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Fig. 1 | Algorithms for Molecular Biology

Fig. 1

From: Coordinate systems for supergenomes

Fig. 1

Projections of a supergenome graph. An example how the projection of an artificial MSA \(\mathfrak{A}\) to a supergenome graph \(\Gamma (\mathfrak{A})\) can be done. Starting point is the MSA \(\mathfrak{A}\) shown in (i), which comprises five blocks (\(B_1\), ..., \(B_5\)), each consisting of up to four intervals from the four genome assemblies (distinguished by colors: \(\mathcal {G}_1\) blue, \(\mathcal {G}_2\) green, \(\mathcal {G}_3\) orange, \(\mathcal {G}_4\) purple) with one contig each (\(c_1\), ..., \(c_4\)). The intervals are designated as \(\beta _{k,l}=(\mathcal {G}_l,c_l,i_{k,l},j_{k,l},+1) \in B_k\) and \(\bar{\beta }_{k,l}=(\mathcal {G}_l,c_l,i_{k,l},j_{k,l},-1) \in B_k\).       To construct the supergenome graph first the predecessor of each interval is determined by sorting the intervals separately for each assembly. By assumption, intervals do not overlap. The ordered set of each assembly is shown in panel (ii). Only these orders are relevant in subsequent steps, hence we suppress the positional information from now on. The interval order implies a separate predecessor relation among blocks (iii), with a colored arrow from \(B_1\) to \(B_2\) implying that \(B_1\) is a predecessor of \(B_2\) w.r.t. the assembly indicated by the color. The supergenome graph \(\Gamma (\mathfrak{A})\) has all blocks of \(\mathfrak{A}\) as its vertices (iv). The predecessor relations among the blocks define the colored, directed edges (v)

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