Motif dynamics in non-Erdös-Rényi networks.

<p>(A) Degree distribution of the finite-size Erdös-Rényi networks used in Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004458#pcbi.1004458.g002" target="_blank">2</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004458#pcbi.1004458.g009" target="_blank">9</a>, showing each neuron’s number of incoming synapses (in-degree) and outgoing synapses (out-degree). (B) Correlated, truncated power degree distributions. From left to right, the frequency of chain motifs increases. The degree distributions at either end of the “Chain Frequency” axis correspond to highly anti-correlated (left) and highly correlated (right) in- and out-degrees, with correlation coefficient <i>ρ</i> = ±.9 (Methods: Neuron and network models). The networks in columns ii-iv are drawn from the labelled points on this axis, with <i>ρ</i> = −.1 (ii), <i>ρ</i> = .1 (iii) and <i>ρ</i> = .5 (iv). In each column, we sample networks from each side of threshold for potentiation of <i>p</i>. For the network in column ii, </p><p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>div</p><mo>=</mo><mo>.</mo><mn>0149</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>con</p><mo>=</mo><mo>.</mo><mn>0163</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>ch</p><mo>=</mo><mo>−</mo><mo>.</mo><mn>0012</mn><p></p><p></p><p></p>. For the network in column iii, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>div</p><mo>=</mo><mo>.</mo><mn>0165</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>con</p><mo>=</mo><mo>.</mo><mn>0157</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>ch</p><mo>=</mo><mn>7</mn><mo>.</mo><mn>7</mn><mi>x</mi><p><mn>10</mn></p><p><mo>−</mo><mn>4</mn></p><p></p><p></p><p></p><p></p>. For the potentiating network in column iv, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>div</p><mo>=</mo><mo>.</mo><mn>0161</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>con</p><mo>=</mo><mo>.</mo><mn>0157</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>ch</p><mo>=</mo><mo>.</mo><mn>0062</mn><p></p><p></p><p></p>. For the depressing network in column iv, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>div</p><mo>=</mo><mo>.</mo><mn>0148</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>con</p><mo>=</mo><mo>.</mo><mn>0156</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>q</mi><mn>0</mn>ch</p><mo>=</mo><mo>.</mo><mn>0068</mn><p></p><p></p><p></p>. (C) Dynamics of the mean synaptic weight. (D) Dynamics of divergent motifs. (E) Dynamics of convergent motifs. (F) Dynamics of chain motifs. In all panels, the STDP rule is the balanced, depression-dominated one (−<i>δ</i> in Figs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004458#pcbi.1004458.g006" target="_blank">6</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004458#pcbi.1004458.g009" target="_blank">9</a>).<p>