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DataBase Searching Dynamic Programming Reloaded Database Searching Fasta Blast Statistics Practical Guide Extentions PSI-Blast PHI-Blast Local Blast BLAT
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Needleman-Wunsch-edu.plThe Score Matrix---------------- Seq1(j)1 2 3 4 5 6 7Seq2 * C K H V F C R(i) * 0 -1 -2 -3 -4 -5 -6 -71 C -1 1 a 0 -1 -2 -3 -4 -52 K -2 0c 2b 1 0 -1 -2 -33 K -3 -1 1 1 0 -1 -2 -34 C -4 -2 matrix(i,j) = matrix(i-1,j-1) + (MIS)MATCH A: 0 0 0 -1 0 -15 F -5 -3 -1(substr(seq1,j-1,1) eq substr(seq2,i-1,1) if -1 -1 1 0 -16 C -6 -4 up_score = matrix(i-1,j) + GAP 2 B: -2 -2 -2 0 17 K -7 -5 -3 -3 -3 -1 1 18 C -8 -6 left_score =-4 C: -4 matrix(i,j-1) +-2 -4 GAP 0 09 V -9 -7 -5 -5 -3 -3 -1 -1
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Multiple Alignment Method • The most practical and widely used method in multiple sequence alignment is the hierarchical extensions of pairwise alignment methods. • The principal is that multiple alignments is achieved by successive application of pairwise methods. – First do all pairwise alignments (not just one sequence with all others) – Then combine pairwise alignments to generate overall alignment
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Database Searching • Consider the task of searching SWISS-PROT against a query sequence: – say our query sequence is 362 amino- acids long – SWISS-PROT release 38 contains 29,085,265 amino acids – finding local alignments via dynamic programming would entail O(1010) matrix operations • Given size of databases, more efficient methods needed
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Heuristic approaches to DP for database searchingFASTA (Pearson 1995) BLAST (Altschul 1990, 1997)Uses heuristics to avoid Uses rapid word lookup calculating the full dynamic methods to completely skip programming matrix most of the database entriesSpeed up searches by an order of magnitude Extremely fast compared to full Smith- One order of magnitude Waterman faster than FASTA Two orders of magnitude faster than Smith-The statistical side of FASTA is Waterman still stronger than BLAST Almost as sensitive as FASTA
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FASTA « Hit and extend heuristic» • Problem: Too many calculations “wasted” by comparing regions that have nothing in common • Initial insight: Regions that are similar between two sequences are likely to share short stretches that are identical • Basic method: Look for similar regions only near short stretches that match exactly
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FASTA-Stages 1. Find k-tups in the two sequences (k=1,2 for proteins, 4-6 for DNA sequences) 2. Score and select top 10 scoring “local diagonals” 3. Rescan top 10 regions, score with PAM250 (proteins) or DNA scoring matrix. Trim off the ends of the regions to achieve highest scores. 4. Try to join regions with gapped alignments. Join if similarity score is one standard deviation above average expected score 5. After finding the best initial region, FASTA performs a global alignment of a 32 residue wide region centered on the best initial region, and uses the score as the optimized score.
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FastA • Sensitivity: the ability of a program to identify weak but biologically significant sequence similarity. • Selectivity: the ability of a program to discriminate between true matches and matches occurring by chance alone. – A decrease in selectivity results in more false positives being reported.
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FastA (http://www.ebi.ac.uk/fasta33/)Gap opening penalty Blosum50-12, -16 by default default.for fasta with Lower PAMproteins and DNA, higher blosumrespectively to detect close sequencesGap extension Higher PAM andpenalty -2, -4 by lower blosumdefault for fasta to detect distantwith proteins and sequencesDNA, respectively The larger theMax number of word-length thescores and less sensitive, butalignments is 100 faster the search will be
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FastA Output Initn, init1, opt, z- score calculated during runDatabase E score -code expectationhyperlinked value, howto the SRS many hits aredatabase at expected to beEBI found by chance with such a score while comparing this query to this database. E() does not represent the Accession Description Length % similarity number
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FastA is a family of programs FastA, TFastA, FastX, FastY Query: DNA Protein Database:DNA Protein
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FASTA problems FASTA can miss significant similarity since – For proteins, similar sequences do not have to share identical residues • Asp-Lys-Val is quite similar to • Glu-Arg-Ile yet it is missed even with ktuple size of 1 since no amino acid matches • Gly-Asp-Gly-Lys-Gly is quite similar to Gly-Glu-Gly-Arg-Gly but there is no match with ktuple size of 2
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FASTA problems FASTA can miss significant similarity since – For nucleic acids, due to codon “wobble”, DNA sequences may look like XXyXXyXXy where X’s are conserved and y’s are not • GGuUCuACgAAg and GGcUCcACaAAA both code for the same peptide sequence (Gly-Ser- Thr-Lys) but they don’t match with ktuple size of 3 or higher
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DataBase Searching Dynamic Programming Reloaded Database Searching Fasta Blast Statistics Practical Guide Extentions PSI-Blast PHI-Blast Local Blast Blast
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What does BLAST do?• Search a large target set of sequences...• …for hits to a query sequence...• …and return the alignments and scores from those hits...• Do it fast.Show me those sequences that deserve a second look. Blast programs were designed for fast database searching, with minimal sacrifice of sensitivity to distant related sequences.
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The big red button Do My Job It is dangerous to hide too much of the underlying complexity from the scientists.
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Overview • Approach: find segment pairs by first finding word pairs that score above a threshold, i.e., find word pairs of fixed length w with a score of at least T • Key concept “Neigborhood”: Seems similar to FASTA, but we are searching for words which score above T rather than that match exactly • Calculate neigborhood (T) for
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OverviewCompile a list of words which give a scoreabove T when paired with the query sequence.– Example using PAM-120 for query sequence ACDE (w=4, T=17): A C D E A C D E = +3 +9 +5 +5 = 22 • try all possibilities: A A A A = +3 -3 0 0 = 0 no good A A A C = +3 -3 0 -7 = -7 no good • ...too slow, try directed change
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Overview A C D E A C D E = +3 +9 +5 +5 = 22 • change 1st pos. to all acceptable substitutions g C D E = +1 +9 +5 +5 = 20 ok n C D E = +0 +9 +5 +5 = 19 ok I C D E = -1 +9 +5 +5 = 18 ok k C D E = -2 +9 +5 +5 = 17 ok • change 2nd pos.: cant - all alternatives negative and the other three positions only add up to 13 • change 3rd pos. in combination with first position gCnE = 1 9 2 5 = 17 ok • continue - use recursion• For "best" values of w and T there are typically about 50 words in the list for every residue in the query sequence
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Neighborhood.pl# Calculate neighborhoodmy %NH;for (my $i = 0; $i < @A; $i++) { my $s1 = $S{$W[0]}{$A[$i]}; for (my $j = 0; $j < @A; $j++) { my $s2 = $S{$W[1]}{$A[$j]}; for (my $k = 0; $k < @A; $k++) { my $s3 = $S{$W[2]}{$A[$k]}; my $score = $s1 + $s2 + $s3; my $word = "$A[$i]$A[$j]$A[$k]"; next if $word =~ /[BZX*]/; $NH{$word} = $score if $score >= $T; } }}# Output neighborhoodforeach my $word (sort {$NH{$b} <=> $NH{$a} or $a cmp $b} keys %NH) { print "$word $NH{$word}n";}
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indexed * Trim to max Score S Length of extension*Two non-overlapping HSP’s on a diagonal within distance A
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indexed * Trim to max Score S Length of extension*Two non-overlapping HSP’s on a diagonal within distance A
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The BLAST algorithm• Break the search sequence into words – W = 3 for proteins, W = 12 for DNA MCGPFILGTYC MCG, CGP, GPF, PFI, FIL, CGP ILG, LGT, GTY, TYC MCG• Include in the search all words that score above a certain value (T) for any search word MCG CGP MCT MGP … MCN CTP This list can be … … computed in linear time
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The Blast Algorithm (2)• Search for the words in the database – Word locations can be precomputed and indexed – Searching for a short string in a long string• HSP (High Scoring Pair) = A match between a query word and the database• Find a “hit”: Two non-overlapping HSP’s on a diagonal within distance A• Extend the hit until the score falls below a threshold value, S
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BLAST parameters• Lowering the neighborhood word threshold (T) allows more distantly related sequences to be found, at the expense of increased noise in the results set.• Choosing a value for w – small w: many matches to expand – big w: many words to be generated – w=4 is a good compromise• Lowering the segment extension cutoff (S) returns longer extensions for each hit.• Changing the minimum E-value changes the threshold for reporting a hit.
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Critical parameters: T,W and scoring matrix • The proper value of T depends ons both the values in the scoring matrix and balance between speed and sensitivity • Higher values of T progressively remove more word hits and reduce the search space. • Word size (W) of 1 will produce more hits than a word size of 10. In general, if T is scaled uniformly with W, smaller word sizes incraese sensitivity and decrease speed. • The interplay between W,T and the scoring matrix is criticial and choosing them wisely is the most effective way of controlling the speed and sensiviy of blast
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DataBase Searching Dynamic Programming Reloaded Database Searching Fasta Blast Statistics Practical Guide Extentions PSI-Blast PHI-Blast Local Blast BLAT
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Database Searching• How can we find a particular short sequence in a database of sequences (or one HUGE sequence)?• Problem is identical to local sequence alignment, but on a much larger scale.• We must also have some idea of the significance of a database hit. – Databases always return some kind of hit, how much attention should be paid to the result?• How can we determine how “unusual” a particular alignment score is?
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Significance Sentence 1: “These algorithms are trying to find the best way to match up two sequences” Sentence 2: “This does not mean that they will find anything profound” ALIGNMENT: THESEALGRITHMARETR--YINGTFINDTHEBESTWAYTMATCHPTWSEQENCES :: :.. . .. ...: : ::::.. :: . : ... THISDESNTMEANTHATTHEYWILLFINDAN-------YTHIN-GPRFND------ 12 exact matches 14 conservative substitutions Is this a good alignment?
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Overview • A key to the utility of BLAST is the ability to calculate expected probabilities of occurrence of Maximum Segment Pairs (MSPs) given w and T • This allows BLAST to rank matching sequences in order of “significance” and to cut off listings at a user-specified probability
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Mathematical Basis of BLAST • Model matches as a sequence of coin tosses • Let p be the probability of a “head” – For a “fair” coin, p = 0.5 • (Erdös-Rényi) If there are n throws, then the expected length R of the longest run of heads is R = log1/p (n). • Example: Suppose n = 20 for a “fair” coin R=log2(20)=4.32 • Trick is how to model DNA (or amino acid) sequence alignments as coin tosses.
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Mathematical Basis of BLAST• To model random sequence alignments, replace a match with a “head” and mismatch with a “tail”. AATCAT HTHHHT ATTCAG• For DNA, the probability of a “head” is 1/4 – What is it for amino acid sequences?
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Mathematical Basis of BLAST• So, for one particular alignment, the Erdös-Rényi property can be applied• What about for all possible alignments? – Consider that sequences are being shifted back and forth, dot matrix plot• The expected length of the longest match is R=log1/p(mn) where m and n are the lengths of the two sequences.
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Karlin-Alschul Statistics E=kmn-λS This equation states that the number of alignments expected by chance (E) during the sequence database search is a function of the size of the search space (m*n), the normalized score (λS) and a minor constant (k mostly 0.1) E-Value grows linearly with the product of target and query sizes. Doubling target set size and doubling query length have the same effect on e-value
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Scoring alignments• Score: S (~R) – S= M(qi,ti) - gaps• Any alignment has a score• Any two sequences have a(t least one) optimal alignment
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• For a particular scoring matrix and its associated gap initiation and extention costs one must calculate λ and k• Unfortunately (for gapped alignments), you can’t do this analytically and the values must be estimated empirically – The procedure involves aligning random sequences (Monte Carlo approach) with a specific scoring scheme and observing the alignment properties (scores, target frequencies and lengths)
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Significance“Monte Carlo” Approach:• Compares result to randomized result, similarly to results generated by a roulette wheel at Monte Carlo• Typical procedure for alignments – Randomize sequence A – Align to sequence B – Repeat many times (hundreds) – Keep track op optimal score• Histogram of scores …
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Assessing significance requires a distribution• I have an pumpkin of diameter 1m. Is that unusual? Frequency Diameter (m)
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Significance Normal Distribution does NOT Fit Alignment Scores !! • In seeking optimal Alignments between two sequences, one desires those that have the highest score - i.e. one is seeking a distribution of maxima • In seeking optimal Matches between an Input Sequence and Sequence Entries in a Database, one again desires the matches that have the highest score, and these are obtained via examination of the distribution of such scores for the entries in the database - this is again a distribution of maxima. “A Normal Distribution is a distribution of Sums of independent variables rather than a sum of their Maxima.“
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Comparing distributions Gaussian: Extreme Value: 2 x x x 1 2 2 1 e f x e f x e e 2
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Alignment scores follow extreme value distributionsAlignment of unrelated/random sequences result in scoresfollowing an extreme value distribution x P = 1 –e-E E P(x S) = 1-exp(-k m n e- S) m, n: sequence lengths. k, free parameters. E=-ln(1-P)This can be shown analytically for ungapped alignments and hasbeen found empirically to also hold for gapped alignments undercommonly used conditions.
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Alignment scores follow extreme value distributionsAlignment algorithms will always producealignments, regardless of whether it is meaningful or not=> important to have way of selecting significant alignmentsfrom large set of database hits.Solution: fit distribution of scores from database search toextreme value distribution; determine p-value of hit from thisfitted distribution. Example: scores fitted to extreme value distribution. 99.9% of this distribution is located below score=112 => hit with score = 112 has a p-value of 0.1%
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Significance BLAST uses precomputed extreme value distributions to calculate E- values from alignment scores For this reason BLAST only allows certain combinations of substitution matrices and gap penalties This also means that the fit is based on a different data set than the one you are working on A word of caution: BLAST tends to overestimate the significance of its matches E-values from BLAST are fine for identifying sure hits One should be careful using BLAST’s E-values to judge if a marginal hit can be trusted (e.g., you may want to use E-values of 10-4 to 10-5).
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Determining P-values• If we can estimate and , then we can determine, for a given match score x, the probability that a random match with score x or greater would have occurred in the database.• For sequence matches, a scoring system and database can be parameterized by two parameters, k and , related to and . – It would be nice if we could compare hit significance without regard to the scoring system used!
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Bit Scores• The expected number of hits with score S is: E = Kmn e s – Where m and n are the sequence lengths• Normalize the raw score using: S ln K S ln 2• Obtains a “bit score” S’, with a standard set of units.• The new E-value is: E mn 2 S
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FastA Output • The distribution of scores graph of frequency of observed scores • expected curve (asterisks) according to the extreme value distribution –the theoretic curve should be similar to the observed results • deviations indicate that the fitting parameters are wrong –too weak gap penalties –compositional biases
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FastA Output • A summary of the statistics and of the program parameters follows the histogram. – An important number in this summary is the Kolmogorov-Smirnov statistic, which indicates how well the actual data fit the theoretical statistical distribution. The lower this value, the better the fit, and the more reliable the statistical estimates. – In general, a Kolmogorov-Smirnov statistic under 0.1 indicates a good fit with the theoretical model. If the statistic is higher than 0.2, the statistics may not be valid, and it is recommended to repeat the search, using more stringent (more negative) values for the gap penalty parameters.
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Statistics summary• Optimal local alignment scores for pairs of random amino acid sequences of the same length follow and extreme-value distribution. For any score S, the probability of observing a score >= S is given by the Karlin-Altschul statistic (P(score>=S)=1-exp(-kmne(- lambda.S))• k en Lambda are parameters related to the position of the maximum and the with of the distribution,• Note the long tail at the right. This means that a score serveral standard deviations above the mean has higher probability of arising by chance (that is, it is less significant) than if the scores followed a normal distribution.
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P-values• Many programs report P = the probability that the alignment is no better than random. The relationship between Z and P depends on the distribution of the scores from the control population, which do NOT follow the normal distributions – P<=10E-100 (exact match) – P in range 10E-100 10E-50 (sequences nearly identical eg. Alleles or SNPs – P in range 10E-50 10E-10 (closely related sequenes, homology certain) – P in range 10-5 10E-1 (usually distant relatives) – P > 10-1 (match probably insignificant)
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E• For database searches, most programs report E-values. The E-value of an alignemt is the expected number of sequences that give the same Z-score or better if the database is probed with a random sequence. E is found by multiplying the value of P by the size of the database probed. Note that E but not P depends on the size of the database. Values of P are between 0 and 1. Values of E are between 0 and the number of sequences in the database searched: – E<=0.02 sequences probably homologous – E between 0.02 and 1 homology cannot be ruled out – E>1 you would have to expect this good a match by just chance
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DataBase Searching Dynamic Programming Reloaded Database Searching Fasta Blast Statistics Practical Guide Extentions PSI-Blast PHI-Blast Local Blast Blast
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Blast BLAST is actually a family of programs: • BLASTN - Nucleotide query searching a nucleotide database. • BLASTP - Protein query searching a protein database. • BLASTX - Translated nucleotide query sequence (6 frames) searching a protein database. • TBLASTN - Protein query searching a translated nucleotide (6 frames) database. • TBLASTX - Translated nucleotide query (6 frames) searching a translated nucleotide (6 frames) database.
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Tips • Be aware of what options you have selected when using BLAST, or FASTA implementations. • Treat BLAST searches as scientific experiments • So you should try your searches with the filters on and off to see whether it makes any difference to the output
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Tips: Low-complexity and Gapped Blast Algorithm • The common, Web-based ones often have default settings that will affect the outcome of your searches. By default all NCBI BLAST implementations filter out biased sequence composition from your query sequence (e.g. signal peptide and transmembrane sequences - beware!). • The SEG program has been implemented as part of the blast routine in order to mask low-complexity regions • Low-complexity regions are denoted by strings of Xs in the query sequence
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Tips • The sequence databases contain a wealth of information. They also contain a lot of errors. Contaminants … • Annotation errors, frameshifts that may result in erroneous conceptual translations. • Hypothetical proteins ? • In the words of Fox Mulder, "Trust no one."
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Tips • Once you get a match to things in the databases, check whether the match is to the entire protein, or to a domain. Dont immediately assume that a match means that your protein carries out the same function (see above). Compare your protein and the match protein(s) along their entire lengths before making this assumption.
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Tips • Domain matches can also cause problems by hiding other informative matches. For instance if your protein contains a common domain youll get significant matches to every homologous sequence in the database. BLAST only reports back a limited number of matches, ordered by P value. • If this list consists only of matches to the same domain, cut this bit out of your query sequence and do the BLAST search again with the edited sequence (e.g. NHR).
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Tips • Do controls wherever possible. In particular when you use a particular search software for the first time. • Suitable positive controls would be protein sequences known to have distant homologues in the databases to check how good the software is at detecting such matches. • Negative controls can be employed to make sure the compositional bias of the sequence isnt giving you false positives. Shuffle your query sequence and see what difference this makes to the matches that are returned. A real match should be lost upon shuffling of your sequence.
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Tips • Perform Controls #!/usr/bin/perl -w use strict; my ($def, @seq) = <>; print $def; chomp @seq; @seq = split(//, join("", @seq)); my $count = 0; while (@seq) { my $index = rand(@seq); my $base = splice(@seq, $index, 1); print $base; print "n" if ++$count % 60 == 0; } print "n" unless $count %60 == 0;
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Tips • Read the footer first • View results graphically • Parse Blasts with Bioperl
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FastA vs. Blast • BLASTs major advantage is its speed. – 2-3 minutes for BLAST versus several hours for a sensitive FastA search of the whole of GenBank. • When both programs use their default setting, BLAST is usually more sensitive than FastA for detecting protein sequence similarity. – Since it doesnt require a perfect sequence match in the first stage of the search.
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FastA vs. Blast Weakness of BLAST: – The long word size it uses in the initial stage of DNA sequence similarity searches was chosen for speed, and not sensitivity. – For a thorough DNA similarity search, FastA is the program of choice, especially when run with a lowered KTup value. – FastA is also better suited to the specialised task of detecting genomic DNA regions using a cDNA query sequence, because it allows the use of a gap extension penalty of 0. BLAST, which only creates ungapped alignments, will usually detect only the longest exon, or fail altogether. • In general, a BLAST search using the default parameters should be the first step in a database similarity search strategy. In many cases, this is all that may be required to yield all the information needed, in a very short time.
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DataBase Searching Dynamic Programming Reloaded Database Searching Fasta Blast Statistics Practical Guide Extentions PSI-Blast PHI-Blast Local Blast BLAT
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PSI-Blast 1. Old (ungapped) BLAST 2. New BLAST (allows gaps) 3. Profile -> PSI Blast - Position Specific Iterated Strategy:Multiple alignment of the hits Calculates a position-specific score matrix Searches with this matrix In many cases is much more sensitive to weak but biologically relevant sequence similarities PSSM !!!
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PSI-Blast • Patterns of conservation from the alignment of related sequences can aid the recognition of distant similarities. – These patterns have been variously called motifs, profiles, position-specific score matrices, and Hidden Markov Models. For each position in the derived pattern, every amino acid is assigned a score. (1) Highly conserved residue at a position: that residue is assigned a high positive score, and others are assigned high negative scores. (2) Weakly conserved positions: all residues receive scores near zero. (3) Position-specific scores can also be assigned to potential insertions and deletions.
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Pattern• a set of alternative sequences, using “regular expressions”• Prosite (http://www.expasy.org/ prosite/)
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PSI-Blast • The power of profile methods can be further enhanced through iteration of the search procedure. – After a profile is run against a database, new similar sequences can be detected. A new multiple alignment, which includes these sequences, can be constructed, a new profile abstracted, and a new database search performed. – The procedure can be iterated as often as desired or until convergence, when no new statistically significant sequences are detected.
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PSI-Blast (1) PSI-BLAST takes as an input a single protein sequence and compares it to a protein database, using the gapped BLAST program. (2) The program constructs a multiple alignment, and then a profile, from any significant local alignments found. The original query sequence serves as a template for the multiple alignment and profile, whose lengths are identical to that of the query. Different numbers of sequences can be aligned in different template positions. (3) The profile is compared to the protein database, again seeking local alignments using the BLAST algorithm. (4) PSI-BLAST estimates the statistical significance of the local alignments found. Because profile substitution scores are constructed to a fixed scale, and gap scores remain independent of position, the statistical theory and parameters for gapped BLAST alignments remain applicable to profile alignments. (5) Finally, PSI-BLAST iterates, by returning to step (2), a specified number of times or until convergence.
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PSI-BLAST pitfalls • Avoid too close sequences: overfit! • Can include false homologous! Therefore check the matches carefully: include or exclude sequences based on biological knowledge. • The E-value reflects the significance of the match to the previous training set not to the original sequence! • Choose carefully your query sequence. • Try reverse experiment to certify.
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Reduce overfitting risk by Cobbler • A single sequence is selected from a set of blocks and enriched by replacing the conserved regions delineated by the blocks by consensus residues derived from the blocks. • Embedding consensus residues improves performance • S. Henikoff and J.G. Henikoff; Protein Science (1997) 6:698- 705.
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DataBase Searching Dynamic Programming Reloaded Database Searching Fasta Blast Statistics Practical Guide Extentions PSI-Blast PHI-Blast Local Blast BLAT
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PHI-Blast Local Blast(Pattern-Hit Initiated BLAST)
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From: http://bioweb.pasteur.fr/seqanal/blast/intro-uk.html PHI-Blast Local Blast
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BLAT method • Align sequence with BLAT, get alignment info • Per BLAT hit, pick up additional info from connected databases: – mRNAs – ESTs – RepeatMasker – CpG Islands – RefSeq Genes
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Weblems W5.1: Submit the amino acid sequence of papaya papein to a BLAST (gapped and ungapped) and to a PSI-BLAST search. What are the main difference in results? W5.2: Is there a relationship between Klebsiella aerogenes urease, Pseudomonas diminuta phosphotriesterase and mouse adenosine deaminase ? Also use DALI, ClustalW and T-coffee. W5.3: Yeast two-hybrid typically yields DNA sequences. How would you find the corresponding protein ? W5.4: When and why would you use tblastn ? W5.5: How would you search a database if you want to restrict the search space to those entries having a secretion signal consisting of 4 consecutive (N- terminal) basic residues ?
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