Ratio of left action selection relatively to the two previous trials history for D1L (left column) and D2L (right column) stimulation.

<p><b>A</b> and <b>B</b> show our modelling results and <b>C</b> reproduces results from Tai & Lee et al. (2012). RP was not affected by the stimulation in <b>A</b>, whereas it was the case in <b>B</b>, but only if the selected action was the one contralateral to the stimulation. All error bars represent s.e.m., * and ** means p<0.05 and p<0.001 respectively for the difference in left ratio with and without stimulation, for each reward history condition.</p

Schematic representation of the model in relation to biology.

<p>As not all the different nuclei are implemented in the model, we represented only relevant biological structures. We arbitrarily labelled output actions as “right” and “left”. Only one SNc is shown here, as in our model there is no difference in the feedback (RPE) any D1 or D2 units get. Only one unit in SNc gets active per trial, representing the reward prediction for the current state and the selected action.</p

Ratio of left action selection relatively to ten intervals averages of the left action value, without and with added stimulation.

<p>Top row (<b>A</b>) shows modelling results for three different intensities: 0.15, 0.50 and 2.00, bottom row (<b>B</b>) is reproduced from Tai & Lee et al. (2012) with also three different intensities. All error bars represent s.e.m.</p

Average change in the weights at the beginning (first two trials) and at the end (last two trials) of blocks of 20 trials.

<p>Results group trials where no reward was delivered are presented in <b>A</b>, whereas in <b>B</b>, a reward was obtained. Error bars represent standard deviation and all differences for a same timing are significant (p<0.001).</p

Frequency-dependent discharge of Martinotti cells (MCs).

<p>(A) Microcircuitry modeled as described in Silberberg & Markram (2007) showing the disynaptic pathway between pyramidal cells (PCs) (black) mediated by 3 MCs (red, blue and green). The PC1 to MC excitatory synapses are facilitating. (B) The presynaptic PC1 was stimulated by a train of APs at different frequencies (40, 50 and 70 Hz), shown for a 40 Hz input. The overlaid voltage traces of 3 post-synaptic MCs are shown. Firstly, higher frequency evoked post-synaptic APs with higher probability and shorter onset latency. Secondly, higher frequency recruited more intermediate MCs, in accordance with experiments (Silberberg & Markram, 2007). Rarely do all 3 MCs discharge for 40 Hz input, 2 MCs discharge in ninety percent of the trials during 50 Hz and all 3 MCs discharge in ninety percent of the trials during 70 Hz. The MC membrane potential jitter is due to the presence of background activity. (C) The increase in amplitude and decrease in latency of disynaptic response on PC2 membrane potential as a function of presynaptic AP train frequency. The monosynaptic excitation between pyramidal cells is turned off to present how the disynaptic response of MCs in experiment and model coincide. (D) Individual traces of MCs receiving synaptic input from PCs demonstrating membrane depolarization following different presynaptic discharge frequencies.</p

Synapse parameters.

<p>Synapse parameters.</p

Teasing out the parameters that cause attractor termination.

<p>Every point on the figure is an average of the attractor duration of all stored patterns calculated for each trial. The error bar gives their variation in each trial. Interspersed between the three conditions ((A), (B), (C)) are the control conditions (Ct) to show the sensitivity of attractor duration in the absence of MCs (blue) and presence of MCs with different facilitation time constants (red and green). Throughout this analysis, we have used the “40/80” paradigm for the connections between PCs and MCs. The short-term plasticity values at various synapses during ‘Ct’ are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030752#pone-0030752-t003" target="_blank">Table 3</a>. The numbers just above the error bar are the values assumed by the varying quantity during (A), (B) and (C); the values at (C) are the percentage difference from ‘Ct’. In the absence of MCs, the attractor duration is sensitive to the lower values of depression between PC-PC synapses, brought about by lowering ‘U’ (A) or lowering τ_rec (B), and changes in <i>g_M</i> of PCs (C), inasmuch as these factors results in increase in PCs firing. The height of the errorbar at the lower values of depression ((A), (B)) is also high implying a large variation in the attractor duration of all stored patterns in every trial. When MCs inhibition is included (red), sensitivity to change in STD and adaptation are minimal, there are no strong peaks apart from trial-to-trial variation of attractor duration. Besides, the presence of MCs inhibition also prevents the scatter of data from its mean value in every trial (note the steady values of green and red errorbars). Decreasing the τ_facil of PC-MC synapses (green) shows a similar response.</p

Schematic of the network arrangement and all the excitatory and inhibitory pathways between different cell types and their connection densities in the model.

<p>(A) Cartoon of a network of 9 hypercolumns with 5 minicolumns each. The model used had 36 hypercolumns. Each hypercolumn has 5 circularly arranged minicolumns. A minicolumn, represented by red discs, contains 30 densely connected (25%) PCs denoting local re-entry. The minicolumns in a hypercolumn receive inhibition from the cell population represented by blue discs, the excitatory (red) and inhibitory synapses (blue) are also shown. Dashed lines show minicolumns that are connected and distributed in different hypercolumns, which forms a pattern. (B) A small segment of the network blown-up to show the particulars, only here we see each blue disc houses 2 inhibitory cell types.</p

The activity of cells in the network. The output of different cell types are colour-coded for the sake of clarity; PCs (blue), BCs (red) and MCs (green).

<p>(A,C) Rastergram and average discharge rate of PCs and BCs versus time when inhibition from MCs is turned off. (A) When the network is subjected to a low background noise (0.25 – 0.5 Hz), it started hopping through the stored attractor states. PCs that form a pattern and are active (near) synchronously in different hypercolumns are grouped for visual aid. The x axis represents time, while the y axis represents neuron label. A dot in the rastergram means a spike of a neuron y at time x. (C) The time varying firing rate of all the cells is not evident in the rastergram. Average discharge rate versus time, bin size of 25 ms, makes it clearer. BCs fire at every attractor cycle since they receive excitation from all minicolumns in a hypercolumn. PCs from different patterns, represented by various blue line-strokes, took turns getting active. BCs, keeping step with PCs, had a high firing rate at the beginning of the attractor and tapered off maintaining the excitation - inhibition balance. (B, D) Same as above after the inclusion of MCs inhibition. (D) The late activity of MCs is apparent in the average firing rate. BCs with their characteristic depressing synapses are the first to respond (red). MCs receiving facilitating synapses discharge with a delay (green), and similar to BCs, as mentioned above, are active at every attractor cycle. MCs due to their strong projection to the neighbouring PCs within 100 µm radius (Silberberg & Markram, 2007), shut the activity thereby shifting the excitation - inhibition balance. Thus, presence of MCs inhibition controls the dwell time of the attractor.</p

Attractor duration and peak firing rate of PCs during different connection paradigms when connection strengths are varied.

<p>See the text for a description of these connection paradigms. The value at the bottom of each subfigure is the varying quantity and on the top is the quantity that is held constant. (A,C) PCs attractor duration showed a linear response to increase in PC -> PC (0.8, 1.2, 1.5 mV) and PC -> MC (0.2, 0.4, 0.6 mV) epsp size. (A) The attractor duration decreased as PC -> PC strength increased. The response to “without MC” paradigm was similar to “15/80”, but “50/80” and “80/80” paradigms showed marked reduction in the attractor duration. (C) Increase in PC -> MC connection strength also showed a similar trend. (B,D) It takes about 80 ms after PCs enter an attractor state before spike-frequency adaptation and synaptic depression take effect causing a reduction in average firing rate. (B) If the MCs become active before the above factors take effect, the peak-firing rate will be affected as in the case of “80/80” paradigm when the PC -> PC Epsp size is 1.5 mV. Apart from this single exception, the peak firing rate showed a linear response. (D) The onset of MC firing was quicker when PC -> MC connection strength was doubled and tripled.</p