Last lecture summary

1. Last lecture summary

3. Window size? • Stringency? • Color mapping? Frame shifts?

4. Limits of detection of alignment • Homology, similarity • Twilight zone

5. 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. • What are H0and Ha? • Significance of local alignment • gapless • gapped • Significance of global alignment

6. Gumbel distribution … location parameter … scale parameter wikipedia.org

7. New stuff

8. Database similarity searching

9. 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. • Determining the identity of a DNA or protein sequence. • Determining what variants have been described for a particular gene or protein. • Investigating ESTs. • Exploring amino acid residues that are important in the function and/or structure of a protein (multiple alignment of BLAST results, conserved residues).

10. 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-Watermannis too computationally intensive. • Instead, heuristicis utilized, significant speed up.

11. 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 sensitivityleads to decrease in specificity, improvement in speed often comes at the cost of lowered sensitivity and selectivity

12. Types of algorithms • exhaustive • uses a rigorous algorithm to find the best or 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

13. 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.

14. 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.

15. BLAST - list • Compile a list of “words” of a fixed length wthat 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

17. 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.

18. 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.

19. 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.

20. 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.

21. 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.

22. BLAST Statistics • quantitative measure of whether the alignments represent significant matches or whether they would be expected to occur by chance alone • For two random sequences mand n, the cumulative distribution function of scores Sis described by the formula – characteristic value – decay constant Gumbel distribution

23. To use this equation, we need to estimate the values of and . • m, n … sequence lengths, K … constant • Probability of observing a score S equal to or greater than x by chance is then given by the formula

24. In the context of a database search, m and n refer to the length (in residues) of the query sequence and the length of the entire database, respectively. • The product m.ndefines the size of the search space. • The search space represents all the sites at which a query sequence can be aligned to any sequence in the database. • The expected number of HSPs having some score S (or better) by chance alone is described using the equation • Erefers to the expect value, which is the number of different alignments with scores equivalent to or better than S that are expected to occur by chance in a database search. • This provides an estimate of the number of false positive results from a BLAST search.

25. E-value • E depends on score S and parameter which scale the scoring system. • It also depends on the length of query sequence and on the length of the database. • The parameter K is a scaling factor for the search space. • The parameters K and were described by Karlinand Altschuland so are often called Karlin–Altschulstatistics. Karlin S., Altschul S. F. Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes. PNAS87, 2264–2268, 1990

26. Properties of E-value I • Decreases exponentially with increasing S. Thus, a high score corresponds to a low E-value. As E approaches zero, the probability that the alignment occurred by chance approaches zero. • The expected score for aligning a random pair of amino acids must be negative. Otherwise, very long alignments of two sequences could accumulate large positive scores and appear to be significantly related when they are not. • The size of the database that is searched influences the likelihood that particular alignments will occur by chance. Consider a result with an E = 1. This value indicates that in a database of this particular size one match with a similar score is expected to occur 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.

27. Properties of E-value II • The theory was developed for ungapped alignments. For these, BLAST calculates values for, and . • The same equation can be used for gapped local alignments (such as the results of a BLAST search). However, for gapped alignments , and cannot be calculated analytically, but instead they are estimated by simulation and looked up in a table of precomputed values.

28. 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 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.

29. Relation between E and p values I • What is p-value? • Probability of a chance alignment occurring with the score in question or better. • The most highly significant p values are those close to zero. The p and E values are different ways of representing the significance of the alignment. • The probability of finding an HSP with a given E value is

30. Relation between E and p values II • While BLAST reports Evalues rather than p values, the two measures are nearly identical, especially for very small values associated with strong database matches. • An advantage of using E values is that it is easier to think about E values of 5 versus 10 rather than 0.99326205 versus 0.99995460. • A p-value below 0.05 is usually used to define statistical significance (what does it mean?) • Thus, an E value of 0.05 or less may be considered significant.

31. Multiple comparisons correction I • The significance level … p-value of 0.05 suggests that some observation (e.g., the score of a protein query to a match in a database) is likely to have occurred by chance 1 time in 20. • Ho … your query is not homologous to the database match, Ha … it is homologous • If p-value < , which hypothesis is true? • When you search a database that has one million proteins, there are many opportunities for your query to find matches. Five percent of 1 million proteins is 50,000 proteins, and we might expect to obtain that many matches by chance.

32. Multiple comparisons correction II • This situation involves multiple comparisons: you are not hypothesizing that your query will match one particular database entry, you are interested in knowing if it matches any entries. • A solution is to correct for multiple comparisons by adjusting the level. • A very conservative way to do this (Bonferroni correction) is to divide by the size of the database. • In the case of BLAST searches this is done automatically, because the E value is multiplied by the effective search space.

33. E-value interpretation • 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 • 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.