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Can be expressed as a product of mutation operators on an
Can be expressed as a product of mutation operators on an initial (extended) AZD-8055 manufacturer sequence state. For example, the indel history illustrated in panels a and b of Fig. 4 can be represented as a series ??^ ^ ^ ^ of indel events, M D ?; 3? M I ?; 2? M D ?; 3? M I ?; 1?, on the initial basic state sI (given above). Then, the final result of this indel history is expressed as: ^ ^ ^ ^ hsI jM D ?; 3 I ?; 2 D ?; 3 I ?; 1?. Figure 4c shows the MSA among the initial, intermediate and final sequence states. Figure 4d shows the resulting PWA between the initial and final sequence states. These new tools, the ancestry indices and the operator representation of mutations, will play essential roles in our theoretical development described below. In the SID models [21], each evolutionary process was expressed as a (time-recorded) trajectory of sequence states, each of which was represented by an array of residues (without ancestry assignments). In consequence, an instantaneous transition from a state to the next state was often expressed as a summation of multiple possible muta tions. (For example, the transition from ? ; A to 0 ^ ^ ? could result from either M D ?; 1?or M D ?; 2?). Ancestry indices help avoid such ambiguous channels byEzawa BMC Bioinformatics (2016) 17:Page 8 of^ Fig. 3 Operator representation of mutations. a A substitution operator, M S ?; T C ? The residues before and after the substitution are in boldface in blue ^ ^ and red, respectively. b An insertion operator, M I ?; 3? and a fill-in operator, F ?; ; A; C ? The inserted sites are shaded in cyan. (Note that “A” at the top ^ of the rightmost inserted column means the ancestry index of 10, not the residue state of A). c A deletion operator, M D ?; 4? The sites to be deleted are shaded in magenta. In this figure, the extended sequence states were used for illustration. The bra-vector below each array denotes the state. The extended state, s, is identical to that in Fig. 2b. Each vertical arrow indicates the action of the mutation operator beside it. Note that the first arguments of all operators and the second argument of the deletion operator specify positions along the sequence, and not ancestries (specified at the top of the sites)uniquely defining each instantaneous state-to-state transition as an action of a single mutation. (In the above ex ample, the former causes the transition from ??; 2 to ?? ??, and the latter yields the transition fromto ?? ??). This, in conjunction with the operator representation of mutations, enables us to shift the focus from the trajectory of sequence states to the history of mutations, especially indels. This shift of focus, as wellFig. 4 Example indel history and resulting alignments. a An example indel history in terms of the bra-vectors of sequence states and indel operators. b The graphical illustration of the history using basic sequence states. Each sequence state in panel a is horizontally aligned with its graphical representation in panel b. c The resulting MSA among the sequence states that the indel history went through. d The resulting PWA between the initial and final sequences. In both c and d, the bold italicized characters in the leftmost column are the suffixes indicating the sequence states in panel a. In panels b, c, and d, the number in each site (cell) represents its ancestry, but not necessarily its position PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/28404814 along the sequence. The `A’ in the final sequence abbreviates 10. The same shading scheme as in Fig. 1 is used.

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