Metrics of structured activity vs post-synaptic time duration.

<p>a) Metrics <i>Q</i>₀ (in solid line) and <i>Q</i>_<i>d</i> (dashed) as a function of the pulse time scale for the parameter values {Δ<i>V</i>,<i>g</i>} = {5 mV,8} corresponding to the maximum <i>Q</i>₀ value in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g002" target="_blank">Fig 2(d)</a>. Probability distribution functions <i>P</i>(<i>CV</i>) (<i>P</i>(<i>CV</i>₂)) for the coefficient of variation <i>CV</i> (local coefficient of variation <i>CV</i>₂) are shown in b) (in c)) for three representative <i>τ</i>_<i>α</i> = {2, 9, 20} ms, indicated in the three panels with red squares, blue triangles-up and black circles respectively. For these three cases the average firing rate in the network is 〈<i>ν</i>〉 = {8.81,7.65,7.35} Hz ordered for increasing <i>τ</i>_<i>α</i>-values. Other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g001" target="_blank">Fig 1</a>.</p

Cell assemblies and connectivity.

<p>a) Cross-correlation matrix <i>C</i>(<i>ν</i>_<i>i</i>, <i>ν</i>_<i>j</i>) of the firing rates organized according to the clusters generated via the <i>k-means</i> algorithm with <i>k</i> = 15, the clusters are ordered as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g001" target="_blank">Fig 1(c)</a> from the highest to the lowest correlated one. b) Connectivity matrix with the indices ordered as in panel a). Here, a black (copper) dot denotes a 1 (0) in , i.e. the presence(absence) of a synaptic connection from <i>j</i> to <i>i</i>. c) Average cross-correlation 〈<i>C</i>〉_<i>ml</i> among the elements of the matrix block (<i>m</i>, <i>l</i>), versus the probability <i>p</i>_<i>ml</i> to have synaptic connections from neurons in the cluster <i>l</i> to neurons in the cluster <i>m</i>. d) 〈<i>C</i>〉_<i>ml</i> versus the block averaged similarity metrics <i>e</i>_<i>ml</i>. Black squares indicate the blocks along the diagonal delimited by black borders in panel a) and b); blue triangles denote the ten blocks with the lowest 〈<i>C</i>〉_<i>ml</i> values, which are also delimited by blue edges in a) and b). The vertical red dashed line in panel c) denotes the average probability to have a connection <i>p</i> = 5% and in panel d) the value of the metrics <i>e</i>_<i>ml</i> averaged over all the blocks. The black solid line in panel c) is the linear regression to the data (〈<i>C</i>〉_<i>ml</i> ≈ 0.15–3.02<i>p</i>_<i>ml</i>, correlation coefficient <i>R</i> = −0.72). Other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g001" target="_blank">Fig 1</a>.</p

Cell activity characterization.

<p>a) Firing rates <i>ν</i>_<i>i</i> of 6 selected neurons belonging to two anti-correlated assemblies, the color identifies the assembly and the colors correspond to the one used in b) for the different clusters; b) raster plot activity, the firing times are colored according to the assembly the neurons belong to; c) cross-correlation matrix <i>C</i>(<i>ν</i>_<i>i</i>, <i>ν</i>_<i>j</i>) of the firing rates. The neurons in panel b) and c) are clustered according to the correlation of their firing rates by employing the <i>k-means</i> algorithm; the clusters are ordered in terms of their average correlation (inside each cluster) from the highest to the lowest one (for more details see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#sec011" target="_blank">Methods</a>). The firing rates are calculated over overlapping time windows of duration 1 s, the origins of successive windows are shifted by 50 ms. The system is evolved during 10⁷ spikes, after discarding an initial transient of 10⁵ spike events. Other parameters used in the simulation: <i>g</i> = 8, <i>K</i> = 20, <i>N</i> = 400, <i>k</i>_<i>mean</i> = <i>N</i>_<i>act</i>/15, Δ<i>V</i> = 5 mV and <i>τ</i>_<i>α</i> = 20 ms. The number of active neurons is 370, corresponding to <i>n</i>* ≃ 93%.</p

Metrics of structured activity vs lateral inhibition strength.

<p>a) Metrics entering in the definition of <i>Q</i>₀ versus the synaptic strength <i>g</i>. From top to bottom: Averaged coefficient of variation 〈<i>CV</i>〉_<i>N</i>, standard deviation of the cross-correlation matrix <i>σ</i>(<i>C</i>), and the fraction of active neurons <i>n</i>*. The solid (dashed) line refers to the case Δ<i>V</i> = 1 mV (Δ<i>V</i> = 5 mV). The minimum number of active neurons is achieved at <i>g</i> = <i>g</i>_<i>min</i>, this corresponds to a peak amplitude of the PSP <i>A</i>_<i>PSP</i> = 0.064 mV (<i>A</i>_<i>PSP</i> = 0.184 mV) for Δ<i>V</i> = 1 mV (Δ<i>V</i> = 5 mV) (for more details see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#sec011" target="_blank">Methods</a>). b) Distributions of the average <i>ISI</i> for a fixed Δ<i>V</i> = 5 mV and for two different coupling strengths, <i>g</i> = 4 (red triangle-up symbol) and <i>g</i> = 10 (blue triangle-down). Inset, the distribution <i>P</i>(<i>CV</i>) of the <i>CV</i> of the single neurons for the same two cases. c) <i>Q</i>₀ and <i>Q</i>_<i>d</i>, as defined in Eqs (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.e001" target="_blank">1</a>) and (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.e061" target="_blank">20</a>), versus <i>g</i> for Δ<i>V</i> = 1 mV. d) Same as c) for Δ<i>V</i> = 5 mV. Other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g001" target="_blank">Fig 1</a>.</p

Single neuron statistics.

<p>a) Distribution <i>P</i>(<i>ISI</i>) at short values of <i>ISI</i>s for one representative cell in the network, by setting <i>τ</i>_<i>α</i> = 20 ms. Inset: same as main figure for the whole range of <i>ISI</i>s. b) Same as a) for <i>τ</i>_<i>α</i> = 2 ms. c-d) Corresponding Poissonian reconstruction of the <i>P</i>(<i>ISI</i>) for the same cases depicted in a) and b). e-f) Single neuron distribution of the for the same considered cases as in a) and b) calculated from the simulation (black solid lines with circles) and the Poissonian reconstruction (red dashed line with squares). The network parameters are Δ<i>V</i> = 5 mV and <i>g</i> = 8, remaining parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g001" target="_blank">Fig 1</a>. Both the examined neurons have <i>I</i>_<i>s</i> = −45.64 mV. For the Poissonian reconstruction the frequencies of the incoming uncorrelated spike trains are set to 〈<i>ν</i>〉_<i>N</i> ≈ 7.4 Hz (〈<i>ν</i>〉_<i>N</i> ≈ 8.3 Hz) for <i>τ</i>_<i>α</i> = 20ms (<i>τ</i>_<i>α</i> = 2ms), as measured from the corresponding network dynamics. The distributions are obtained by considering a sequence of 10⁹ spikes in the original network, and 10⁷ events for the Poissonian reconstruction.</p

Computational capability of the network.

<p>Characterization of the firing activity of the network, obtained as response to three consecutive inputs presented in succession. a) Percentage of the variance of the neuronal firing activity reproduced by each of the first 10 principal components. The inset displays the corresponding cumulative percentage as a function of the considered component. Filled black and shaded red (bar or symbols) correspond to <i>τ</i>_<i>α</i> = 20 ms and <i>τ</i>_<i>α</i> = 2 ms, respectively. Projection of the neuronal response along the first three principal components for b) <i>τ</i>_<i>α</i> = 20 ms and c) <i>τ</i>_<i>α</i> = 2 ms. Each point in the graph correspond to a different time of observation. The three colors denote the response to the three different inputs, which are quenched stimulation currents randomly taken as <i>I</i>^(<i>j</i>) ∈ [<i>V</i>_<i>th</i>, <i>V</i>_<i>th</i> + Δ<i>V</i>] for <i>j</i> = 1, 2, 3, the experiment is then performed as explained in the text.</p

Pattern separation.

<p>Average dissimilarity as a function of the fraction <i>f</i> of inputs differing from the control input, for the values of <i>τ</i>_<i>α</i> = 20ms (black circles) and <i>τ</i>_<i>α</i> = 2ms (red squares) with two different observation windows <i>T</i>_<i>E</i> = 2s (solid line) and <i>T</i>_<i>E</i> = 10s (dashed line). Other parameters used: Δ<i>T</i> = 50ms, Δ<i>V</i> = 5 mV. Remaining parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g001" target="_blank">Fig 1</a>.</p

Sequential switching.

<p>a) Raster plot associated to the two input protocols <i>I</i>⁽¹⁾ and <i>I</i>⁽²⁾. The circles denote the clusters of active neurons appearing repetitively after the presentation of the stimulus <i>I</i>⁽¹⁾. Vertical lines denote the switching times between stimuli. The clustering algorithm employed to identify the different groups is applied only during the presentation of the stimulus <i>I</i>⁽¹⁾, therefore the sequential dynamics is most evident for that particular stimulus. b) Averaged State Transition Matrix , obtained by considering a 4<i>T</i>_<i>sw</i> × 4<i>T</i>_<i>sw</i> sub-matrix averaged over <i>r</i> = 5 subsequent time windows of duration 4<i>T</i>_<i>sw</i> (see the section <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#sec011" target="_blank">Methods</a> for details). The inputs <i>I</i>⁽¹⁾ and <i>I</i>⁽²⁾ are different realization of the same random process, they are obtained by selecting <i>N</i> current values <i>I</i>_<i>i</i> from the flat interval [<i>V</i>_<i>th</i>, <i>V</i>_<i>th</i> + Δ<i>V</i>]. The input stimuli are switched every <i>T</i>_<i>sw</i> = 2 s. Number of clusters <i>k</i> = 35 in a). Other parameters as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004778#pcbi.1004778.g001" target="_blank">Fig 1</a>.</p

Single neuron stimulation (SNS) can stop population bursting activity in presence of type T1 plus T2 correlations.

<p>A sketch of a SNS experiment for a network with type T1 plus T2 correlations is reported in (A) and (B): the neuron is stimulated with a DC step for a time interval (as shown by the red line on the top panel). Average firing rate of neuron (A) and network activity (B) as measured during the experiment. (C) and (D) refer to correlated and uncorrelated networks, respectively. Upper panels display the number of population bursts, PBs, delivered during SNS experiments versus the stimulated neuron, ordered accordingly to their average firing rates under control conditions (bottom panels). Each neuron was stimulated with a DC step (switching its excitability from to ) for an interval s. The critical neurons are signaled by red circles. The number of PBs, emitted in control conditions within an interval s, are also displayed: red dashed lines indicate their averages, while the shaded gray areas correspond to three standard deviations. The data refer to mV and neurons.</p

The critical neurons precede the population bursts in a network with correlations of type plus .

<p>(A) Raster plot of the network activity: every dot denotes a firing event. The dashed green lines and black dots refer to the four critical neurons. (B) Enlargement of a representative population burst: PBs are anticipated by the ordered firing sequence . For clarity reasons, in the raster plots, at variance with all the other figures, the neuronal labels are not ordered accordingly to their firing rates.</p