1. Yueyi Irene Liu CS374 Lecture Oct. 17, 2002
Motif Finding
Yueyi Irene Liu
CS374 Lecture
Oct. 17, 2002

2. Outline Background biology Motif-finding methods Word enumeration
Gibbs sampling
Random projection
Phylogenetic footprinting
Reducer

4. 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

5. Typical Structure of an Eukaryotic mRNA Gene

6. Control of Transcription Initiation

7. 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

8. Models for Representing Motifs
Regular expression
Consensus
TGACGCA
Degenerate
WGACRCA
Position Specific Matrix
TGACGCA
AGACGCA
TGACACA 1 2 3 4 5 6 7 A
0.4
0.2 T
0.6 G
0.8 C

9. 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

10. Microarrays experiments genes Cells of Interest Known DNA sequences10
Microarrays
Isolate mRNA
Cells of Interest
Reference sample
Known DNA sequences
Glass slide
genes
Resulting data
experiments
Proteins can be measured by measuring DNA-like molecule called mRNA.
Labeled mRNA (cdna) can selectively hybridize to matching DNA sequence on slide.
Quantitate the data and represent it as a matrix, although we tend to display it in terms of colors, as shown here.
Results usually shown as a ratios matrix (sample/reference)
Experiments appear in columns
Genes appear in rows
Sizes range, 10,000 x 30 reasonable

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

12. 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: n*P(ATTGA)
Observed frequency in the data set
Statistical significance of enrichment
Z = (O - E) / sqrt[np  (1 - p)] ~ N(0, 1)
Disadvantage: only consider exact word
E.g, YCTGCA: TCTGCA and CCTGCA

13. 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

14. 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

15. Gibbs Sampling Initialization Pick random start position, compute motif matrixak
a1'
a3'
a4'
ak'
a2'
Liu, X

16. Gibbs Sampling Iteration Steps 1) Take out one sequence, calculate the fitness score of every subsequence relative to the current motif
a1'
?????????????????
a2'
a3'
a4'
ak'
Liu, X

17. Fitness Score Ax = Qx / Px
Current Motif
Ax = Qx / Px
Qx: probability of generating subsequence x from current motif
Px: probability of generating subsequence x from background 1 2 3 A
0.1
0.3
0.7 T
0.2 G
0.4 C
Background:
P(A) = P(T) = 0.4
P(G) = P(C) = 0.1
X = GGA:
Q? P?

18. Gibbs Sampling Iteration Steps 2) Pick new start position sampling from fitness score
ak'
Liu, X

19. Recent Development
Random Projection
Phylogenetic Footprinting
Reducer

20. 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

21. 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.
ATGCGTC
...ccATCCGACca...
...ttATGAGGCtc...
...ctATAAGTCgc...
...tcATGTGACac...
(7,2) motif
x(1)
x(2)
x(5)
x(8) =M
Buhler, J

22. 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.
l = 15
k = 7 P
ATGGCATTCAGATTC
TGCTGAT
Buhler, J
P = (2, 4, 5, 7, 11, 12, 13)

23. 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...
Bucket TGCT
TGCACCT
Buhler, J

24. Example l = 7 (motif size) , k = 4 (projection size)
Choose projection (1,2,5,7)
Input Sequence
...TAGACATCCGACTTGCCTTACTAC...
ATGC
ATCCGAC
GCTC
Buckets
GCCTTAC
Buhler, J

25. 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.
ATTC
CATC
GCTC
ATGC
Buhler, J

26. 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
ATGC
ATCCGAC
ATGAGGC
ATAAGTC
ATGTGAC
Local refinement algorithm
ATGCGTC
Candidate motif
Buhler, J

27. Parameter Selection Projection size k
Choose k small so several motif instances hash to same bucket. (k < l - d)
Choose k large to avoid contamination by spurious l-mers. ( 4k > t (n - l + 1)
Bucket threshold s: (s = 3, s = 4)
Buhler, J

28. Recent Development
Random Projection
Phylogenetic Footprinting
Reducer

29. Conservation of Regulatory Elements in Upstream of ApoAI Gene
Hepatic site C
CCAAT box
Mouse
Rabbit
Human
Chicken
TATA box
TATA box
TATA box

30. AAGCA
ACGCA

31. 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

32. Parsimony Score s1 s2 s`34 s6 s5 s4 s3 Tree T:
Minimum (all possible labelings of internal nodes)
l(v) – label of node v
d(l1, l2) – Hamming distance
Blanchette, M

33. String Parsimony Problem
S1: AAAGCATTC
S2: TACGCACCC
S3: GAAGCAGGG
AAGCA
ACGCA
k = 5
d = 1 S1 S2 S3

34. Algorithm: version I Root the tree at arbitrary internal node r
Compute table Wu of size 4k for each node u, where Wu[s] – best parsimony score for subtree rooted at u when u is labeled with s
Direct implementation of this recursion gives O(n∙k∙(42k + l), where l – average sequence length
Blanchette, M

35. Algorithm: version II u labeled s w v
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

36. 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: Wv[s] = 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(k∙4k)
Blanchette, M

37. 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

38. 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

39. Recent Development
Random Projection
Phylogenetic Footprinting
Reducer

40. Reducer (Bussemaker, et al 2001)
Links motif finding to expression level
Ag = C + Σ 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

41. Reducer (Cont’d) Log ratio of expression levels Gene1 Gene2 Gene3
Expression vector
Log ratio of expression levels
Gene1
Gene2
Gene3
Gene4 …
GeneN
1.3
-3.7
10.3
4.5
-2.3
Motif vector
Number of times that motif occurs in the upstream region of the gene
AAAAA 2 5 3
AAAAT 1
Liu, X

42. Reducer (Cont’d) 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

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

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

46. Information Content of Motifs
Uncertainty
Information = Hbefore - Hafter

47. 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

48. Clinical Importance of Defects in Regulatory Elements
Burkitt’s Lymphoma

49. Statistical Methods Expectation Maximization (EM) Gibbs sampling MEME
BioProspector
AlignACE

50. 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

51. Sequence Logo

52. Why is this Problem Hard?
Motif information content low
Hamming distance between each motif instance high