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:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and right parsimonious and left aligned. (definition of left parsimony) <br>
:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and right parsimonious and left aligned. (definition of left parsimony) <br>
:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and each allele does not end with the same type of nucleotide. (lemma 1) <br>
:⇒ A variant is normalized if and only if it is has no superfluous nucleotides on the left side and each allele does not end with the same type of nucleotide. (lemma 1) <br>
== Uniqueness ==
It is important that the normalization results in a unique representation of the variant. Before we begin the proof, intuitively, accept that any representation of a variant can be
transformed to another representation by adding nucleotides from the reference sequence to either ends of all the alleles at the same time or removing equivalent nucleotides from the ends of
all the alleles at the same time.
Now suppose there are 2 normalized variants A and B. Suppose A is at a different position from B and B is to the right of A (without loss in generality), this is not possible because by the definition of a normalized variant, it is left aligned,
and if they were at different positions, that means B may be left aligned to A since they represent the same variants leading to a contradiction. So A and B must be at the same position.
Now, suppose that A and B are at the same position but are of different lengths where B is longer than A (without loss in generality), this is not possible as B is then not parsimonious, so B can be trimmed to the same length as A.
Thus A and B have to be at the same position and have the same length and variant normalization is unique.
= Implementation =
= Implementation =
*GATK v3.1-1-g07a4bf8
*GATK v3.1-1-g07a4bf8
*vt normalize v0.5
*vt normalize v0.5
= Here is an example where this normalization algorithm fails =
We distinguish the concepts of normalization and decomposition/reconstruction of variants as follows:
Normalization involves reducing representations of a variant to a canonical representation. Normalization can be applied to biallelic variants or multiallelic variants. The problem of normalization is solvable and there exists a unique representation that is left aligned and parsimonious. Mathematical proof is published. [http://bioinformatics.oxfordjournals.org/content/suppl/2015/02/19/btv112.DC1/VtNormApplicationNote_supp_20141113_1346.pdf]
Decomposition of variants involves the breaking down of a variant record into multiple records. It may be done vertically - as in multiallelics becoming biallelics or it can be done horizontally - a cluster of indels and SNPs represented as a complex variant being splitted up into several records. Horizontal decompositions in general do not have a unique solution. Similarly, reconstruction combines several variant records into a single record and can be done vertically and horizontally too. Vertical decomposition of a multiallelic variant to a set of biallelic records is a many to one function. Construction of a set of biallelic variants into a multiallelic record is not unique as you need to considered all possible permutations of the haplotypes containing your alleles.
If your example contains the decomposition or reconstruction of variants, then it is probable that you can find inconsistencies.
It is important to distinguish the difference between normalization and decomposition/reconstruction. The notion of normalization implies that a variant can be reduced to a standardized form. If you were to include decomposition and reconstruction in your notion of normalization, you are bound to find inconsistencies simply due to the inherent issues of identifiability.
When performing decomposition and construction, I think the following factors should be considered:
* Are your variants describing just a single individual or a population?
* Are the genotypes (if any) in your individual(s) phased?
Depending on the context, you will obtain different answers.
[https://github.com/atks/vt/issues/16 An example of inconsistent variant representation due to using vt normalize]
= Citation =
[http://bioinformatics.oxfordjournals.org/content/31/13/2202 Adrian Tan, Gonçalo R. Abecasis and Hyun Min Kang. (2015) Unified Representation of Genetic Variants. Bioinformatics.]
= Translations =
A mandarin translation can be found [http://www.lyon0804.com/fan-yi-variant-normalization.html here]
= Maintained by =
= Maintained by =
This page is maintained by [mailto:atks@umich.edu Adrian].
This page is maintained by [mailto:atks@umich.edu Adrian].
