A Statistical Method for Finding Transcriptional Factor Binding Sites

A Statistical Method for Finding Transcriptional Factor Binding Sites

Authors: Saurabh Sinha and Martin Tompa

Presenter: Christopher Schlosberg

CS598ss

Regulation of Gene Expression

Difficulties of Motif Finding

Regulatory sequences don’t follow same orientation as the coding sequence or each other

Multiple binding sites might exist for each regulated gene

Large variation in the binding sites of a single factor. Variations are not well understood.

Previous & Proposed Methods for Finding Motifs

Previous Methods: Find longer, general motifs Use local search algorithms (Gibbs

sampling, Expectation Maximization, greedy algorithms)

Proposed Method: TFBS is small enough to use enumerative

methods Enumerative statistical methods guarantee

global optimality and affordability

Proposed Method Highlights Allows variations in the binding site instances of a

given transcription factor

Allows for motifs to include “spacers”

Allows for overlapping occurrences (in both orientations), which lends to complex dependencies

Statistical significance of a motif (s) is based on the frequencies of shorter (more frequent) oligonucleotides

Use of Markov chain to model background genomic distribution

Use of z-score to measure statistical significance

Allows for multiple binding sites

Characteristics of a Motif

Any single TFBS has significant variation

Many motifs have spacers from 1-11bp

Variation often occurs as a transition (e.g. purine purine) rather than a transversion (e.g. pyrimidine purine)

Variation occurs less between a pair of complementary bases.

Indels are uncommon

Proposed Motif Definition

Motif will be a string with Σ= {A,C,G,T, R,Y,S,W,N}

A,C,G,T (DNA bp), R (purine), Y (pyrimidine), S (strong), W (weak), N (spacer)

TF database (SCPD) confirms this model of variation Of 50 binding site consensi, 31 exact fits (62%) Another 10 fit if slight variations allowed

Measure of Statistical Significance

Given set of corregulated S. cerevisiae genes, the input to the problem is corresponding set of 800bp upstream sequences having 3’ end on start site of gene translation.

Model must measure from input sequences: Absolute number of occurrences (Ns) of motif (s) Background genomic distribution

X is a set of random DNA sequences in the same number and lengths of the input sequences Generated by Markov chain of order m Transition probabilities determined by (m+1)-mer

frequencies in fully complement of 6000+ (800bp in length) Background model chooses m=3

z-score

Xs – r.v. is number of occurrences of motif (s) in X

E(Xs) – expectation, σ(Xs) – standard deviation

zs – number of S.D. by which observed value Ns exceeds expectation

Implications

Possibility of overlap of a motif with itself (in either orientation)

Previous study of pattern autocorrelation

Generalized computation of SD, treating motif as a finite set of strings Higher order Markov chains Spacers handled at no extra computational cost Handles motif in either orientation

Algorithm

Enumerates over each input sequence

Tabulates number Ns of occurrences of each motif in either direction

Compute expectation and SD for each motif s.t. Ns>0

Calculate z-score

Rank motifs by z-score

Algorithm Analysis

For single motif, complexity is O(c2k2) k – # of nonspacer characters in motif c – # of instantiations of R, Y, S, W in motif

Only modest values of k

Linear dependence on genome size

Can trim variance calculation to optimize

Number of Occurrences

Convert motif s into a multiset W

Add reverse complements for each string in W

Motif s only occurs at position in X iff some string in W occurs at same position

Xs - # of occurrences (in X) of each member of W

Handling Palindromes

Wi – member of W

|W| = T

Number of Occurrences Con’t

Expectation

Linearity of Expectation

Variance

B term

C term

C Term

A term

A Term

Overlapping Concatenation

CW (like W) is potentially a multiset

One-to-one correspondence

C Term Simplification

A Term Revisited

Si1Si2 Term & Approximation

Kleffe and Borodovsky (1992) Approximation

B Term

B Term Con’t

Summary

Higher Order Markov Models

Variance calculations remain the same except for Si1Si2 term

Experimental m = 3

Experimental Results & Future Considerations

17 coregulated sets of genes

Known TF with known binding site consensus

In 9 experiments, known consensus was one of 3 highest scoring motifs

Future Topics: Non-centered spacers Enumeration Loop optimization Filtering repeats

Question

E(Xs) is more straight-forward to calculate compared to σ(Xs). Under the assumptions given in the paper, name one of the reasons for this complication.