Y.C.%20Wong%20Public%20Lecture%20040611

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1, 2, 3, and Beyond

• A slideshow for HKU Open Day in 1980
• I did the narration and background music
• The experience has a great impact on my journey
• Mathematics is beyond numbers
• We find it in buildings, banks, and
  supermarkets
• in atoms, molecules, and genes

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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 palindrome clusters 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
in DNA Viruses

• 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 proteomic data

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Acknowledgements
Collaborators Louis H. Y. Chen (National
University of Singapore) David Chew (National
University of Singapore) Kwok Pui Choi (National
University of Singapore) Aihua Xia (University of
Melbourne, Australia) Funding Support NIH
Grants S06GM08194-23, S06GM08194-24, and
2G12RR008124 NSF DUE9981104 W.M. Keck Center of
Computational Struct. Biol. at Rice University
National Univ. of Singapore ARF Research Grant
(R-146-000-013-112) Singapore BMRC Grants
01/21/19/140 and 01/1/21/19/217
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St. Stephens Girls College
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University of Hong Kong
Department of Mathematics A Beach Picnic
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Continuing to Find Mathematics in Genes and
Diseases
Ming-Ying Leung Department of Mathematical
Sciences University of Texas at El Paso (UTEP)