# Bioinformatics

## In the previous classes

• Hamming distance: count mismatches
• Levenstein distance: count mismatches and indels
• Dot plots
• Global and semi-global alignment

# Different questions need different alignments

## Different alignments for different questions

• Global alignment compares genes to genes, or proteins to proteins
• We expect that both sequences are similar
• Semi-global alignment compares genes to genomes
• We expect that query is similar to part of subject
• Local alignment compares genomes to genomes
• We expect that part of the query is similar to part of subject

## Global, Semi-Global and Local alignment

Global
all sequences must match.
Each gap is penalized
Semi-global
all sequences must match, but one may be shorter than the other.
external gaps are not penalized
Local
Some part of the sequence must match
external gaps are not penalized
can be with or without internal gaps

Wikipedia

## Part of query to part of subject

ABRACADABRA
CHUPACABRA

We have two alignments

      ABRACADABRA      ABRACADABRA
||||                    ||||
CHUPACABRA              CHUPACABRA

External gaps do not count

# Dot plots show the alignments

## Looking the diagonals

For local alignment we have two cases

• Ungapped, where we can only move in diagonal
• Gapped, where we can move diagonal, horizontal, and vertical
• Horizontal and vertical movement gives gaps

Global and semi-global alignments always have gaps

# Local alignment is not like global alignment

## We found global alignment using distances

“Distance” means that smaller numbers are better

If the distance is 0, then the two sequences are identical

If the distance is small, the two sequences are similar

If the distance is big, the sequences are different

## Local alignment is not a distance

Since external gaps do not count, we can always use them

In this case the smallest distance is always 0

The smallest cost is achieved taking one letter

         ABRACADABRA
|
CHUPACABRA

We cannot find local alignments using small values

(it is not a minimization problem)

Instead of finding a minimum, we look for a maximum

• Matching places get positive score
• Mismatch and gaps get negative score

The philosophy is the same, but we look for big numbers instead of small numbers

# We look for the Optimal Alignment

## Dot plot becomes a matrix

Initially we placed 1 or 0 on each cell depending on match or mismatch

Now we put positive or negative numbers, depending of single-letter scores

$D_{i,j} = \text{Score}(q_i,s_j)$

## We can find optimal alignment efficiently

Once the “dot plot matrix” is complete, it is easy to find the optimal score

• Global alignment: find the largest sum from corner to corner

• Semi-global alignment: find the largest sum from side to side

• Local alignment: find the largest sum in any diagonal

## Local alignment score formula

We have three options as before, but not negative values

$M_{i,j} = \max\begin{cases} M_{i-1,j-1} + \text{Score}(q_i,s_j)\\ M_{i-1,j} + \text{gap} \\ M_{i,j -1} + \text{gap}\\ 0\end{cases}$

Notice we use $$\max$$ instead of $$\min$$

# Gaps

## Gap penalty

We prefer this alignment

GGGTAACCTACCTC
||| ||||| ||||
GGGCAACCTGCCTC

GGGT-AACCTA-CCTC
|||  |||||  ||||
GGG-CAACCT-GCCTC

Thus, gap penalty must be greater than mismatch penalty

## Long gaps instead of short ones

We prefer this alignment

TCAAAGAG---GATA
|||  |||   ||||
TCA--GAGGGGGATA

TCAAAGA-G-G-ATA
|| | || | | |||
TC-A-GAGGGGGATA

We want few long gaps instead of many short gaps

## Affine gaps

Gap values must reflect how real insertions and deletions occur in nature

We observe that, once an indel event starts, it can easily grow

If the polymerase jumps, then it can jump a long distance

To represent this, we use affine gaps

## Linear v/s affine

So far we considered only linear gaps

The penalty of $$n$$ consecutive gaps is $$n\cdot G$$
($$G$$ is the gap penalty)

Now we consider affine gaps, where the first gap is expensive, but the consecutive are cheap

The penalty of $$n$$ consecutive gaps is $$I + n\cdot E$$

$$I$$ is the initial gap penalty, $$E$$ is the gap extension penalty

# BLAST

## BLAST

The most common tool for local alignment is BLAST

Basic Local Alignment Search Tool

BLAST is not Global Alignment

## Using BLAST

There are two ways of using BLAST

• Going to NCBI’s website: https://blast.ncbi.nlm.nih.gov/
• Runs in NCBI servers with NCBI databases
• Using a command line version
• can also send jobs in NCBI servers with NCBI databases

For today we can look at NCBI page

## Types of BLAST

Depending on the alphabet of the query and subject

BlastN
Search nucleotides in nucleotide databases
BlastP
Search proteins in protein databases

There are others. Today we only use these ones

## NCBI protein databases

nr
Non-redundant protein sequences
refseq_protein
Reference proteins
refseq_select
Reference Select proteins

There are others. Today we only use these ones

## What is “Non-Redundant”?

These databases get data from several sources

Sometimes two people upload the same sequence but with different ID

For example, EMBL ID, GenBank ID, RefSeq ID, etc.

This database combines all identical entries into one, and keeps all the alternative IDs

## Let’s test it

Let’s look for Terje Steinum’s data

This is a 16S gene amplified by PCR

(see the course’s Homepage)