Regulatory Motif Finding

1
Regulatory Motif Finding

• Mohammed AlQuraishi

2
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance

3
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance

4
Cell Factory, Proteins Machines
Biovisions, Harvard
5
DNA

• Instructions for making the machines

Coding Regions
Regulatory Regions (Regulons)

• Instructions for when and where to make them

6
Transcriptional Regulation

• Regulatory regions are comprised of binding
  sites
• Binding sites attract a special class of
  proteins, known as transcription factors
• Bound transcription factors can inhibit DNA
  transcription

7
DNA Regulation
Source Richardson, University College London
8
Cell Regulation

• Transcriptional regulation is one of many
  regulatory mechanisms in the cell

Focus of Talk
Source Mallery, University of Miami
9
Structural Basis of Interaction
10
Structural Basis of Interaction

• Key Feature
• Transcription factors are not 100 specific when
  binding DNA
• Not one sequence, but family of sequences, with
  varying affinities

0.54
0.48
0.32
0.25
0.11
0.08
11
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance

12
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance

13
Motif Finding

• Basic Objective
• Find regions in the genome that bind
  transcription factors
• Many classes of algorithms, differ in
• Types of input data
• Motif representation

14
Input Data

• Single sequence

• Evolutionarily related set of sequences

• Sequence other data
• Microarray expression profile
• ChIP-chip
• Others

15
Motif Representation

• Probabilistic
• Word-Based

Focus of Talk
16
Motif Representation

• Structural discussion immediately raises
  difficulties

17
Structural Basis of Interaction

• Key Feature
• Transcription factors are not 100 specific when
  binding DNA
• Not one sequence, but family of sequences, with
  varying affinities

0.54
0.48
0.32
0.25
0.11
0.08
18
Motif Representation

• Structural discussion immediately raises
  difficulties
• Least Expressive
• Single sequence

• Most Expressive
• 4k-dimensional probability distribution
• Independently assign probability for each
  possible kmer

19
Motif Representation

• Standard Solution
• Position-Specific Scoring Matrix (PSSM)
• Assuming independence of positions, assign a
  probability for each position

• Fraught with problems (Will revisit this)

20
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance

21
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance

22
Reference

• Authors
• Eugene Fratkin, Brian T. Naughton, Douglas L.
  Brutlag, and Serafim Batzoglou
• Title
• MotifCut regulatory motifs finding with maximum
  density subgraphs
• Publication
• Bioinformatics Vol. 22 no. 14 2006, pages
  e150e157

23
Overview

• Motif Finding Algorithm (MotifCut)
• Motivation
• Oversimplicity of PSSMs
• Intractability of more complex models

24
Oversimplicity of PSSMs

• Assumes independence between positions
• 25 of TRANSFAC motifs have been shown to
  violate this assumption
• Two Examples ADR1 and YAP6

25
Oversimplicity of PSSMs

• Assumes independence between positions
• Generates potentially unseen motifs

26
Basic Features of MotifCut

• Does not assume an underlying PSSM
• Represents a motif with a graph structure
• In principle maximally expressive
• In practice not quite
• Motif finding cast as maximum density subgraph
• Subquadratic complexity

27
Motif Graph Representation

• Nodes are kmers
• Edge weights are distances between kmers

AGTGCGAC
1
AGTGGGAC
1
1
0
2
AGTGGGAC
AGTGCTAC
2

• Generative model Frequency of kmer node equal to
  frequency of generating kmer
• Distance definition is complicated (Will come
  back to)
• Same kmer node can appear multiple times

28
Motif Finding

• Find highest density subgraph

• Density is defined as sum of edge weights per
  node
• Somewhat limits representational power

29
Motif Finding

• Read new sequence
• Generate graph as previously described
• Kmers are generated by shifting one base pair
• Each kmer in the sequence gets a node, including
  identical kmers
• Graph contains as many nodes as there are base
  pairs
• Connect edges with weights based on distances
  between nodes
• Find densest subgraph

30
Edge Weights

• Heart of the algorithm, will focus on this
• Semantics
• Edge weight is the likelihood of two kmers to be
  in the same motif
• Use Hamming distance as a way to quantify
  distance between kmers

0
1
2
3
T
A
C
31
Edge Weights

• Heart of the algorithm, will focus on this
• Semantics
• Edge weight is the likelihood of two kmers to be
  in the same motif
• Use Hamming distance as a way to quantify
  distance between kmers
• Interpret hamming distance as a measure of the
  likelihood of two kmers to be in same motif
• F(hamming distance) likelihood of two kmers to
  be in same motif

32
Edge Weights

• Lets make this a bit more precise
• But how to compute ?
• Simulate it!
• Way too many variables to account for
  analytically Background model, kmer length,
  hamming distance, etc

33
Genome Simulation

• Background Motifs
• No genes, promoters, signaling sequences, etc.
• Background Model
• 3rd order Markov model
• Probability of next base depends on previous 3
  bases
• Modeled on the yeast genome
• Incorporates GC bias
• Motif Model
• PSSM
• Based on empirically observed information content
  of yeast motifs

34
Genome Simulation

• Use Markov model to generate 10k 20k length
  sequences of background

• Seed with 20 motifs generated by the PSSM
• Result is a simulated genome of yeast
• We know which parts are the real motifs, and
  which are not

35
Edge Weights

• Back to
• is number of true motifs of k-length
  that are l-distance away
• is number of non-motifs of k-length
  that are l-distance away

36
Edge Weights
True Motifs
False Motifs (Part of Background)
37
Edge Weights
Lets perform calculation from the perspective of
this motif

• All 1 distance away (Hamming distance)
• a(k 6, l 1) 1
• ß(k 6, l 1) 1

38
Edge Weights

• Computation provides an empirical estimate for
• Parameterized by two quantities
• k, the kmer length
• l, the Hamming distance between two kmers
• Fit to a sigmoidal function

39
Edge Weights

• Normalization step
• Wont go into details
• This covers problem formulation
• How is motif finding actually done?

40
Maximum Density Subgraph

• Standard graph theory method
• Max-flow / min-cut
• O(nm log(n2m))
• Need faster method
• Developed heuristic approach that utilizes
  max-flow / min-cut method with modifications

41
Maximum Density Subgraph

• Remove all edges below a certain threshold

42
Maximum Density Subgraph

• Pick one vertex (do this for every vertex)

43
Maximum Density Subgraph

• Put back all neighboring edges for that vertex

44
Maximum Density Subgraph

• Use standard algorithm to calculate densest
  subgraph

45
Results

• Synthetic Tests
• Plenty of test cases
• Measure performance as data set size grows
• Avoid over biasing on empirical data
• Know real answer, can unambiguously test
  performance
• Yeast Test
• Gold standard data (Harbinson et al., 2004)

46
Synthetic Tests

• Varied
• Motif length
• Information content
• Simulated genome (as before)
• Correlated predicted PSSMs to real ones, counted
  as true positive if correlation gt 0.7

47
Synthetic Tests Results
48
Yeast Test Results
49
Performance
50
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance

51
Talk Outline

• Biology Background
• Algorithmic Problem
• Papers
• New Motif Finding Algorithm (MotifCut)
• Analysis of Motif Finders Performance
• Shorter but more drier (no pretty pictures)

52
Reference

• Authors
• Patrick Ng, Niranjan Nagarajan, Neil Jones, and
  Uri Keich
• Title
• Apples to apples improving the performance of
  motif finders and their significance analysis in
  the Twilight Zone
• Publication
• Bioinformatics Vol. 22 no. 14 2006, pages
  e393e401

53
Overview

• Twilight Zone
• Non-negligible probability that a maximally
  scoring random motif would have a higher score
  than motifs that overlap the real motif
• Motivation
• Behavior of Motif Finders in Twilight Zone is
  poorly understood
• Understanding would aid in development of Motif
  Finders
• Sheds light on whether it is theoretically
  possible

54
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding

55
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding

56
E-value

• E-value is defined in terms of information
  content
• Information Content
• E-value
• Expected number of random alignments exhibiting
  an information content at least as high as that
  of the given alignment

57
Analysis

• Generate 400 random datasets
• Dataset 40 sequences totaling 1485 bases
• Implant a single motif of length 13 per dataset
• High likelihood that motif finders would miss it

58
Results

• Reported E-value
• 8 x 1015
• Very high, very statistically insignificant
• In principle, theoretically impossible to find
• Search results
• Alignment covering 30 of motif found in 288/400
  cases!
• Data generated exactly in accordance with E-value
  model

59
Whats going on?

• They dont know, hand-waive it
• Many satellite alignments boost up effective
  score
• Difficult to characterize analytically

60
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding

61
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding

62
New Metric OPV

• Also defined in terms of Information Content
• OPV(s) (Overall p-value)
• Probability that a random sample of the same size
  as the input set will contain an alignment with
  at least as much information content as s
• Contrast
• E-value Expected number of alignments (in
  general)
• OPV Probability of finding an alignment in a
  dataset

63
Estimation

• Caveat
• Random sample (no biasing)
• Difficult to calculate analytically
• Estimate empirically
• General OPV
• Finder-specific OPV

64
General OPV Estimation

• Generate 1600 random datasets
• No implants
• Run a collection of motif finders on each dataset
• Pick highest scoring motif in each dataset
• Out of all finders
• Sort scores, then pick score with 95 quantile

65
General OPV Estimation
Score such that 95 of scores are below it, 5
above it
66
General OPV Estimation

• Meaning
• 95 of the time, highest scoring random motif
  scored less than s0
• Obtaining a score s0 means 5 chance for the
  motif to be random

67
General OPV Results

• Run on previous 400 datasets
• 90 of correct runs (288/400) were classified as
  noise
• Not good

68
Finder-Specific OPV Estimation

• Same as before, but use only one finder
• Better biased toward the parameter space of the
  specific finder

69
Finder-Specific OPV Results

• Tested it on Gibbs
• Same 400 datasets
• 228 TPs
• 13 FPs
• Much better

70
Using OPV

• Impractical
• A priori generation is prohibitive given
  parameter space of motif finders
• Per problem estimation is prohibitive
• Requires 100x more runs
• Not theirs

71
Another Metric ILR (Incomplete Likelihood Ratio)

• Not defined in terms of Information Content

72
Another Metric ILR (Incomplete Likelihood Ratio)

• Not defined in terms of Information Content
• Ratio of null hypothesis to OOPS hypothesis
• OOPS Once occurrence per sequence
• Intuition behind it

73
Another Metric ILR (Incomplete Likelihood Ratio)
74
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding

75
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding

76
Motif Finding using ILR

• Used existing algorithms, ranked final output by
  ILR
• Developed simple new algorithm that uses ILR as
  objective function

77
ILR Motif Finding Results
78
ILR Motif Finding Results
79
ILR Motif Finding Results

• Promising

80
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding

81
Objectives

• Analyze existing standard (E-value)
• Statistical significance of motifs in Twilight
  Zone
• Examine and suggest new metrics
• Employ new metric for motif finding
• One More Thing!

82
(No Transcript)
83
Thank You