Sequence database searching – Homology searching Dynamic Programming (DP) too slow for repeated database searches. Therefore fast heuristic methods: FASTA BLAST and PSI-BLAST QUEST HMMER SAM-T98 Fast heuristics Hidden Markov modelling

FASTA Compares a given query sequence with a library of sequences and calculates for each pair the highest scoring local alignment Speed is obtained by delaying application of the dynamic programming technique to the moment where the most similar segments are already identified by faster and less sensitive techniques FASTA routine operates in four steps:

FASTA Operates in four steps: 1.Rapid searches for identical words of a user specified length occurring in query and database sequence(s) (Wilbur and Lipman, 1983, 1984). For each target sequence the 10 regions with the highest density of ungapped common words are determined. 2.These 10 regions are rescored using Dayhoff PAM-250 residue exchange matrix (Dayhoff et al., 1983) and the best scoring region of the 10 is reported under init1 in the FASTA output. 3.Regions scoring higher than a threshold value and being sufficiently near each other in the sequence are joined, now allowing gaps. The highest score of these new fragments can be found under initn in the FASTA output. 4.full dynamic programming alignment (Chao et al., 1992) over the final region which is widened by 32 residues at either side, of which the score is written under opt in the FASTA output.

FASTA output example DE METAL RESISTANCE PROTEIN YCF1 (YEAST CADMIUM FACTOR 1).... SCORES Init1: 161 Initn: 161 Opt: 162 z-score: E(): 3.4e-06 Smith-Waterman score: 162; 35.1% identity in 57 aa overlap test.seq MQRSPLEKASVVSKLFFSWTRPILRKGYRQRLE :| :|::| |:::||:|||::|: | YCFI_YEAST CASILLLEALPKKPLMPHQHIHQTLTRRKPNPYDSANIFSRITFSWMSGLMKTGYEKYLV test.seq LSDIYQIPSVDSADNLSEKLEREWDRE :|:|::| |:::||:|||::|: | YCFI_YEAST EADLYKLPRNFSSEELSQKLEKNWENELKQKSNPSLSWAICRTFGSKMLLAAFFKAIHDV

FASTA (1) Rapid identical word searches: Searching for k-tuples of a certain size within a specified bandwidth along search matrix diagonals. For not-too-distant sequences (> 35% residue identity), little sensitivity is lost while speed is greatly increased. Technique employed is known as hash coding or hashing: a lookup table is constructed for all words in the query sequence, which is then used to compare all encountered words in each database sequence.

FASTA The k-tuple length is user-defined and is usually 1 or 2 for protein sequences (i.e. either the positions of each of the individual 20 amino acids or the positions of each of the 400 possible dipeptides are located). For nucleic acid sequences, the k-tuple is 5-20, and should be longer because short k-tuples are much more common due to the 4 letter alphabet of nucleic acids. The larger the k-tuple chosen, the more rapid but less thorough, a database search.

BLAST blastp compares an amino acid query sequence against a protein sequence database blastn compares a nucleotide query sequence against a nucleotide sequence database blastx compares the six-frame conceptual protein translation products of a nucleotide query sequence against a protein sequence database tblastn compares a protein query sequence against a nucleotide sequence database translated in six reading frames tblastx compares the six-frame translations of a nucleotide query sequence against the six-frame translations of a nucleotide sequence database.

BLAST Generates all tripeptides from a query sequence and for each of those the derivation of a table of similar tripeptides: number is only fraction of total number possible. Quickly scans a database of protein sequences for ungapped regions showing high similarity, which are called high-scoring segment pairs (HSP), using the tables of similar peptides. The initial search is done for a word of length W that scores at least the threshold value T when compared to the query using a substitution matrix. Word hits are then extended in either direction in an attempt to generate an alignment with a score exceeding the threshold of S, and as far as the cumulative alignment score can be increased.

BLAST Extension of the word hits in each direction are halted when the cumulative alignment score falls off by the quantity X from its maximum achieved value the cumulative score goes to zero or below due to the accumulation of one or more negative-scoring residue alignments upon reaching the end of either sequence The T parameter is the most important for the speed and sensitivity of the search resulting in the high-scoring segment pairs A Maximal-scoring Segment Pair (MSP) is defined as the highest scoring of all possible segment pairs produced from two sequences.

PSI-BLAST Query sequences are first scanned for the presence of so-called low-complexity regions (Wooton and Federhen, 1996), i.e. regions with a biased composition likely to lead to spurious hits; are excluded from alignment. The program then initially operates on a single query sequence by performing a gapped BLAST search Then, the program takes significant local alignments found, constructs a multiple alignment and abstracts a position specific scoring matrix (PSSM) from this alignment. Rescan the database in a subsequent round to find more homologous sequences Iteration continues until user decides to stop or search has converged

PSI-BLAST iteration Q ACD..YACD..Y Pi Px Query sequence PSSM Q Query sequence Gapped BLAST search Database hits Gapped BLAST search ACD..YACD..Y Pi Px PSSM Database hits xxxxxxxxxxxxxxxxx

PSI-BLAST output example

Multiple alignment profiles Gribskov et al A way to represent multiple alignment consensus ACDWYACDWY Gap penalties i  Position dependent gap penalties

Normalised sequence similarity The p-value is defined as the probability of seeing at least one unrelated score S greater than or equal to a given score x in a database search over n sequences. This probability follows the Poisson distribution (Waterman and Vingron, 1994): P(x, n) = 1 – e -n  P(S  x), where n is the number of sequences in the database Depending on x and n (fixed)

Normalised sequence similarity Statistical significance The E-value is defined as the expected number of non- homologous sequences with score greater than or equal to a score x in a database of n sequences: E(x, n) = n  P(S  x) if E-value = 0.01, then the expected number of random hits with score S  x is 0.01, which means that this E- value is expected by chance only once in 100 independent searches over the database. if the E-value of a hit is 5, then five fortuitous hits with S  x are expected within a single database search, which renders the hit not significant.

Normalised sequence similarity Statistical significance Database searching is commonly performed using an E-value in between 0.1 and Low E-values decrease the number of false positives in a database search, but increase the number of false negatives, thereby lowering the sensitivity of the search.

HMM-based homology searching Most widely used HMM-based profile searching tools currently are SAM-T98 (Karplus et al., 1998) and HMMER2 (Eddy, 1998) formal probabilistic basis and consistent theory behind gap and insertion scores HMMs good for profile searches, bad for alignment HMMs are slow

The HMM algorithms Questions: 1.What is the most likely die (predicted) sequence? Viterbi 2.What is the probability of the observed sequence? Forward 3.What is the probability that the 3 rd state is B, given the observed sequence? Backward Forward:  (i) = P(observed sequence, ending in state i at base t) Backward:  ß (i) = P(obs. after t | ending in state i at base t)  Viterbi:  (i) = max P(obs., ending in state i at base t) t t t

HMM-based homology searching Transition probabilities and Emission probabilities Gapped HMMs also have insertion and deletion states

Profile HMM: m=match state, I-insert state, d=delete state; go from left to right. I and m states output amino acids; d states are ‘silent”. d1d1 d2d2 d3d3 d4d4 I0I0 I2I2 I3I3 I4I4 I1I1 m0m0 m1m1 m2m2 m3m3 m4m4 m5m5 Start End

Homology-derived Secondary Structure of Proteins (HSSP) Sander & Schneider, 1991