DNA Sequence Alignment

1
DNA Sequence Alignment

• Lecture 19 DNA Sequence Alignment
• Review Primer of Genome Science Handout
• Needleman/Wunsch example
• Review Assignment 5

• Lecture 18 Introduction to Dynamic Programming
• Structure of Dynamic Programs
• Calculating Binomial Coefficient
• Pascals Triangle
• Coins Revisited

2
Needleman/Wunsch

• Score for aligning i residues of sequence 1
  against j residues of sequence 2 given by
• c(i,j) is the cost of matching (or mismatching)
  residues I from sequence 1 with j from sequence 2
• Build table with (i,j)th entry being the best
  score for aligning the first i residues of
  sequence 1 with first j residues of sequence 2

3
Example

• Align (ACGCTGA) with (ACTGT) using scoring
  function substitution, 1 indel, 5, match, -3.

4
Example

• Initialize first row and column using scoring
  function substitution, 1 indel, 5, match, -3.

5
Example

• S(1,1) is the minimum of S(i-1,j-1)-33,

6
Example

• S(1,1) is the minimum of S(i-1,j-1)-33,
  S(i-1,j)510,

7
Example

• S(1,1) is the minimum of S(i-1,j-1)-33,
  S(i-1,j)510, S(i,j-1)510

8
Example

• S(1,1) is the minimum of S(i-1,j-1)-33,
  S(i-1,j)510, S(i,j-1)510

9
Example

• S(i,1) is the score for aligning i elements of
  sequence 1 against the initial A from sequence 2
  followed by gaps

10
Example

• S(1,j) is the score for aligning the initial A
  from sequence 1 followed by gaps, with j elements
  of sequence 2

11
Example

• S(2,2) is the minimum of S(i-1,j-1)-3-6,
  S(i-1,j)57, S(i,j-1)57

12
Example

• S(i,2) and S(2,j) consider alignment, appending
  gaps

13
Example

• S(3,3) is the minimum of S(i-1,j-1)1-5,
  S(i-1,j)54, S(i,j-1)54

14
Example

• S(i,j) is the minimum of S(i-1,j-1)c(i,j),
  S(i-1,j)5,
• S(i,j-1)5

15
Example

• S(i,j) is the minimum of S(i-1,j-1)c(i,j),
  S(i-1,j)5,
• S(i,j-1)5

16
Example

• Traceback to find alignments yielding optimal
  score

17
Example

• Two optimal alignments, ACGCTGA or ACGCTGA
• A -
  - CTGT AC - - TGT