Trial-to-trial variability of granule cell firing reduces noise correlations under global stimulation.

<p><b>A</b>) Raster plots showing responses of four different granule cells to repeated cycles of the sinusoidal stimulus in the deterministic regime for the granule cells (i.e. <i>ρ</i> = 0). <b>B</b>) Raster plots showing trial-to-trial variability in the responses of four different granule cells to repeated cycles of the sinusoidal stimulus in the stochastic regime for the granule cells (i.e. <i>ρ</i>>0). <b>C</b>) Ratio of the noise correlation coefficients obtained under simulated local and global stimulation as a function of the noise intensity <i>ρ</i>. Note that the ratio decreases from 1 as <i>ρ</i> is increased from 0. <b>D</b>) Ratio of the signal correlation coefficients obtained under simulated local and global stimulation as a function of the noise intensity <i>ρ</i>.</p

Effect of RF center overlap on correlations in the three parallel ELL segments.

<p><b>(A)</b> We modeled differences in RF center size and overlap by varying the number of afferents converging onto pyramidal cells (LS: blue; CLS: magenta; CMS: green). We used phenomenological and accurate models of peripheral afferent activity and summed their spiking activities to obtain two input signals. The input signals to both pyramidal cells consisted of independent (bright magenta) and common (dark magenta) afferent populations. The signals served as inputs into two model ELL pyramidal neurons. We computed correlations between the spiking outputs of these two model ELL pyramidal neurons on different timescales t ranging between 10⁻³ s and 1.5 s. RFs consisted of 640, 105, and 25 afferents for LS, CLS, and CMS, respectively. RF overlap were 56.9, 33.3, and 13.2% for LS, CLS, and CMS as per anatomical data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005716#pcbi.1005716.ref030" target="_blank">30</a>] respectively. <b>(B)</b> Correlations between the spiking activities of the model ELL pyramidal neurons as a function of time window for the three different segments (see legend). Shown are mean (white lines), SEM (colored areas) and STD (gray shaded areas) across 250 random model realizations for 20 s duration. The correlation coefficients increased with time window size in a non-linear fashion. The overall correlation magnitude strongly decreased from LS to CMS (at t = 100 ms: median LS: 0.32, range: -0.10–0.74; CLS: 0.17, -0.27–0.77; CMS: 0.08, -0.43–0.59). <b>(C)</b> Distributions of correlation coefficients for the three ELL segments for t = 100 ms (see vertical dotted line in B). At this time scale the means of the distributions differed significantly (Kruskal-Wallis dF = 2; Chi² = 97.48; p = 6.8 · 10⁻²²). Qualitatively similar results were obtained for other time windows (e.g.: t = 10 ms; Chi² = 130.8; p = 3.8 · 10⁻²⁹; or t = 1 s; Chi² = 22.73; p = 1.16 · 10⁻⁵).</p

Pharmacological inactivation of indirect feedback input onto ELL pyramidal cells increases noise correlations.

<p><b>A</b>) Schematic of the pharmacological inactivation technique. <b>B</b>) Noise CCG from an example pair of same type ELL pyramidal cells under 4 Hz global stimulation before (control, blue) and after (block, red) pharmacological inactivation of feedback pathways. <b>C</b>) Population-averaged noise correlation coefficients under control (blue) and during the block (red). “*” indicates statistical significance at the p = 0.05 level using a signrank test with N = 14. <b>D</b>) Change in signal correlation coefficient (block-control) as a function of the change in noise correlation coefficient (block-control). No significant correlation was observed between both quantities (R = 0.32, p = 0.18, N = 14).</p

Anatomical and model schematic.

<p>Peripheral electroreceptor afferents receive the sinusoidal stimulus and project to both deep pyramidal (DP) as well as superficial pyramidal (SP) cells. The DPs relay the stimulus faithfully to a set of granule cells within the Eminentia Granularis posterior (EGp) that make direct excitatory synaptic contact onto SPs via parallel fibers as well as indirect inhibitory synaptic contact via local interneurons. It is assumed that each granule cell responds to a given phase of the sinusoidal stimulus and project via excitation and inhibition to SPs.</p

Different RF center-surround geometries give rise to similar correlations.

<p><b>(A-C)</b> Spike-count correlations for t = 100 ms for LS (A), CLS (B), and CMS (C) as a function of RF surround relative gain (x-axis) and size (y-axis). At the intersection of the dashed horizontal and vertical lines RF center-surround balance is at equilibrium (i.e. equal gain and size between surround and center). Correlation magnitudes like those found experimentally (≈ 0.19; green color) were obtained for multiple and very different combinations of RF surround relative gain and size in all segments. Roman numerals (I—V) in each panel show example selected combinations of surround relative gain and size that were considered for further analyses.</p

The formation of a negative image mediated by anti-Hebbian burst time dependent plasticity reduces signal but not noise correlations.

<p><b>A</b>) One cycle of the 4 Hz sinusoidal stimulus (top, red trace) and synaptic weights (bottom, blue traces) as a function of time for (black traces from top to bottom), t = 0, t = 0.5 sec, t = 1 sec, t = 1.5 sec, t = 2 sec, t = 2.5 sec, t = 3 sec, t = 3.5 sec, t = 4 sec, t = 4.5 sec, t = 5 sec, t = 5.5 sec. The red trace (bottom) shows the synaptic weights at t = 1000 sec (steady state) for comparison. The vertical arrow shows the progression of time. <b>B</b>) Time series of 5 synaptic weights during training. <b>C</b>) Cycle histograms from one SP cell neuron for the synaptic weights corresponding to (from top to bottom): t = 25 sec, 50 sec, 75 sec, 100 sec, 150 sec, and 200 sec. The vertical arrow shows the progression of time. Note the progressive reduction in response modulation as the negative image forms. <b>D</b>) Raw and noise correlation computed for the synaptic weights values obtained during training for the same time shown on the x-axis. Note the progressive decrease in signal correlations but the relative constancy of noise correlations.</p

Correlations between ELL pyramidal cell activities are nearly identical across the ELL segments.

<p><b>(A)</b> Simultaneous extracellular recordings of baseline activity (i.e. in the absence of stimulation) from pairs of pyramidal cells were obtained in all three ELL segments. Recordings were performed using two metal-filled micropipettes inserted into the pyramidal-cell layer of the respective ELL map (mean recording duration: 105 s; range: 39–318 s). <b>(B)</b> Absolute spike-count correlation coefficient for LS (blue), CLS (magenta), and CMS (green) as a function of the time window t. Shown are mean (white lines), SEM (colored areas) and STD (gray shaded areas) correlation coefficients across the populations of pairs recorded in each segment (LS: N = 23; CLS: N = 108; CMS: N = 24). The correlation coefficients obtained for the three segments were similar and thus largely overlapped with one another. (at t = 100 ms: median LS: 0.14, range: 0.009–0.44; CLS: 0.16, 0.001–0.48; CMS: 0.22, 0.003–0.5). <b>(C)</b> Population-averaged absolute correlation coefficient for t = 100 ms (see vertical dotted line in B). At this time scale, the means of the distributions were not significantly different from one another (Kruskal-Wallis; df = 2; Chi² = 1.66; p = 0.44). Qualitatively similar results were obtained for other time windows (e.g.: t = 10 ms; Chi² = 1.64; p = 0.44; or t = 1 s; Chi² = 2.78; p = 0.25).</p

Reduction of noise correlations by granule cell activity is dependent on stimulation frequency.

<p><b>A</b>) Noise correlation coefficient as a function of <i>c</i> and the sinusoidal stimulation frequency <i>f</i> for local stimulation. <b>B</b>) Noise correlation coefficient as a function of <i>c</i> and <i>f</i> for global stimulation. <b>C</b>) Reduction (local-global) in noise correlation coefficient as a function of <i>c</i> and <i>f</i>.</p

Experimentally measured differences in RF structure across the ELL maps give rise to similar levels of correlation in our model.

<p><b>(A)</b> RF organization for our model LS, CLS and CMS neurons. These are based on previously published experimental data [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005716#pcbi.1005716.ref028" target="_blank">28</a>] and our numerical simulations. The impact of RF surround on correlations was small in LS (size relation = 1:0.065; gain relation = 1:1.47), moderate in CLS (size = 1:12; gain = 1:0.4), and strong in CMS (size = 1:6; gain = 1:12). <b>(B)</b> Spike-count correlations for LS (blue), CLS (magenta) and CMS (green) as a function of time window corresponding to the RF structures shown in (A). Shown are mean (white lines), SEM (colored areas) and STD (gray shaded areas) correlation coefficients calculated across 50 realizations of the model. The correlation coefficients predicted for the three segments were similar and thus largely overlapped with one another. (at T = 100 ms: median LS: 0.24, range: -0.44–0.79; CLS: 0.24, -0.57–0.67; CMS: 0.26, -0.20–0.71). <b>(C)</b> Distribution of correlation coefficients calculated for t = 100 ms (see vertical dotted line in B). At this timescale, the means of the distributions were not significantly different from one another (Kruskal-Wallis; dF = 2; Chi² = 1.8; p = 0.41). Qualitatively similar results were obtained for other time windows (e.g.: t = 10 ms; Chi² = 4.27; p = 0.12; or t = 1 s; Chi² = 1.23; p = 0.54).</p

Correlated variability between SPs and granule cells influences noise correlations.

<p><b>A</b>) Noise correlation coefficient as a function of the input noise correlation coefficient <i>c</i> for the SP cells and of the fraction of shared noise with the SPs <i>e</i> for local stimulation. <b>B</b>) Noise correlation coefficient as a function of <i>c</i> and <i>e</i> for global stimulation. <b>C</b>) Reduction (local-global) in noise correlation coefficient as a function of <i>c</i> and <i>e</i>.</p