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Fig. 2 | BMC Bioinformatics

Fig. 2

From: Progressive multiple sequence alignment with indel evolution

Fig. 2

Overview of the progressive algorithm. The algorithm traverses a guide tree (indicated by the shadow in Panel a) in postorder. At each internal node, the evolutionary paths from the two children down to the leaves (doted lines in Panel a) are aligned by full maximum likelihood under the PIP model, using a dynamic programming approach (DP). Since the likelihood function does not increase monotonically in the MSA length (see Fig. 1), the DP accommodates the MSA length along a third dimension (indicated by k in Panels a, b); thus, it works with cubic matrices (in contrast to the traditional quadratic DP alignment). The forward phase of the DP stores likelihood values in three sparse matrices (Panel b: SM for matching columns; SX and SY to introduce new indel events). Further, matrix TR (Panel a) at position (i,j,k) records the name of the DP matrix (either “ SM”, “ SX”, or “ SY”) with highest likelihood at (i,j,k). An optimal alignment is determined by backtracking along TR (indicated in Panel a by the arrows in the projection of TR onto the plane). Note that the likelihood function marginalises over all indel scenarios compatible with putative homology (Panel c)

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