# Introduction to Bioinformatics 2. Biology Background

Biotechnology

Oct 2, 2013 (4 years and 9 months ago)

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Sequence Alignments with Indels

Evolution produces insertions and deletions (indels)

Good example:

MHHNALQRRTVWVNAY MHHNALQRRTVWVNAY

MHHALQRRTVWVNAY
-

MHH
-
ALQRRTVWVNAY

Blosum Score = 2 (end =
-
6) Score = 79 (gap =
-
6)

An alignment must have equal length aligned sequences

So, we must add gaps at the start and the ends

Combinatorially difficult problem to find best indel solution

Gap

So far we ignored gaps

A gap corresponds to an insertion or a deletion
of a residue

A conventional wisdom dictates that the
penalty for a gap must be several times greater
than the penalty for a mutation. That is
because a gap/extra residue

Interrupts the entire polymer chain

In DNA shifts the reading frame

Gap Penalties

Gaps are penalised

Write w
x

to indicate the penalty for a gap of length x

For example, each gap scores
-
6, so w
x

=
-
6*x

One common scheme is

Score
-
12 for opening a gap

And
-
2 for every subsequent gap

i.e., w
x

=
-
12
-

2*(x
-
1)

Start and end gap penalties often set to zero

But this can leave a doubt

Dot Matrix Representations (Dotplots)

To help visualise best alignments

Plot where each pair is the same, then draw best line

M

N

A

L

S

Q

L

N

N

A

L

M

S

Q

N

H

M

N

A

L

S

Q

L

N

N

A

L

M

S

Q

N

H

Getting Alignments

from Dotplot Paths

M

N

A

L

S

Q

L

N

N

A

L

M

S

Q

N

H

Indicates that M
matches with a gap

Indicates that L
matches with a gap

Stage 1:

Align middle

Use triangles

To indicate gaps

NAL
-
SQLN

NALMSQ
-
N

Stage 2:

Sort the ends out

MNAL
-
SQLN
-

-
NALMSQ
-
NH

Dotplots for Real Proteins

Need a way to automatically find the best path(s)

Dynamic Programming Approach

BLAST is quick

But not guaranteed to find best alignment

Gapped blast has indels, but no guarantee…

Dynamic Programming:

Also known as: Needleman
-
Wunsch Algorithm

Can use it to draw the Dotplot paths

From that we can get the alignment

Mathematically guaranteed

To find the best scoring alignment

Given a substitution scheme (scoring scheme, e.g., BLOSUM)

And given a gap penalty

The Needleman
-
Wunsch algorithm

A smart way to reduce the massive number of
possibilities that need to be considered, yet still
guarantees that the best solution will be found (Saul
Needleman and Christian Wunsch, 1970).

The basic idea is to build up the best alignment by
using optimal alignments of smaller subsequences.

The Needleman
-
Wunsch algorithm is an example of
dynamic programming, a discipline invented by
Richard Bellman (an American mathematician) in
1953!

Dynamic Programming

A divide
-
and
-
conquer strategy:

Break the problem into smaller
subproblems
.

Solve the smaller problems optimally.

Use the sub
-
problem solutions to construct an
optimal solution for the original problem.

Dynamic programming can be applied only to problems
exhibiting the properties of overlapping
subproblems
.

Examples include

Trevelling

salesman problem

Finding the best chess move

Overview of Needleman
-
Wunsch

Four Stages

1.
Initialise a matrix for the sequences

2.
Fill in the entries of that matrix (call these S
i,j
)

At the same time drawing arrows in the matrix

3.
Use the arrows to find the best scoring path(s)

4.
Interpret the paths as alignments as before

Illustrate with: MNALQM & NALMSQA

Stage 1

Initialising the Matrix

Draw the grid

Put in increasing gap penalties

Then put in BLOSUM scores

Stage 2

Putting Scores and Arrows in

Put the score in Draw the arrow

Mathematically, we are calculating:

Where:

S
i,j

is the matrix entry at (i,j) [the one we want to fill in]

S
i
-
1,j
-
1

is above and to the left of this

s(a
i
,b
j
) is the BLOSUM score for the

i
-
th residue from the horizontal sequence and

j
-
th residue from the vertical sequance

(i.e., just the scores we have written in brackets)

This diagram might help:

Fill in the next row and column

A Close up View

Continue filling in the S
i,j

entries

Stage 3

Finding the best path

Scores S
i,j

in the matrix

Are the BLOSUM scores for alignments

However!

We must take into account final gap penalties

Look down the final column and along the final row

Find the highest scoring number

Remembering to take off the gap penalty the correct
number of times

Finding the best path

So, the best path is:

Stage 4: Generating the Alignment

Firstly, draw the Dotplot

Secondly, Generate the Alignment

Using the technique previously mentioned

This path gives us an alignment with three gaps

M N A L
-

-

Q M

-

N A L M S Q A

S =
-
6 6 4 4
-
6
-
6 5
-
1 = 0

Should check that you get the same score

As on the diagram

Other Alignments

MNALQ
-
M
-

MNALQM
--

-
NALMSQA (score=
-
4)
-
NALMSQA (score=
-
5)

Smith
-

Waterman Alterations

To make the algorithm find best
local

alignments

Adjustments only to the scoring scheme for S
i,j
:

The scoring scheme must include:

Some negative scores for mismatches

When S
i,j

becomes negative, set it to zero

So local paths are not penalised for earlier bad routes

To find best local alignment

Find highest scoring matrix position (anywhere)

And work backwards until a zero is reached

Local and Global Alignments

Needleman & Wunsch

best global alignments

Smith & Waterman

best local alignments

For illustration purposes only

Calculations done slightly differently (don’t worry)