Subnetworks size ranking.

<p>In linear-logarithmic scale, ranking distribution of subnetwork sizes. Colors indicate the number of base pairs <i>L_p</i> in the secondary structure: one pair (black), two pairs (red), three pairs (green) and four pairs (blue). The solid line corresponds to an exponential fitting. Insets show for each group of structures (with the same <i>L_p</i>) the size of the subnetworks (in the <i>y</i>-axis) that belong to the same neutral network as a function of the corresponding neutral network size (in the <i>x</i>-axis). Note changes of scale in both axes.</p

Sketches of two typical output networks.

<p>These two networks are constructed for <i>n</i>₁ = 100, <i>n</i>₂ = 1000, and <i>δ</i> = <i>π</i>. The nodes of the original graph are depicted in black, the forcing nodes are depicted in blue. The left (right) network corresponds to a case in which the forcing nodes are unable (able) to lock the phases of the oscillators in G₀.</p

Description of the main parameters of the sequence space.

<p><<i>k_rnd</i>> is the expected average degree if the probability of folding into a structure different from the open structure would not depend on the position in the space of sequences.</p

Structures and neutral networks obtained from the folding of all sequences of length <i>l</i> = 12.

<p>Additional properties of the <i>l</i> = 12 RNA neutral networks space can be found in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026324#pone.0026324-Cowperthwaite1" target="_blank">[10]</a>.</p

Ensemble average of the final degree distribution in the parameter space.

<p>(a)–(c): Log-log plots of (see text for definition) <i>vs. k.</i> obtained after an ensemble average over 50 different realizations of the growing process (<i>n</i>₁ = 1000, <i>n</i>₂ = 10000, <i>d</i>₁ = 0.2). In all cases, solid (dashed) lines correspond to the locked (non locked) regime, obtained for high (low) values of <i>d_p</i>, and solid red lines indicate the best power-law fits. (d): final number of connections <i>k_i</i>(<i>t_fin</i>) acquired by each node as a function of its initial frequency <i>ω</i>_0<i>i</i> = 0.5 for, <i>δ</i> = <i>π</i>, and <i>d_p</i> = 0.2 (upper plot, unlocked case) and <i>d_p</i> = 0.5 (lower plot, locked case).</p

Probability of mutation.

<p>Probability of mutation at each position of the sequence for two different secondary structures (see <i>x</i>-axis labels of both plots). (A) corresponds to the largest subnetwork <i>N</i> = 57481, whose secondary structure is fourth by abundance. (B) corresponds to the largest subnetwork <i>N</i> = 35594 of the most abundant secondary structure. We plot the sequences grouped by degree (dotted, dashed and dashed-dotted lines) together with their averages (solid lines).</p

Comparison of neutral networks of <i>l</i> = 12 with classical random and scale-free networks.

<p>Comparison of neutral networks of <i>l</i> = 12 with classical random and scale-free networks.</p

Time averaged phase synchronization order parameter <i>R</i> in the parameter space <i>ω_p</i>−<i>d_p</i>.

<p>Time averaged phase synchronization order parameter <i>R</i> (see text for definition) as a function of both the pacemaker frequency <i>ω_p</i> and the coupling strength <i>d_p</i>. Parameters: <i>n</i>₁ = 100, <i>d</i>₁ = 0.2, <i>m</i>₀ = 2, <i>n</i>₂ = 200, <i>δ</i> = <i>π</i> and each point is an average over 10 different realizations of the growing process.</p

Sequence centrality.

<p>Evaluation of the sequence centrality for the largest subnetwork <i>N</i> = 57481, whose secondary structure is ((....))..... In (A), degree <i>k_i</i> versus eigenvector centrality <i>v</i>₁(<i>i</i>). In (B), degree <i>k_i</i> versus betweenness centrality <i>B</i>(<i>i</i>). Colors and shapes denote the type of base pairs the sequences have (see Figure's legend). Note the community division created by the eigenvector centrality, which is related to the type of nucleotides participating in the base pair: GC+UA and AU+CG for low eigenvector centrality, GU+CG and GC+UG and for intermediate <i>v</i>₁(<i>i</i>) and GC+CG for high <i>v</i>₁(<i>i</i>).</p

Eigenvector centrality.

<p>Largest eigenvalue <i>λ</i>₁ of the adjacency matrix <b>A</b> as a function of the network size <i>N</i>. The inset shows the linear relationship between <i>λ</i>₁ and the network average degree . Solid line in the inset is .</p