Protein Quaternary Fold Recognition Using Conditional Graphical Models

Carnegie MellonSchool of Computer Science

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Protein Quaternary Fold Recognition Using Conditional Graphical Models

Yan Liu, Jaime CarbonellVanathi Gopalakrishnan (U Pitt), Peter Weigele (MIT)

Language Technologies InstituteSchool of Computer ScienceCarnegie Mellon University

IJCAI-2007 – Hyderabad, India


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Snapshot of Cell BiologyNobelprize.org

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Protein function

DSCTFTTAAAAKAGKAKAG

Protein sequence

Protein structure


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Example Protein Structures

Adenovirus Fibre Shaft Virus Capsid

Triple beta-spiral fold in Adenovirus Fiber Shaft


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Predicting Protein Structures• Protein Structure is a key determinant of protein function

• Crystalography to resolve protein structures experimentally in-vitro is very expensive, NMR can only resolve very-small proteins

• The gap between the known protein sequences and structures: 3,023,461 sequences v.s. 36,247 resolved structures (1.2%) Therefore we need to predict structures in-silico


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Quaternary Folds and Alignments

• Protein fold Identifiable regular arrangement of secondary structural elements

• Thus far, a limited number of protein folds have been discovered (~1000)

Very few research work on quaternary folds • Complex structures and few labeled data

• Quaternary fold recognition

Seq 1: APA FSVSPA … SGACGP ECAESGSeq 2 : DSCTFT…TAAAAKAGKAKCSTITL

Biology task

Protein fold Membership and non-membership proteins

Will the protein take the fold?

AI task Pattern to be induced

Training data (seq-struc pairs + physics)

Does the pattern appear in the testing sequence?


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Previous Work• Sequence similarity perspective

Sequence similarity searches, e.g. PSI-BLAST [Altschul et al, 1997]

Profile HMM, .e.g. HMMER [Durbin et al, 1998] and SAM [Karplus et al, 1998]

Window-based methods, e.g. PSI_pred [Jones, 2001]

• Physical forces perspective Homology modeling or threading, e.g. Threader [Jones, 1998]

• Structural biology perspective Painstakingly hand-engineered methods for specific structures, e.g. αα- and ββ- hairpins, β-turn and

β-helix [Efimov, 1991; Wilmot and Thornton, 1990; Bradley at al, 2001]

Generative models based on rough approximation of free-energy, perform very poorly on complex structures

Very Hard to generalize due to built-in constants, fixed features

Fail to capture the structure properties and long-range dependencies


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Conditional Random Fields• Hidden Markov model (HMM) [Rabiner, 1989]

• Conditional random fields (CRFs) [Lafferty et al, 2001]

Model conditional probability directly (discriminative models, directly optimizable)

Allow arbitrary dependencies in observation Adaptive to different loss functions and

regularizers Promising results in multiple applications But, need to scale up (computationally) and

extend to long-distance dependencies

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( ) ( | ) ( | )N

i i i ii

P P x y P y y

x, y

11 10

1( ) exp( ( , , , ))

N K

k k i ii k

P f i y yZ

y | x x

1 1( , , , ) ' ( , ) ( , ')k i i k i if i y y f i I y s y s x x


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• Outputs Y = {M, {Wi} }, where Wi = {pi, qi, si}

• Feature definition Node feature

Local interaction feature

Long-range interaction feature

Our Solution: Conditional Graphical Models

1 1 1( , , ) ( , ', 1)k i i i i i if w w x I s s s s p q

( , ) '( , , ) ( ', 1 ')k i k i i i i if w x f x p q I s s q p d

Long-range dependencyLocal dependency

1( , , ) '( , , , , ) ( , ')k i j k i i j j i if w w x g x p q p q I s s s s


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Linked Segmentation CRF

• Node: secondary structure elements and/or simple fold• Edges: Local interactions and long-range inter-chain and

intra-chain interactions• L-SCRF: conditional probability of y given x is defined as

, , ,

1 1 , , ,,

1( ,..., | ,..., ) exp( ( , )) exp( ( , , , ))

i j G i j a b G

R R k k i i j l k i a i j a bV k lE

P f g yZ

y y y

y y x x x y x x y

Joint Labels


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• Classification:

• Training : learn the model parameters λ Minimizing regularized negative log loss

Iterative search algorithms by seeking the direction whose empirical values agree with the expectation

• Complex graphs results in huge computational complexity

Linked Segmentation CRF (II)

( | )( ( , ) [ ( , )]) ( ) 0G

k c p k cc Ck

Lf E f

y xx y x y

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( , ) log ( )G

K

k k cc C k

L f Z

x y

1

* arg max ( , )G

K

k k cc C k

y f Y

x


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Approximate Inference of L-SCRF

• Most approximation algorithms cannot handle variable number of nodes in the graph, but we need variable graph topologies, so…

• Reversible jump MCMC sampling [Greens, 1995, Schmidler et al,

2001] with Four types of Metropolis operators State switching Position switching Segment split Segment merge

• Simulated annealing reversible jump MCMC [Andireu et al, 2000]

Replace the sample with RJ MCMC Theoretically converge on the global optimum


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Experiments: Target Quaternary Fold

• Triple beta-spirals [van Raaij et al. Nature 1999]

Virus fibers in adenovirus, reovirus and PRD1

• Double barrel trimer [Benson et al, 2004]

Coat protein of adenovirus, PRD1, STIV, PBCV


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Features for Protein Fold Recognition


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Tertiary Fold Recognition: β-Helix fold

• Histogram and ranks for known β-helices against PDB-minus dataset

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Chain graph model reduces the real running time of SCRFs model by around 50 times


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Fold Alignment Prediction: β-Helix• Predicted alignment for known β -helices on cross-family

validation


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Discovery of New Potential β-helices

• Run structural predictor seeking potential β-helices from Uniprot (structurally unresolved) databases Full list (98 new predictions) can be accessed at

www.cs.cmu.edu/~yanliu/SCRF.html

• Verification on 3 proteins with later experimentally resolved structures from different organisms 1YP2: Potato Tuber ADP-Glucose Pyrophosphorylase 1PXZ: The Major Allergen From Cedar Pollen GP14 of Shigella bacteriophage as a β-helix protein

No single false positive!


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Experiment Results: Fold Recognition

Double barrel-trimerTriple beta-spirals


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Experiment Results: Alignment Prediction

Triple beta-spirals

Four states: B1, B2, T1 and T2

Correct Alignment:

B1: i – o B2: a - h

Predicted Alignment

B1 B2


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Experiment Results:Discovery of New Membership Proteins

• Predicted membership proteins of triple beta-spirals can be accessed at

http://www.cs.cmu.edu/~yanliu/swissprot_list.xls

• Membership proteins of double barrel-trimer suggested by biologists [Benson, 2005] compared with L-SCRF predictions


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Conclusion• Conditional graphical models for protein structure

prediction Effective representation for protein structural properties Feasibility to incorporate different kinds of informative

features Efficient inference algorithms for large-scale applications

• A major extension compared with previous work Knowledge representation through graphical models Ability to handle long-range interactions within one chain

and between chains

• Future work Automatic learning of graph topology Applications to other domains


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Graphical Models

• A graphical model is a graph representation of probability dependencies [Pearl 1993; Jordan 1999]

Node: random variables Edges: dependency relations

• Directed graphical model (Bayesian networks)

• Undirected graphical model (Markov random fields)

11..

( ,.., ) ( | parents( ))n i ii n

P x x P x x

1

1 1( ,.., ) ( ) exp( ( ))n c c c

c C c C

P x x x H xZ Z

Documents

Protein Quaternary Fold Recognition Using Conditional Graphical Models