Scoring Matrices

1
Scoring Matrices

• Scoring matrices, PSSMs, and HMMs

Reading Ch 6.1
BIO520 Bioinformatics Jim Lund
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Alignment scoring matrix

• DNA matrix
• A C G T
• A 5 -4 -4 -4
• C -4 5 -4 -4
• G -4 -4 5 -4
• T -4 -4 -4 5

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Alignment scoring matrix

• Protein matrix

4
Use of a scoring matrix

• P L S - - C F G
• G L T - A C H L
• 111-2-1111
• Score 3

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Consensus sequences

• Different ways to describe a consensus, from
  crude to refined
• Consensus site
• Sequence logos
• Position Specific Score Matrix (PSSM)
• Hidden Markov Model (HMM)

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Consensus sequences and sequence logos
GTMGFGLPAAIGAKLARPDRRVVAIDGDGSFQMTVQELST
Consensus sequence
Sequence logo
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Constructing (and using) a consensus sequence

1. Collect sequences
2. Align sequences (consensus sites are descriptions
   of the alignment)
3. Condense the set of sequences into a consensus
   (to a consensus, PSSM, HMM).
4. Apply the scoring matrix in alignments/searches.

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Position Specific Score Matrix (PSSM)

• A position specific scoring matrix (PSSM) is a
  matrix based on the amino acid frequencies (or
  nucleic acid frequencies) at every position of a
  multiple alignment.
• From these frequencies, the PSSM that will be
  calculated will result in a matrix that will
  assign superior scores to residues that appear
  more often than by chance at a certain position.

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Creating a PSSM Example

• NTEGEWI
• NITRGEW
• NIAGECC

Amino acid frequencies at every position of the
alignment
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Creating a PSSM Example

• Amino acids that do not appear at a specific
  position of a multiple alignment must also be
  considered in order to model every possible
  sequence and have calculable log-odds scores. A
  simple procedure called pseudo-counts assigns
  minimal scores to residues that do not appear at
  a certain position of the alignment according to
  the following equation
• Where
• Frequency is the frequency of residue i in column
  j (the count of occurances).
• pseudocount is a number higher or equal to 1.
• N is the number of sequences in the multiple
  alignment.

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Creating a PSSM Example

• In this example, N 3 and lets use pseudocount
  1
• Score(N) at position 1 3/3 1.
• Score(I) at position 1 0/3 0.
• Readjust
• Score(I) at position 1 -gt (01) / (320) 1/23
  0.044.
• Score(N) at position 1 -gt (31) / (320) 4/23
  0.174.
• The PSSM is obtained by taking the logarithm of
  (the values obtained above divided by the
  background frequency of the residues).
• To simplify for this example well assume that
  every amino acid appears equally in protein
  sequences, i.e. fi 0.05 for every i)
• PSSM Score(I) at position 1 log(0.044 / 0.05)
  -0.061.
• PSSM Score(N) at position 1 log(0.174 / 0.05)
  0.541.

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Creating a PSSM Example

• The matrix assigns positive scores to residues
  that appear more often than expected by chance
  and negative scores to residues that appear less
  often than expected by chance.

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Using a PSSM

• To search for matches to a PSSM, scan along a the
  sequence using a window the length (L) of the
  PSSM.
• The matrix is slid on a sequence one residue at a
  time and the scores of the residues of every
  region of length L are added.
• Scores that are higher than an empirically
  predetermined threshold are reported.

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Advantages of PSSM

• Weights sequence according to observed diversity
  specific to the family of interest
• Minimal assumptions
• Easy to compute
• Can be used in comprehensive evaluations.

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More sophisticated PSSMs
From less to more complicated

1. PSSM with pseudocounts.
2. Giving pseudocounts less weight when more
   alignment data is available.
3. Weight pseudocount amino acids by their frequency
   of occurrence in proteins.
4. Instead of giving pseudocounts all the same
   value, weight them by their similarity to the
   consensus (like BLOSUM62 does) at each position.
   (PSI-BLAST method).
5. Combine 2 4 (Dirichlet mixture method).

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A PSSM column with a perfectly conserved
isoleucine with different methods used to
calculate the scores.
Method 1 and standard BLOSUM62 matrix
Method 5
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Using Hidden Markov models to describe sequence
alignment profiles

• A profile HMM can represent a sequence alignment
  profile similar to how a PSSM does.
• A profile HMM includes information on the amino
  acid consensus at each position in the alignment
  like a PSSM.
• A profile HMM also has position-specific scores
  for gap insertion and extensions.

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Background Creating HMMs

• To create an HMM to model data we need to
  determine two things
• The structure/topology of the HMMstates and
  transitions
• The values of the parametersemission and
  transition probabilities.
• Determining the parameters is called training.

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A HMM structure/topology
M match state (score the aa in the sequence at
this position in the profile) I insertion
(w.r.t profile - insert gap characters in
profile) D deletion (w.r.t sequence - insert
gap characters in sequence) M1 is first aa in
the profile, M2 is second, etc.
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Example HMMER parameters

• NULE 595 -1558 85 338 -294 453 -1158 (...) -21
  -313 45 531 201 384
• HMM A C D E F G H (...) m-gtm m-gti m-gtd i-gtm i-gti
  d-gtm d-gtd b-gtm m-gte
• 1 -1084 390 -8597 -8255 -5793 -8424 -8268
  (...) 1
• - -149 -500 233 43 -381 399 106 (...)
• C -1 -11642 -12684 -894 -1115 -701 -1378 -16
  
• 2 -2140 -3785 -6293 -2251 3226 -2495 -727
  (...) 2
• - -149 -500 233 43 -381 399 106 (...)
• C -1 -11642 -12684 -894 -1115 -701 -1378
  (...)
• 76 -2255 -5128 -302 363 -784 -2353 1398 (...)
  103
• - -149 -500 233 43 -381 399 106 (...)
• E -1 -11642 -12684 -894 -1115 -701 -1378
• 77 -633 879 -2198 -5620 -1457 -5498 -4367
  (...) 104
• - (...)
• C 0
• //

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A profile HMM with match state probabilities shown
AAs PATH is the consensus sequence.
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Building a profile HMM

• Pick a HMM structure/topology.
• Estimate initial parameters.
• Train the HMM by running sequences through it.
• Transitions that get used are given higher
  probabilities, those rarely used are given lower
  probabilities.

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Protein profile HMMs

• Better (in theory) representations than PSSMs.
• More complicated.
• Not hand-tuned by curators.
• Used in some protein profile databases
• Pfam (http//pfam.sanger.ac.uk/)
• SMART (http//smart.embl-heidelberg.de/)
• Difficult to describe in human readable formats.

Schuster-Böckler et al., 2004 (http//www.biomedce
ntral.com/1471-2105/5/7)