CS5263 Bioinformatics

Lecture 20

Practical issues in motif finding

Final project

Homework problem 3.1

• Count separately the number of character comparisons and the number of steps needed to find the next matching character using the bad character rule

• Question: can you give an example?

Extended bad character rule

char Position in P

a 6, 3

b 7, 4

p 2

t 1

x 5

T: xpbctbxabpqqaabpqz

P: tpabxab *^^

P: tpabxab

Find T(k) in P that is immediately left to i, shift P to align T(k) with that position

k

In this iteration:

# of comparison = 3

Table lookup: 2

Results for some real genes

llr = 394     E-value = 2.0e-023

llr = 347     E-value = 9.8e-002

llr = 110     E-value = 1.4e+004

Strategies to improve results

• Combine results from different algorithms usually helpful– Ones that appeared multiple times are

probably more interesting• Except simple repeats like AAAAA or ATATATATA

– Cluster motifs into groups according to their similarities

Strategies to improve results

• Compare with known motifs in database– TRANSFAC– JASPAR

• Issues: – How to determine similarity between motifs?

• Alignment between matrices

– How similar is similar?• Empirically determine some threshold

Strategies to improve results

• Statistical test of significance– Enrichment in target sequences vs

background sequences

Target setT

Background setB

Assumed to contain a common motif, P

Assumed to not contain P, or with very low frequency

Ideal case: every sequence in T has P, no sequence in B has P

Statistical test for significance

• Intuitively: if n / N >> m / M– P is enriched (over-represented) in T– Statistical significance?

Target setT

Background set + target setB + T

Size = NSize = M

P

Appear in n sequences

Appear in m sequences

Hypergeometric distribution

• A box with M balls, of which N are red, and the rest are blue.

– Red ball: target sequences– Blue ball: background sequences

• If we randomly draw m balls from the box,

• what’s the probability we’ll see n red balls?

– If probability very small, we are probably not drawing randomly

• Total # of choices: (M choose m)• # of choices to have n red balls:

(N choose n) x (M-N choose m-n)

m

M

nm

NM

n

N

nmNMHypegeom ),,,(

Cumulative hypergeometric test for motif significance

• We are interested in: if we randomly pick m balls, how likely that we’ll see at least n red balls?

1

0

),min(

1

),,,(

n

i

Nm

ni

m

M

im

NM

i

N

m

M

im

NM

i

N

nmNMcHypegeom

This can be interpreted as the p-value for the null hypothesis that we are randomly picking.

Alternative hypothesis: our selection favors red balls.

Equivalent: the target set T is enriched with motif P.

Or: P is over-represented in T.

Examples• Yeast genome has 6000 genes• Select 50 genes believed to be co-regulated by a common TF• Found a motif for these 50 genes• It appeared in 20 out of these 50 genes• In the whole genome, 100 genes have this motif• M = 6000, N = 50, m = 100+20 = 120, n = 20• Intuition:

– m/M = 120/6000. In Genome, 1 out 50 genes have the motif– N = 50, would expect only 1 gene in the target set to have the motif – 20-fold enrichment

• P-value = 6 x 10-22

• n = 5. 5-fold enrichment. P-value = 0.003• Normally a very low p-value is needed, e.g. 10-10

0 2 4 6 8 1010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

n

hypegeom(6000, 50, 120, n)

chypegeom(6000, 50, 120, n)

0 10 20 30 40 5010

-100

10-80

10-60

10-40

10-20

100

n

hypegeom(6000, 50, 120, n)

chypegeom(6000, 50, 120, n)

ROC curve for motif significance

• Motif is usually a PWM• Any word will have a score

– Typical scoring function: Log P(W | M) / P(W | B)– W: a word. – M: a PWM. – B: background model

• To determine whether a sequence contains a motif, a cutoff has to be decided– With different cutoffs, you get different number of

genes with the motif– Hyper-geometric test first assumes a cutoff– It may be better to look at a range of cutoffs

ROC curve for motif significance

• With different score cutoff, will have different m and n• Assume you want to use P to classify T and B• Sensitivity: n / N• Specificity: (M-N-m+n) / (M-N)• False Positive Rate = 1 – specificity: (m – n) / (M-N)• With decreasing cutoff, sensitivity , FPR

Target setT

Background set + target setB + T

Size = NSize = M

P

Appeared in n sequences

Appeared in m sequences

Given a score cutoff

ROC curve for motif significance

ROC-AUC: area under curve. • 1: perfect separation. • 0.5: random.

Motif 1 is better than motif 2.

1-specificity

sens

itivi

ty

Motif 1Motif 2Random

A good cutoff

Highest cutoff. No motif can pass the cutoff. Sensitivity = 0. specificity = 1.

Lowest cutoff. Every sequence has the motif. Sensitivity = 1. specificity = 0.

0

1

10

Other strategies

• Cross-validation– Randomly divide sequences into 10 sets, hold 1 set

for test. – Do motif finding on 9 sets. Does the motif also appear

in the testing set?

• Phylogenetic conservation information– Does a motif also appears in the homologous genes

of another species?– Strongest evidence– However, will not be able to find species-specific ones

Other strategies

• Finding motif modules– Will two motifs always appear in the same gene?

• Location preference– Some motifs appear to be in certain location

• E.g., within 50-150bp upstream to transcription start

– If a detect motif has strong positional bias, may be a sign of its function

• Evidence from other types of data sources– Do the genes having the motif always have similar activities

(gene expression levels) across different conditions?– Interact with the same set of proteins?– Similar functions?– etc.

To search for new instances

• Usually many false positives• Score cutoff is critical• Can estimate a score cutoff from the “true”

binding sites

Motif finding

Scoring function

A set of scores for the “true” sites. Take mean - std as a cutoff. (or a cutoff such that the majority of “true” sites can be predicted).

To search for new instances

• Use other information, such as positional biases of motifs to restrict the regions that a motif may appear

• Use gene expression data to help: the genes having the true motif should have similar activities

• Phylogenetic conservation is the key

Final project

• Write a review paper on a topic that we didn’t cover in lecturesOr

• Implement an algorithm and do some experiments• Compare several algorithms (existing implementation ok)• Combine several algorithms to form a pipeline (e.g. gene

expression + motif analysis)

• Final: – 5 -10 pages report (single space, single column, 12pt) + 15

minutes presentation

Possible topics for term paper

• Possible topics:– Haplotype inferencing– Computational challenges associated with new

microarray technologies – Phylogenetic footprinting – Small RNA gene / target prediction (siRNA, mRNA,

…) – Biomedical text mining – Protein structure prediction– Topology of biological networks

An example project

• Given a gene expression data (say cell cycle)• Cluster genes using k-means• Find motifs using several algorithms• (Cluster and combine similar motifs)• Rank motifs according to their specificity to the

target sequences comparing to the other clusters

• Get their logos• Use the sequences to search the whole genome

for more genes with the motif• Do they have any functional significance?