1. Blosum matrices What are they
Blosum matrices What are they? Morten Nielsen Depart of systems biology, DTU IIB-INTECH, UNSAM, Argentina

2. Alignment scoring matrices
Outline
Alignment scoring matrices
How are Blosum matrices constructed?
What is a BLOSUM50 matrix and how is it different from a BLOSUM80 matrix?
What is the difference between a Blosum scoring matrix and the Blosum frequency substitution matrix?

3. Sequence Alignment
1PLC._
1PLB._

4. Where is the active site?
Sequence alignment. Infer function (and functional residues) from one protein to another
1K7C.A TVYLAGDSTMAKNGGGSGTNGWGEYLASYLSATVVNDAVAGRSARSYTREGRFENIADVVTAGDYVIVEFGHNDGGSLSTDN
S G N
1WAB._ EVVFIGDSLVQLMHQCE---IWRELFS---PLHALNFGIGGDSTQHVLW--RLENGELEHIRPKIVVVWVGTNNHG------
1K7C.A GRTDCSGTGAEVCYSVYDGVNETILTFPAYLENAAKLFTAK--GAKVILSSQTPNNPWETGTFVNSPTRFVEYAEL-AAEVA
1WAB._ HTAEQVTGGIKAIVQLVNERQPQARVVVLGLLPRGQ-HPNPLREKNRRVNELVRAALAGHP
1K7C.A GVEYVDHWSYVDSIYETLGNATVNSYFPIDHTHTSPAGAEVVAEAFLKAVVCTGTSL H
1WAB._ RAHFLDADPG---FVHSDG--TISHHDMYDYLHLSRLGYTPVCRALHSLLLRL---L

5. Homology modeling and the human genome

6. BLOSUM = BLOck SUbstitution Matrices
Focus on conserved domains, MSA's (multiple sequence alignment) are ungapped blocks.
Compute pairwise amino acid alignment counts
Count amino acid replacement frequencies directly from columns in blocks
Sample bias:
Cluster sequences that are x% similar.
Do not count amino acid pairs within a cluster.
Do count amino acid pairs across clusters, treating clusters as an "average sequence".
Normalize by the number of sequences in the cluster.
BLOSUMXX matrices
Sequences that are xx% similar are clustered during the construction of the matrix.

7. Log-odds scores Log-odds scores are given by
Log( Observation/Expected)
The log-odd score of matching amino acid j with amino acid i in an alignment is
where Pij is the frequency of observing amino i aligned with j, and Qi, Qj are the frequencies of amino acids i and j in the data set.
The log-odd score is (in half bit units)

8. So what does this mean? An example
NAA = 14
NAD = 5
NAV = 5
NDA = 5
NDD = 8
NDV = 2
NVA = 5
NVD = 2
NVV = 2
PAA = 14/48
PAD = 5/48
PAV = 5/48
PDA = 5/48
PDD = 8/48
PDV = 2/48
PVA = 5/48
PVD = 2/48
PVV = 2/48
1: VVAD
2: AAAD
3: DVAD
4: DAAA
MSA
QA = 8/16
QD = 5/16
QV = 3/16

9. So what does this mean? PAA = 0.29 QAQA = 0.25 PAD = 0.10 QAQD = 0.16
PAV = 0.10
PDA = 0.10
PDD = 0.17
PDV = 0.04
PVA = 0.10
PVD = 0.04
PVV = 0.04
QAQA = 0.25
QAQD = 0.16
QAQV = 0.09
QDQA = 0.16
QDQD = 0.10
QDQV = 0.06
QVQA = 0.09
QVQD = 0.06
QVQV = 0.03
1: VVAD
2: AAAD
3: DVAD
4: DAAA
MSA
QA=0.50
QD=0.31
QV=0.19

10. So what does this mean? PAA = 0.29 PAD = 0.10 PAV = 0.10 PDA = 0.10
PDD = 0.17
PDV = 0.04
PVA = 0.10
PVD = 0.04
PVV = 0.04
QAQA = 0.25
QAQD = 0.16
QAQV = 0.09
QDQA = 0.16
QDQD = 0.10
QDQV = 0.06
QVQA = 0.09
QVQD = 0.06
QVQV = 0.03
SAA = 0.44
SAD =-1.17
SAV = 0.30
SDA =-1.17
SDD = 1.54
SDV =-0.98
SVA = 0.30
SVD =-0.98
SVV = 0.49
BLOSUM is a log-likelihood matrix:
Sij = 2log2(Pij/(QiQj))

11. The Scoring matrix A D V 0.44 -1.17 0.30 1.54 -0.98 0.49 1: VVAD
2: AAAD
3: DVAD
4: DAAA
MSA

12. And what does the BLOSUMXX mean?
Cluster sequence Blocks at XX% identity
Do statistics only across clusters
Normalize statistics according to cluster size AV AP AL VL
} min XX % identify A) B) AV GL GV

13. And what does the BLOSUMXX mean?AV AP AL VL A) B) AV GL GV

14. And what does the BLOSUMXX mean?
High Blosum values mean high similarity between clusters
Conserved substitution dominate
Low Blosum values mean low similarity between clusters
Less conserved substitutions dominate

15. BLOSUM80 <Sii> = 9.4 <Sij> = -2.9
A R N D C Q E G H I L K M F P S T W Y V A R N D C Q E G H I L K M F P S T W Y V
<Sii> = 9.4
<Sij> = -2.9

16. BLOSUM30 <Sii> = 8.3 <Sij> = -1.16
A R N D C Q E G H I L K M F P S T W Y V A R N D C Q E G H I L K M F P S T W Y V
<Sii> = 8.3
<Sij> = -1.16

17. The different Blosum matrices
The BLOSUM alignment scoring matrix is a log-likelihood matrix
The Blosum frequency substitution matrix, is a conditional probability matrix of matching amino acids j given you have amino acid i
and

18. The way from frequencies to log-odds
A R N D C Q E G H I L K M F P S T W Y V A R N D C Q E G H I L K M F P S T W Y V
The weight matrix is identical to the Blosum row for each amino adis