Expectation Maximization for DNA motif discovery
Alastair M. Kilpatrick
Centre for Intelligent Systems and their Applications, University of Edinburgh
http://www.cisa.inf.ed.ac.uk
Sequence motifs are short, reasonably well conserved patterns of DNA known to have biological functions,
serving as transcription factor binding sites, for example. Discovery of these motifs is an important task in the
wider challenge of understanding the mechanisms of gene expression. Considerable effort has been invested into
computational methods for motif discovery; these methods have been applied successfully in this area.
The Expectation-Maximization (EM) algorithm is a classic general optimisation technique used in a number of
motif discovery algorithms, including the popular MEME algorithm. Given a number of input DNA sequences, two
models are created, one representing a recurring pattern within the sequences (the 'motif') and the other
representing the remainder of the sequences (the 'background'). An initial estimation for the motif model
parameters is made, then two iterative steps are carried out repeatedly to simultaneously optimise both the motif
and the background model.
We have implemented the EM algorithm for DNA motif discovery in alphaproteobacteria (Magnetospirillum
magneticum sp.strain AMB-1), with promising results.
The EM algorithm and MEME
Experimental Work
The basic EM algorithm for motif discovery (Lawrence and
Reilly, 1990) assumes that each subsequence within the
input dataset arises from either the motif or the
background model; at the outset, it is not known which one
(this knowledge is known as the ‘missing data’). Given an
initial estimate of the motif model parameters, EM allows
us to discover which subsequences arise from which
model and hence any motifs within the (observed) dataset.
In the expectation step (E-step), the current parameter
values are used to evaluate the probability of the missing
data given the observed data. This probability is then used
in the maximization step (M-step) to re-estimate the model
parameters. These steps are carried out iteratively until
convergence is reached.
The MEME algorithm was implemented and tested on both
synthetic data and selected promoter sequences of genes
from the M. magneticum sp. strain AMB-1 genome (a
member of the alphaproteobacteria, a class of bacteria
currently researched in the Ward lab, School of Biological
Sciences at The University of Edinburgh). The results
confirmed previously proposed regulatory motifs and
proposed several new motifs potentially important in gene
expression (Kilpatrick, 2009).
(a)
(b)
Results of tests on AMB-1 confirm previously proposed iron
regulatory motifs. Results are visualised to show percentage
weights (a) and rescaled to show motif information content (b).
Using the EM algorithm to iteratively estimate the two
components in the ‘Old Faithful’ dataset. Figures show EM
iterations 1, 2 & 30 (convergence). Note that although the
initial estimates are poor, EM still converges to a good
estimation.
The original EM algorithm for motif discovery forms the
basis of the popular MEME algorithm (Bailey and Elkan,
1995), which incorporates a number of novel features,
including a method for discovering multiple motifs within a
dataset and a method for automatically discovering the
length of motifs. MEME can also successfully model
alternative motif forms, including (quasi-)palindromic
motifs and spaced dyad (‘gapped’) motifs. Wet-lab work
has confirmed that MEME works well in unsupervised
motif discovery (i.e. no prior knowledge is required).
However, we have shown that if prior information about
motifs is available, it can be exploited and incorporated
within MEME in order to improve results (Kilpatrick, 2009).
Two novel extensions to the MEME algorithm have been
implemented (Kilpatrick, 2009). A method to score motifs
based on information content has been successful in
increasing the significance of returned motifs, particularly
when searching for multiple motifs in a single dataset. A
method to incorporate prior knowledge of motif positions
based on the concept of the energy of a motif has also been
successfully implemented, further improving results.
Future work will consider stochastic methods and other forms
of prior biological knowledge in order to improve the results of
motif discovery algorithms.
References
Bailey, T.L. & Elkan, C. (1995) Unsupervised learning of multiple
motifs in biopolymers using expectation maximization. Machine
Learning.
Lawrence, C.E. & Reilly, A.A. (1990) An EM algorithm for the
identification and characterisation of common sites in unaligned
biopolymer sequences. Proteins.
Kilpatrick, A.M. (2009) Regulatory motif discovery in magnetic
bacteria. MSc Thesis The University of Edinburgh
AMK is supported by an EPSRC Doctoral Studentship.