Figure 2

<p>Period histogram (a and b) and dependence of R on τ (c) for 10³ cells. (a) k = 0.0, (b and c) k = 2.0. For (b), σ = 10, and for (c), T₀ = 12.2 (representing the intrinsic period). The lifetime ratio β in the different cells is chosen to obey the Gaussian distribution of mean <β> = 2 and standard deviation Δβ = 0.05.</p

Figure 9

<p>The effect of impulsive stimulus on synchronization of 10³ repressilators: Achieving synchronization due to coupling (see stages I and IV); Ruining the achieved synchronization by some external impulses with moderate strength (stage II), and recovering synchronization with the suppressed oscillation amplitude by some strong enough impulses (stage III). The protein TetR concentrations of 10 cells are plotted. k = 20, η = η<i>_e</i> = 3 and τ = 6<<i>T</i>₀. Other parameters are the same as those described for <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000231#pone-0000231-g006" target="_blank">Fig. 6</a>.</p

The number of genes used in the analysis.

<p>The number of genes used in the analysis.</p

Adjacency inference in H (i.e., gray dashed edges in graph B) from matched vertices u, v in graph A.

<p>Vertices a, b are matched vertices that have not been contracted. Vertices c, d are unmatched. Black solid edges are derived from PG(G_obs), CPG(G_obs) or contracted edges. The four different paths found by <b>find_path(u, v)</b> are as follows: (1) (u, v) (green), (2) (u, a, b, v) (blue), (3) (u, b, a, c, v) (orange), and (4) (u, d, v) (pink). In graph A, the first two paths are odd and form two even cycles – (u, v, u) and (u, a, b, v, u) – by adding the gray edge (u, v) in the top right panel. The former disappears after contraction, while the latter generates a new black edge (a, b) in the bottom left panel. The last two paths are merged by two same gray edges (u, v) to form an even cycle – (u, b, a, c, v, u, d, v, u) – that is contracted and generates two new black edges, (b, d) and (c, d). Two numbers on each edge of graph A indicate the copy IDs of the two corresponding vertices in graph B.</p

Figure 7

<p>Oscillation death appearing in region I of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000231#pone-0000231-g006" target="_blank">Fig. 6</a>, where the maximum and minimum of concentration of protein TetR are plotted. (a) σ = 100; (b) τ = 2. Other parameters are the same as those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000231#pone-0000231-g006" target="_blank">Fig. 6</a>.</p

Comparison of inferred distance computed using Sankoff-Warren’s algorithm and our own algorithm.

<p>Each red point is a simulation data point. The proportions of data points calculated using our method with inferred distances larger than those calculated using the Sankoff-Warren method are 0.7%, 5.9%, 0.5% and 3.2% (from the upper to bottom panels, respectively). Green line: y = 0. The variable <i>n</i> is the number of gene families, and <i>r</i> is the duplicated size of G_obs.</p

Representation of a genome, a PG and a CPG.

<p>(A) A rearranged duplicated genome with duplicated size of 3 is represented as a sequence of signed integers, where a positive (negative) sign is represented by the direction of the colored arrow. (B) The same genome is represented as a sequence of extremities (i.e., heads, tails or cap genes). (C) PG of the above genome. Each non-cap gene is cut into head and tail, which becomes two vertices in the partial graph. (D) The vertex reposition of the PG in (C). (E) The contracted PG that is converted from the PG showed in (C) and (D). Each vertex corresponds to an extremity family. Numbers on each edge indicate the copy IDs (i.e., subscripts) of the two extremities connected by the corresponding adjacency. Note that the edge (1^h, 2^t) in (E) corresponds to 2 adjacencies (or edges) in (C), so its multiplicity is 2.</p

Figure 5

<p>Scheme of the respressilator network coupled to a quorum-sensing mechanism.</p

DCJ distance-based NJ tree of human, chicken, mouse and their WGD ancestor.

<p>DCJ distance-based NJ tree of human, chicken, mouse and their WGD ancestor.</p

Figure 6

<p>Impulse-induced dynamics in the coupled system governed by Eqs. 1, 2, 4 and 5: 10³ cells are simulated. (a) Resonance regions (forming Arnold tongues), where two cases corresponding to k = 2 (labeled by red boundaries) and k = 8 (labeled by blue boundaries), respectively, are displayed; (b) The time evolution of TetRs of 10 cells in resonance region II. η = η<i>_e</i> = 0.1 (a and b), k = 8, σ = 10, and τ = <i>T</i>₀ (b); (c) The effect of parameter k on the mean intrinsic period and amplitude. Other parameters are α = 216 and n = 2, The lifetime ratio β in the different cells is chosen to obey the Gaussian distribution of mean <β> = 2 and standard deviation Δβ = 0.05.</p