Motif Finding

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Motif Finding

• Yueyi Irene Liu
• CS374 Lecture
• Oct. 17, 2002

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Outline

• Background biology
• Motif-finding methods
• Word enumeration
• Gibbs sampling
• Random projection
• Phylogenetic footprinting
• Reducer

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Regulation of Gene Expression

• Chromatin structure
• Transcription initiation
• Transcript processing and modification
• RNA transport
• Transcript stability
• Translation initiation
• Post-Translational Modification
• Protein Transport
• Control of Protein Stability

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Typical Structure of an Eukaryotic mRNA Gene
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Control of Transcription Initiation
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Motif

• A conserved pattern that is found in two or more
  sequences
• Can be found in
• DNA (e.g., transcription factor binding sites)
• Protein
• RNA

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Models for Representing Motifs

• Regular expression
• Consensus
• TGACGCA
• Degenerate
• WGACRCA
• Position Specific Matrix

TGACGCA TGACGCA AGACGCA TGACACA AGACGCA
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Where to look for motifs?

• Gene families a set of genes controlled by a
  common transcription factor or common
  environmental stimulus
• How do you construct gene families?
• Microarray experiments

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Microarrays
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Motif-finding Methods

• Goal Look for motifs (5-15bp) in the data set
• Methods
• Word enumeration method
• Gibbs sampling
• Random projection
• Phylogenetic footprinting
• Reducer

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Word Enumeration

• For every word w, calculate
• Expected frequency based on entire upstream
  region of the yeast genome
• E.g., P(ATTGA) (0.4)4(0.1)1, given P(A) P(T)
  0.4,
• P(G)P(C) 0.1
• Expected number of occurrences of ATTGA
  nP(ATTGA)
• Observed frequency in the data set
• Statistical significance of enrichment
• Z (O - E) / sqrtnp ? (1 - p) N(0, 1)
• Disadvantage only consider exact word
• E.g, YCTGCA TCTGCA and CCTGCA

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Gibbs Sampling

• Matrix to capture a motif
• Goal find the best ak to maximize the difference
  between motif and background base distribution.

a1
a2
a3
a4
ak
Liu, X
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Gibbs Sampling (Lawrence, et al, 1993)

• Step 1 Pick random start position, compute
  current motif matrix
• Step 2 Iterative update
• Take one sequence out, update motif matrix
• Calcuate fitness score of each position of out
  sequence
• Pick start position in out sequence based on
  weight Ax
• Take out another sequence, , until converge
• Step 3 Reset starting position

Liu, X
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Gibbs Sampling InitializationPick random start
position, compute motif matrix
Liu, X
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Gibbs Sampling Iteration Steps1) Take out one
sequence, calculate the fitness score of every
subsequence relative to the current motif
a1'
?????????????????
a2'
a3'
a4'
ak'
Liu, X
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Fitness Score
Current Motif

• Ax Qx / Px
• Qx probability of generating subsequence x from
  current motif
• Px probability of generating subsequence x from
  background

Background P(A) P(T) 0.4 P(G) P(C) 0.1
X GGA Q? P?
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Gibbs Sampling Iteration Steps2) Pick new start
position sampling from fitness score
a1''
a2'
a3'
a4'
ak'
Liu, X
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Recent Development

• Random Projection
• Phylogenetic Footprinting
• Reducer

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Random Projection (Buhler, 2002)

• (l, d)-motif problem
• M is an (unknown) motif of length l
• Each occurrence of M is corrupted by exactly d
  point substitutions in random positions
• No known biological motifs are
• of (l, d)-motif

CCcaAG CCcgAG CCgcAG CCtaAG CCtgAG
CtATgG CCctAc tCtTAG CaAcAG CCAgAa
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Random Projection Algorithm

• Guiding principle Some instances of a motif
  agree on a subset of positions.
• Use information from multiple motif instances to
  construct model.

Buhler, J
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k-Projections

• Choose k positions in string of length l.
• Concatenate nucleotides at chosen k positions to
  form k-tuple.
• In l-dimensional Hamming space, projection onto k
  dimensional subspace.

k 7
l 15
P
ATGGCATTCAGATTC
TGCTGAT
Buhler, J
P (2, 4, 5, 7, 11, 12, 13)
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Random Projection Algorithm

• Choose a projection by selecting k positions
  uniformly at random.
• For each l-tuple in input sequences, hash into
  bucket based on letters at k selected positions.
• Recover motif from bucket containing multiple
  l-tuples.

Input sequence x(i) TCAATGCACCTAT...
Buhler, J
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Example

• l 7 (motif size) , k 4 (projection size)
• Choose projection (1,2,5,7)

Input Sequence
...TAGACATCCGACTTGCCTTACTAC...
Buckets
GCCTTAC
Buhler, J
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Hashing and Buckets

• Hash function h(x) obtained from k positions of
  projection.
• Buckets are labeled by values of h(x).
• Enriched buckets contain more than s l-tuples,
  for some parameter s.

Buhler, J
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Motif Refinement

• How do we recover the motif from the sequences in
  the enriched buckets?
• k nucleotides are known from hash value of
  bucket.
• Use information in other l-k positions as
  starting point for local refinement scheme, e.g.
  EM or Gibbs sampler

Local refinement algorithm
ATGCGTC
Candidate motif
Buhler, J
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Parameter Selection

• Projection size k
• Choose k small so several motif instances hash to
  same bucket. (k lt l - d)
• Choose k large to avoid contamination by spurious
  l-mers. ( 4k gt t (n - l 1)
• Bucket threshold s (s 3, s 4)

Buhler, J
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Recent Development

• Random Projection
• Phylogenetic Footprinting
• Reducer

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Conservation of Regulatory Elements in Upstream
of ApoAI Gene
TATA box
TATA box
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Substring Parsimony Problem

• Given
• orthologous upstream sequences S1,Sn
• phylogenetic tree T of the n species
• size k of the motif, threshold d
• Problem
• Find all sets of substrings s1,sn of S1,Sn ,
  each of size k, such that the parsimony score of
  s1,sn on T is at most d

Blanchette, M
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Parsimony Score
s1
Tree T
s2
s34
s3
s4
s5
s6
Minimum (all possible labelings of internal nodes)

• l(v) label of node v
• d(l1, l2) Hamming distance

Blanchette, M
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String Parsimony Problem
S1 AAAGCATTC S2 TACGCACCC S3 GAAGCAGGG
k 5 d 1
S1
S2
S3
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Algorithm version I

• Root the tree at arbitrary internal node r
• Compute table Wu of size 4k for each node u,
  where Wus best parsimony score for subtree
  rooted at u when u is labeled with s
• Direct implementation of this recursion gives
  O(nk(42k l), where l average sequence
  length

Blanchette, M
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Algorithm version II

• Define X(u, v)s best parsimony score for
  subtree consisting of edge (u,v) and the subtree
  rooted at v

u labeled s
w
v
Blanchette, M
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Algorithm version II (continued)

• Update X(u, v) in phases in phase p maintain set
  Bp of sequences t, such that X(u, v)t p
• Define
• Ra s Wvs a
• N(s) t in ?k d(s, t) 1
• Start in phase m and let Bm Rm
• Update
• Computation of X(u, v) takes O(k4k)

Blanchette, M
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Improvements

• Reduce the size of Bp when sequences contribute
  to X(u, v) greater than threshold d
• In phase p, only care for sequence X(u, v) s if
• Leads to significant reductions in stages d/2 d
• Reduce the number of substrings inserted in W at
  the leaves
• For substring s of Si, if its best match against
  any Sj, has Hamming distance at least d, s can be
  discarded

Blanchette, M
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Results

• Practical limit on k 10
• There appeared to be a threshold d0 with very few
  solutions below and many above
• Algorithm found 80 known binding sites
• Performed better than ClustalW, MEME, Consensus

Blanchette, M
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Recent Development

• Random Projection
• Phylogenetic Footprinting
• Reducer

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Reducer (Bussemaker, et al 2001)

• Links motif finding to expression level
• Ag C S Fu Nug
• Ag gene expression level (logarithm of
  expression ratio)
• M number of significant motifs
• Ng number of occurrences of motif u in gene g
• C baseline expression level (same for all genes)
• F increase/decrease of expression level caused
  by presence of motif

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Reducer (Contd)
Liu, X
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Reducer (Contd)

• Normalize expression (A) and motif (n) vectors
• Linear regression between A vector and every n
  vector to find the best fit n to A
• Step-wise regression to combine effects of motifs
• Subtract the effect of one motif
• Find the next best motif

Liu, X
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Acknowlegement

• People from whom I borrowed slides
• Xiaole Liu (Reducer)
• Olga Troyanskaya (Microarray)
• Jeremy Buhler (Random projections)
• Mathieu Blanchette (Phylogenetic footprinting)
• Various web sources

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excitation
scanning
cDNA clones (probes)
laser 1
laser 2
PCR product amplification purification
emission
printing
mRNA target)
overlay images and normalise
0.1nl/spot
Hybridise target to microarray
microarray
analysis
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Information Content of Motifs

• Uncertainty
• Information Hbefore - Hafter

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Improvement on Original Gibbs sampler

• 0 n copies of sites in each sequence
• Iterative masking to find multiple motifs
• Use higher order Markov models to improve motif
  specificity

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Clinical Importance of Defects in Regulatory
Elements
Burkitts Lymphoma
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Statistical Methods

• Expectation Maximization (EM)
• MEME
• Gibbs sampling
• BioProspector
• AlignACE

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Motifs are not limited to DNAs

• RNA motifs
• RNA RNA interaction motifs, e.g., intron-exon
  splice sites
• RNA protein interaction motifs, e.g., binding
  of proteins to RNA polyA tail
• Protein motifs
• E.g., Helix-turn-helix motif

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Sequence Logo
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Why is this Problem Hard?

• Motif information content low
• Hamming distance between each motif instance high