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Sequence Alignments

Introduction to Bioinformatics. Sequence Alignments. Sequence Alignments. Cornerstone of bioinformatics What is a sequence? Nucleotide sequence Amino acid sequence Pairwise and multiple sequence alignments We will focus on pairwise alignments What alignments can help

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Sequence Alignments

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  1. Introduction to Bioinformatics Sequence Alignments

  2. Sequence Alignments • Cornerstone of bioinformatics • What is a sequence? • Nucleotide sequence • Amino acid sequence • Pairwise and multiple sequence alignments • We will focus on pairwise alignments • What alignments can help • Determine function of a newly discovered gene sequence • Determine evolutionary relationships among genes, proteins, and species • Predicting structure and function of protein Intro to Bioinformatics – Sequence Alignment Acknowledgement: This notes is adapted from lecture notes of both Wright State University’s Bioinformatics Program and Professor Laurie Heyer of Davidson College with permission.

  3. DNA Replication • Prior to cell division, all the genetic instructions must be “copied” so that each new cell will have a complete set • DNA polymerase is the enzyme that copies DNA • Reads the old strand in the 3´ to 5´ direction Intro to Bioinformatics – Sequence Alignment

  4. Over time, genes accumulate mutations • Environmental factors • Radiation • Oxidation • Mistakes in replication or repair • Deletions, Duplications • Insertions, Inversions • Translocations • Point mutations Intro to Bioinformatics – Sequence Alignment

  5. Deletions • Codon deletion:ACG ATA GCG TAT GTA TAG CCG… • Effect depends on the protein, position, etc. • Almost always deleterious • Sometimes lethal • Frame shift mutation:ACG ATA GCG TAT GTA TAG CCG…ACG ATA GCG ATG TAT AGC CG?… • Almost always lethal Intro to Bioinformatics – Sequence Alignment

  6. Indels • Comparing two genes it is generally impossible to tell if an indel is an insertion in one gene, or a deletion in another, unless ancestry is known:ACGTCTGATACGCCGTATCGTCTATCTACGTCTGAT---CCGTATCGTCTATCT Intro to Bioinformatics – Sequence Alignment

  7. The Genetic Code Substitutions are mutations accepted by natural selection. Synonymous: CGC CGA Non-synonymous: GAU  GAA Intro to Bioinformatics – Sequence Alignment

  8. Comparing Two Sequences • Point mutations, easy:ACGTCTGATACGCCGTATAGTCTATCTACGTCTGATTCGCCCTATCGTCTATCT • Indels are difficult, must align sequences:ACGTCTGATACGCCGTATAGTCTATCTCTGATTCGCATCGTCTATCTACGTCTGATACGCCGTATAGTCTATCT----CTGATTCGC---ATCGTCTATCT Intro to Bioinformatics – Sequence Alignment

  9. Why Align Sequences? • The draft human genome is available • Automated gene finding is possible • Gene: AGTACGTATCGTATAGCGTAA • What does it do? • One approach: Is there a similar gene in another species? • Align sequences with known genes • Find the gene with the “best” match Intro to Bioinformatics – Sequence Alignment

  10. Gaps or No Gaps • Examples Intro to Bioinformatics – Sequence Alignment

  11. Scoring a Sequence Alignment Given • Match score: +1 • Mismatch score: +0 • Gap penalty: –1 • SequencesACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || ||||||||----CTGATTCGC---ATCGTCTATCT  • Matches: 18 × (+1) • Mismatches: 2 × 0 • Gaps: 7 × (– 1) Score = +11 Intro to Bioinformatics – Sequence Alignment

  12. Origination and Length Penalties • Note that a bioinformatics computational model or algorithm must be “biologically meaningful” or even “biologically significant” • We want to find alignments that are evolutionarily likely. • Which of the following alignments seems more likely to you?ACGTCTGATACGCCGTATAGTCTATCTACGTCTGAT-------ATAGTCTATCTACGTCTGATACGCCGTATAGTCTATCTAC-T-TGA--CG-CGT-TA-TCTATCT • We can achieve this by penalizing more for a new gap, than for extending an existing gap   Intro to Bioinformatics – Sequence Alignment

  13. Scoring a Sequence Alignment (2) Given • Match/mismatch score: +1/+0 • Gap origination/length penalty: –2/–1 • Sequences ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || ||||||||----CTGATTCGC---ATCGTCTATCT  • Matches: 18 × (+1) • Mismatches: 2 × 0 • Origination: 2 × (–2) • Length: 7 × (–1) • Caution: Sometime “gap extension” used instead of “gap length” … Score = +7 Intro to Bioinformatics – Sequence Alignment

  14. How can we find an optimal alignment? • Finding the alignment is computationally hard:ACGTCTGATACGCCGTATAGTCTATCTCTGAT---TCG-CATCGTC--T-ATCT • C(27,7) gap positions = ~888,000 possibilities • It’s possible, as long as we don’t repeat our work! • Dynamic programming: The Needleman & Wunsch algorithm Intro to Bioinformatics – Sequence Alignment

  15. Dynamic Programming • Technique of solving optimization problems • Find and memorize solutions for subproblems • Use those solutions to build solutions for larger subproblems • Continue until the final solution is found • Recursive computation of cost function in a non-recursive fashion Intro to Bioinformatics – Sequence Alignment

  16. Dynamic Programming • Example • Solving Fibonacci number f(n) = f(n-1) + f(n-2) recursively takes exponential time • Because many numbers are recalculated • Solving it using dynamic programming only takes a linear time • Use an array f[] to store the numbers f[0] = 1; f[1] = 1; for (i = 2; i <= n; i++) f[i] = f[i – 1] + f[i – 2]; Intro to Bioinformatics – Sequence Alignment

  17. i-1 i j j-1 Global Sequence Alignment • Needleman-Wunsch algorithm • Suppose we are aligning:a with a … Di,j= max{ Di-1,j+ d(Ai, –), Di,j-1+ d(–, Bj), Di-1,j-1+ d(Ai, Bj)} B A Seq1 Seq2 Intro to Bioinformatics – Sequence Alignment

  18. Dynamic Programming (DP) Concept • Suppose we are aligning:CACGA CGA Intro to Bioinformatics – Sequence Alignment

  19. G +1 ACTCG ACAGTAG -1 ACTC- ACAGTAG- -1 ACTCGG ACAGTA DP – Recursion Perspective • Suppose we are aligning:ACTCGACAGTAG • Last position choices: Intro to Bioinformatics – Sequence Alignment

  20. What is the optimal alignment? • ACTCGACAGTAG • Match: +1 • Mismatch: 0 • Gap: –1 Intro to Bioinformatics – Sequence Alignment

  21. Needleman-Wunsch: Step 1 • Each sequence along one axis • Gap penalty multiples in first row/column • 0 in [1,1] (or [0,0] for the CS-minded) Intro to Bioinformatics – Sequence Alignment

  22. Needleman-Wunsch: Step 2 • Vertical/Horiz. move: Score + (simple) gap penalty • Diagonal move: Score + match/mismatch score • Take the MAX of the three possibilities Intro to Bioinformatics – Sequence Alignment

  23. Needleman-Wunsch: Step 2 (cont’d) • Fill out the rest of the table likewise… Intro to Bioinformatics – Sequence Alignment

  24. Needleman-Wunsch: Step 2 (cont’d) • Fill out the rest of the table likewise… • The optimal alignment score is calculated in the lower-right corner Intro to Bioinformatics – Sequence Alignment

  25. But what is the optimal alignment • To reconstruct the optimal alignment, we must determine of where the MAX at each step came from… Intro to Bioinformatics – Sequence Alignment

  26. A path corresponds to an alignment • = GAP in top sequence • = GAP in left sequence • = ALIGN both positions • One path from the previous table: • Corresponding alignment (start at the end):AC--TCG ACAGTAG Score = +2 Intro to Bioinformatics – Sequence Alignment

  27. Algorithm Analysis • Brute force approach • If the length of both sequences is n, number of possibility = C(2n, n) = (2n)!/(n!)2 22n / (n)1/2, using Sterling’s approximation of n! = (2n)1/2e-nnn. • O(4n) • Dynamic programming • O(mn), where the two sequence sizes are m and n, respectively • O(n2), if m is in the order of n Intro to Bioinformatics – Sequence Alignment

  28. Practice Problem • Find an optimal alignment for these two sequences: GCGGTT GCGT • Match: +1 • Mismatch: 0 • Gap: –1 Intro to Bioinformatics – Sequence Alignment

  29. Practice Problem • Find an optimal alignment for these two sequences: GCGGTT GCGT GCGGTTGCG-T- Score = +2 Intro to Bioinformatics – Sequence Alignment

  30. Semi-global alignment • Suppose we are aligning:GCGGGCG • Which do you prefer?G-CG -GCGGGCG GGCG • Semi-global alignment allows gaps at the ends for free. • Terminal gaps are usually the result of incomplete data acquisition  no biologically significant Intro to Bioinformatics – Sequence Alignment

  31. Semi-global alignment • Semi-global alignment allows gaps at the ends for free. • Initialize first row and column to all 0’s • Allow free horizontal/vertical moves in last row and column Intro to Bioinformatics – Sequence Alignment

  32. Local alignment • Global alignments – score the entire alignment • Semi-global alignments – allow unscored gaps at the beginning or end of either sequence • Local alignment – find the best matching subsequence • CGATGAAATGGA • This is achieved by allowing a 4th alternative at each position in the table: zero. Intro to Bioinformatics – Sequence Alignment

  33. Local Sequence Alignment • Why local sequence alignment? • Subsequence comparison between a DNA sequence and a genome • Protein function domains • Exons matching • Smith-Waterman algorithm Initialization: D1,j= , Di,1=  Di,j= max{ Di-1,j+ d(Ai, –), Di,j-1+ d(–,Bj), Di-1,j-1+ d(Ai,Bj), 0} Intro to Bioinformatics – Sequence Alignment

  34. c g a t g 0 0 0 0 0 0 a 0 0 0 1 0 0 a 0 0 0 1 0 0 a 0 0 0 1 0 0 t 0 0 0 0 2 1 g 0 0 1 0 1 3 g 0 0 1 0 0 2 a 0 0 0 2 1 1 Local alignment • Score: Match = 1, Mismatch = -1, Gap = -1 CGATGAAATGGA Intro to Bioinformatics – Sequence Alignment

  35. Local alignment • Another example Intro to Bioinformatics – Sequence Alignment

  36. -- A C G G C T C -- -4 -8 -12 -16 -20 -24 -28 A -4 1 -3 -7 -11 -15 -19 -23 T -8 -3 -2 -6 -10 -14 -14 -18 G -12 -7 -6 -1 -5 -9 -13 -17 G -16 -11 -10 -5 0 -4 -8 -12 C -20 -15 -10 -9 -4 1 -3 -7 C -24 -19 -14 -13 -8 -3 -2 -2 T -28 -23 -18 -17 -12 -7 -2 -5 C -32 -27 -22 -21 -16 -11 -6 -1 More Example • Align ATGGCCTC ACGGCTC Mismatch = -3 Gap  = -4 0 Global Alignment: ATGGCCTC ACGGC-TC Intro to Bioinformatics – Sequence Alignment

  37. -- A C G G C T C -- 0 0 0 0 0 0 0 A 0 1 0 0 0 0 0 0 T 0 0 0 0 0 0 1 0 G 0 0 0 1 1 0 0 0 G 0 0 0 1 2 0 0 0 C 0 0 1 0 0 3 0 1 C 0 0 1 0 0 1 0 1 T 0 0 0 0 0 0 2 0 C 0 0 1 0 0 1 0 3 More Example Local Alignment: ATGGCCTC ACGG CTC or ATGGCCTC ACGGC TC 0 Intro to Bioinformatics – Sequence Alignment

  38. Scoring Matrices for DNA Sequences • Transition: A  G C  T • Transversion: a purine (A or G) is replaced by a pyrimadine (C or T) or vice versa Intro to Bioinformatics – Sequence Alignment

  39. Scoring Matrices for Protein Sequence • PAM 250 Intro to Bioinformatics – Sequence Alignment

  40. Scoring Matrices for Protein Sequence • PAM (Percent Accepted Mutations) • 1 PAM unit can be thought of as the amount of time in which an “average” protein mutates 1 out of every 100 amino acids. • Perform multiple sequence alignment on a “family” of proteins that are at least 85% similar. Find the frequency of amino acid i and j are aligned to each other and normalize it. • Entry mij in PAM1 represents the probability of amino acid i substituted by amino acid j in 1 PAM unit • PAM 2 = PAM 1 × PAM 1 • PAM n = (PAM 1)n, e.g., PAM 250 = (PAM 1)250 • Questions • Why are values in a PAM matrix integers? Shouldn’t a probability be between 0 and 1? • Why is PAM250 possible? Shouldn’t a probability be less than or equal to 100%? Intro to Bioinformatics – Sequence Alignment

  41. Scoring Matrices for Protein Sequence • BLOSUM (BLOcks SUbstitution Matrix) 62 Intro to Bioinformatics – Sequence Alignment

  42. Using Protein Scoring Matrices • Divergence BLOSUM 80 BLOSUM 62 BLOSUM 45 PAM 1 PAM 120 PAM 250 Closely related Distantly related Less divergent More divergent Less sensitive More sensitive • Looking for • Short similar sequences → use less sensitive matrix • Long dissimilar sequences → use more sensitive matrix • Unknown → use range of matrices • Comparison • PAM – designed to track evolutionary origin of proteins • BLOSUM – designed to find conserved regions of proteins Intro to Bioinformatics – Sequence Alignment

  43. Multiple Sequence Alignment • Why multiple sequence alignment (MSA) • Two sequences might not look very similar. • But, some “similarity” emerges with more sequences, however. • Is dynamic programming still applicable? • CLUSTALW • One of most popular tools for MSA • Heuristic-based approach • Basic 1) Calculate the distance matrix based on pairwise alignments 2) Construct a guide tree NJ (unrooted tree)  Mid-point (rooted tree) 3) Progressive alignment using the guide tree

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