1 / 25

250 likes | 316 Views

Definitions. Optimal alignment - one that exhibits the most correspondences. It is the alignment with the highest score . May or may not be biologically meaningful.

Download Presentation
## Definitions

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Definitions**Optimal alignment - one that exhibits the most correspondences. It is the alignment with the highest score. May or may not be biologically meaningful. Global alignment - Needleman-Wunsch (1970) maximizes the number of matches between the sequences along the entire length of the sequences. Local alignment - Smith-Waterman (1981) gives the highest scoring local match between two sequences.**Pairwise Global Alignment**• Global alignment - Needleman-Wunsch (1970) • maximizes the number of matches between the sequences along the entire length of the sequences. • Reason for making a global alignment: • checking minor difference between two sequences • Analyzing polymorphisms (ex. SNPs) between closely related sequences • …**Pairwise Global Alignment**• Computationally: • Given: a pair of sequences (strings of characters) • Output: an alignment that maximizes the similarity**How can we find an optimal alignment?**• ACGTCTGATACGCCGTATAGTCTATCTCTGAT---TCG-CATCGTC--T-ATCT • How many possible alignments? C(27,7) gap positions = ~888,000 possibilities • Dynamic programming: The Needleman & Wunsch algorithm 27 1**= (2n)!/(n!)2 = (22n /n ) = (2n)** 2n n Time Complexity Consider two sequences: AAGT AGTC How many possible alignments the 2 sequences have?**Scoring a sequence alignment**• Match/mismatch score: +1/+0 • Open/extension penalty: –2/–1ACGTCTGATACGCCGTATAGTCTATCT ||||| ||| || ||||||||----CTGATTCGC---ATCGTCTATCT • Matches: 18 × (+1) • Mismatches: 2 × 0 • Open: 2 × (–2) • Extension: 5 × (–1) Score = +9**Pairwise Global Alignment**• Computationally: • Given: a pair of sequences (strings of characters) • Output: an alignment that maximizes the similarity**Needleman & Wunsch**• Place each sequence along one axis • Place score 0 at the up-left corner • Fill in 1st row & column with gap penalty multiples • Fill in the matrix with max value of 3 possible moves: • Vertical move: Score + gap penalty • Horizontal move: Score + gap penalty • Diagonal move: Score + match/mismatch score • The optimal alignment score is in the lower-right corner • To reconstruct the optimal alignment, trace back where the max at each step came from, stop when hit the origin.**empty**A A A C empty 0 -2 -4 -6 -8 A -2 1 -1 -3 -5 G -4 -1 0 -2 -4 C -3 -2 -1 -1 -6 Example • Let gap = -2 match = 1 mismatch = -1. AAAC A-GC AAAC -AGC**Time Complexity Analysis**• Initialize matrix values: O(n), O(m) • Filling in rest of matrix: O(nm) • Traceback: O(n+m) • If strings are same length, total time O(n2)**Local Alignment**• Problem first formulated: • Smith and Waterman (1981) • Problem: • Find an optimal alignment between a substring of s and a substring of t • Algorithm: • is a variant of the basic algorithm for global alignment**Motivation**• Searching for unknown domains or motifs within proteins from different families • Proteins encoded from Homeobox genes (only conserved in 1 region called Homeo domain – 60 amino acids long) • Identifying active sites of enzymes • Comparing long stretches of anonymous DNA • Querying databases where query word much smaller than sequences in database • Analyzing repeated elements within a single sequence**GATCACCT**GAT_ACCC empty G A T C A C C T 0 0 0 0 0 0 0 0 empty 0 0 0 0 0 G 0 0 0 0 0 A 0 0 0 0 1 T 0 0 0 0 0 A 0 0 C 0 0 0 0 C 0 0 0 C Local Alignment GATCACCT GATACCC • Let gap = -2 match = 1 mismatch = -1. 0 1 0 0 0 0 2 0 0 1 0 3 1 0 1 1 2 2 0 0 2 1 3 1 0 1 1 2 4 2 1 0 2 3 3**Smith & Waterman**• Place each sequence along one axis • Place score 0 at the up-left corner • Fill in 1st row & column with 0s • Fill in the matrix with max value of 4 possible values: • 0 • Vertical move: Score + gap penalty • Horizontal move: Score + gap penalty • Diagonal move: Score + match/mismatch score • The optimal alignment score is the max in the matrix • To reconstruct the optimal alignment, trace back where the MAX at each step came from, stop when a zero is hit**exercise**• Let: gap = -2 match = 1 mismatch = -1. • Find the best local alignment: CGATGAAATGGA**Semi-global Alignment**Example: CAGCA-CTTGGATTCTCGG –––CAGCGTGG–––––––– CAGCACTTGGATTCTCGG CAGC––––G––T––––GG We like the first alignment much better. In semiglobal comparison, we score the alignments ignoring some of the end spaces.**Global Alignment**Example: AAACCC A CCC • Prefer to see: • AAACCC • ACCC Do not want to penalize the end spaces**SemiGlobal Alignment**Example: s = AAACCC t = ACCC**SemiGlobal Alignment**Example: s = AAACCCG t = ACCC G 0 -1 -2 -1 2**SemiGlobal Alignment**• Summary of end space charging procedures:**Pairwise Sequence Comparison over Internet**Bioinformatics for Dummies**Significance of Sequence Alignment**• Consider randomly generated sequences. What distribution do you think the best local alignment score of two sequences of sample length should follow? • Uniform distribution • Normal distribution • Binomial distribution (n Bernoulli trails) • Poisson distribution (n, np=) • others**Extreme Value Distribution**• Yev = exp(- x - e-x )**“Twilight Zone”**Some proteins with less than 15% similarity have exactly the same 3-D structure while some proteins with 20% similarity have different structures. Homology/non-homology is never granted in the twilight zone.

More Related