Last lecture summary

• identity vs. similarity• homology vs. similarity• gap penalty

• affine gap penalty• gap penalty high

• fewer gaps, if investigating related sequences

• low• more gaps, larger gaps, distantly related sequences

BLOSUM• blocks• focuse on substitution patterns only in blocks• BLOSUM62 – 62, what does it mean?• BLOSUM vs. PAM

• BLOSUM matrices are based on observed alignments• BLOSUM numbering system goes in reversing order as the PAM

numbering system

Selecting an Appropriate MatrixMatrix Best use Similarity (%)

Pam40 Short highly similar alignments 70-90

PAM160 Detecting members of a protein family 50-60

PAM250 Longer alingments of more divergent sequences ~30

BLOSUM90 Short highly similar alignments 70-90

BLOSUM80 Detecting members of a protein family 50-60

BLOSUM62 Most effective in finding all potential similarities 30-40

BLOSUM30 Longer alingments of more divergent sequences <30

Similarity column gives range of similarities that the matrix is able to best detect.

Dynamic programming (DP)

• Recursive approach, sequential dependency.• 4th piece can be solved using solution of the 3rd piece, the 3rd piece can be solved by using solution of the 2nd piece and so on…

Sequence B

Sequence ABest previous alignment

New best alignment = previous best + local best

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...

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...If you already have the optimal solution to:

X…YA…B

then you know the next pair of characters will either be:

X…YZ or X…Y- or X…YZA…BC A…BC A…B-

You can extend the match by determining which of these has the highest score.

• Window size?• Stringency?• Color mapping?

Frame shifts?

New stuff

Homology vs. similarity again• Just a reminder of the important concept in sequence

analysis – homology. It is a conclusion about a common ancestral relationship drawn from sequence similarity.

• Sequence similarity is a direct result of observation from the sequence alignment. It can be quantified using percentages, but homology can not!

• It is important to understand this difference between homology and similarity.

• If the similarity is high enough, a common evolutionary relationship can be inferred.

Limits of the alignment detection• However, what is enough? What are the detection limits of

pairwise alignments? How many mutations can occur before the differences make two sequences unrecognizable?

• Intuitively, at some point are two homologous sequences too divergent for their alignment to be recognized as significant.

• The best way to determine detection limits of pairwise alignment is to use statistical hypothesis testing. See later.

Twilight zone• However, the level one can infer homologous relationship

depends on type of sequence (proteins, NA) and on the length of the alignment.• Unrelated sequences of DNA have at least 25% chance to be

identical. For proteins it is 5%. If gaps are allowed, this percentage can increase up to 10-20%.

• The shorter the sequence, the higher the chance that some alignment can be attributed to random chance.

• This suggest that shorter sequences require higher cuttof for inferring homology than longer sequences.

Essential bioinformatics, Xiong

Statistical significance• Key question – Constitutes a given alignment evidence for

homology? Or did it occur just by chance?• The statistical significance of the alignment (i.e. its score)

can be tested by statistical hypotheses testing.

Significance of global alignment• We align two proteins: human beta globin and myoglobin.

We obtain score S.• And we want to know if such a score is significant or if it

appeared just by a chance. How to proceed?• State H0

• two sequences are not related, score S represents a chance occurrence

• State Ha

• Choose a significance level • Statistics of distribution.

• i.e. sample mean, sample standard deviation

Database similarity searching

BLAST• Basic Local Alignment Search Tool (BLAST) – Google of the

sequence world.• Compare a protein or DNA sequence to other sequences in

various databases, main tool of NCBI.• Why to search database

• Determine what orthologs and paralogs are known for a particular sequence.

• Determine what proteins or genes are present in a particular organism.• Determine the identity of a DNA or protein sequence.• Determine what variants have been described for a particular gene or

protein.• Investigate ESTs.• Explore amino acid residues that are important in the function and/or

structure of a protein (multiple alignment of BLAST results, conserved residues).

Database searching requirements I• query sequence, perform pairwise alignments between

the query and the whole database (target)• Typically, this means that millions of alignments are

analyzed in a BLAST search, and only the most closely related matches are returned.

• We are usually more interested in identifying locally matching regions such as protein domains. Global alignment (Needlman-Wunsch) is not often used.

• Smith-Watermann is too computationally intensive.• Instead, heuristic is utilized, significant speed up.

Database searching requirements II• sensitivity – the ability to find as many correct hits (TP)

as possible• selectivity (specificity) – ability to exclude incorrect hits

(FP)• speed

• ideally: high sensitivity, high specificity, high speed• reality: increase in sensitivity leads to decrease in

specificity, improvement in speed often comes at the cost of lowered sensitivity and selectivity

Types of algorithms• exhaustive

• uses a rigorous algorithm to find the exact solution for a particular problem by examining all mathematical combinations

• example: DP

• heuristic• computational strategy to find an empirical or near optimal solution

by using rules of thumb• this type of algorithms take shortcuts by reducing the search space

according to some criteria• the shortcut strategy is not guaranteed to find the best or most

accurate solution

Heuristic algorithms• Perform faster searches because they examine only a

fraction of the possible alignments examined in regular dynamic programming

• currently, there are two major algorithms:• FASTA• BLAST

• Not guaranteed to find the optimal alignment or true homologs, but are 50–100 times faster than DP.

• The increased computational speed comes at a moderate expense of sensitivity and specificity of the search, which is easily tolerated by working molecular biologists.

BLAST• Parts of algorithm

• list, scan, extend

• BLAST uses word method for pairwise alignment• Find short stretches of identical (or nearly identical) letters

in two sequences – words (similar to window in dot plot)• Basic assumption: two related sequences must have at

least one word in common• By first identifying word matches, a longer alignment can be

obtained by extending similarity regions from the words.• Once regions of high sequence similarity are found,

adjacent high-scoring regions can be joined into a full alignment.

BLAST - list• Compile a list of “words” of a fixed length w that are

derived from the query sequence.• protein searches – word size = 3, NA searches = 11• A threshold value T is established for the score of aligned

words (true for proteins, for NAs exact matches are used).• Those words either at or above the threshold are collected

and used to identify database matches; those words below threshold are not further pursued.

• The threshold score T can be lowered to identify more initial pairwise alignments. This will increase the time required to perform the search and may increase the sensitivity

BLAST - scan• After compiling a list of word pairs at or above threshold T,

the BLAST algorithm scans a database for hits.• This requires BLAST to search an index of the database

to find entries that correspond to words on the compiled list.

BLAST - extend• Extend hits to find alignments called high-scoring

segment pairs (HSPs).• Extend in both directions (ungapped originally, gapped

BLAST is newer), count the alignment score.• The extension process is terminated when a score falls

below a cutoff.

BLAST strategy• Compare a protein or DNA query sequence to each

database entry and form pairwise alignments (HSPs).

• When the threshold parameter is raised, the speed of the search is increased, but fewer hits are registered, and so distantly related database matches may be missed.

• When the threshold parameter is lowered, the search proceeds more slowly, but many more word hits are evaluated, and thus sensitivity is increased.

• Recent improvement – gapped BLAST• Variants

• BLASTN – nucleotide sequences• BLASTP – protein sequences• BLASTX – uses nucleotide sequences as queries and translates

them in all six reading frames to produce translated protein sequences, which are used to query a protein sequence database

• TBLASTN – queries protein sequences to a nucleotide sequence database with the sequences translated in all six reading frames

• TBLASTX – uses nucleotide sequences, which are translated in all six frames, to search against a nucleotide sequence database that has all the sequences translated in six frames.

Which sequence to search?• The choice of the type of sequences also influences the

sensitivity of the search.• Clear advantage of using protein sequences in detecting

homologs• If the input sequence is a protein-encoding DNA sequence, use

BLASTX (six open reading frames before sequence comparisons)

• If you’re looking for protein homologs encoded in newly sequenced genomes, you may use TBLASTN. This may help to identify protein coding genes that have not yet been annotated.

• If a DNA sequence is to be used as the query, a protein-level comparison can be done with TBLASTX.

• TBLASTN, TBLASTX are very computationally intensive and the search process can be very slow.

E-value I• expected value• a parameter that describes the number of hits one can

'expect' to see by chance when searching a database of a particul

• decreases exponentially as the score of the match increasesar size

• an E value of 1 assigned to a hit can be interpreted as meaning that in a database of the current size one might expect to see 1 match with a similar score simply by chance• If the database were twice as big, there would be twice the

likelihood of finding a score equal to or greater than S by chance.

E-value II• E < 10-50 … extremely high confidence that the database match is

a result of homologous relationships• E is from (10-50 , 0.01) … the match can be considered a result of

homology (for proteins, conclusive are E-values < 0.001)• E is from (0.01, 10) … the match is considered not significant, but

may hint tentative remote homology• E > 10 … the sequences under consideration are either unrelated

or related by extremely distant relationships that fall below the limit of detection with the current method.

• E-value is proportional to the database size, as database grows E-value for a given sequence match increases. However, the evolutionary relationship between two sequences remains constant. As the db grows, one may lose previously detected homologs.

Bit score• A typical BLAST output reports both E values and scores. • There are two kinds of scores: raw and bit scores.

• Raw scores are calculated from the substitution matrix and the gap penalty parameters that are chosen.

• The bit score S’ is calculated from the raw score by normalizing with the statistical variables that define a given scoring system.

• Bit scores from different alignments, even those employing different scoring matrices in separate BLAST searches, can be compared.