79 research outputs found

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

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    <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<sub>obs</sub>.</p

    Relative DCJ distance among the WGD ancestor, chicken, mouse and human.

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    <p>Relative DCJ distance among the WGD ancestor, chicken, mouse and human.</p

    Reconstructing G<sub>dup</sub> from the genome (G<sub>obs</sub>) of <b>Figure 1A</b>.

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    <p>This figure shows how graph A changes during the solution. In this simple example, step 2 is not necessary, but here we still calculate the weights N<sub>p</sub>, C<sub>p</sub> and use step 2 to infer the last two adjacencies , , , , and of G<sub>dup</sub> (or H) ahead of linearizing circular chromosomes, to show how step 2 works. Different vertex colors indicate different gene families. Edges with multiplicity <i>k</i> are represented as <i>k</i> edges for a clear display. The numbers on each edge are the copy IDs of the two vertices incident to the corresponding edge in graph B. Blue numbers are the weights N<sub>p</sub>, C<sub>p</sub> for the pair of vertices linked by gray dotted edge.</p

    Transforming paths to black cycles.

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    <p>Vertices u, v are matched. The upper path is (u, a, b, c, d, e, f, v), and the bottom path is (u, g, h, e, d, i, j, k, v). Four colored subpaths on the left are contracted into four edges in the right cycles, respectively. An odd path is transformed into an even cycle, while an even path is transformed into an odd cycle. Solid and dashed edges correspond to black and gray edges, respectively.</p

    Application of the heuristic algorithm to four simulation datasets.

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    <p>Each light blue point in each panel corresponds to a data point. Green line: x = y. Inner axis labels represent DCJ distance, whereas outer labels show relative DCJ distance. The Y value of the dark blue dot is 0.1 (relative DCJ distance) in each plot, where <i>n</i> is the number of gene families and <i>r</i> is the duplicated size of G<sub>obs</sub>, and the blue numbers (DCJ distance and relative DCJ distance) below each blue cycle represent the corresponding X values. Note that the inferred and simulated distances are almost the same when the relative simulated distance is smaller than 0.4. The distance is less than 0.1, until the relative simulated distance increases to approximately 0.6. The relative DCJ distance between simulated and inferred G<sub>dup</sub> is small when the simulated distance is smaller than 0.25 (<i>r</i> = 3) or 0.33 (<i>r</i> = 4).</p

    The number of genes used in the analysis.

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

    Representation of a genome, a PG and a CPG.

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    <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<sup>h</sup>, 2<sup>t</sup>) in (E) corresponds to 2 adjacencies (or edges) in (C), so its multiplicity is 2.</p

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

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

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

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    <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<sub>obs</sub>), CPG(G<sub>obs</sub>) 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

    Revealing Solid–Liquid Equilibrium Behavior of 4‑Fluorobenzoic Acid in 12 Pure Solvents from 283.15 to 323.15 K by Experiments and Molecular Simulations

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    The solubility of 4-fluorobenzoic acid (4FBA) in 12 pure solvents (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, isobutanol, 1-pentanol, ethyl formate, methyl acetate, ethyl acetate, acetonitrile, and acetone) from 283.15 to 323.15 K at atmospheric pressure was determined using the gravimetric method. Within the experimental temperature range, the solubility of 4FBA increased with increasing temperature in all solvents. Four thermodynamic models (modified Apelblat model, NRTL model, Van’t Hoff model, and λh model) were selected to correlate the experimental solubility data of 4FBA and assess the goodness of fit. The results revealed that the modified Apelblat equation exhibited the highest fitting accuracy. Furthermore, the mixing thermodynamic properties (mixing Gibbs free energy, mixing enthalpy, and mixing entropy) derived from the NRTL equation indicated that the mixing process of 4FBA in the selected solvents is spontaneous and entropy-driven. To elucidate the solid–liquid equilibrium behavior of 4FBA in pure solvents, the structural properties of the solute–solvent molecules were investigated. The physicochemical properties of solvents, solvation free energies, and radial distribution functions were studied to explain the solid–liquid equilibrium behavior of 4FBA
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