Sequence Similar Similar Function
Charles Yan Spring 2006
From Sequence to Function
Protein sequence determine protein function. Thus similar protein sequences have similar functions One approach to predict function for a new protein is to search for similar proteins (homologues) whose functions are known. If the similarities are high, it is likely that the new protein has the same functions as its homologues
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Homologue Search
Basic Local Alignment Search Tool (BLAST) finds regions of local similarity between sequences. The program compares nucleotide or protein sequences to sequence databases and calculates the statistical significance of matches. BLAST can be used to infer functional and evolutionary relationships between sequences as well as help identify members of gene families
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Dynamic Programming
a1a2a3...am b1b2b3...bn
Mi,j = MAX { Mi1, j1 + Si,j (match/mismatch) Mi,j1 + w (gap in sequence #1) Mi1,j + w (gap in sequence #2) }
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Dynamic Programming
G A A T T C A G T T A (sequence #1) G G A T C G A (sequence #2) Si,j = 1 (match) Si,j = 0 (mismatch score) w = 0 (gap penalty)
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Dynamic Programming
M1,1 = MAX[M0,0 + 1, M1, 0 + 0, M0,1 + 0] = MAX [1, 0, 0] = 1
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Dynamic Programming
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Dynamic Programming
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Global and Local Alignment
A global alignment is an optimal alignment that includes all characters from each sequence, whereas a local alignment is an optimal alignment that includes only the most similar local region or regions.
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BLAST
The BLAST programs (Basic Local Alignment Search Tools) are a set of sequence comparison algorithms introduced in 1990 that are used to search sequence databases for optimal local alignments to a query.
Break the query and database sequences into fragments ("words"), and initially seek matches between fragments. The initial search is done for a word of length "W" that scores at least "T" when compared to the query using a given 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". The "T" parameter dictates the speed and sensitivity of the search.
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BLAST
Web interface: http://www.ncbi.nlm.nih.gov/BLAST/ Download http://www.ncbi.nlm.nih.gov/BLAST/download.shtml
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BLAST
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BLAST
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BLAST
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Substitution Matrix
A substitution matrix containing values proportional to the probability that amino acid i mutates into amino acid j for all pairs of amino acids
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Substitution Matrix
The BLOSUM family BLOSUM matrices are based on local alignments. BLOSUM 62 is a matrix calculated from comparisons of sequences with no less than 62% divergence. All BLOSUM matrices are based on observed alignments; they are not extrapolated from comparisons of closely related proteins. BLOSUM 62 is the default matrix in BLAST 2.0. Though it is tailored for comparisons of moderately distant proteins, it performs well in detecting closer relationships. A search for distant relatives may be more sensitive with a different matrix.
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Substitution Matrix
The PAM family PAM matrices are based on global alignments of closely related proteins. The PAM1 is the matrix calculated from comparisons of sequences with no more than 1% divergence. Other PAM matrices are extrapolated from PAM1.
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Substitution Matrix
The relationship between BLOSUM and PAM substitution matrices. BLOSUM matrices with higher numbers and PAM matrices with low numbers are both designed for comparisons of closely related sequences. BLOSUM matrices with low numbers and PAM matrices with high numbers are designed for comparisons of distantly related proteins. If distant relatives of the query sequence are specifically being sought, the matrix can be tailored to that type of search.
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Raw Score S
The raw score S for an alignment is calculated by summing the scores for each aligned position and the scores for gaps
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Bit Score S'
Raw scores have little meaning without detailed knowledge of the scoring system used, or more simply its statistical parameters K and lambda. Unless the scoring system is understood, citing a raw score alone is like citing a without distance specifying feet, meters, or light years. By normalizing a raw score using the formula
one attains a "bit score" S', which has a standard set of units.
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Bit Score S'
The value S' is derived from the raw alignment score S in which the statistical properties of the scoring system used have been taken into account. Because bit scores have been normalized with respect to the scoring system, they can be used to compare alignment scores from different searches.
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Significance
The significance of each alignment is computed as a P value or an E value
E value: Expectation value. The number of different alignents with scores equivalent to or better than S that are expected to occur in a database search by chance. The lower the E value, the more significant the score. P value :The probability of an alignment occurring with the score in question or better. The p value is calculated by relating the observed alignment score, S, to the expected distribution of HSP scores from comparisons of random sequences of the same length and composition as the query to the database. The most highly significant P values will be those close to 0. P values and E values are different ways of representing the significance of the alignment.
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Evalue
In the limit of sufficiently large sequence lengths m and n, the statistics of HSP scores are characterized by two parameters, K and lambda. Most simply, the expected number of HSPs with score at least S is given by the formula We call this the Evalue for the score S. This formula makes eminently intuitive sense. Doubling the length of either sequence should double the number of HSPs attaining a given score. Also, for an HSP to attain the score 2x it must attain the score x twice in a row, so one expects E to decrease exponentially with score. The parameters K and lambda can be thought of simply as natural scales for the search space size and the scoring system respectively.
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Pvalue
The number of random HSPs with score >= S is described by a Poisson distribution. This means that the probability of finding exactly a HSPs with score >=S is given by where E is the Evalue of S given by equation (1) above. Specifically the chance of finding zero HSPs with score >=S is eE, so the probability of finding at least one such HSP is This is the Pvalue associated with the score S. For example, if one expects to find three HSPs with score >= S, the probability of finding at least one is 0.95. The BLAST programs report Evalue rather than P values because it is e...