Bioinformatics

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Lecture 10
Bioinformatics

• Finding signals and motifs in DNA and proteins
• Expectation Maximization Algorithm
• MEME
• The Gibbs sampler

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Finding signals and motifs in DNA and proteins

• An alignment of sequences is intrinsically
  connected with another essential task, which is
  finding certain signals and motifs (highly
  conservative ungapped blocks) shared by some
  sequences.
• A motif is a sequence pattern that occurs
  repeatedly in a group of related protein or DNA
  sequences. Motifs are represented as
  position-dependent scoring matrices that describe
  the score of each possible letter at each
  position in the pattern.
• Another related task is searching biological
  databases for sequences that contain one or more
  of known motifs.
• These objectives are critical in analysis of
  genes and proteins, as any gene or protein
  contains a set of different motifs and signals.
  Complete knowledge about locations and structure
  of such motifs and signals leads to a
  comprehensive description of a gene or protein
  and indicates at a potential function.

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The eMOTIF method of motif analysis

• eMotif is very useful method of identifying
  motifs in proteins
• MSA of a particular set of proteins is submitted
  to eMotif, which essentially searches for
  consensus sequence(s) and identifies the
  conservative motifs.
• The probability of a motif is estimated from the
  frequencies of the individual amino acids in the
  SwissProt DB as a product of probabilities of
  each position in the consensus
• The result could be as follows This motif
  matches 25 out of the 30 sequences supplied. It
  will match 1 in 10 19 random sequences, or less
  than 1 sequence in the current SWISS-PROT
  database.
• Then a motif can be searched in the Swiss-Prot DB

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eMOTIF

True positives
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eMOTIF search of sequences with certain emotif
in the DB
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Expectation Maximization (EM) Algorithm

• This algorithm is used to identify conserved
  areas in unaligned DNA and proteins.
• Assume that a set of sequences is expected to
  have a common sequence pattern.
• An initial guess is made as to location and size
  of the site of interest in each of the sequences
  and these parts are loosely aligned.
• This alignment provides an estimate of base or
  aa composition of each column in the site.
• The EM algorithm consists of the two steps,
  which are repeated consecutively.
• Step 1, the expectation step, the
  column-by-column composition of the site is used
  to estimate the probability of finding the site
  at any position in each of the sequences. These
  probabilities are used to provide new information
  as to expected base or aa distribution for each
  column in the site.
• Step 2, the maximization step, the new counts
  for bases or aa for each position in the site
  found in the step 1 are substituted for the
  previous set.

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Expectation Maximization (EM) Algorithm
OOOOOOOOXXXXOOOOOOOOOOOOOOOOXXXXOOOOOOOO o o o o
o o o o o o o o o o o o o o o o o o o
o OOOOOOOOXXXXOOOOOOOO OOOOOOOOXXXXOOOOOOOO
IIII IIIIIIII IIIIIII
Columns defined by a preliminary alignment of
the sequences provide initial estimates of
frequencies of aa in each motif column
Columns not in motif provide background
frequencies
Bases Background Site column 1 Site column 2
G 0.27 0.4 0.1
C 0.25 0.4 0.1
A 0.25 0.2 0.1
T 0.23 0.2 0.7
Total 1.00 1.00 1.00
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Expectation Maximization (EM) Algorithm
A
B
The resulting score gives the likelihood that the
motif matches positions A, B or other in seq 1.
Repeat for all other positions and find most
likely locator. Then repeat for the remaining
seqs.
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EM Algorithm 1st expectation step calculations

• Assume that the seq1 is 20 bases long and the
  length of the site is 20 bases.
• Suppose that the site starts in the column 1 and
  the first two positions are A and T.
• The site will end at the position 20 and
  positions 21 and 22 do not belong to the site.
  Assume that these two positions are A and T also.
  
• The Probability of this location of the site in
  seq1 is given by
• Psite1,seq1 0.2 (for A in position 1) x 0.7
  (for T in position 2) x Ps (for the next 18
  positions in site) x 0.25 (for A in first
  flanking position) x 0.23 (for T in second
  flanking position x Ps (for the next 78 flanking
  positions).
• The same procedure is applied for calculation of
  probabilities for Psite2,seq1 to Psite78,
  seq1, thus providing a comparative set of
  probabilities for the site location.
• The probability of the best location in seq1,
  say at site k, is the ratio of the site
  probability at k divided by the sum of all the
  other site probabilities.
• Then the procedure repeated for all other
  sequences.

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EM Algorithm 2nd optimisation step calculations

• The site probabilities for each seq calculated
  at the 1st step are then used to create a new
  table of expected values for base counts for each
  of the site positions using the site
  probabilities as weights.
• Suppose that P (site 1 in seq 1) Psite1,seq1 /
  (Psite1,seq1 Psite2,seq1 Psite78,seq1 )
  0.01 and P (site 2 in seq 1) 0.02.
• Then this values are added to the previous table
  as shown in the table below.
• This procedure is repeated for every other
  possible first columns in seq1 and then the
  process continues for all other sequences
  resulting in a new version of the table.
• The expectation and maximization steps are
  repeated until the estimates of base frequencies
  do not change.

Bases Background Site column 1 Site column 2
G 0.27 0.4 0.1
C 0.25 0.4 0.1
A 0.25 0.2 0.01 0.1
T 0.23 0.2 0.7 0.02
Total/ weighted 1.00 1.00 1.00
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Multiple EM for Motif Elicitation - MEME
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MEME Summary Line

• This line gives the width (width), number of
  occurrences in the training set (sites), log
  likelihood ratio (llr) and E-value of the
  motif. Each motif describes a pattern of a fixed
  width and no gaps are allowed in MEME motifs.
  MEME numbers the motifs consecutively from one as
  it finds them. MEME usually finds the most
  statistically significant (low E-value) motifs
  first.
• The statistical significance of a motif is based
  on its log likelihood ratio, its width and number
  of occurrences, the background letter
  frequencies (given in the command line summary),
  and the size of the training set.
• The E-value is an estimate of the expected
  number of motifs with the given log likelihood
  ratio (or higher), and with the same width and
  number of occurrences, that one would find in a
  similarly sized set of random sequences. (In
  random sequences each position is independent
  with letters chosen according to the background
  letter frequencies.)
• The log likelihood ratio is the logarithm of
  the ratio of the probability of the occurrences
  of the motif given the motif model (likelihood
  given the motif) versus their probability given
  the background model (likelihood given the null
  model). (Normally the background model is a
  0-order Markov model using the background letter
  frequencies, but higher order Markov models may
  be specified via the -bfile option to MEME.)
• Clicking on the buttons to the left of the motif
  summary line takes you to the previous motif (P)
  or next motif (N).

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MEME Summary Line
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MEME
MOTIF 1 width 26 sites 5 llr
244 E-value 5.0e-006
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MEME
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The Gibbs Sampler

• The Gibbs sampler algorithm is slightly
  different from the EM approach. The method also
  searches for the statistically most probable
  motifs and can find the optimal width and the
  number of motifs in each sequence.
• The method iterates through two steps. In the
  first step a random start position for the motif
  is chosen for all sequences but for one. These
  seq. are then aligned and used to find an initial
  guess of the motif.
• The objective of the next step is to find the
  most probable pattern common to left out sequence
  (and on the next iterations to all of the
  sequences) by sliding them back and forth until
  the ratio of the motif probability to the
  background probability is a maximum.
• Then the next sequence is left out and the
  process is repeated until the residue frequencies
  in each motif do not change. The number of
  iterations may range from several hundred to
  several thousand.
• Several additional statistical procedure are
  used to improve the performance of the algorithm.
  The Gibbs sampler was used to align sequences
  with very little sequences similarity.

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Steps of the Gibbs sampler algorithm
A. Estimate the aa or base frequencies in the
motif columns of all but the 1 sequence. Also
obtain background
Motif
xxxxxxxMxxxxxxx
xxxxxxxMxxxxxxx xxxxxxxxxxMxxxx
xxxxxxxxxxMxxxx xMxxxxxxxxxxxxx
xMxxxxxxxxxxxxx xxxxxxxxxxxxxxM
xxxxxxxxxxxxxxM xxxxxMxxxxxxxxx
xxxxxMxxxxxxxxx Random start
Location of motif in each sequence
provides positions chosen first
estimate of motif composition
All sequences except the outlier
x is equal to n seq. positions M indicates
random location of the motif in each seq. -
indicates initially aligned motif positions
B. Use the estimate from A to calculate the
ratio of probability of motif to background score
at each position in the left out
sequence. This ratio for each possible location
in the sequence is the weight of the position.
xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx
xxxxxxxxxxxxxxx M - gt
M - gt M
- gt M - gt
M - gt C. Choose a new
location for the motif in the left out sequence
by a random selection using the weights to bias
the choice. xxxxxxxxxxMxx
Estimated locations of the motif in left out
sequence D. Repeat steps A to C gtgttimes
The outlier sequence