Last lecture summary Flavors of sequence alignment pair-wise alignment × multiple sequence alignment Flavors of sequence alignment global alignment × local alignment global local align entire sequence stretches of sequence with the highest density of matches are aligned, generating islands of matches or subalignments in the aligned sequences Evolution of sequences • The sequences are the products of molecular evolution. • When sequences share a common ancestor, they tend to exhibit similarity in their sequences, structures and biological functions. DNA1 DNA2 Protein1 Protein2 Sequence similarity Similar 3D structure Similar function Similar sequences produce similar proteins However, this statement is not a rule. See Gerlt JA, Babbitt PC. Can sequence determine function? Genome Biol. 2000;1(5) PMID: 11178260 Homology • homology, orthology, paralogy • orthologs – from different spcies, posses same function • paralogs – different function in the same organism • How it happens? • orthology – speciation • paralogy – gene duplication • gene duplication – unequal cross-over, chromosome replication, retrotrasposition • The degree of sequence conservation in the alignment reveals evolutionary relatedness of different sequences • The variation between sequences reflects the changes that have occurred during evolution in the form of substitutions and/or indels. Scoring systems • DNA and protein sequences can be aligned so that the number of identically matching pairs is maximized. A T T G - - - T A – - G A C A T • Counting the number of matches gives us a score (3 in this case). Higher score means better alignment. • This procedure can be formalized using substitution matrix. A Identity matrix T C A 1 T 0 1 C 0 0 1 G 0 0 0 G 1 Scoring DNA sequence alignment • Match score: • Mismatch score: • Gap penalty: +1 +0 –1 • ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT • Matches: 18 × (+1) • Mismatches: 2 × 0 • Gaps: 7 × (– 1) Score = +11 Scoring DNA sequence alignment (2) • Match/mismatch score: • Origination/length penalty: +1/+0 –2/–1 • ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || |||||||| ----CTGATTCGC---ATCGTCTATCT • Matches: 18 × (+1) • Mismatches: 2 × 0 • Origination: 2 × (–2) • Length: 7 × (–1) Score = +7 Substitution matrices • Should reflect: • Physicochemical properties of amino acids. • Different frequencies of individual amino acids occuring in proteins. • Interchangeability of the genetic code. • PAM • Manual alignments of 71 groups of very similar (at least 85% identity) protein sequences. 1572 substitutions were found. • These mutations do not significantly alter the protein function. Hence they are called accepted mutations. • Two sequences are 1 PAM apart if they have 99% identical residues. • PAM1 matrix is the result of computing the probability of one substitution per 100 amino acids. • Higher PAM matrices Zvelebil, Baum, Understanding bioinformatics. PAM 120 Positive score – frequency of substitutions is greater than would have occurred by random chance. Zero score – frequency is equal to that expected by chance. small, polar Negative score – frequency is less than would have occurred by random chance. small, nonpolar polar or acidic basic large, hydrophobic aromatic Selzer, Applied bioinformatics. How to calculate score? 2 substitution matrix New stuff Similarity vs. identity • Similarity refers to the percentage of aligned residues that can be more readily substituted for each other. • have similar physicochemical characteristics and • the selective pressure results in some mutations being accepted and others being eliminated S = [(Ls × 2)/(La + Lb)] × 100 number of aligned residues with similar characteristics total lengths of each sequence Homology vs. similarity • Two sequences are homologous when they descended from a common ancestor sequence. • Similarity can be quantified: “two sequences share 40% similarity”. • But NOT “two sequences share 40% homology”. Just “two sequences are homologous” • Qualitative statement • And it is a conclusion about a common ancestral relationship drawn from sequence similarity comparison Gaps • How will I score this alignment? V D S - C Y V E S L C Y • The gaps can’t be inserted freely. • Indels are relatively slow evolutionary processes. • And alignments with large gaps do not make biological sense. • Each gap is penalized – a gap penalty • The gap penalty is an adjustable parameter. • Let’s use the gap penalty equaling to -11. V D S V E S L 4 2 4 -11 C Y C Y 9 7 S = 4 + 2 + 4 – 11 + 9 + 7=15 Gap penalty • Affine gap penalty • different for opening and extending • constant for extending • The gap penalty is high – fewer gaps will be inserted • If you’re searching for sequences that are a strict match for your query sequence, the gap penalty should be set high. • This will retrieve regions with very closely related sequences. • The gap penalty is low – more and larger gaps will be inserted • If you are searching for similarity between distantly related sequences, the gap penalty should be set low. (A) High gap penalty. Gaps has been inserted only at the beginning and end. Percentage identity = 10% (B) Low gap penalty. More gaps. Percentage identity = 18% Zvelebil, Baum, Understanding bioinformatics. BLOSUM matrices I • BLOck SUbstitution Matrix by Henikoff and Henikoff, 1992. • They used the BLOCKS database containing multiple alignments of ungapped segments (blocks). • These alignments correspond to the most highly conserved regions of proteins. • Blocks are ungapped sequence motifs. Sequence motif is a conserved stretch of amino acids confering a specific function to a protein. • Any given protein can contain one or more blocks corresponding to its structural/functional motifs. Blocks .. . BLOSUM matrices II • Thus the Hanikoffs focused on substitution patterns only in the most conserved regions of a protein. These regions are (presumably) least prone to change. • The substitution patterns of 2000 blocks (block is the whole alignment, not individual sequences within it) representing more than 500 groups were examined, and BLOSUM matrices were generated. • Sequences sharing no more than 62% identity were used to calculate BLOSUM62 matrix. Short and clear explanation of BLOSUM62 derivation: Eddy SR. Where did the BLOSUM62 alignment score matrix come from? Nat Biotechnol. 2004 22(8):1035-6. PMID: 15286655. BLOSUM matrices III • BLOSUM matrices are based on entirely different type of sequence analysis (local ungapped alignment vs. global gapped alignment in PAM) and on a much larger data than PAM. • All BLOSUM matrices are based on observed alignments. They are not based on extrapolations like PAM !!! • BLOSUM numbering system goes in reversing order as the PAM numbering system. • The lower the BLOSUM number, the more divergent sequence they represent. PAM vs. BLOSUM I • However, you may ask a question which particular matrix • • • • • should be used? Dayhoff et al. (1978) defined terms protein families and superfamilies. A protein family is formed by sequences 85% (or greater) identical to each other. A protein superfamily is defined as sequences related from 30% or greater. Superfamily may clearly contain many families. These terms are widely used in contemporary literature, however with different meanings (we’ll come to that later). Guidance in the choice of scoting matrix: Wheeler D. Selecting the right protein-scoring matrix. Curr Protoc Bioinformatics. 2002;Chapter 3:Unit 3.5. www.nshtvn.org/ebook/molbio/Current%20Protocols/CPB/bi0305.pdf PAM vs. BLOSUM II – PAM • At the time of deriving PAM matrices, most known • • • • proteins were small, globular and hydrophilic. If resercher believes his protein contain substantial hydrophobic regions, PAM matrices are not that useful. Most widely used is PAM250. It is capable of detecting similarities in the 30% range (i.e. superfamilies). Another point of view – PAM250 provides the best lookback in evolutionary time. PAM250 is most effective if the goal is to know the widest possible range of proteins similar to the given protein. PAM vs. BLOSUM III – PAM • Assume a protein is a known member of the serine • • • • protease family. Using the protein as a query against protein databases with PAM 250 will detect virtually all serine proteases, but also considerable amount of irrelevant hits. In this case, the PAM160 matrix should be used. It detects similarities in the 50% to 60% range (Altschul, 1991). And to find only those proteins most similar (70% - 90%) to the query protein, use PAM40. Let’s summarize: • Locate all potential similarities – PAM250 • Determine if the protein belongs to the protein family – PAM160 • Determine the most similar proteins – PAM40 PAM vs. BLOSUM IV – BLOSUM • Most widely used is BLOSUM62. • BLOSUM62 appears to be superior to PAM250 in detecting distant relationships even if the PAM method is updated with current data sets. • BLOSUM62 is capable of accurately detecting similarities down to the 30% range (superfamilies). • Determine if the protein belongs to protein family – BLOSUM80 (detects identities at the 50% level) • Determine the most similar proteins – BLOSUM90 Selecting an Appropriate Matrix Matrix 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. PAM vs. BLOSUM V – battle • Careful information theory analysis showed that the following matrices are equivalent: • PAM250 is equivalent to BLOSUM45 • PAM160 is equivalent to BLOSUM62 • PAM120 is equivalent to BLOSUM80 • Compared to the PAM160 matrix, BLOSUM62 is less tolerant to substitutions involving hydrophilic amino acids, and more tolerant to substitutions involving hydrophobic amino acids. • Although both PAM250 and BLOSUM62 detect similarities at the 30% level, since BLOSUM uses much wider range of proteins, PAM250 is actually equivalent to BLOSUM45 when considering all proteins, not just those that are hydrophilic. Scoring DNA Alignment • The concept of similarity has little relevance here. • Though transitions (R → R or Y → Y) occur more often than transversions (R → Y or Y → R), this is usually not helpful for sequence alignment. • Instead, concept of identity is used. • Frequencies of mutations are equal for all bases: • match score +5 • mismatch score -4 • gap penalty (usually a parameter) • opening -10 • extending -2 Pairwise alignment algorithms • Dynamic programming • Slow, but formally optimizing • Heuristic methods • Efficient, but not as thorough • Word (also k-tuples) methods • Used in database searches • Dot plot (dot matrix) • Graphical way of comparing two sequences Dynamic programming (DP) • General class of algorithms typically applied to optimization problems. • Recursive approach. • Original problem is broken into smaller subproblems and then solved. • Pieces of larger problem have a 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… We want to align two following sequences: ABCDE PQRST If you already have the optimal solution to: A…D P…R then you know the next pair of characters will be either: A…DE P…RS or A…DP…RS or A…DE P…R- You can extend the match by determining which of these has the highest score. New best alignment = previous best + local best Best previous alignment Sequence A ... ... ... ... Sequence B DP algorithms • Global alignment - Needlman-Wunsch • Local alignment - Smith-Waterman • Guaranteed to provide the optimal alignment. • Disadvantages: • Slow due to the very large number of computational steps: O(n 2). • Computer memory requirement also increases with the square of the sequence lengths. • Therefore, it is difficult to use the method for very long sequences. • Many alignments may give the same optimal score. And none of these correspond to the biologically correct alignment.