Scoring Matrices

1
Scoring Matrices

• Scoring matrices, PSSMs, and HMMs

BIO520 Bioinfromatics Jim Lund
2
Alginment scoring matrix

• DNA matrix
• A C G T
• A 5 -4 -4 -4
• T -4 5 -4 -4
• C -4 -4 5 -4
• G -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
Constructing a consensus

• 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.

7
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.

8
Creating a PSSM Example

• NTEGEWI
• NITRGEW
• NIAGECC

Amino acid frequencies at every position of the
alignment
9
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.

10
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(N) at position 1 log(0.044 / 0.05)
  -0.061.
• PSSM Score(I) at position 1 log(0.174 / 0.05)
  0.541.

11
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.

12
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.

13
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.

14
Review 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.

15
HMMER structure/topology
M match state I insertion (w.r.t profile -
insert gap characters in profile) D deletion
(w.r.t sequence - insert gap characters in
sequence) N N-terminal un-aligned C
C-terminal un-aligned J Joining segment,
un-aligned
16
Example HMMER parameters

• HMMER2.0 2.3
• NAME rrm
• ACC PF00076
• DESC RNA recognition motif. (a.k.a. RRM, RBD, or
  RNP domain)
• LENG 77
• ALPH Amino
• RF no
• CS yes
• MAP yes
• COM ../src/hmmbuild -F rrm.hmm rrm.sto
• NSEQ 90
• DATE Tue Apr 29 110143 2003
• CKSUM 8325
• GA 15.2 0.0
• TC 15.2 0.3
• XT -8455 -4 -1000 -1000 -8455 -4 -8455 -4
• NULT -4 -8455
• NULE 595 -1558 85 338 -294 453 -1158 (...) -21
  -313 45 531 201 384 -1998 -644
• 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 -16 -649

17
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
• //