1. Protein Classification

2. PDB Growth
New PDB structures

3. Protein classification
Number of protein sequences grow exponentially
Number of solved structures grow exponentially
Number of new folds identified very small (and close to constant)
Protein classification can
Generate overview of structure types
Detect similarities (evolutionary relationships) between protein sequences
SCOP release 1.67, Class
# folds
# superfamilies
# families
All alpha proteins
202
342
550
All beta proteins
141
280
529
Alpha and beta proteins (a/b)
130
213
593
Alpha and beta proteins (a+b)
260
386
650
Multi-domain proteins 40 55
Membrane & cell surface 42 82 91
Small proteins 72
104
162
Total
887
1447
2630
Morten Nielsen,CBS, BioCentrum, DTU

4. Protein structure classification
Protein fold
Protein world
Protein superfamily
Protein family
Morten Nielsen,CBS, BioCentrum, DTU

5. Structure Classification Databases
SCOP
Manual classification (A. Murzin)
scop.berkeley.edu
CATH
Semi manual classification (C. Orengo)
FSSP
Automatic classification (L. Holm)
Morten Nielsen,CBS, BioCentrum, DTU

6. Morten Nielsen,CBS, BioCentrum, DTU
Major classes in SCOP
Classes
All alpha proteins
Alpha and beta proteins (a/b)
Alpha and beta proteins (a+b)
Multi-domain proteins
Membrane and cell surface proteins
Small proteins
Morten Nielsen,CBS, BioCentrum, DTU

7. All a: Hemoglobin (1bab)
Morten Nielsen,CBS, BioCentrum, DTU

8. All b: Immunoglobulin (8fab)
Morten Nielsen,CBS, BioCentrum, DTU

9. a/b: Triosephosphate isomerase (1hti)
Morten Nielsen,CBS, BioCentrum, DTU

10. Morten Nielsen,CBS, BioCentrum, DTU
a+b: Lysozyme (1jsf)
Morten Nielsen,CBS, BioCentrum, DTU

11. Morten Nielsen,CBS, BioCentrum, DTU
Families
Proteins whose evolutionarily relationship is readily recognizable from the sequence
(>~25% sequence identity)
Families are further subdivided into Proteins
Proteins are divided into Species
The same protein may be found in several species
Fold
Superfamily
Family
Proteins
Morten Nielsen,CBS, BioCentrum, DTU

12. Morten Nielsen,CBS, BioCentrum, DTU
Superfamilies
Proteins which are (remote) evolutionarily related
Sequence similarity low
Share function
Share special structural features
Relationships between members of a superfamily may not be readily recognizable from the sequence alone
Fold
Superfamily
Family
Proteins
Morten Nielsen,CBS, BioCentrum, DTU

13. Morten Nielsen,CBS, BioCentrum, DTU
Folds
Proteins which have >~50% secondary structure elements arranged the in the same order in the protein chain and in three dimensions are classified as having the same fold
No evolutionary relation between proteins
Fold
Superfamily
Family
Proteins
Morten Nielsen,CBS, BioCentrum, DTU

14. Protein Classification
Given a new protein, can we place it in its “correct” position within an existing protein hierarchy?
Methods
BLAST / PsiBLAST
Profile HMMs
Supervised Machine Learning methods
Fold
Superfamily
new protein ?
Family
Proteins

15. PSI-BLAST Given a sequence query x, and database D
Find all pairwise alignments of x to sequences in D
Collect all matches of x to y with some minimum significance
Construct position specific matrix M
Each sequence y is given a weight so that many similar sequences cannot have much influence on a position (Henikoff & Henikoff 1994)
Using the matrix M, search D for more matches
Iterate 1–4 until convergence
Profile M

16. Profile HMMs M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1
Protein profile H
Each M state has a position-specific pre-computed substitution table
Each I and D state has position-specific gap penalties
Profile is a generative model:
The sequence X that is aligned to H, is thought of as “generated by” H
Therefore, H parameterizes a conditional distribution P(X | H)

17. Classification with Profile HMMs
Fold M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1
Superfamily
“The statistical modeling approach to protein sequence analysis involves constructing a generative protein model, such as an HMM, for a protein family or superfamily. Sequences known to be members of the protein family are used as positive training examples, and the parameters of a statistical model representing the family are estimated using these training examples, in conjunction with general a priori information about properties of proteins. The model assigns a probability to any given protein sequences. If it is a good model for the family it is trained on, then sequences from that family, including sequences that were not used as training examples, yield a higher probability score than those outside the family. The probability score can thus be interpreted as a measure of the extent to which a new protein sequence is homologous to the protein family of interest.” Jaakkola, Diekhans, Haussler, 1999.
Family
new protein M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1 M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1 ?

18. Classification with Profile HMMs
How generative models work
Training examples ( sequences known to be members of family ): positive
Model assigns a probability to any given protein sequence.
The sequence from that family yield a higher probability than that of outside family.
Log-likelihood ratio as score
P(X | H1) P(H1) P(H1|X) P(X) P(H1|X)
L(X) = log = log = log
P(X | H0) P(H0) P(H0|X) P(X) P(H0|X)
This approach is perfectly reasonable if we assume that the models we have constructed, Hnull and Hfamily are excellent and give a very accurate posterior probability of the model given a sequence. As is usually the case with oversimplifying models of biological sequences, this is not a very reasonable assumption.

19. Generation of a protein by a profile HMM
P(X | H) ??
To generate sequence x1…xn by profile HMM H:
We will find the sum probability of all possible ways to generate X
Define
AjM(i): probability of generating x1…xi and ending with xi being emitted from Mj
AjI(i): probability of generating of x1…xi and ending with xi being emitted from Ij
AjD(i): probability of generating of x1…xi and ending in Dj
(xi is the last character emitted before Dj)

20. Alignment of a protein to a profile HMM
AjM(i) = εM(j)(xi) * { Aj-1M(i – 1) + log αM(j-1)M(j) +
Aj-1I(i – 1) + log αI(j-1)M(j) +
Aj-1D(i – 1) + log αD(j-1)M(j) }
AjI(i) = εI(j)(xi) * { AjM(i – 1) + log αM(j)I(j) +
AjI(i – 1) + log αI(j)I(j) +
AjD(i – 1) + log αD(j)I(j) }
AjD(i) = { Aj-1M(i) + log αM(j-1)D(j) +
Aj-1I(i) + log αI(j-1)D(j) +
Aj-1D(i) + log αD(j-1)D(j) }

21. Generative Models

22. Generative Models

23. Generative Models

24. Generative Models

25. Generative Models

26. Discriminative Methods
Instead of modeling the process that generates data, directly discriminate between classes
Give up trying to provide a likelihood function (a generative model) of the input data. Instead, focus on separating the different classes.
More direct way to the goal
Better if model is not accurate

27. Discriminative Models -- SVM
If x1 … xn training examples,
sign(iixiTx) “decides” where x falls
Train i to achieve best margin
margin
Give up trying to provide a likelihood function (a generative model) of the input data. Instead, focus on separating the different classes.
Decision Rule:
red: vTx > 0 v
Large Margin for |v| < 1 
Margin of 1 for small |v|

28. Discriminative protein classification
Jaakkola, Diekhans, Haussler, ISMB 1999
Define the discriminating function to be
L(X) = XiH1 i K(X, Xi) - XjH0 j K(X, Xj)
We decide X  family H whenever L(X) > 0
For now, let’s just assume K(.,.) is a similarity function
Then, we want to train i so that this classifier makes as few mistakes as possible in the new data
Similarly to SVMs, train i so that margin is largest for 0  i  1

29. Discriminative protein classification
Ideally, for training examples, L(Xi) ≥ 1 if Xi  H1, L(Xi)  -1 otherwise
This is not always possible; softer constraints are obtained with the following objective function
J() = XiH1 i(2 - L(Xi)) - XjH0 j(2 + L(Xj))
Training: for Xi  H, try to “make” L(Xi) = 1
1 - L(Xi) + i K(Xi, Xi)
i  ; with minimum allowable value 0, and maximum 1
K(Xi, Xi)
Similarly, for Xi  H0 try to “make” L(Xi) = -1

30. The Fisher Kernel The function K(X, Y) compares two sequences
Acts effectively as an inner product in a (non-Euclidean) space
Called “Kernel”
Has to be positive definite
For any X1, …, Xn, the matrix K: Kij = K(Xi, Xj) is such that
For any X  Rn, X ≠ 0, XT K X > 0
Choice of this function is important
Consider P(X | H1, ) – sufficient statistics
How many expected times X takes each transition/emission M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1

31. The Fisher Kernel Fisher score
UX =  log P(X | H1, )
Quantifies how each parameter contributes to generating X
For two different sequences X and Y, can compare UX, UY
D2F(X, Y) = ½ 2 |UX – UY|2
Given this distance function, K(X, Y) is defined as a similarity measure:
K(X, Y) = exp(-D2F(X, Y))
Set  so that the average distance of training sequences Xi  H1 to sequences Xj  H0 is 1
Question:
Is partial derivative larger when
X “uses” a given parameter I
more or less often?
Question:
Is partial derivative larger when
a given parameter I is
larger or smaller? M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1

32. The Fisher Kernel
In summary, to distinguish between family H1 and (non-family) H0, define
Profile H1
UX =  log P(X | H1, ) (Fisher score)
D2F(X, Y) = ½ 2 |UX – UY|2 (distance)
K(X, Y) = exp(-D2F(X, Y)), (akin to dot product)
L(X) = XiH1 i K(X, Xi) – XjH0 j K(X, Xj)
Iteratively adjust  to optimize
J() = XiH1 i(2 - L(Xi)) – XjH0 j(2 + L(Xj))

33. The Fisher Kernel
If a given superfamily has more than one profile model,
Lmax(X) = maxi Li(X) = maxi (XjHi j K(X, Xj) – XjH0 j K(X, Xj))
Superfamily
Family M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1 M1 M2 Mm
BEGIN I0 I1
Im-1 D1 D2 Dm
END Im
Dm-1

34. Benchmarks Methods evaluated
BLAST (Altschul et al. 1990; Gish & States 1993)
HMMs using SAM-T98 methodology (Park et al. 1998; Karplus, Barrett, & Hughey 1998; Hughey & Krogh 1995, 1996)
SVM-Fisher
Measurement of recognition rate for members of superfamilies of SCOP (Hubbard et al. 1997)
PDB90 eliminates redundant sequences
Withhold all members of a given SCOP family
Train with the remaining members of SCOP superfamily
Test with withheld data
Question: “Could the method discover a new family of a known superfamily?”
O. Jangmin

35. O. Jangmin

36. Other methods SAM-T98 method
WU-BLAST version 2.0a16 (Althcshul & Gish 1996)
PDB90 database was queried with each positive training examples, and E-values were recorded.
BLAST:SCOP-only
BLAST:SCOP+SAM-T98-homologs
Scores were combined by the maximum method
SAM-T98 method
Same data and same set of models as in the SVM-Fisher
Combined with maximum methods
O. Jangmin

37. Results Metric : the rate of false positives (RFP)
RFP for a positive test sequence : the fraction of negative test sequences that score as good of better than positive sequence
Result of the family of the nucleotide triphosphate hydrolases SCOP superfamily
Test the ability to distinguish 8 PDB90 G proteins from 2439 sequences in other SCOP folds
O. Jangmin

38. Table 1. Rate of false positives for G proteins family
Table 1. Rate of false positives for G proteins family. BLAST = BLAST:SCOP-only, B-Hom = BLAST:SCOP+SAMT-98-homologs, S-T98 = SAMT-98, and SVM-F = SVM-Fisher method
O. Jangmin

40. Running time of Fisher kernel SVM on query X?
QUESTION
Running time of Fisher kernel SVM
on query X?