A Statistical Method for Finding Transcriptional Factor Binding Sites

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A Statistical Method for Finding Transcriptional
Factor Binding Sites

• Authors Saurabh Sinha and Martin Tompa
• Presenter Christopher Schlosberg
• CS598ss

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Regulation of Gene Expression
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Difficulties of Motif Finding

• Regulatory sequences dont follow same
  orientation as the coding sequence or each other
• Multiple binding sites might exist for each
  regulated gene
• Large variation in the binding sites of a single
  factor. Variations are not well understood.

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Previous Proposed Methods for Finding Motifs

• Previous Methods
• Find longer, general motifs
• Use local search algorithms (Gibbs sampling,
  Expectation Maximization, greedy algorithms)
• Proposed Method
• TFBS is small enough to use enumerative methods
• Enumerative statistical methods guarantee global
  optimality and affordability

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Proposed Method Highlights

• Allows variations in the binding site instances
  of a given transcription factor
• Allows for motifs to include spacers
• Allows for overlapping occurrences (in both
  orientations), which lends to complex
  dependencies
• Statistical significance of a motif (s) is based
  on the frequencies of shorter (more frequent)
  oligonucleotides
• Use of Markov chain to model background genomic
  distribution
• Use of z-score to measure statistical
  significance
• Allows for multiple binding sites

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Characteristics of a Motif

• Any single TFBS has significant variation
• Many motifs have spacers from 1-11bp
• Variation often occurs as a transition (e.g.
  purine ? purine) rather than a transversion (e.g.
  pyrimidine ? purine)
• Variation occurs less between a pair of
  complementary bases.
• Indels are uncommon

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Proposed Motif Definition

• Motif will be a string with S A,C,G,T,
  R,Y,S,W,N
• A,C,G,T (DNA bp), R (purine), Y (pyrimidine), S
  (strong), W (weak), N (spacer)
• TF database (SCPD) confirms this model of
  variation
• Of 50 binding site consensi, 31 exact fits (62)
• Another 10 fit if slight variations allowed

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Measure of Statistical Significance

• Given set of corregulated S. cerevisiae genes,
  the input to the problem is corresponding set of
  800bp upstream sequences having 3 end on start
  site of gene translation.
• Model must measure from input sequences
• Absolute number of occurrences (Ns) of motif (s)
• Background genomic distribution
• X is a set of random DNA sequences in the same
  number and lengths of the input sequences
• Generated by Markov chain of order m
• Transition probabilities determined by (m1)-mer
  frequencies in fully complement of 6000 (800bp
  in length)
• Background model chooses m3

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z-score

• Xs r.v. is number of occurrences of motif (s)
  in X
• E(Xs) expectation, s(Xs) standard deviation
• zs number of S.D. by which observed value Ns
  exceeds expectation

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Implications

• Possibility of overlap of a motif with itself (in
  either orientation)
• Previous study of pattern autocorrelation
• Generalized computation of SD, treating motif as
  a finite set of strings
• Higher order Markov chains
• Spacers handled at no extra computational cost
• Handles motif in either orientation

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Algorithm

• Enumerates over each input sequence
• Tabulates number Ns of occurrences of each motif
  in either direction
• Compute expectation and SD for each motif s.t.
  Nsgt0
• Calculate z-score
• Rank motifs by z-score

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Algorithm Analysis

• For single motif, complexity is O(c2k2)
• k of nonspacer characters in motif
• c of instantiations of R, Y, S, W in motif
• Only modest values of k
• Linear dependence on genome size
• Can trim variance calculation to optimize

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Number of Occurrences

• Convert motif s into a multiset W
• Add reverse complements for each string in W
• Motif s only occurs at position in X iff some
  string in W occurs at same position
• Xs - of occurrences (in X) of each member of W
• Handling Palindromes
• Wi member of W
• W T

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Number of Occurrences Cont

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Expectation

• Linearity of Expectation

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Variance
? B term
? C term

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C Term

? A term
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A Term

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Overlapping Concatenation

• CW (like W) is potentially a multiset

• One-to-one correspondence

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C Term Simplification

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A Term Revisited

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Si1Si2 Term Approximation

• Kleffe and Borodovsky (1992) Approximation

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B Term

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B Term Cont

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Summary
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Higher Order Markov Models

• Variance calculations remain the same except for
  Si1Si2 term
• Experimental m 3

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Experimental Results Future Considerations

• 17 coregulated sets of genes
• Known TF with known binding site consensus
• In 9 experiments, known consensus was one of 3
  highest scoring motifs
• Future Topics
• Non-centered spacers
• Enumeration Loop optimization
• Filtering repeats

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Question

• E(Xs) is more straight-forward to calculate
  compared to s(Xs). Under the assumptions given in
  the paper, name one of the reasons for this
  complication.