Types of alignments.

Assumptions:

1. I assume that positions of all neighbors are detected.

2. Neighbors are defined as closest aligned pairs of nucleotides on the flanking sequence. It is not decided yet should neighbors have matching nucleotides or not.

3. Left neighbor is always less then corresponding right one.

4. SNP position on the flanking sequence is always between neighbors. SNP position on the subject sequence is always between left and right neighbors.

5. Allele is the part of the sequence between neighbors, excluding neighbors themselves.

Loctype 1: Insertion on the subject sequence.

In this case single nucleotide on the flanking sequence is substituted with the sequence of nucleotides with total length more than one. In this case the following equations are always true:

Rs – Ls – 1 > 1

Rf – Lf – 1 = 1

	Left neighbor	SNP position	Right neighbor	Distance between neighbors
Flanking sequence (Q)	Lf = 199	Sf = 200	Rf = 201	201-199-1 = 1
Subject sequence (S)	Lc = 2034	Sc = 0	Rc = 2062	2062-2034 -1 = 27

Loctype 2: True SNP.

This is a restricted situation of Loctype 1. In this case exactly one nucleotide on the flanking sequence is replaced with exactly one nucleotide on the subject sequence. For this case the following equations are always true:

Rs – Ls – 1 = 1

Rf – Lf – 1 = 1

	Left neighbor	SNP position	Right neighbor	Distance between neighbors
Flanking sequence (Q)	Lf = 199	Sf = 200	Rf = 201	201 – 199 – 1
Subject sequence (S)	Lc = 2051	Sc = 2052	Rc = 2053	2053 – 2051 -1

Loctype 3: Deletion on the subject sequence.

In this situation part of the flanking sequence, which includes SNP site is deleted from the contig. For such case it is always true:

Rs – Ls – 1

Rf – Lf – 1 >= 1

	Left neighbor	SNP position	Right neighbor	Distance between neighbors
Flanking sequence (Q)	Lf = 163	Sf = 200	Rf = 201	201-163-1 = 27
Subject sequence (S)	Lc = 2034	Sc = 0	Rc = 2035	0

Loctype 4: Range insertion.

In this case shorter part of flanking sequence, containing SNP site is replaced with longer subsequence on the subject. Neighbours are not adjacent to the declared SNP site.

Rc – Lc – 1 > 1

Rf – Lf – 1 > 1

Rc – Lc < Rf - Lf

	Left neighbor	SNP position	Right neighbor	Distance between neighbors
Flanking sequence (Q)	Lf = 197	Sf = 200	Rf = 202	202-197-1 = 4
Subject sequence (S)	Lc = 2033	Sc = 2036	Rc = 2038	2038-2033-1=4

Loctype 5: Range substitution.

Here the part of the flanking sequence is replaced with another sequence of nucleotides having exactly the same length. Left and right flanking neighbors are not adjacent to the declared SNP site.

Rc - Lc – 1 >= 1

Rf – Lf – 1 >= 1

Rc – Lc = Rf – Lf

	Left neighbor	SNP position	Right neighbor	Distance between neighbors
Flanking sequence (Q)	Lf = 197	Sf = 200	Rf = 202	202-197-1 = 4
Subject sequence (S)	Lc = 2033	Sc = 2036	Rc = 2038	2038-2033-1=4

Loctype 6: Range deletion.

Part of the flanking sequence containing SNP site is replaced with shorter subsequence on the subject. Neighbors are not adjacent to the declared SNP site.

Rc – Lc – 1 > 1

Rf – Lf – 1 > 1

Rc – Lc > Rf - Lf

	Left neighbor	SNP position	Right neighbor	Distance between neighbors
Flanking sequence (Q)	Lf = 183	Sf = 200	Rf = 202	202 -183 -1 = 18
Subject sequence (S)	Lc = 2033	Sc = 0	Rc = 2044	2044 -2033 -1=10

Alignment Profiling: Profiling function.

Weights of the mismatches should not be equal along the flanking sequence. The weight should be assigned according to some profiling function. Because of the nature of the sequencing process it is normal to have more errors concentrated on the tails of the flanking sequence. We have to take this fact in count to save alignments which can easily be disregarded because of the errors in the tails of the query sequence. Let assume, that the distribution of the errors follow the rule of natural distribution starting some point of the flank. This can be approximated with the function F(x):

Quality of the alignment can be calculated using the following equation:

Having:

Optimistic identity rate can be calculated by this function. I named it “optimistic”, because I didn’t include mismatches:

Mismatch will affect the numerator of the function. The function to describe mismatches will have parts of unmovable discontinuations. Strictly speaking we have to take an integral for this function to get the effect of the mismatches, but due to corpuscular nature of the alignment we can easily replace it with the sum of elementary functions.

; where m – vector of mismatch positions.

Thus, the final function: