Finding regulatory modules: A statistical approach

1
Finding regulatory modules A statistical approach

• Mikhail Velikanov
• Linnaeus Centre for Bioinformatics

2
Introduction

• Regulatory modules (RMs) sets of regulatory
  sites that work cooperatively
• TF binding sites and promoter elements
• Splicing enhancers and suppressors
• Site clusters
• site A AND (site B OR site C) AND (NOT site D)
• Beads on a spring
• site B is 20 3 bp downstream of site A
• Distance distributions have a short range and a
  well-defined peak

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Searching for RMs Setup of the Problem
Motifs
Annotations

• Seq. length constant and small (0.5 kb)
• Num. of sites 20
• No overlapping sites
• Sites characterized by
• Identity
• P-values ( pt)
• shown by width

Look for annotation patterns that occur
consistently in all or some of the sequences.
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RMs as Annotation Alignments

• Align sites by identity
• Find sequences of 2 or more sites shared across a
  number of annotations (common annotations)
• Conditions
• Distances between sites are similar
• P-values of aligned sites are similar
• P-values of aligned sites are small

Need a function that measures how well conditions
(1-3) are satisfied (strength of common
annotation).
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Strength of common annotation site p-values

• Assume a common annotation of S sites supported
  by N sequences
• For the i-th site, let pimin, pimax be the
  smallest and the largest of the N p-values
• pimax measure of how small p-values are
• Ri pimax/pimin measure of similarity
• Probability pi of observing p-values as similar
  and as small in N random annotations

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Strength of common annotationdistances between
sites

• Account for no overlaps between sites
• renormalization of pi for each site
• p0 1 - ?pi positions between sites
• Compute approximately probability of common
  annotation PCA as a function of p0, p1, , pS
• Strength of common annotation
• Z -ln PCA

S


i1



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Searching for the strongest common annotations

• Given an input set of annotations, define groups
  of annotations such that
• each group has at least one common annotation
• the strongest common annotation of each group is
  distinct
• NB Groups may fully or partially overlap!

Cannot use standard clustering algorithms.
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Classification Algorithm

• Find pairs of annotations with at least one
  common annotation
• Each pair is a nucleus of a potential group
• Each group grows by adding annotations one at a
  time
• the group retains its strongest common annotation
  at each step
• each addition maximizes the group strength
• annotation added to one group remains available
  for addition to other groups
• Where does the growth stop?

(strength group strength, Zg)
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Stopping criterion

• No more annotations can be added
• group contains all annotations in the input set
• change in the strongest common annotation
• Formed during growth of another group
• ignore current group (pruning)
• Group strength is too small
• adding an unrelated annotation
• group strength Zg is a score (Zg gt 0)
• can be computed for groups of random annotations
• by the extremal types theorem
• lim Prob(Zgrand gt Zg) 1 - exp-(Zg/b)-a
• threshold on Zg
• numerical calibration of a, b for all possible N,
  S

n ? 8
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From annotation groups to RMs

• Need a way to
• account for optional sites
• search for homologous RMs

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RMs as generalized HMMs

• Generalized (duration) HMMs (gHMMs or dHMMs)
  consist of 2 types of states
• motif states (PSSMs)
• annotation sites
• spacer states (distance distributions)
• gaps between sites
• States are connected according to certain
  topology
• Transitions probabilities depend only on the
  present state
• Common annotations of groups are simple gHMMs

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RMs as generalized HMMs
Can make a single model because of the overlap!

• Common annotations define gHMM states
• Overlaps define topology and provide estimates of
  transition probabilities
• Multiple matches to the model

13
From annotations to RMs
RMs
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Testing the Method Test 1

• 25 random DNA sequences, 20 are seeded with an
  RM
• 2 sites with low p-value (lt 10-3) separated by 20
  25 bp
• Scan sequences with unrelated motif subject to
  p-value threshold
• 3rd site (random noise in annotations)

m0
m1
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Testing the Method Test 2

• 25 random DNA sequences, 2 non-overlapping groups
  of 10 and 11 sequences
• each group is seeded with a distinct RM (2
  sites)
• distance between sites is 20 25 bp or 52 55
  bp
• Extra site added as before

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Testing the Method Test 3

• 25 random DNA sequences, 2 overlapping groups of
  12 and 14 sequences
• same RMs as in previous test
• groups overlap by 5 sequences
• Extra site added as before

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Summary

• A method for discovery of regulatory modules
  given a set of annotated sequences
• Builds RMs from recurrent annotation patterns
• Treats site p-values and distances in consistent
  statistical framework
• Can use prior information on RMs (Bayesian
  approach)
• RMs are output as gHMMs
• flexibility of RMs structure (topology)
• searching for homologous RMs

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Future developments

• Testing the method on real data
• upstream regions of bacterial operons
• bacterial Fe-regulons
• other benchmark sets?
• Algorithm improvements
• better stopping criterion (use properties of
  distance distributions)
• more precise computation of common annotation
  strength
• better similarity measure for site p-values
  (reduce compensation)

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Acknowledgements

• Thanks to David Ardell (LCB, Uppsala) and
  Georgiy Sofronov (Univ. of Queensland, Brisbane)
  for many fruitful discussions