Motif finding problem

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Motif finding problem

• Some important conserved sequences come in short
  dispersed blocks called motifs.
• How can we find such motifs? If examples of the
  sequence exist this is relatively
  straightforward but what if they dont?
• Problem is common in DNA motif finding, e.g.
  transcription-factor binding sites, splicing
  regulators.
• Usually cannot just multiply align and take the
  best aligning region because spacing, order, and
  information content too variable.
• We need a method that will scan through all the
  sequences at all positions looking for short
  regions of similarity.

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Short motifs may be anywhere in sequences
We want to find the position of this motif AND
we dont know where it is or what its sequence
is.
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Motif-finding Approaches

• Expectation maximization (EM)
• Gibbs sampling
• Phylogeny-accountable methods (variants of what
  we will discuss, but account for how related
  target sequences are).

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Sequence Probability

• We need to define the probability of seeing a
  particular residue sequence of interest in a
  larger sequence block.
• For this to make sense, we need a specific
  expectation (a model) for the sequence and a
  background model for the complete sequence.
• This is similar to amino acid score matrices,
  but we will define a different scoring method for
  motif finding, based on entropy.

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A simple example model for a 3-nucleotide sequence
Consider a case in which the model favors A then
T then T
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Computer algorithm digression
Using
The P-value quickly becomes extremely small. Even
using double precision, it will exceed available
precision for protein sequences longer than about
20 residues. So
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Sequence matches and backgrounds

• If the sequences we are searching have a
  composition identical to our expected sequence,
  background model not needed.
• But to generalize we will assume the background
  might NOT have the same composition.

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Computing background probability
Simplest case is where all nucleotides are
equally frequent
General case make residue counts for the entire
sequence set that you are analyzing.
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Differentiating from background
Now consider a test sequence that is nearly all A
and T. This background predicts
Compared to one that is nearly all C and G
Clearly we should be much more impressed if we
find ATT in the second case
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Putting them together
We want to know the DEGREE to which our model
favors a particular sequence compared to
background
This can be a very large number (gtgt1) if the
sequence matches the model much better or a small
number (lt1) if the sequence matches the
background better.
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Entropy measure

• this method uses a pure entropy measure of
  residue conservation in each column.
• the less variable the column is, the better it
  scores (low entropy).
• takes no account of amino acid similarities
  (e.g. L, V, I all have very similar side chains).

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For entropy measures, where do the model qi come
from?
note this is a strict entropy definition of
conservation
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Deriving one column of the motif model
12 sequences, pseudocounts are commonly taken to
be proportional to the general amino acid
frequency (Fi)
(for this example I have also taken background
from the general amino acid frequencies)
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Gibbs Sampler starting state
A single motif of fixed width chosen at random
from each of many sequences
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One round of Gibbs Sampling

• one sampled motif is removed from the set of N
  motifs.
• the remaining N-1 motifs are aligned and a motif
  model is derived from them as before.
• the motif model is used to test the match
  quality at every position in the removed sequence
  by

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Selecting a motif match
Assign a quality value according to
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sampling round cont.

• Select one among all possible positions
  according to their match quality.
• Can be either probabilistic (strict sampling
  approach) or fixed at single best match
  (converges a little faster but more prone to
  getting stuck at local maxima).

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Iterate!!
At each iteration, simply remove a randomly
chosen sequence from the model set and 1)
recompute the model 2) scan along the removed
sequence 3) probabilistically select a
match The removed sequence can be chosen in a
fixed order and/or the best match can be chosen
probabilistically or strictly. note fixed
order and fixed best match is close to an EM
(expectation maximization) algorithm
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early iterations have no real pattern
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but by chance two real motifs line up

• once two real motif alignments occur, they
  induce a slight bias toward selecting other
  copies of similar sequences during the iterative
  process.
• here for example is an early Gibbs Sampler run
  where some likely real matches have been made.
• two of them have probably recruited additional
  members

note in this example, motif regions are in
similar positions in all the sequences not
necessary
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After two real motifs align, they bias new choices
Match quality
probabilistically favored because slightly better
match
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If a good set of motifs is found
Match quality
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End point of a run
Overview
Alignment
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Local optima, noise, and sliding
Two very different types of local optima can
occur
The easy one is really a pseudo-optimum and is
solved by motif sliding
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Local optima, noise, and sliding (cont).

• The more difficult local optima are true
  (favorably scoring) motif alignments that are not
  the best (might not even be close in space or
  score quality).
• Reduced by the noisy algorithm tends to
  jiggle out of poor local optima.
• Require multiple independently-started runs to
  solve you simply take the best motif set found
  (but no guarantee!).

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Run graphic sampler example