Bioinformatics: Buzzword or Discipline (???)

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Bioinformatics Buzzword or Discipline (???)
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Outline of the course

• Analysis of one DNA sequence Shotgun sequencing,
  Markov-Chain modeling, patterns and repeats.
• Analysis of multiple DNA or protein sequences
  Dynamic programming alignments, substitution
  matrices.
• BLAST Algorithm for sequence retrieval and
  comparison.
• Refresher on Markov Chains Capsule theory,
  Markov-Chain Monte Carlo algorithms.
• Hidden Markov Models Viterbi Algorithm and its
  applications.
• Evolutionary Models Models of nucleotide
  mutation and substitution, recombination and
  genetic drift, with applications to genome
  evolution and gene mapping.
• Molecular phylogenetics (tree making) distance
  matrix, maximum likelihood and parsimony.
• Special topics Gene and protein networks,
  analysis of DNA-microarray data,

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30,000
Genes make up only 3 of the genome
BCM- HGSC
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Genome Sizes
Human 3.0 x 109 base pairs
Mouse 3.0 x 109
Drosophila 1.1 x 108
Worm 1.0 x 108
Dictyostelium 3.4 x 107
Yeast 1.2 x 107
Bacteria 1.0 - 5.0 x 106
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Shotgun Sequencing
High Accuracy Sequence lt 1 error/ 10,000 bases
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The Human Genome 3 Billion Base PairsWhole
Genome Shotgun Strategy
Genome 3 billion bases
Libraries of clones 3kb, 10kb, 50kb base pairs
DNA sequence reads 500 bases each
AGGCTCACTG
BCM- HGSC
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Statistical issues in shotgun strategy

• Model for the random fragments Binomial/Poisson
  process
• Coverage of sequence by random fragments
• Mean number of contigs
• Mean size of contigs
• Coverage by anchored contigs

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Binomial/Poisson Process

• N fragments, of length L each, randomly scattered
  in the interval of length G.
• Coverage a NL/G
• Contig Union of overlapping fragments. We want
  to have them cover as much of G as possible.
• Prfrags with left end in (x, x-h) k is
  binomial(N,h/G) or approximately Poisson(Nh/G)
  (when?).

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Mean number of contigs

• Econtigs N ? Pra frag is rightmost in a
  contig
• N ? Prfrag does not include the left end of
  any other frag
• N ? exp(- NL/G) (aG/L) ? exp(- a)

L 800 G 100,000
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Mean contig size

• ES Efrags-1 Einter-epoch distance L

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Mean contig size
E(S)
a
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Number of anchored contigs
anchors M frags N a NL/G b ML/G
Eanchored contigs Nb exp(-a)-exp(-b)/(b-a
)
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Conclusions

• Expected number of contigs first increases, then
  decreases with coverage.
• Expected size of contig increases with coverage.
• Expected number of anchored contigs first
  increases then decreases with anchor density .
• Attention Computations do not involve boundary
  effects.