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If the ends of each allele is the same nucleotide, it is not left aligned or parsimonious on the right side.
 
If the ends of each allele is the same nucleotide, it is not left aligned or parsimonious on the right side.
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==== Proof of property ====
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ProofSuppose an indel is already left aligned. In order to shift the variant to the right, we have to be able to truncate the first leftmost nucleotide in each allele without any loss of information (i.e. we can reconstruct the original   alleles from the right aligned version of the variant given the reference genome). In order to guarantee this, the first leftmost nucleotide in each allele should be the same type of nucleotide (in other words, the same as the reference nucleotide). The truncation of the first leftmost nucleotide should not result in any empty allele. To achieve this, we need to first extend the rightmost end of each allele by the base observed on the reference sequence and then attempting to truncate the alleles simultaneously on the leftmost end. Thus, an indel is not left aligned if the rightmost nucleotide of each allele is represented by the same type of nucleotide.  This procedure also ensures parsimony on the right side of the variants.
 
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Suppose an indel is already left aligned. In order to shift the variant to the right, we have to be able to truncate the first leftmost nucleotide in each allele without any loss of information (i.e. we can reconstruct the original alleles from the right aligned version of the variant given the reference genome). In order to guarantee this, the first leftmost nucleotide in each allele should be the same type of nucleotide (in other words, the same as the reference nucleotide).
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The truncation of the first leftmost nucleotide should not result in any empty allele. To achieve this, we need to first extend the rightmost end of each allele by the base observed on the reference sequence and then attempting to truncate the alleles simultaneously on the leftmost end. Thus, an indel is not left aligned if the rightmost nucleotide of each allele is represented by the same type of nucleotide.  This procedure also ensures parsimony on the right side of the variants.
      
= Algorithm for Normalization =
 
= Algorithm for Normalization =
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