Scoring Matrices

1
Scoring Matrices

• Scoring matrices, PSSMs, and HMMs

BIO520 Bioinfromatics Jim Lund
2
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

3
Alginment 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

5
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)

6
Consensus sequences and sequence logos
GTMGFGLPAAIGAKLARPDRRVVAIDGDGSFQMTVQELST
Consensus sequence
Sequence logo
7
Constructing (and using) a consensus sequence

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

8
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.

9
Creating a PSSM Example

• NTEGEWI
• NITRGEW
• NIAGECC

Amino acid frequencies at every position of the
alignment
10
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.

11
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.

12
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.

13
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.

14
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.

15
More sophisticated PSSMs
From less to more complicated

• PSSM with pseudocounts.
• Giving pseudocounts less weight when more
  alignment data is available.
• Weight pseudocount amino acids by their frequency
  of occurrence in proteins.
• 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).
• Combine 2 4 (Dirichlet mixture method).

16
A PSSM column with a perfectly conserved
isoleucine with different methods used to
calculate the scores.
Method 1 and standard BLOSUM62 matrix
Method 5
17
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.

18
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.

19
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.
20
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
• //

21
A profile HMM with match state probabilities shown
AAs PATH is the consensus sequence.
22
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.

23
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)