Application of Algorithm Research to Molecular Biology

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Application of Algorithm Research to Molecular
Biology

• R. C. T. Lee
• Dept. Of Computer Science
• National Chinan University

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• There is one peculiar characteristics of all
  living organisms We can reproduce ourselves.
• Yet, it is important that what we reproduce have
  to be the same as we are.
• That is, wild flowers produce the same kind of
  wild flowers and birds reproduce the same kind of
  birds.

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• Information about ourselves must be passed to our
  descendants.
• Question How is this done?
• Answer Through DNA.

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• DNA(Deoxyribonucleic Acid) can be viewed as two
  strands of nucleic acids formed as a double helix.

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• There are only four types of nucleic acids in
  every DNA
• A Adenine
• G Guanine
• C Cytosine
• T Thymine

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• Each strand of a DNA is a sequence of A, G, C and
  T.
• Yet, in each strand, A is paired with T in the
  other strand.
• Similarly, G is paired with C.

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Human Mitochondrial DNA Control Region

• TTCTTTCATGGGGAAGCAAA
• AAGAAAGTACCCCTTCGTTT

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• DNA exists in cells.
• For each living organism, there are a lot of
  different kinds of cells. For instance, in human
  beings, we have muscle cells, blood cells, neural
  cells etc.
• How can different cells perform different
  functions?

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Genes

• In each DNA sequence, there are subsequences
  which are called genes.
• Each gene corresponds to a distinct protein and
  it is the protein which determines the function
  of the cell.
• For instance, in red blood cells, there must be
  oxygen carrying protein haemoglobin and the
  production of this protein is controlled by a
  certain gene.

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Proteins

• Each protein consists of amino acids.
• There are 20 different amino acids

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The Relationship between a Gene and its
Corresponding Protein
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• As shown above, each amino acid is coded by a
  triplet. For instance, TTC denotes
  PHE(Phenylalanine).
• Each triplet is called a codon.
• There are three codons, namely TAA, TGA and TAG
  which represent end of gene.

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• Protein Rnase AKETAAAKFER
• Its corresponding DNA sequence isAAA GAA ACT
  GCT GCT GCT AAA TTT GAA CGT

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How Is a Protein Produced?

• RNA (Ribonucleic Acid)
• Each cell is able to recognize all of the
  starting points of genes relevant to the proteins
  important to the functions of the cell.

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• The RNA system scans a gene. For each codon being
  scanned, it produces a corresponding amino acid.
• After all codons have been scanned, the
  corresponding protein is produced.

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• AAA GAA ACT GCT GCT GCT AAA TTT GAA CGT
• KETAAAKFER
• Note that codon AAA corresponds to amino acid K
  and CGT corresponds to R.
• Remember TAA, TGA and TAG signify end of gene.

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Problems

• 1. String Matching Problem
• 2. Sequence Alignment Problem
• 3. Evolution Tree Problem
• 4. RNA Secondary Structure Prediction Problem
• 5. Protein Structure Problem
• 6. Physical Mapping Problem

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Exact String Matching Problems

• Exact String Matching Problems
• Instance A text T of length n and a pattern P
  of length m, where n gt m.
• Question Find all occurrences of P in T.
• Example If T ttaptaap and P ap, then P
  occurs in T starting at 3 and 7.
• Linear time (O(nm) time) Algorithms
• Knuth-Morris-Pratt (KMP) algorithm
• Boyer-Moore algorithm

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Approximate String Matching Problems

• Approximate String Matching Problems
• Instance A text T of length n, a pattern P of
  length m and a maximal number of errors allowed k
• Question Find all text positions where the
  pattern matches the text up to k errors, where
  errors can be substituting, deleting, or
  inserting a character.
• Example
• Let T pttapa, P patt and k 2.
• The substrings T1..2, T1..3, T1..4 and
  T5..6 are up to 2 errors with P.
• Algorithms
• Dynamic Programming approach
• NFA approach

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Sequence Alignment Problem

• ATTCATTACAACCGCTATGACCCATCAACAACCGCTATG
• It appears that these two sequences are quite
  different.
• An alignment will produce the followingATTCATTA-
  CAACCGCTATGACCCATCAACAACCGCTATG

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• Given two sequences, any alignment will have a
  corresponding score.
• For each exact match, the score is equal to 2.
• For each mismatch, the score is equal to -1.
• AGC- AG-CAAAC AAAC2-3-1
  2x2-2x(-1)2

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• The sequence alignment problem Given two
  sequences, find an alignment which produces the
  highest score.
• Approach Dynamic Programming
• The multiple sequence alignment problem is NP-hard

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The Evolution Tree Problem
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• The evolution tree problem Given a distance
  matrix of n species, find an evolution tree under
  some criterion.
• Usually, the criteria are such that all of the
  tree distances reflect the original distances.
• That is, when two species are close to each other
  in the distance matrix, they should be close in
  the evolution tree.

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• Each criterion corresponds to a distinct
  evolution tree problem.
• Most of them are NP-complete.
• Algorithms which produce optimal evolution trees
  in polynomial time are mostly based upon the
  minimal spanning tree approach.

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A Partial Evolution Tree of the Homo Sapien
(Intelligent Human Beings, also Modern Men) Our
ancestors are from Africa.
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Secondary Structure of RNA

• Due to hydrogen bonds, the primary structure of a
  RNA can fold back on itself to form its secondary
  structure.
• Base pairs (formed by hydrogen bonds) 1. A?U
  (Watson-Crick base pair) 2. C?G (Watson-Crick
  base pair)3. G?U (Wobble base pair)

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AGGCCUUCCU
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2D 3D Structures of Yeast Phenylalanyl-Transfer
RNA
3D Structure
2D Structure
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Secondary Structure Prediction Problem

• Given an RNA sequence, determine the secondary
  structure of the minimum free energy from this
  sequence.
• Approach Dynamic Programming

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Protein Structure Problem

• Each amino acid of a protein can be classified
  into either of the following two types
• H (hydrophobic, non-polar) (hating water)
• P (hydrophilic, polar) (loving water)
• Then the amino acid sequence of a protein can be
  viewed as a binary sequence of Hs (1s) and Ps
  (0s).

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Example

• Instance 011001001110010

0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
Score 5
Score 3
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H-P Model

• Instance A sequence of 1s (Hs) and 0s (Ps).
• Question To find a self-avoiding paths embedded
  in either a 2D or 3D lattice which maximizes
  score, where the score is the number of pairs of
  1s that are adjacent in the lattice without
  being adjacent in the sequence.
• NP-complete even for 2D lattice.

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Physical Mapping Problem
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Shortest Common Superstring

• Input A collection F of strings.
• Output A shortest possible string S such that
  for every f ? F, S is a superstring of f.
• For example
• NP-complete

ACT CTA AGTACTAGT
F
S
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• Suppose the target is too long and its contents
  are unknown.
• What can we do?
• Enzyme A ? 6, 8, 3, 10Enzyme B ? 7, 11, 4,
  5Enzymes A and B ? 1, 5, 2, 6, 7, 3, 3

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This problem is called the two digest problem
which is NP-complete.
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• TAA, TGA, or TAG.
• Do you know what they mean?

• End of Gene.
• Thank you for your patience. Have a good
  conference.