Transcription factor binding motifs (part I) 10/17/07

Steps of gene transcription TATA activator TFIID 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 where  m is the entries in the frequency matrix    is the background model: p 0 (A), …, p 0 (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.

Third-order Markov model The probability of generating a new base is dependent on the previous three bases. 3rd order Markov dependency p( )

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 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 = {Y i } –For a fixed length w, partition Y into overlapping w-mers: X = {X i } –A set of alphabets: A = {a j } = {A,C,G,T} Mixture Model –  m Motif model: –  0 Background model: 0 th or 3 rd Markov

Missing data: Z = { Z i } 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 EMGibbs Sampling Maximum likelihoodPosterior DeterministicStochastic FrequenistBayesian Initialize seed for  Initialize prior for 

Gibbs Motif Sampler  3131 4141 5151 2121 11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 Without  11 Segment Take out one sequence with its sites from current motifTake out one sequence with its sites from current motif 3131 4141 5151 2121  11

Segment (2-7): 3 Sequence 1 Gibbs Motif Sampler Score each possible segment of this sequenceScore each possible segment of this sequence 3131 4141 5151 2121  1 Without  11 Segment

 12 Modified  1 Gibbs Motif Sampler Sample a new segment to put the sequence backSample a new segment to put the sequence back 3131 4141 5151 21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)

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 TGTAACGT8-mer TGTAACGTmatched 8 AGTAACGTmatched 7 TGCAACATmatched 6 TGACACGGmatched 5 AATAACAGmatched 4 m-matches for TGTAACGT Pick a reasonable m to call two w-mers similar

MDscan Algorithm: Finding candidate motifs Seed1m-matches Significance of differential gene expression

MDscan Algorithm: Finding candidate motifs Seed2m-matches Significance of differential gene expression

Maximum a posteriori (MAP) score function: Prefer: conserved motifs with many sites, but are not often seen in the genome background Keep best candidate motifs MDscan Algorithm: Scoring candidate motifs Motif Signal Abundant Positions Conserved Specific (unlikely in genome background)

MDscan Algorithm: Update motifs with remaining seqs Seed1m-matches Significance of differential gene expression

Seed1m-matches MDscan Algorithm: Refine the motifs Significance of differential gene expression

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(n 2 ) –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.