Transcription factor binding motifs (part I)

10/17/07

Steps of gene transcription

TATA

activator

TFIID

Pol II Pol II

The term “transcription factor” (TF) usually means an activator or repressor.

Understand Regulation

• Which TFs are involved in the regulation?

• Does a TF enhance / repress gene expression?

• Which genes are regulated by this TF?

• Are there binding partner / competitor for the TF?

• Why disease when a TF went wrong?

Understand Regulation

• Which TFs are involved in the regulation?

• Does a TF enhance / repress gene expression?

• Which genes are regulated by this TF?

• Are there binding partner / competitor for the TF?

• Why disease when a TF went wrong?

Sequence specificity of TF binding

Motif representation

• Consensus: GCGAA

• PWM

Alignment matrix

Motif representation

• Consensus: GCGAA

• PWM

frequency matrix

Motif representation

• Consensus: GCGAA

• PWM

• Logo

Objectives of motif finding

• Known motif mapping– Given a known motif, find all the matches over

a query sequence.

• De novo motif discovery– Both motif patterns and match positions are

unknown– much harder

Known Motif Mapping

• The matching score for a new sequence x is given by

wherem is the entries in the frequency matrix

is the background model: p0(A), …, p0(T), or can be

third-order Markov model (see next slide).

• Calculate the matching score for all genomic sequences.

Motif sites correspond to highest scores.

) model background | Pr(

) model motif | Pr(log

)|Pr(

)|Pr(log 2

02 x

x

x

xS m

i

xim ipx ,)|Pr(

TGCAjwiijm p ,,,;,,1)(

Third-order Markov model

• The probability of generating a new base is dependent on the previous three bases.

3rd order Markov dependencyp( )

)|(

)|(

)|(

)|(

)|()(

TGTAP

ATGTP

TATGP

TTATP

CTTAPATGTAP

De novo motif discovery

• Statistical approach– Identify sequence patterns that occur more frequently

than random.– Target regions:

• Promoters regions of co-regulated genes• Promoters regions of differentially expressed genes• Experimentally identified TF binding sites

– Very common

• Biophysical approach– Calculate protein-DNA binding affinities from first

principles.– See Roider et al. 2006 for an example.

Methods

• PWM modeling– MEME, GMS, AlignACE, BioProspector

• Word enumeration– YMF, MDScan

• Use negative control– REDUCE, Motif Regressor

• Comparative genomic– MCS, ComparProspector, Phylocon

• CHIP-chip (will discuss later)

The challenges

no motif sites

The challenges

multiple motif sites

The challenges

variable relative positions

The challenges

variable sequence pattern

ATCCG

ATTCG

MEME

(Bailey and Elkan 1994)

• Input– A set of sequences: Y = {Yi}

– For a fixed length w, partition Y into overlapping w-mers: X = {Xi}

– A set of alphabets: A = {aj} = {A,C,G,T}

• Mixture Model

m Motif model:

0 Background model: 0th or 3rd Markov

TGCAjwiijm p ,,,;,...,1)(

0)1(~ mX

• Missing data: Z = { Zi }

• The log-likelihood is

• Select and to maximize the log-likelihood, but how?

Log-likelihood

Expectation-Maximization (EM)

• Iteratively update hidden states and parameter values. Commonly used in bioinformatics research.

• E-step:– Under current estimate of , , and the observed

data, evaluate the expected value of log-likelihood over the values of the missing data Z.

Expectation Maximization (EM)

• M-step:– Update the parameters so that expected log-

likelihood is maximized.

For

For

Iterative E- and M- steps until convergence

Issue with EM algorithm

• Can get trapped into local minimum

• Results depend on initial guess

• Often need to do multiple runs starting with difference initial guesses. Then pick the best one.

Gibbs sampling

• Gibbs sampling is an algorithm to generate a sequence of samples from the joint probability distribution of two or more random variables

• Gibbs sampling is applicable when the joint distribution is not known explicitly, but the conditional distribution of each variable is known.

• The sequence of samples comprises a Markov Chain.

• As the iteration number goes to infinity, the asymptotic distribution approaches the underlying joint distribution.

Key differences between EM and Gibbs sampling

EM Gibbs Sampling

Maximum likelihood Posterior

Deterministic Stochastic

Frequenist Bayesian

Initialize seed for Initialize prior for

Gibbs Motif Sampler

31

41

51

21

11

(Lawrence et al. 1993; Liu et al. 1995)

Assume each sequence contains one motif. But the position and the motif frequency matrix are unknown.

Gibbs Motif Sampler

1 Without11 Segment

• Take out one sequence with its sites from current motifTake out one sequence with its sites from current motif

31

41

51

21

11

Segment (2-7): 3

Segment Scores of Sequence 1

0

10

20

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Starting Position of Segment

Se

gm

en

t S

core

Sequence 1

Gibbs Motif Sampler• Score each possible segment of this sequenceScore each possible segment of this sequence

31

41

51

21

1 Without11 Segment

Segment Scores of Sequence 1

0

10

20

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Starting Position of Segment

Se

gm

en

t S

core

12

Modified 1

Gibbs Motif Sampler• Sample a new segment to put the sequence backSample a new segment to put the sequence back

31

41

51

21

Advantage of Gibbs sampling

• Stochastic sampling permits the algorithm to escape from local minima. More robust than determinstic sampling as in EM.

• Fast.

Transcription level changes in glucose vs galactose

(Roth 1998)

(Roth 1998)

MDscan

(Liu et al. 2002)• Basic idea

– True targets are likely to be more differentially expressed than other genes.

• Procedure:– Rank genes according to p-values, gene expression

levels, etc. – Search TF motif from highest ranking targets first

(high signal / background ratio)– Refine candidate motifs with all targets

Similarity defined by m-match

For a given w-mer and any other random w-mer

TGTAACGT 8-mer

TGTAACGT matched 8

AGTAACGT matched 7

TGCAACAT matched 6

TGACACGG matched 5

AATAACAG matched 4

m-matches for TGTAACGT

Pick a reasonable m to call two w-mers similar

MDscan Algorithm:Finding candidate motifs

Seed1 m-matches

Sig

nific

ance

of d

iffer

entia

l gen

e ex

pres

sion

MDscan Algorithm:Finding candidate motifs

Seed2 m-matches

Sig

nific

ance

of d

iffer

entia

l gen

e ex

pres

sion

• Maximum a posteriori (MAP) score function:

• Prefer: conserved motifs with many sites, but are not often seen in the genome background

• Keep best 30-50 candidate motifs

MDscan Algorithm:Scoring candidate motifs

Motif Signal Abundant

PositionsConserved

Specific (unlikely in genome background)

MDscan Algorithm:Update motifs with remaining seqs

Seed1 m-matches

Sig

nific

ance

of d

iffer

entia

l gen

e ex

pres

sion

Seed1 m-matches

MDscan Algorithm:Refine the motifs

Sig

nific

ance

of d

iffer

entia

l gen

e ex

pres

sion

MDscan Algorithm

• Check high signal/background ratio sequences first, more likely to find the correct motif

• Algorithm summary:– Seed with w-mer in top, find m-match to make matrix– Keep good motifs to be update by remaining

sequences– Refine motifs by removing bad sites

• Can check motif of any width very fast– Only consider existing w-mers, finite dataset– Seed in top sequences O(n2)– Update motifs with all sequences O(n)

Word enumeration

YMF (Sinha and Tompa 2002)• Search in ALL possible w-mers. For each w-mer,

calculate a z-score measuring whether it is over-represented in the selected sequences vs the background.

• Rank the words by the z-score.• Select the top ones.

Advantage:• Global optimum

Drawback:• Computational time grows exponentially with w, so can

only be used to search short motifs. 6~10 mer.