BCB 444/544

1
BCB 444/544

• Lecture 5
• Dynamic Programming
• 5_Aug29

2
Required Reading (before lecture)

• Mon Aug 27 - for Lecture 4
• Pairwise Sequence Alignment
• Chp 3 - pp 31-41
• Wed Aug 29 - for Lecture 5
• Dynamic Programming
• Eddy What is Dynamic Programming?
• 2004 Nature Biotechnol 22909
• Thurs Aug 30 - Lab 2
• Databases, ISU Resources Pairwise Sequence
  Alignment
• Fri Aug 31 - for Lecture 6
• Scoring Matrices and Alignment Statistics
• Chp 3 - pp 41-49

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Review Chp 2- Biological Databases

• Xiong Chp 2
• Introduction to Biological Databases
• What is a Database?
• Types of Databases
• Biological Databases
• Pitfalls of Biological Databases
• Information Retrieval from Biological
  Databases

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Types of Databases

• 3 Major types of electronic databases
• Flat files - simple text files
• no organization to facilitate retrieval
• Relational - data organized as tables
  ("relations")
• shared features among tables allows rapid search
• Object-oriented - data organized as "objects"
• objects associated hierarchically

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Examples of Biological Databases

• 1- Primary
• DNA sequences
• GenBank - USA
• European Molecular Biology Lab - EMBL
• DNA Data Bank of Japan - DDBJ
• Structures (Protein, DNA, RNA)
• PDB - Protein Data Bank
• NDB - Nucleic Acid Data Bank

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Examples of Biological Databases

• 2- Secondary
• Protein sequences
• Swiss-Prot, TreEMBL, PIR
• these recently combined into UniProt
• 3- Specialized
• Species-specific (or "taxonomic" specific)
• Flybase, WormBase, AceDB, PlantDB
• Molecule-specific, disease-specific
• See http//www.oxfordjournals.org/nar/database/c
  /

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SUMMARY 2- Biological Databases
BEWARE!
Who was that Icelandic fellow?
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Chp 3- Sequence Alignment

• SECTION II SEQUENCE ALIGNMENT
• Xiong Chp 3
• Pairwise Sequence Alignment
• Evolutionary Basis
• Sequence Homology versus Sequence Similarity
• Sequence Similarity versus Sequence Identity
• Methods
• Scoring Matrices
• Statistical Significance of Sequence Alignment

Adapted from Brown and Caragea, 2007, with some
slides from Altman, Fernandez-Baca, Batzoglou,
Craven, Hunter, Page.
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Motivation for Sequence Alignment

• "Sequence comparison lies at the heart of
  bioinformatics analysis." Jin Xiong
• Sequence comparison is important for drawing
  functional evolutionary inferences re new
  genes/proteins
• Pairwise sequence alignment is fundamental it
  used to
• Search for common patterns of characters
• Establish pair-wise correspondence between
  related sequences
• Pairwise sequence alignment is basis for
• Database searching (e.g., BLAST)
• Multiple sequence alignment (MSA)

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Homology

• Homology has a very specific meaning in
  evolutionary computational biology - term is
  often used incorrectly
• For us
• Homology similarity due to descent from a
  common evolutionary ancestor
• But, HOMOLOGY ? SIMILARITY
• When 2 sequences share a sufficiently high degree
  of sequence similarity (or identity), we may
  infer that they are homologous
• We can infer homology from similarity (can't
  prove it!)

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Orthologs vs Paralogs

• 2 types of homologous sequences
• Orthologs - "same genes" in different species
• result of common ancestry
• corresponding proteins have "same" functions
• (e.g., human ?-globin mouse ?-globin)
• Paralogs - "similar genes" within a species
• result of gene duplication events
• proteins may (or may not) have similar functions
• (e.g., human ?-globin human ?-globin)

A
A is the parent gene Speciation leads to B
C Duplication leads to C
Speciation
Duplication
B and C are Orthologous C and C are Paralogous
B
C
C'
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Sequence Homology vs Similarity

• Homologous sequences - sequences that share a
  common evolutionary ancestry
• Similar sequences - sequences that have a high
  percentage of aligned residues with similar
  physicochemical properties
• (e.g., size, hydrophobicity, charge)

• IMPORTANT
• Sequence homology
• An inference about a common ancestral
  relationship, drawn when two sequences share a
  high enough degree of sequence similarity
• Homology is qualitative
• Sequence similarity
• The direct result of observation from a sequence
  alignment
• Similarity is quantitative can be described
  using percentages

13
Sequence Similarity vs Identity

• For nucleotide sequences (DNA RNA), sequence
  similarity and identity have the "same" meaning
  
• Two DNA sequences can share a high degree of
  sequence identity (or similarity) -- means the
  same thing
• Drena's opinion Always use "identity" when
  making quantitative comparisons re DNA or RNA
  sequences (to avoid confusion!)
• For protein sequences, sequence similarity and
  identity have different meanings
• Identity of exact matches between two aligned
  sequences
• Similarity of aligned residues that share
  similar characteristics (e.g, physicochemical
  characteristics, structural propsensities,
  evolutionary profiles)
• Drena's opinion Always use "identity" when
  making quantitative comparisons re protein
  sequences (to avoid confusion!)

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What is Sequence Alignment?

• Given 2 sequences of letters, and a scoring
  scheme for evaluating matching letters, find an
  optimal pairing of letters in one sequence to
  letters of other sequence.

Align 1 THIS IS A RATHER LONGER SENTENCE THAN
THE NEXT. 2 THIS IS A SHORT SENTENCE.
1 THIS IS A RATHER LONGER SENTENCE THAN THE
NEXT. 2 THIS IS A SHORTSENTENCE
. OR 1 THIS IS A RATHER LONGER SENTENCE
THAN THE NEXT. 2 THIS IS A SHORTSENTENC
E.
Is one of these alignments "optimal"? Which is
better?
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Goal of Sequence Alignment

• Find the best pairing of 2 sequences, such that
  there is maximum correspondence between residues
• DNA 4 letter alphabet ( gap)
• TTGACAC
• TTTACAC
• Proteins 20 letter alphabet ( gap)
• RKVA-GMA
• RKIAVAMA

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Statement of Problem

• Given
• 2 sequences
• Scoring system for evaluating match (or mismatch)
  of two characters
• Penalty function for gaps in sequences
• Find Optimal pairing of sequences that
• Retains the order of characters
• Introduces gaps where needed
• Maximizes total score

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Types of Sequence Variation

• Sequences can diverge from a common ancestor
  through various types of mutations
• Substitutions ACGA ? AGGA
• Insertions ACGA ? ACCGA
• Deletions ACGA ? AGA
• Insertions or deletions ("indels") result in gaps
  in alignments
• Substitutions result in mismatches
• No change? match

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Gaps

• Indels of various sizes can occur in one sequence
  relative to the other
• e.g., corresponding to a shortening of the
  polypeptide chain in a protein

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Avoiding Random Alignments with a Scoring
Function

• Introducing too many gaps generates nonsense
  alignments
• s--e-----qu---en--cesometimesquipsentice
• Need to distinguish between alignments that occur
  due to homology and those that occur by chance
• Define a scoring function that accounts for
  mismatches and gaps

Scoring Function (F) e.g. Match
w 1 Mismatch - x 0
Gap - y -1 F w(matches)
x(mismatches) y(gaps)
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Not All Mismatches are the Same

• Some amino acids are more "exchangeable" than
  others (physicochemical properties are similar)
• e.g., Ser Thr are more similar than Trp Ala
• Substitution matrix can be used to introduce
  "mismatch costs" for handling different types of
  substitutions
• Mismatch costs are not usually used in aligning
  DNA or RNA sequences, because no substitution is
  "better" than any other (in general)

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Substitution Matrix

• s(a,b) corresponds to score of aligning character
  a with character b
• Match scores are often calculated
• based on frequency of mutations in very similar
  sequences
• (more details later)

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Methods

• Global and Local Alignment
• Alignment Algorithms
• Dot Matrix Method
• Dynamic Programming Method
• Gap penalities
• DP for Global Alignment
• DP for Local Alignment
• Scoring Matrices
• Amino acid scoring matrices
• PAM
• BLOSUM
• Comparisons between PAM BLOSUM
• Statistical Significance of Sequence Alignment

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Global vs Local Alignment

• Global alignment
• Finds best possible alignment across entire
  length of 2 sequences
• Aligned sequences assumed to be generally similar
  over entire length

• Local alignment
• Finds local regions with highest similarity
  between 2 sequences
• Aligns these without regard for rest of sequence
• Sequences are not assumed to be similar over
  entire length

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Global vs Local Alignment - example
S CTGTCGCTGCACG T TGCCGTG
Which is better?
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Global vs Local Alignment Which should be used
when?

• Both are important
• but it is critical to use right method for a
  given task!
• Global alignment
• Good for aligning closely related sequences of
  similar length
• Not good for divergent sequences or sequences
  with different lengths
• Local Alignment
• Good for searching for conserved patterns
  (domains or motifs) in DNA or protein sequences
• Not good for generating an alignment of closely
  related sequences
• Global and local alignments are fundamentally
  similar they differ only in optimization
  strategy used to align similar residues

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Alignment Algorithms

• 3 major methods for pairwise sequence alignment
• Dot matrix analysis
• Dynamic programming
• Word or k-tuple methods (later, in Chp 4)

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Dot Matrix Method (Dot Plots)

• Place 1 sequence along top row of matrix
• Place 2nd sequence along left column of matrix
• Plot a dot each time there is a match between an
  element of row sequence and an element of column
  sequence
• For proteins, usually use more sophisticated
  scoring schemes than "identical match"
• Diagonal lines indicate areas of match
• Contiguous diagonal lines reveal alignment
  "breaks" gaps (indels)

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Interpretation of Dot Plots

• When comparing 2 sequences
• Diagonal lines of dots indicate regions of
  similarity between 2 sequences
• Reverse diagonals (perpendicular to diagonal)
  indicate inversions
• What do similar patterns mean when comparing a
  sequence with itself (reverse complement)?
• e.g. Reverse diagonals crossing diagonals (X's)
  indicate palindromes

Exploring Dot Plots
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Dot Matrix Variations

• Compare 2 sequences
• Identify matching regions
• Identities for DNA seqs
• Similarities for protein seqs
• Compare sequence with itself
• Identify repeated regions
• Identify inverted repeats
• Identify palindromes
• For long sequences?
• Too many dots! Noisy!
• Instead of per "residue," plot one dot per
  "window" of n matching residues to reduce noise

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Strengths Weakneses of Dot Plots

• Strengths
• Fast and easy
• Allows direct visual identification of regions of
  similarity
• Repeats, inversions, etc. are readily apparent
• Displays all possible matches
• Weaknesses
• Doesn't generate full alignment - user must
  "connect the diagonals"
• No statistical assessment of quality of alignment
  (score)
• Impractical and noisy for long sequences
• Difficult to scale up to muliple alignment

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Dynamic Programming
For Pairwise sequence alignment
Idea Display one sequence above another with
spaces inserted in both to reveal similarity

• A C A T - T C A - C
• B C - T C G C A G C

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Global alignment Scoring
CTGTCG-CTGCACG -TGC-CG-TG----
Reward for matches ? Mismatch penalty
? Space/gap penalty ?
Score ?w ?x - ?y
w matches x mismatches y spaces
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Global alignment Scoring
Reward for matches 10 Mismatch penalty
2 Space/gap penalty 5
C T G T C G C T G C - T G C
C G T G -
-5 10 10 -2 -5 -2 -5 -5 10 10 -5
Total 11
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Optimum Alignment

• Score of an alignment is a measure of its quality
• Optimum alignment problem Given a pair of
  sequences X and Y, find an alignment (global or
  local) with maximum score

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Alignment algorithms

• Global Needleman-Wunsch
• Local Smith-Waterman
• Both NW and SW use dynamic programming
• Variations
• Gap penalty functions
• Scoring matrices

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Dynamic Programming (DP)

• As computer science concept - formalized in early
  1950's by Bellman at RAND Corporation
• Frequently, however, there are only a
  polynomial number of subproblems If we keep
  track of the solution to each subproblem solved,
  and simply look up the answer when needed, we
  obtain a polynomial-time algorithm.
• ----Aho, Hopcroft, Ullman
• Reported to biologists for sequence alignment
  problems by Needleman Wunsch, 1969

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Key Idea

• Score of the best possible alignment that ends
  at a given pair of positions (i,j) in two
  sequences is the score of the best alignment
  previous to those two positions PLUS the score
  for aligning those two positions

Next best alignment previous best local best
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Problem Formulation and Notations

• Given two sequences (strings)
• X x1x2xN of length N x AGC N 3
• Y y1y2yM of length M y AAAC M 4
• Construct a matrix with (N1) x (M1) elements,
  where
• S(i,j) score of best alignment of
  x1..ix1x2xi with y1..jy1y2yj

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Dynamic Programming 4 Components

1. Recursive definition for optimal score
2. Matrix for storing optimal scores of subproblems
3. Bottom-up approach for filling the matrix, by
   solving smallest subproblems first
4. Traceback of path through matrix to recover the
   optimal alignment(s) that gave the optimal score

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Global Alignment Algorithm
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Calculating Score of Optimum Alignment
S(i,j) satisfies the following relationships
Initial conditions
Recursive definition For 1 ? i ? n, 1 ? j ?
m
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Computing the best current score
0
1
N
0
S(0,0)0
1
S(i,j)
S(N,M)
M
Recursion
Initialization
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What happens at the last step in the alignment of
x1..i to y1..j?
1 of 3 cases
yj aligns to a gap
xi aligns to a gap
xi aligns to yj
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DP Implementationn - 3 steps

1. Construct sequence vs sequence matrix and fill in
   from 0,0 to N,M, the best possible scores for
   alignments including the residues at i,j. Also,
   keep track of dependencies of scores (in a
   pointer matrix).
2. For a global alignment of the sequences, find the
   score S(N,M)
3. Trace back through pointer matrix to get the
   optimal alignment. Do this position by position
   to retrieve alignment of all residues of
   sequences, including gaps (i.e., repeat alignment
   calculations in reverse order, following path
   back through matrix, starting at from position
   with highest score.

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Example
Case 1 Line up xi with yj
i
i - 1
x C A T T C A C y C - T T C A
G
j
j -1
Case 2 Line up xi with space
i - 1
i
x C A T T C A - C y C - T T
C A G -
j
Case 3 Line up yj with space
i
x C A T T C A C - y C - T T
C A - G
j
j -1
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? C T C G C
A G C
0 -5 -10 -15 -20 -25 -30 -35 -40
?
10
5
C
A
T
T
C
A
C
10 for match, -2 for mismatch, -5 for space
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? C T C G C
A G C
0 -5 -10 -15 -20 -25 -30 -35 -40
-5 10 5 0 -5 -10 -15 -20 -25
-10 5 8 3 -2 -7 0 -5 -10
-15 0 15 10 5 0 -5 -2 -7
-20 -5 10 13 8 3 -2 -7 -4
-25 -10 5 20 15 18 13 8 3
-30 -15 0 15 18 13 28 23 18
-35 -20 -5 10 13 28 23 26 33
?
C
A
T
T
C
A
C
Traceback can yield both optimal alignments
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Affine Gap Penalty Functions

• Gap penalty h gk
• where
• k length of gap
• h gap opening penalty
• g gap continuation penalty

Can also be solved in O(nm) time using dynamic
programming