Protein Classification New PDB structures PDB Growth Protein
Protein Classification
New PDB structures PDB Growth
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 40 55 Membrane & cell surface 42 82 91 Small proteins 72 104 162 Total 887 1447 2630 Morten Nielsen, CBS, Bio. Centrum, DTU
Protein structure classification Protein fold Protein world Protein superfamily Protein family Morten Nielsen, CBS, Bio. Centrum, DTU
Structure Classification Databases • SCOP § Manual classification (A. Murzin) § scop. berkeley. edu • CATH § Semi manual classification (C. Orengo) § www. biochem. ucl. ac. uk/bsm/cath • FSSP § Automatic classification (L. Holm) § www. ebi. ac. uk/dali/fssp. html Morten Nielsen, CBS, Bio. Centrum, 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, Bio. Centrum, DTU
All a: Hemoglobin (1 bab) Morten Nielsen, CBS, Bio. Centrum, DTU
All b: Immunoglobulin (8 fab) Morten Nielsen, CBS, Bio. Centrum, DTU
a/b: Triosephosphate isomerase (1 hti) Morten Nielsen, CBS, Bio. Centrum, DTU
a+b: Lysozyme (1 jsf) Morten Nielsen, CBS, Bio. Centrum, DTU
Families • Proteins whose evolutionarily relationship is readily recognizable from the sequence (>~25% sequence identity) Fold Superfamily • Families are further subdivided into Proteins Family • Proteins are divided into Species § The same protein may be found in several species Proteins Morten Nielsen, CBS, Bio. Centrum, DTU
Superfamilies • Proteins which are (remote) evolutionarily related § Sequence similarity low Fold Superfamily § Share function § Share special structural features • Relationships between members of a superfamily may not be readily recognizable from the sequence alone Family Proteins Morten Nielsen, CBS, Bio. Centrum, DTU
Folds • Proteins which have >~50% secondary structure elements Fold arranged the in the same order in the protein chain and in three dimensions are classified as having Superfamily the same fold • No evolutionary relation between proteins Family Proteins Morten Nielsen, CBS, Bio. Centrum, DTU
Protein Classification • Given a new protein, can we place it in its “correct” position within an existing protein hierarchy? Fold Methods • BLAST / Psi. BLAST new protein Superfamily ? Family • Profile HMMs • Supervised Machine Learning methods Proteins
PSI-BLAST Given a sequence query x, and database D 1. 2. 3. 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 • 4. 5. 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
Profile HMMs D 1 BEGIN I 0 D 2 I 1 M 1 Dm-1 Dm Im-1 M 2 Im END Mm 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)
Classification with Profile HMMs Fold D 1 Superfamily BEGIN I 0 Dm-1 D 2 I 1 M 1 Dm Im-1 END Im Mm M 2 Family new protein ? D 1 BEGIN I 0 D 2 I 1 M 1 Dm-1 Dm Im-1 M 2 D 1 Im Mm END BEGIN I 0 D 2 I 1 M 1 Dm-1 Dm Im-1 M 2 Im Mm END
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 | H 1) P(H 1|X) L(X) = log ------------- = log -------P(X | H 0) P(H 0|X)
Generation of a protein by a profile HMM P(X | H) ? ? To generate sequence x 1…xn by profile HMM H: We will find the sum probability of all possible ways to generate X • Define § Aj. M(i): probability of generating x 1…xi and ending with xi being emitted from Mj § Aj. I(i): probability of generating of x 1…xi and ending with xi being emitted from Ij § Aj. D(i): probability of generating of x 1…xi and ending in Dj • (xi is the last character emitted before Dj)
Alignment of a protein to a profile HMM Aj. M(i) = εM(j)(xi) * { Aj-1 M(i – 1) + log αM(j-1)M(j) + Aj-1 I(i – 1) + log αI(j-1)M(j) + Aj-1 D(i – 1) + log αD(j-1)M(j) } Aj. I(i) = εI(j)(xi) * { Aj. M(i – 1) + log αM(j)I(j) + Aj. I(i – 1) + log αI(j) + Aj. D(i – 1) + log αD(j)I(j) } Aj. D(i) = { Aj-1 M(i) + log αM(j-1)D(j) + Aj-1 I(i) + log αI(j-1)D(j) + Aj-1 D(i) + log αD(j-1)D(j) }
Generative Models
Generative Models
Generative Models
Generative Models
Generative Models
Discriminative Methods Instead of modeling the process that generates data, directly discriminate between classes • More direct way to the goal • Better if model is not accurate
Discriminative Models -- SVM If x 1 … xn training examples, margin sign( i ixi. Tx) “decides” where x falls • Train i to achieve best margin Decision Rule: red: v. Tx > 0 v Large Margin for |v| < 1 Margin of 1 for small |v|
Discriminative protein classification Jaakkola, Diekhans, Haussler, ISMB 1999 • Define the discriminating function to be L(X) = Xi H 1 i K(X, Xi) - Xj H 0 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
Discriminative protein classification • Ideally, for training examples, L(Xi) ≥ 1 if Xi H 1, L(Xi) -1 otherwise • This is not always possible; softer constraints are obtained with the following objective function J( ) = Xi H 1 i(2 - L(Xi)) - Xj H 0 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 H 0 try to “make” L(Xi) = -1
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 X 1, …, 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 | H 1, ) – sufficient statistics § How many expected times X takes each transition/emission D 1 BEGIN I 0 D 2 I 1 M 1 Dm-1 Dm Im-1 M 2 Im Mm END
The Fisher Kernel • Fisher score Question: § UX = log P(X | H 1, ) Is partial derivative larger when § Quantifies how each parameter contributes to generating X X “uses” a given parameter I more or. Uless § For two different sequences X and Y, can compare X, Uoften? Y • D 2 F(X, Y) = ½ 2 |UX – UY|2 • Given this distance function, K(X, Y) is defined as a similarity measure: Question: § K(X, Y) = exp(-D 2 F(X, Y)) Is partial derivative § Set so that the average distance of training sequences Xi larger H 1 to when a given parameter I is sequences Xj H 0 is 1 larger or smaller? D 1 BEGIN I 0 D 2 I 1 M 1 Dm-1 Dm Im-1 M 2 Im Mm END
The Fisher Kernel • In summary, to distinguish between family H 1 and (non-family) H 0, define § § Profile H 1 UX = log P(X | H 1, ) D 2 F(X, Y) = ½ 2 |UX – UY|2 K(X, Y) = exp(-D 2 F(X, Y)), § L(X) = Xi H 1 i K(X, Xi) – (Fisher score) (distance) (akin to dot product) Xj H 0 j K(X, Xj) • Iteratively adjust to optimize § J( ) = Xi H 1 i(2 - L(Xi)) – Xj H 0 j(2 + L(Xj))
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 H 0 j K(X, Xj)) Superfamily Family D 1 BEGIN I 0 D 2 I 1 M 1 Dm-1 Dm Im-1 M 2 D 1 Im Mm END BEGIN I 0 D 2 I 1 M 1 Dm-1 Dm Im-1 M 2 Im Mm END
Benchmarks • Methods evaluated § BLAST (Altschul et al. 1990; Gish & States 1993) § HMMs using SAM-T 98 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) § § § PDB 90 eliminates redundant sequences Withhold all members of a given SCOP family Train with the remaining members of SCOP superfamily Test withheld data Question: “Could the method discover a new family of a known superfamily? ” O. Jangmin
O. Jangmin
Other methods • WU-BLAST version 2. 0 a 16 (Althcshul & Gish 1996) § PDB 90 database was queried with each positive training examples, and E -values were recorded. § BLAST: SCOP-only § BLAST: SCOP+SAM-T 98 -homologs § Scores were combined by the maximum method • SAM-T 98 method § Same data and same set of models as in the SVM-Fisher § Combined with maximum methods O. Jangmin
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 PDB 90 G proteins from 2439 sequences in other SCOP folds O. Jangmin
Table 1. Rate of false positives for G proteins family. BLAST = BLAST: SCOP-only, B-Hom = BLAST: SCOP+SAMT-98 -homologs, S -T 98 = SAMT-98, and SVM-F = SVM-Fisher method O. Jangmin
QUESTION Running time of Fisher kernel SVM on query X?
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