SSA is limited to a narrow region in parameter space.

<p>(A) CSI as a function of amplitude (<i>A</i>) and ISI (using <i>U</i> = 0.5, <i>τ</i>_rec = 800 ms). Here and in the other panels, an arrow marks the transition from the No-PS regime to the Selective, Periodic and finally the Reliable regime (Rel.), delineated by the black lines. (B) CSI in a network with the same parameters as in (A), but with homogeneous columns (all input-receiving neurons in each column have the same best frequency). Heterogeneity of the tuning curves acted to shift and slightly expand the range of parameters that showed SSA, and specifically its low-<i>A</i> branch. (C) CSI as a function of synaptic parameters <i>U</i> and <i>τ</i>_rec (<i>A</i> = 5 spikes/s, ISI = 350 ms). On this plane there was also a Bursting regime (Burst.), composed of networks that generate spontaneous PSs, crossing the Reliable regime. (D) CSI in a network with the same parameters as in (A), but without thalamocortical depression. Thalamocortical depression thus extended the range of parameters that showed SSA. In all protocols, P = 10% and Δf = 2. Default values were <i>A</i> = 5 spikes/s, ISI = 350 ms, <i>U</i> = 0.5, <i>τ</i>_rec = 800 ms.</p

Regimes of response limit SSA to a narrow range of parameters.

<p>(A-D) Responses to oddball sequences always fell into one of 4 general patterns (regimes). These are demonstrated here with different input amplitudes: (A) No PS to either standard or deviant; (B) Selective PS response, where PSs were evoked mostly by deviants; (C) Periodic PS responses, where some standards evoked PSs and may have prevented PS responses to subsequent deviants; (D) Reliable PS response, with both standard and deviant evoking PS responses. CSI values are large only in the Selective regime. Colored bars under the traces represent presentations of standard (blue) and deviant (red) stimuli (bar widths are not to scale). (E-H) The same set of response regimes is observed when changing different stimulus or network parameters. The parameters are input amplitude <i>A</i> (E), ISI (F), and synaptic properties such as the fraction of resource utilization <i>U</i> (G) and the recovery time-constant <i>τ</i>_rec (H). Colors represent regimes as in (A-D). Gray curves in (E) and (F) show the parameter dependence in a network with homogeneous columns (all input-receiving neurons in each column have the same best frequency). In (H), the red area corresponds to spontaneous PS generation (“Bursting”). In all protocols, P = 10% and Δf = 2; default values were <i>A</i> = 5 spikes/s, ISI = 350 ms, <i>U</i> = 0.5, <i>τ</i>_rec = 800 ms.</p

Thalamocortical synaptic depression.

<p>(A) Changing <i>U</i>_s, the fraction of thalamocortical (ThC) resource utilization, showed three of the four response regimes shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.g006" target="_blank">Fig 6</a>, with SSA present mainly in the Selective regime. (B) Changing <i>τ</i>^s_rec, the time-constant of recovery in ThC synapses, did not take the network out of the Selective regime. (C) An example of periodic PSs in the standard column. Periodic PS responses (top) arise from recurrent network dynamics, as manifest in the dynamics of <i>x</i> and <i>y</i>, the mean fractions of available resources (Res.) in excitatory and inhibitory synapses, respectively (middle), and not from dynamics of the ThC synapses mediating the standard tone (<i>z</i>, mean fraction of available resources; bottom. Dashed lines show analytical values as in D). ThC dynamics show steady oscillations that are substantially faster than the period of PS responses. Stimuli presentations are marked in gray. (D) Onset (left) and offset (middle) <i>z</i> for the steady oscillations reached in the standard column (Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.e019" target="_blank">17</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.e020" target="_blank">18</a>), computed analytically and plotted across the <i>A</i>-ISI plane. The difference between the two (right) is the fraction of ThC resources recovered during each ISI. Borders of the Selective regime are marked in white. In all protocols, P = 10%, Δf = 2, <i>U</i> = 0.5, <i>τ</i>_rec = 800 ms; default values were <i>A</i> = 5 spikes/s, ISI = 350 ms, <i>U</i>_s = 0.7, <i>τ</i>^s_rec = 300 ms.</p

Properties of SSA.

<p>(A) The average response to the deviant tone increased as its probability of occurrence (P) was decreased. Stimulus durations are marked in gray. (B) SSA was present only within a certain range of input amplitudes (<i>A</i>, left) and inter-stimulus intervals (ISI, right). This range was slightly wider for smaller P. (C) Larger frequency separation (Δf) increased the CSI, and allowed SSA to occur over a wider range of input amplitudes (left) or ISIs (right). (D) Examples for the dependence of experimental CSI on stimulus parameters: Left, results of LFP recordings made by Taaseh [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.ref045" target="_blank">45</a>] at different sound intensities (here represented as attenuations); right, intracellular recordings from Hershenhoren et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.ref012" target="_blank">12</a>]. Numbers above the box plots show the number of recording sites or cells for each attenuation or ISI, respectively. (E) Hyperacuity of SSA in the model is demonstrated using a network with tuning curves 10 times wider than Δf (<i>λ</i> = 20; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#sec019" target="_blank">Methods</a>). CSIs were lower and the range of ISIs was more limited (dark gray) compared to those of a network with normal tuning curves (<i>λ</i> = 5, black). Using normal tuning curves but smaller Δf gave no SSA (light gray). Inset: Scheme of tuning curves and stimuli for hyperacuity tests (colors as in the main plot). The <i>y</i>-axis shows input amplitude normalized to that of the best frequency. Default values for all simulation protocols shown here were P = 10%, Δf = 2, <i>A</i> = 5 spikes/s, ISI = 350 ms.</p

Stimulus-specific adaptation (SSA) in the model network.

<p>Presenting the network with two tones with different probabilities of occurrence produced SSA in a column that responds to both tones. (A) The mean firing-rate, <i>E</i>, in column 11 in response to an oddball protocol (stimuli marked as blue and red bars under the plot). Upon presentation of two tones, f1 = 10 and f2 = 12 (tone “frequency” = index of the column most sensitive to the tone), the middle column showed PS responses only to the deviant. (B) Mean firing-rates across multiple columns. PSs were sometimes generated in column 10 (the standard column; blue), but apart from the response to the first tone in the protocol, only PSs from column 12 (deviant column; red) were strong enough to propagate into column 11. (C) The time-course of synaptic resources, <i>x</i>, across the network shows the long-term effects of PS events: the strong resource depletion left in their wake. In (B) and (C), the standard and deviant columns are shown with different color maps from the rest of the network (black), in order to highlight their locations and roles in the network activity. (D) and (E) Close-ups on the mean firing-rate (D) and mean synaptic resources (E) in the deviant (red), middle (black) and standard (blue) columns for the periods marked with the corresponding colored rectangles in B & C, showing that PSs initiated in the deviant column were able to invade the middle column but PSs initiated in the standard column mostly failed to do so. (F) Top: Traces of average responses in column 11 to both frequencies in the two oddball conditions (Deviant f2, Deviant f1) as well as in the Equal condition. The strength of response to each tone depended on its probability of occurrence (represented in the bar graphs above the traces). Bottom: An example for multi-unit activity (MUA) responses from one site in rat auditory cortex to two frequencies (f1 = 13.3, kHz f2 = 19.2 kHz) in the two oddball conditions and the Equal condition. Data replotted from Taaseh et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.ref004" target="_blank">4</a>]. Stimulus duration is marked in gray. In all simulation protocols, input amplitude (<i>A</i>) = 5 spikes/s and inter-stimulus interval (ISI) = 350 ms.</p

Sensitivity to deviance vs. rarity.

<p>Several control protocols were used to check whether the deviant response is due to its rarity alone, or alternatively to the violation of the regularity set by the standard. (A) There are 6 conditions in which a tone, e.g. f1 = 10, may be presented: As the Standard or Deviant in the regular oddball protocol; one out of two tones with equal probabilities (Equal); a deviant presented alone amid periods of silence (Deviant Alone); or a “deviant among many standards”, with multiple tones spanning an either narrow or broad range of frequencies (Diverse Narrow & Diverse Broad, respectively). Bar graphs show the probabilities of occurrence in the different protocols. (B) Left: A histogram of CSIs of single neurons in the middle column of an example network (gray line marks the mean CSI). Right: A histogram of CSIs calculated from the mean firing-rate in the middle column for 12 networks (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.e010" target="_blank">Eq 9</a>). The mean single-neuron CSI of the network from the left-hand panel is marked with a gray line, and the CSI calculated from the average response of all neurons is marked by an arrow. (C) Average responses to f1 (left) and f2 (right) in the six conditions (peri-stimulus firing-rate, with stimulus duration marked in gray). Insets: Total spike counts, normalized to the Deviant Alone condition. Data are averages over 12 networks with different randomizations of tuning curves, each presented with 10 blocks of each protocol. (D) An example for multi-unit activity (MUA) responses from one site in rat auditory cortex to two frequencies (f1 = 13.3 kHz, f2 = 19.2 kHz) presented in the 6 conditions. Data replotted from Taaseh et al. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.ref004" target="_blank">4</a>] (the responses are from the same site used for <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#pcbi.1005437.g003" target="_blank">Fig 3F</a>, with the additional three conditions). (E) Spike counts for the Diverse Broad (DB) vs. Deviant responses of the 12 networks averaged in (C) to f1 (left) and f2 (right). The example network from (B) is marked with a gray dot. Responses to the Deviant condition were significantly stronger. (F) An example of the responses in the middle column (mean firing-rate, top) during a Diverse Broad protocol (bottom; occurrences of frequency 12 are marked in yellow). (G) and (H) Mean firing-rates (G) and synaptic resources (H) across multiple columns during the same protocol as in (F). Column 12, whose responses to presentations of its best frequency are highlighted in (F), is shown with a yellow colormap. Stimulus durations are marked in gray. In all simulation protocols, <i>A</i> = 5 spikes/s and ISI = 350 ms.</p

Predictions for experimental studies.

<p>(A,B) SSA was strong in the middle column (no. 11) and considerably weaker in the columns most sensitive to the stimulus frequencies. In columns farther away from the middle, the CSI was high but dominated by one of the two conditions (e.g. low-index columns showed high CSI mainly due to strong responses to f1 as the deviant). Dependence of CSI on column is shown for different values of P (A) and Δf (B). Arrows in (B) mark the different pairs of frequencies presented. (C) Color map of CSI values for different combinations of stimulus duration and offset-to-onset interval. Solid lines show the borders of the different response regimes. An arrow shows the transition from the No-PS regime to the Selective, Periodic and finally the Reliable regime (Rel.). Dotted lines mark constant ISIs (onset-to-onset). The dashed curve marks the line on which the interval and duration are equal. Default values were P = 10%, Δf = 2, <i>A</i> = 5 spikes/s, ISI = 350 ms.</p

Dynamics of single-neuron and population activity.

<p>(A) The firing-rate, <i>E</i>, of selected neurons in column 11 in response to an oddball protocol (stimuli shown as blue and red bars under the plot). PS responses were usually evoked by deviant stimuli (red) and only rarely by standard stimuli (blue). (B) Single neurons were highly correlated in their single-trial responses, showing either a small transient increase in firing-rate (left) or a sharp concerted increase in firing-rate, which marks a PS (right). (C) All responses of a single neuron (no. 75, marked with an asterisk in (A)) to the standard condition (left, light blue curves) and to the deviant condition (right, light red) during 5 blocks similar to the one shown in (A). Blue and red curves show the average response of this neuron in each condition. In all blocks, input amplitude (<i>A</i>) = 5 spikes/s and inter-stimulus interval (ISI) = 350 ms.</p

Adaptation shapes the SSA Region by subtractive or divisive operation on the input of column response curves.

<p>(A) Adaptation might affect the response curve of a cortical column in a subtractive (left) or divisive (right) manner. The potential SSA region lies between the response curves of the weakly-adapted deviant column and the strongly-adapted standard column. (B) Response curves of the deviant column and standard column, each to its own best-frequency stimulus (light red and light blue, respectively) for ISI (left) and input amplitude <i>A</i> (right). Red and blue curves show the responses within the middle column to the deviant and standard tones, respectively. Curves demonstrate the effect of adaptation, suggesting a subtractive operation on the logarithmic ISI-scale and divisive operation on the logarithmic <i>A</i>-scale. Responses to the deviant tone were attenuated more strongly in the process of propagating to the middle column compared to standard responses. In all protocols shown here, P = 10%, Δf = 2, <i>U</i> = 0.5, <i>τ</i>_rec = 800 ms.</p

Architecture and activity of the model network.

<p>(A) The primary auditory cortex is represented by a recurrent neural network divided into cortical columns. Columns are arranged tonotopically by their best frequencies (BFs), but the BFs of neurons within each column show some variability (BFs are represented by color). Arrows illustrate the connectivity of one column. (B) Upon sensory stimulation a column may generate a population spike (PS), shown here as a transient increase in the column’s mean firing-rate, <i>E</i> (top). The inhibitory population (mean firing-rate, <i>I</i>) lags behind the excitatory activity. A PS depletes the synaptic resources, which recover gradually (bottom; <i>x</i> is the mean fraction of available resources in excitatory synapses, <i>y</i> in inhibitory synapses). Stimulus duration shown in gray. (C) The threshold for PS generation. Left: Time course of responses for stimuli of varying amplitude. Response strength is displayed using a color scale. Right: Spike count (integrated from stimulus onset until 45 ms following offset; see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005437#sec019" target="_blank">Methods</a>) as a function of input amplitude, with (black) and without (cyan) feedback inhibition. (D) A PS that is initiated in one column (here, column 11) can propagate across the network. The color scales of (C) and (D) are identical. Stimulus duration in (C) and (D) is the same as in (B). (E) A low level of synaptic resources (x) may prevent subsequent stimuli from evoking a PS. Stimulus presentations are shown in gray. (F,G) Refractoriness of PS generation. Following a PS, a stimulus has to be stronger (F) or presented at a longer latency (G) in order to evoke a PS. Stimuli marked by black bars under the traces. In (F), the first stimulus has <i>A</i> = 5 Spikes/s, and values next to the traces specify the amplitude of the second stimulus. In (G), all stimuli are of the same amplitude, <i>A</i> = 5 Spikes/s. (H) The spike count for the second stimulus. The first stimulus was always presented with <i>A</i> = 5 Spikes/s. The second stimulus varied in amplitude (abscissa) and ISI (ordinate).</p