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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First of all, we need a language to pass the
information about heredity. This language has
existed for 3 billion years, the oldest language
in the world. This language consists of 4
alphabets A, G, C and T.
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We need a mechanism to represent the alphabets.
This is done by using chemical compounds. A
adenine G guanine C cytosine T thymine
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Nature has used DNA to pass the heredity
information to our descendants. A DNA strand is
a sequence of chemical compounds. From our
point of view, a DNA strand is a sequence of A,
G, C and T.
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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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• 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
• Physical Mapping Problem
• Genome Rearrangement 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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Before alignment TTAAAAATAA GAAATTTTTT
TTTTTAAAAA ATTTCTATAA ATTTTATATA TATTTTATAT
TTAAAAATAA GAAATTTTTT TTTTTAAAAA ATTTCTATAA
ATTTTATATA TATTTTATAT TTAAAAATAA GAAATTTTTT
TTTTTAAAAA ATTTCTATAA ATTTTATATA TATTTTATAT
TTAAAAATAA GAAATTTTTT TTTTTAAAAA ATTTCTATAA
ATTTTATATA TATTTTATAT TTAAAAATAA GAAATTTTTT
TTTTTAAAAA ATTTCTATAA ATTTTATATA TATATTTTAT
TTAAAAATAA GAAATTATTT TTTAAAAATA ATTTCTATAA
ATGTTATATA TATATTTTAT TTAAAAATAA GAAATTATTT
TTTAAAAATA ATTTCTATAA ATGTTATATA TATATTTTAT
TTAAAAATAA GAAATTATTT TTTAAAAATA ATTTCTATAA
ATGTTATATA TATATTTTAT TTAAAAATAA GAAATTATTT
TTTAAAATAA TTTCTATAAA TTTTATATAT ATATTTTATA
TTAAAAATAA GAAATTATTT TTTAAAAATA ATTTCTATAA
ATTTTATATA TATATTTTAT TTAAAAATAA GAAATTTTTT
TTTTTAAATT AAATTTCTAT CAATTTTATA TATTTTTTAT
TTAAAAATTA GAAATTTTAT TTTTAAAATT TCTATTAAAA
TTTATATATA TATTTTATAA TTAAAAATTA GAAATTTTAT
TTTTAAAATT TCTATTAAAA TTTATATATA TATATTATAA
TTAAAAATTA GAAATTTTAT TTTTAAAATT TCTATTAAAA
TTTATATATA TTTTTTATAA TTAAAAATTA GAAATTTTAT
TTTTTAAAAT TTCTATTAAA ATTTATATAT ATATTTTTTT
TTAAAAATGA GAAATTTTTA TAAAAAAATT TCTTTAAATT
TTATATATTT TATAAATATA TTAATAATAA GAAATTTTTT
TATTTTTTAA ATAAAAAATT CTTTAAATTT TATATATATA
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After alignment TTAAAAATAA GAAATTATTT
TTTAAA AATAATT TCTATAAAT GTTATATATA
TTAAAAATAA GAAATTATTT TTTAAA AATAATT
TCTATAAAT GTTATATATA TTAAAAATAA GAAATTATTT
TTTAAA AATAATT TCTATAAAT GTTATATATA
TTAAAAATAA GAAATTTTTT TTTTTAA AAAATT
TCTATAAAT TTTATATATA TTAAAAATAA GAAATTTTTT
TTTTTAA AAAATT TCTATAAAT TTTATATATA
TTAAAAATAA GAAATTTTTT TTTTTAA AAAATT
TCTATAAAT TTTATATATA TTAAAAATAA GAAATTTTTT
TTTTTAA AAAATT TCTATAAAT TTTATATATA
TTAAAAATAA GAAATTATTT TTTAAA ATAATT
TCTATAAAT TTTATATATA TTAAAAATAA GAAATTATTT
TTTAAA AATAATT TCTATAAAT TTTATATATA
TTAAAAATTA GAAATTTTAT TTTTAA AATT
TCTATTAAAA TTTATATATA TTAAAAATTA GAAATTTTAT
TTTTAA AATT TCTATTAAAA TTTATATATA
TTAAAAATAA GAAATTTTTT TTTTTAA AAAATT
TCTATAAAT TTTATATATA TTAAAAATTA GAAATTTTAT
TTTTTAA AATT TCTATTAAAA TTTATATATA
TTAAAAATTA GAAATTTTAT TTTTAA AATT
TCTATTAAAA TTTATATATA TTAAAAATAA GAAATTTTTT
TTTTTAA ATTAAATT TCTATCAAT TTTATATATT
TTAAAAATGA GAAATTTTTA TAA AAAAATT
TCTTTAAAT TTTATATATT TTAATAATAA GAAATTTTTT
TATTTTTTAA ATAAAAAAT TCTTTAAAT TTTATATATA
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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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RNA Secondary Structure without Pseudoknots
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Given an RNA sequence, there may be several
secondary structures without pseudoknots, as
shown below
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An optimal RNA secondary structure is one with
the maximum number of base pairs.
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RNA Secondary Structure with Simple Pseudoknots
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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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A genome is a sequence of genes. Chloroplast
genome of Alfafa -8, -7, -6, -5, -4, -3, -2,
-1, -11, -10, -9 Chloroplast genome of garden
pea -4, 3, -2, 8, 7, -1, -5, -6, -11, 10,
9
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Suppose that we can only reverse a substring of
genes. -4, 5, -8, -9 After reversal, we
have 9, 8, -5, 4.
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The sorting by reversal problem The problem of
transforming one sequence to another only by
reversals in the minimum number of steps.
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The transformation of worm Ascaris Suum
mitochondrial DNA into human mitochondrial DNA
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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.