A Statistical Method for Finding Transcription Factor Binding Sites

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A Statistical Method for Finding Transcription
Factor Binding Sites

• S. Sinha M. Tompa
• ISMB 2000

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Transcriptional Regulation

TRANSCRIPTION FACTOR
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Introduction

• Goal
• To understand the mechanisms that determine the
  regulation of gene expression
• Fundamental sub-problem is to identify
  DNA-binding sites for unknown regulatory factors
• Then we can go to find regulatory factors
• Input
• A collection of genes believed to be coregulated
• Non-coding DNA sequences near those regions

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Challenges

• Analysis of non-coding regions in eukaryotic
  genome
• Located quite far from coding region
• Regulatory sequence orientation
• Multiple binding sites
• Great variability in the binding sites, the
  nature of allowable variations not well
  understood
• For S. cerevisiae (subject of experimentation)
• Only the first problem is not severe (800bp
  upstream of the translation starting site, these
  are the input)

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Overview

• Previous Methods local search
• EM
• Gibbs sampling
• etc.
• This paper enumerative statistical method
• Enumerative affordable because of a relatively
  small search space
• Statistical high z-scores suggest good candidates

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Previous Methods

• Aim at finding longer and more general motifs
• Longer motif length
• General represented by weighted matrices,
  alignments, gapped alignments
• Price paid local search, no global optimum
  guaranteed
• More than required for transcription binding
  sites
• Length typically 6 to 10
• Enumerative method?

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Enumerative Methods

• Van Helden et al. (1998)
• Only exact matches
• No spacers N
• Occurrences at distinct positions are assumed to
  be independent
• overlapping structures in both orientations
• Example sequence ATATAT, motif ATAT
• Frequency not normalized
• Brazma et al. (1998)
• Allows 3 Ns

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Enumerative Methods

• Tompa (1999)
• Pro
• Markov chain to model the background genomic
  distribution
• z-score for statistical significance
• Consider the autocorrelation of overlapping motif
  occurrences
• Con
• Subject of prokaryotic ribosome binding site ? no
  spacers, insufficient variability

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For S. cerevisiae

• Spacers in length from 1 to 11 bp, occurring in
  the middle
• Conserved bases (not including spacers) 6-10 bp
• Mutation
• In the way of transition rather than transversion
• Purine for purine, pyrimidine for pyrimidine
• Between complementary bases also possible, A/T or
  G/C
• Other kind of variations are much rarer
• Insertion/deletions uncommon ? gaps unnecessary

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What is a Motif?

• String on alphabet A, C, G, T, R, Y, S, W, N,
  with spacers N in the middle
• This much variation is enough
• Such a motif is suitable for enumeration (not
  like weighted matrix)
• An examination of 50 binding consensi included in
  SCPD (Zhu Zhang 1999)
• 31 exactly fit
• 10 more if slight differences are tolerated

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Statistics

• Consider frequency wrt. background genomic
  distribution
• Hypothesis testing ? how unlikely it is to have
  this many occurrences for a background
  distribution
• Background
• Order m Markov chain from (m1)-mer frequencies
• m3 to account for TATA, AAAA, TTTT
• z-score normalization ? to compare different
  motifs

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Expectation and Variance

• E(Xs) relatively straightforward
• s(Xs) substantially more efforts
• Need to consider overlap of a motif to itself
• Fortunately, autocorrelation well studied in the
  past
• Mathematical basis!
• Generalize to the case where s represents a
  finite set of strings (more complex overlapping
  one string with any other)
• Higher order Markov models
• Spacers handled without extra cost
• Motif occurring in either orientation
• Details in Appendix of the paper

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Preliminary Calculations

• For a given motif s
• String of l over A, C, G, T, R, Y, S, W, N
• For simplicity, only first order Markov model
  here
• Transform into a multiset W
• Replace R, Y, S, W by all possible combinations
  of appropriate instantiations
• For each string in W, add its reverse complement
  (both strands)
• Xs is sum of the of occurrences of each member
  of W
• Overlapping instances are counted as separate
• A simple special case palindrome

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Preliminary Calculations (cont)

• Represent members of W as Wi, TW

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Preliminary Calculations (cont)

• E(Xs) is easy linearity of expectation!
• p stationary distribution of Markov chain
• Skip N (spaces) by looking at higher powers of
  transition matrix

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Preliminary Calculations (cont)

• s(Xs) harder

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Preliminary Calculations (cont)

• First part B, second part 2C

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Preliminary Calculations (cont)

• To compute the first term of C
• One-to-one correspondence between Xi1,j
  Xi2,jk1 and Xij(CW)1
• Autocorrelation factor
• Transfer to expectation on a single variable
  Xij(CW)
• B and A more complex (in appendix)

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Algorithm Summary

• Basic routine
• Enumerating all possibilities
• Capturing of occurrences Ns
• Normalize to z-score with E(Xs) ands(Xs), ranking
• Scalability
• k of non-spacers, c of R, Y, S, W
  instantiations
• of enumerated motifs exponential in k ? small k
• Linear to the genome size ? apply to larger
  regions
• To compute a z-score, O(c2k2)
• Do not need to always pay that , prune based on
  less costly sub-components (details of the
  heuristics in the paper)

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Experiment Settings

• Known regulons
• 17 well studied coregulated sets of gene in S.
  cerevisiae
• All having known transcription factor with a
  known binding site consensus
• Success of experiments can be tested
• Another test set about coexpressed gene clusters
• Details in the paper

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Output Presentation

• Italicized for instances in the programs output
• z-score compared with mean max z-score
• Run on several sets of simulated test data
  (randomly generated), see normally how large a
  z-score can be
• In this sense, our output is statistically
  significant!

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Three Examples - 1
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Three Examples - 2
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Three Examples - 3
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Experiment Results

• Known regulons
• Succeed for all but two experiments
• 9 of them, ranks among three highest
• In 6 others, a very similar looking motif is in
  top three
• Other 2 are families with very few genes in them,
  reported in top 20
• Coexpressed gene clusters
• Similar outcome

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Future Work

• Motif characterization limited
• Spacers may not be centered
• More than one run of spacers
• Move work in the enumeration work out to
  preprocessing step
• Faster
• Filter out well known repeats from the upstream
  regions
• Improve accuracy

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Thank you!