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## PowerPoint Slideshow about 'Sequence alignment algorithms' - Sophia

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Presentation Transcript

Overview

- Biological background / motivation / applications
- Dot matrix / dynamic programming
- FASTA / BLAST

biology

- Biomolecules are strings from a restricted alphabet
- Length=4 DNA
- Length=20 protein
- Proteins are the working part

Proteins

- Protein is a linear sequence of 20 characters (amino acids)
- Proteins do not maintain linearity
- Folding happens
- Folding determines overall 3-D shape
- Shape determines function

Sequence => Structure => Function

- sequence does not reveal structure
- Much less function
- A sequenceARTUVEDYERRWWUHUK…

Structure

- Pic 1
- Pic 2

function

- Protein A is a constituent of muscle, skin, cartilage, or …
- Protein B catalyzes the transformation of glucose to fructose, or …
- How do we find proteins with similar function?

Nature does not solve the same problem twice (usually)

- Short sequence with a specific function (or shape) is called a domain
- The same domain appears in multiple proteins
- If we find the same domain in multiple proteins that provides a clue to function and/or structure

Amino acids

- Each has the same basic chemical configuration but has a functional group that makes it chemically unique
- They occur in families
- Some functional groups are similar

How biologists study proteins

- Expensive (NMR, x-ray crystallography)
- Discovery of function is difficult
- Few proteins are understood in detail
- Many are known by sequence
- Sequence is easier to get than structure or function

A biological scenario

- Biologist discovers the sequence of a new protein with unknown function
- She has no idea of function
- If sequence can be associated with a known protein sequence we have a clue about structure and/or function
- Most proteins have unknown function

Public databases

- Vast quantities of sequence, structure, function info is deposited into public databases
- A new sequence should be compared to the database

Comparing sequences

- Alignment with exact matchABCTUVABUVABCTUVAB----UV

Alignment with inexact match

- InexactGARUIPPRSTGARVVBUIEEYSTGAR------UIPPRSTGARVVBUIEEYST

Global vs. local alignment

- ABQRTASGGBV
- ABRRRASGVBB
- ABQRTASGGBV
- ABQ------SGGBV

A real alignment

- MyoglobinPDLRKY FKG-A ENFTA DDVQ KSDRPDTKAY FPKFG DLSTA AALK SSPK
- Homology: common ancestry

Real alignment

- Pic 3

Scoring pairs of amino acids

- For amino acid pairs assign a score based on frequency of substitutionATRGUVXQATRCVVXTATRGVVEQAT-----VVEQ

Substitution matrices

- Pam and Blosum are standard substitution matrices
- Also include scores for
- Gap opening
- Gap extension

Scoring amino acid strings

- Sum the individual pair scores
- Database is huge
- Spurious match to random sequence is likely
- Try your name
- E-value is probability of getting a given score from a random sequence

Alignment algorithms

- Dot matrix
- Dynamic programming
- FASTA
- BLAST

Dot Matrix

- Locating regions of similarity between two DNA or protein sequences which provide a great deal of information about the function and structure of the query sequence.
- Similar structure indicates homology, or similar evolution, which provides critical information about the functions of these sequences.

Dot Matrix Contd..

- A dot matrix plot is a method of aligning two sequences to provide a picture of the homology between them.
- The dot matrix plot is created by designating one sequence to be the subject and placing it on the horizontal axis and designating the second sequence to be the query and placing it on the vertical axis of the matrix.

Dot Matrix Contd..

- At each position within the matrix, a point is plotted if the horizontal and vertical elements are identical.
- Diagonal lines within the resulting matrix indicate regions of similarity. A simple dot matrix plot is shown in Figure A.

Dot Matrix with noise reduction

- A certain percentage of the matches between sequence elements can be expected to be the result of the random nature of their evolution. These random matches are considered “noise" and are filtered out to enhance the diagonal lines.

Dot Matrix

- Noise Reduction

a) Noise reduction in dot matrix can be done by centering a substring of elements of the query sequence over each element in the subject sequence and determining the number of corresponding elements within this “window”.

Dot Matrix

b) If the number of corresponding elements exceeds a specified threshold then a point is plotted for the center element. This is demonstrated in figure B.

Dot Matrix

- Advantages: Readily reveals the presence of insertions/deletions and direct and inverted repeats that are more difficult to find by the other, more automated methods.
- Disadvantages:Most dot matrix computer programs do not show an actual alignment. Does not return a score to indicate how ‘optimal’ a given alignment is.

Dynamic Programming

- Dynamic programming (DP) algorithms are a general class of algorithms typically applied to optimization problems.
- For DP to be applicable, an optimization problem must have two key ingredients:
- a) Optimal substructure – an optimal solution to the problem contains within it optimal solutions to sub-problems.

b) Overlapping sub-problems – the pieces of larger problem have a sequential dependency.

Dynamic Programming

- DP works by first solving every sub-sub-problem just once, and saves its answer in a table, thereby avoiding the work of re- computing the answer every time the sub-sub-problem is encountered. Each intermediate answer is stored with a score, and DP finally chooses the sequence of solution that yields the highest score.

Dynamic Programming

- Path Matrix

Dynamic Programming

- Both global and local types of alignments may be made by simple changes in the basic DP algorithm.
- Alignments depend on the choice of a scoring system for comparing character pairs and penalty scores (e.g. PAM and BLOSUM matrixes – covered before)

Scoring functions – example:

w (match) = +2 or substitution matrix

w (mismatch) = -1 or substitution matrix

w (gap) = -3

Dynamic Programming

- Global Alignment (Needleman-Wunsch)

a) General goal is to obtain optimal global alignment between two sequences, allowing gaps.b) We construct a matrix F indexed by i and j, one index for each sequence, where the value F(i,j) is the score of the best alignment between the initial segment x1…i of x up to xi and the initial segment y1…j of y up to yj. … We begin by initializing F(0,0) = 0. We then proceed to fill the matrix from top left to bottom right. If F(i-1, j-1), F(i-1,j) and F(i,j-1) are known, it is possible to calculate F(i,j).

Dynamic Programming

F(i,j) = max { F(i-1, j-1) + s(xi , yj );F(i-1,j) – d;F(i, j-1) – d. }

where s(a,b) is the likelihood score that residues a and b occur as an aligned pair, and d is the gap penalty.

- Once you construct the matrix, you trace back the path that leads to F(n,m), which is by definition the best score for an alignment of x1…n to y1…m.

Dynamic Programming

- Global Dynamic programming matrix

Dynamic Programming

- Local alignment (Smith-Waterman)Two changes from global alignment:1. Possibility of taking the value 0 if all other options have value less than 0. This corresponds to starting a new alignment.2. Alignments can end anywhere in the matrix, so instead of taking the value in the bottom right corner, F(n,m) for the best score, we look for the highest value of F(i,j) over the whole matrix and start the trace-back from there.

F(i,j) = max { 0;F(i-1, j-1) + s(xi , yj ); F(i-1,j) – d;F(i, j-1) – d.}

Dynamic Programming

- Local Dynamic programming matrix

Dynamic Programming

- Advantages:Guaranteed in a mathematical sense to provide the optimal (very best or highest-scoring) alignment for a given set of scoringfunctions.
- Disadvantages:

a) Slow due to the very large number of computational steps: O(n 2).b) Computer memory requirement also increases as the square of the sequence lengths.

Therefore, it is difficult to use the method for very long sequences.

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FASTA - Idea -- Problem of Dynamic Programming

D.P. compute the score in a lot of useless area for optimal sequence

- FASTA focuses on diagonal area

FASTA - Heuristic -

- Heuristic

Good local alignment should have some exact match subsequence.

FASTA focus on this area

FASTA - Hi Level Algorithm -

Hi level algorithm

Let q be a query

max 0

For each sequence, s in DB

compare q with s and compute a score, y

if max < y

max y;

bestSequence s ;

Return bestSequence

FASTA - Algorithm -

- Step 1

Find all hot-spots

// Hot spots is pairs of words of length k that exactly match

Sequence 1

Hot Spots

Sequence 2

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Location

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FASTA - Algorithm -- Step 1 in detail

Use look-up Table

Query : G A A T T C A G T T A

Sequence: G G A T C G A

Dot—Matrix

Look-up Table

FASTA - Algorithm -

- Step 2

Score the Hot-spot and locate the ten best diagonal run.

// There is some scoring system; ex. PAM250

FASTA - Algorithm -

- Step 3

Combine sub-alignments into one alignment with GAP

GAP

One of local alignment

FASTA - Algorithm -

- Step 4

# Consider weighted direct graph.

# Let node be a sub-alignment found in step 1

# Let u and v be nodes

# Edge (u,v) exists if alignment u is before in the sequence.

# Each edge has gap penalty (negative)

# Find the maximum weight path

Sub-sequence

Edge

One Sequence

FASTA - Algorithm -

- Step 5

Use the dynamic programming in restricted area around the best-score alignment to find out the higher-score alignment than the best-score alignment

Width of this band is a parameter

FASTA - Algorithm -

- Summary of Algorithm

1: Find all hot-spots

// Hot spots is pairs of words of length k that exactly match

2: Score the Hot-spot and locate the ten best diagonal run.

3: Combine sub-alignments into one alignment

4: Score Each alignment with gap penalty and pick up the best-score alignment

5: Use the dynamic programming in restricted area around the best-score alignment to find out the alignment greater than the best-score alignment.

FASTA - Complexity -

- Complexity

# Step 1 and 2 // select the best 10 diagonal run

Let n be a sequence from DB

O(n) because Step 1 just uses look up the table

O(n) << O(mn) m,n = 100 to 200

FASTA - Complexity -

# Step 3 and 4 // compute the MAX Weight Path

Let r be the number of sub-alignments. (r = 10)

Lets be the number of edges

O(r2) < O(m*n)

n1 n2 n3

n1

n2

n3

1% of D.P because r2 =102

and m*n >= 104

Positive Weight

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Max Weight Path

FASTA - Complexity -

# Step 5 // compute partial D.P.

Depends on the restricted area < O(mn)

Therefore, FASTA is faster than D.P.

Width of this band is a parameter

BLAST - Heuristic -

- Another Heuristic algorithm
- Heuristic but evaluating the result statistically.

Homologous sequence are likely to contain a short high scoring word pair, a hit.

BLAST tries to extend it on the both sides to get optimal sequence.

A T T A G …………….

Sequence

Short high score Word

BLAST - Algorithm -

Neighborhood Word

- Step 1: preprocessing Query

Compile the short-hit scoring word list from query.

The length of query word,w, is 3 for brosom scoring

Threshold T is 13

BLAST - Algorithm -

- Step 1 – 2

Create neighborhood words for each query word

Query Word

Neighborhood words

BLAST - Algorithm -

- Step 2: Scanning DB

For each words list, identify all exact matches with DB sequences

Neighborhood Word list

Query Word

Sequences in DB

Sequence 1

Sequence 2

Step 2

Step 1

The purpose of Step 1 and 2 is as same as FASTA

BLAST - Algorithm -

- Step 2-2

Method 1: Hash Table

Query: LAALLNKCKTPQGQRLVNQWIKQPLMD

Hash Table

Word list

BLAST – Algorithm -

- Step 3 (Search optimal alignment)

Let S be a score of hit-word

For each hit-word, extend ungapped alignmentin both directions.

- Step 4 (Evaluate the alignment statistically)

Stop extension when E-value (depending on score S) become less than threshold. The hit-word is called High Scoring Segment Pair. BLAST return it

E-value = the number of HSPs having score S (or higher) expected to

occur only by chance.

Smaller E-value, more significant in statistics

Bigger E-value , by chance

A T T A G …………….

Sequence

Hit Word

BLAST - Algorithm -

- Step 3 -2

Definition of E-Value

The expected number of HSP with the score at least S is :

E = K*n*m*e-λS

K, λ is constant depending on model

n, m are the length of query and sequence

The probability of finding at least one such HSP is:

P = 1 - eE

If a word is hit by chance (E-value is bigger),

P become smaler.

Running Time

D.P

16.989 [s]

FASTA

0.618 [s]

BLAST

0.118 [s]

BLAST - Running Time -- Running Time

The length of Query : 153

DB size : 5997 sequences

PC : Pentium 4

By Dr. Takeshi Kawabata

Nara Sentan Gijyutu University

Comparison of Algorithm

- Dynamic Programming

1. most sensitive result

D.P uses all information of two sequence

2. Running time is slow

D.P compute the useless area for computing the optimal sequence.

Comparison of Algorithm

- FASTA

1. Less sensitive than D.P and BLAST

FASTA uses partial information to speed up the computaiotn.

FASTA does not evaluatethe resultstatistically.

2. Running time is faster D.P

the same reason as the above.

Comparison of Algorithms

- BLAST

1. Sensitive than FASTA

BLAST evaluate the result statistically.

2.Faster than FASTA

Because BLAST evaluate the entire DB with the same threshold based on statistics. BLAST eliminate noises and reduces the running time.

FASTA vs BLAST

BLAST

Compare the query and sequences in DB

with the same threshold.

FASTA

compare the query and a sequence one by one

And compare the each result.

DB

DB

Query

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