Entropy, Information contents

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Entropy, Information contents Logo plotsBy
Thomas Nordahl Petersen
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Biological information
Exon Intron Exon

• Mutiple alignment of acceptor sites from 268
  yeast DNA sequences
• What is the biological signal around the site ?
• What are the important positions
• How can it be visualized ?

• Logo plot with Information Content

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Entropy - Definition

• Entropy of random variable is a measure of the
  uncertainty
• In Thermodynamics ?GH-T?S
• The entropy S of a system is the degree of
  disorder

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Entropy - Definition

• Entropy of a distribution of amino acids
• The Shannon entropy
• H(p) - ?a pa log2(pa), where p is an amino
• acid distribution.
• H(p) is measured in bits log2(2) 1, log2(4)2
• Mutiple alignment of 3 sequences
• Seq1 A L P K
• Seq2 A V P R
• Seq3 A I K R
• High entropy - high disorder
• Low entropy - low disorder

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Entropy - example

• H(p) - ?a pa log2(pa)
• Mutiple alignment of 3 sequences
• Seq1 A L R
• Seq2 A V R
• Seq3 A I K
• Pos1 H(p) -1log2(1) 0
• Pos2 H(p) -1/3log2(1/3) 1/3log2(1/3)
  1/3log2(1/3)
• Pos3 H(p) -2/3log2(2/3) 1/3log2(1/3)

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Relative EntropyThe Kullback-Leiber distance D

• How different is an amino acid distribution pa
  compared to a background distribution qa - i.e.
  distance D between them.
• D(pq) ?a pa log2(pa/qa)
• Normally a background distribution of the amino
  acids is
• obtained as frequencies from a large database
  like UniProt.
• Ala (A) 7.82 Gln (Q) 3.94 Leu (L) 9.62 Ser
  (S) 6.87
• Arg (R) 5.32 Glu (E) 6.60 Lys (K) 5.93 Thr
  (T) 5.46
• Asn (N) 4.20 Gly (G) 6.94 Met (M) 2.37 Trp
  (W) 1.16
• Asp (D) 5.30 His (H) 2.27 Phe (F) 4.01 Tyr
  (Y) 3.07
• Cys (C) 1.56 Ile (I) 5.90 Pro (P) 4.85 Val
  (V) 6.71

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Information content

• D(pq) ?a pa log2(pa/qa)
• Often the Information content is used as a
  measure of the
• degree of conservation.
• I ?a pa log2(pa/qa)
• A special case is that where all amino acids have
  the same background distribution qa 1/20

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Information content

• I ?a pa log2(pa/(1/20))
• ?a pa log2pa - log2(1/20)
• -H(p) - ?a palog2(1/20)
• -H(p) ?a palog2(20)
• -H(p) log2(20)
• -H(p) 4.32

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Information content

• I -H(p) 4.32 ?a palog2pa 4.32
• The Information content is at its maximum when
  then the entropy is zero - i.e. A fully conserved
  position in a multiple alignment.
• Mutiple alignment of 3 sequences
• Seq1 A L R
• Seq2 A V R
• Seq3 A I K
• Pos1 I -1log2(1) 4.32 4.32
• Pos2 I -1/3log2(1/3) 1/3log2(1/3)
  1/3log2(1/3) 4.32
• Pos3 I -2/3log2(2/3) 1/3log2(1/3) 4.32

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Logo plots - HowTo
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Logo plots - Information Content
Calculate Information Content I ?a?palog2pa
log2(4), Maximal value is 2 bits
Completely conserved
0.5 each

• Total height at a position is the Information
  Content measured in bits.
• Height of letter is the proportional to the
  frequency of that letter.
• A Logo plot is a visualization of a mutiple
  alignment.

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Programs to make a Logo plot

• WebLogo
• Requires a mutiple alignment as input
• Protein or DNA sequences
• More output formats
• Blast2Logo
• Requires a fasta file as input
• Only protein sequences
• Runs PSI-blast and makes a table of frequencies
• pdf logo plot

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WebLogo - http//weblogo.berkeley.edu/
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WebLogo - http//weblogo.berkeley.edu/
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Find important positions
gtspQ00017RHA1_ASPAC Rhamnogalacturonan
acetylesterase MKTAALAPLFFLPSALATTVYLAGDSTMAKNGGGS
GTNGWGEYLASYLSATVVNDAVAGR SARSYTREGRFENIADVVTAGDYV
IVEFGHNDGGSLSTDNGRTDCSGTGAEVCYSVYDGV NETILTFPAYLEN
AAKLFTAKGAKVILSSQTPNNPWETGTFVNSPTRFVEYAELAAEVAG VE
YVDHWSYVDSIYETLGNATVNSYFPIDHTHTSPAGAEVVAEAFLKAVVCT
GTSLKSVL TTTSFEGTCL
What is the next step ?

1. Find homologous sequences - how ?

• Blast or PsiBlast
• Download sequences
• Make a mutiple alignment
• ClustalW or others
• or use Blast2Logo program

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Mutiple alignment programs
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Blast2logo - http//www.cbs.dtu.dk/biotools/Blast2
logo-1.0/
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Important positions

• Important positions in proteins are conserved
• positions gt high Information Content.
• Conserved for a reason
• Functionally important positions
• Catalytic residues
• Structurally important positions
• Manitain the correct fold of the protein

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Blast2logo

• Runs iterative blast i.e. Psi-Blast
• Searching for homologues sequences by use
• of Position Specific Scoring Matrices (PSSM).
• Iteration - use Blosum62 scoring matrix
• Iteration - make profile of seq found in
  iteration 1
• Iteration - make profile of seq found in
  iteration 2
• Iteration - Calculate aa freq at each position
  in
• query sequence. Correct for low counts and weight
• seq such that very similar seq are down weighted

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Important positions - counting
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Example. Where is the active site?

• Sequence profiles might show you where to look!
• The active site could be around
• S9, G42, N74, and H195

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Exercise

1. Calculate nucleotide frequencies from a mutiple
   alignment of human donor sites
2. Calculate Entropy and Information content
3. Draw (by hand) a Logo plot
4. Use 2 Logo plot programs
5. Learn to interpret Logo frequency plots
6. Active site residues structural residues