoidal increase as κ increases, with κ = 1 dividing weakly correlated cortical states from strongly correlated states. To illustrate this trend, we computed the mean pairwise correlation for each experiment and present the mean (line) ± standard error (shaded areas) across all experiments with similar κ. <b>(d)</b> The model undergoes a similar transition from weak to strong population correlations as inhibition is tuned from strong to weak (blue to red, color map the same as <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004576#pcbi.1004576.g002" target="_blank">Fig 2H</a>). <b>(e)</b> Model results match experiments more closely when model state is parameterized by κ.</p

Explaining experiments requires model with activity dependent depression.

<p>Comparison of our model results with and without activity dependent depression. <b>a)</b> Without depression, the supercritical regime (inhibitory modulation at 0) results in sustained, saturated network activity (green). With depression, the system is quiet except during large bursts of activity, but never saturates (brown), similar to our experiments with suppressed inhibition (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004576#pcbi.1004576.g002" target="_blank">Fig 2A</a>, red). <b>b)</b> As in previous studies without depression, dynamic range is maximized near criticality (inhibitory modulation near 1). Color indicates the inhibitory modulation factor as indicated by horizontal axis of right panel. <b>c)</b> With depression, the response curves change shape, decreasing for small stimuli (left). This change in shape mostly occurs in the supercritical regime (inhibitory modulation <1), leaving the critical and subcritical cases largely unchanged. This results in highest dynamic range for the supercritical state (right). However, if large stimuli are excluded (keeping the gray shaded region), which is more realistic compared to our experiments, then dynamic range is again maximized at criticality, as shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004576#pcbi.1004576.g004" target="_blank">Fig 4E–4G</a>. Color indicates the inhibitory modulation factor as indicated by horizontal axis of right panel.</p

Peak dynamic range at intermediate cortical state near κ = 1.

<p><b>(a)</b> MUA spike response for 180 trials of whisker stimulation ranked by stimulus strength (whisker speed) for unaltered (left), enhanced (middle), reduced inhibition (right). Color indicates total population MUA spike count. Gray line (top) indicates stimulus onset and duration. <b>(b)</b> Average speed of dominant whisker during 100 ms following stimulus onset for the 180 trials shown in (a). Color indicates inhibitory condition: none (black), enhanced (blue), or reduced (red). <b>(c)</b> Example stimulus-response curves. Typically, enhanced inhibition (blue) resulted in decreased sensitivity and gain compared to unaltered inhibition (black). Reduced inhibition (red) often increased gain so much that the response curve reached a saturated level for moderate stimuli. Each point represents the average MUA spike response conditioned on whisker speed during the first 100 ms following stimulus onset. Dashed line is a best-fit sigmoid curve. <b>(d)</b> Dynamic range ∆ was highest for an intermediate cortical state close to κ = 1. (inset) Dynamic range was defined based on the best fit sigmoid. <b>(e)</b> Stimulus response curves from our model. Notice that the shapes of response curves change with inhibitory modulation (color code defined in panel f) as seen in experiments (panel c). <b>(f)</b> The highest dynamic range was found near criticality (with unmodulated inhibition). <b>(g)</b> Parameterizing the model state with κ reveals the model dynamic range depends on network state as seen experimentally (d).</p