Motif Finding in Biological Sequences

1
Motif Finding in Biological Sequences

• Xin He
• Dep. of Computer Science, UIUC
• 02/15/06

2
Problem
Given a collection of genes that share a common
TF-binding site motif, find the motif and where
it occurs in each sequence
3
Word Enumeration

• Idea a true motif occurs in all input sequences,
  thus it should be overrepresented in the input
• Algorithm compute the statistical significance
  of all words in the input and output the most
  significant ones
• Statistical significance use the background
  frequency as control
• Extension allow variations of words

4
Combinatorial Searching

• Idea suppose we know where motifs occur, then
  the motif sites should be similar to each other
• Algorithm define a similarity score for the
  alignment and then maximizes it

5
Finding the Best Alignment

• Let A (a1, a2, , aN) be the starting
  positions of motifs at each input sequence, I(A)
  be the similarity of motif sites. Then
• A argmax I(A)

6
CONSENSUS

• f?k frequency of base ? at position k
• q? frequency of base ? in the background
• Information content of an alignment

7
Bayesian Inference Overview

• Perspective data is generated from some
  (unknown) random process, infer the underlying
  process using the observed data
• Procedure let ? be unknown and D be data
• Set up a full probability model the joint
  distribution for all observed and unobserved
  quantities
• Posterior distribution P(? D)
• Model evaluation how good the model fits data

8
Bayesian Missing Data Problem

• Problem let ? be the unknown parameter(s), S be
  observed data and A be missing data, find the
  posterior distribution P(?,AS) or P(AS)
• Step1 probability model P(S,A ?)
• Step2 posterior distribution

9
Gibbs Sampling

• Idea to sample from joint distribution P(A,
  ?S), repeat the two steps
• Sample At P(AS, ?t-1)
• Sample ?t P(?S,At)
• Can be generalized to joint distribution of any
  number (n) of random variables fix (n-1)
  variables, sample the rest cycle through n
  variables

10
Gibbs Motif Sampler

• Motif representation position weight matrix
  (PWM). ? (?ij) where ?ij P( symbol j at
  position i)
• Probability model for any sequence Si
• Select a position for motif start ai with
  probability 1/L, where L is the sequence length
• Plant motif sequence in positions ai, aiw-1
  using PWM ?, where w is the motif width
• Plant background sequence in the other positions
  using background distribution ?0

11
Gibbs Motif Sampler

• Posterior distribution sample from P(AS)
• Gibbs sampling procedure
• Repeat choose a sequence z, sample
• az P( azS, A\az)
• Approximation of conditional probability find
  the PWM ? using A\az and S then sample az using
  this value of ?
• Predictive update ? argmax P(?S, A\az)
• Sampling az P(azS, ?)

12
Extensions of Basic Model

• Multiple or zero occurrences of motif per
  sequence
• Multiple types of motifs Stochastic Dictionary
  model
• Regulatory modules a cluster of motifs (multiple
  types, multiple occurrences of each type)
  CisModule
• Regulatory modules with motif dependency
  EMCModule