Y.C. Wong Public Lecture 040611

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Outline

• DNA and RNA
• Genome, genes, and diseases
• Palindromes and replication origins in viral
  genomes
• Mathematics for prediction of replication origins

Cytomegalovirus (CMV) Particle
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DNA and RNA

• DNA is deoxyribonucleic acid, made up of 4
  nucleotide bases Adenine, Cytosine, Guanine, and
  Thymine.
• RNA is ribonucleic acid, made up of 4 nucleotide
  bases Adenine, Cytosine, Guanine, and Uracil.
• For uniformity of notation, all DNA and RNA data
  sequences deposited in GenBank are represented as
  sequences of A, C, G, and T.
• The bases A and T form a complementary pair, so
  are C and G.

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Genes and Genome
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Genes and Diseases
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Virus and Eye Diseases
CMV Particle

• CMV Retinitis
• inflammation of the retina
• triggered by CMV particles
• may lead to blindness

Genome size 230 kbp
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Replication Origins and Palindromes

• High concentration of palindromes exists around
  replication origins of other herpesviruses
• Locating clusters of palindromes (above a minimal
  length) on CMV genome sequence might reveal
  likely locations of its replication origins.

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Palindromes in Letter Sequences
Odd Palindrome

• A nut for a jar of tuna

ANUTFORA
AROFTUNA
J
Even Palindrome
Step on no pets
STEPON
NOPETS
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DNA Palindromes
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Association of Palindrome Clusters with
Replication Origins
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Computational Prediction of Replication Origins

• Palindrome distribution in a random sequence
  model
• Criterion for identifying statistically
  significant palindrome clusters
• Evaluate prediction accuracy
• Try to improve

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Random Sequence Model

• A mathematical model can be used to generate a
  DNA sequence
• A DNA molecule is made up of 4 types of bases
• It can be represented by a letter sequence with
  alphabet size 4

• Adenosine
• Cytosine
• Guanine
• Thymine

Wheel of Bases (WOB)
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Random Sequence Model
Each type of the bases has its chance (or
probability) of being used, depending on the base
composition of the DNA molecule.

• Adenosine
• Cytosine
• Guanine
• Thymine

Wheel of Bases (WOB)
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Random Sequence Model
Each type of the bases has its chance (or
probability) of being used, depending on the base
composition of the DNA molecule.

• Adenosine
• Cytosine
• Guanine
• Thymine

Wheel of Bases (WOB)
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Poisson Process Approximation of Palindrome
Distribution
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Use of the Scan Statistic to Identify Clusters of
Palindromes
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Measures of Prediction Accuracy

• Attempts to improve prediction accuracy by
• Adopting the best possible approximation to the
  scan statistic distribution
• Taking the lengths of palindromes into
  consideration when counting palindromes
• Using a better random sequence model

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Markov Chain Sequence Models

• More realistic random sequence model for DNA and
  RNA
• It allows neighbor dependence of bases (i.e., the
  present base will affect the selection of bases
  for the next base)
• A Markov chain of nucleotide bases can be
  generated using four WOBs in a Sequence
  Generator (SG)

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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Sequence Generator (SG)
Wheels of Bases (WOB)
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Results Obtained for Markov Sequence Models

• Probabilities of occurrences of single
  palindromes
• Probabilities of occurrences of overlapping
  palindromes
• Mean and variance of palindrome counts

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Related Work in Progress

• Finding the palindrome distribution on Markov
  random sequences
• Investigating other sequence patterns such as
  close repeats and inversions in relation to
  replication origins

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Other Mathematical Topics in Genes and Diseases

• Optimization Techniques prediction of molecular
  structures
• Differential Equations molecular dynamics
• Matrix Theory analyzing gene expression data
• Fourier Analysis proteomics data