Post on 14-Jan-2016
description
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.