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

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

Assortativity.

<p>(A) Average nearest neighbors degree <i>k_nn</i>(<i>k</i>) as a function of <i>k</i> for fifteen networks of different sizes. (B) Assortativity parameter <i>r</i> as a function of the network size. As in previous figures, colors correspond to the number of base pairs of the subnetwork: one (black), two (red), three (green) and four (blue). The <i>r</i> for equivalent random networks are plotted in black squares.</p

Construction of neutral networks.

<p>In (A), we show an example of how neutral networks are constructed: sequences that fold into the same secondary structure are connected if they are at a Hamming distance of one. In (B), we show all sequences of length 12 that fold into the secondary structure (.(....))..., which is ranked in the 46th position. Although all sequences fold into the same secondary structure, the neutral network splits into 3 isolated subnetworks of sizes <i>N</i> = 404, 341, and 55.</p

Degree distribution <i>p</i>(<i>k</i>) and average degree

<p>(A) Degree distribution <i>p</i>(<i>k</i>) of fifteen subnetworks. They are the five largest (black curves), five of intermediate size (brown curves, one order of magnitude smaller) and five small subnetworks (blue curves, two orders of magnitude smaller). (B) Average degree as a function of the subnetwork size <i>N</i>. Colors correspond to one (black), two (red), three (green) and four (blue) base pairs in the secondary structure. The solid line corresponds to the numerical fitting (note the logarithmic-linear scale). The analytical approximation to making use of the values of , and <i>α</i> obtained from all the 12-nt folded sequences (and implying <i>A_S</i> = 0.53) is plotted in long-dashed black line. The upper and lower bounds to coefficient <i>A_S</i> yield and (plotted in short-dashed red lines).</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

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

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

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

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