Protein Quaternary Fold Recognition Using Conditional Graphical Models

1. Protein Quaternary Fold Recognition Using Conditional Graphical Models Yan Liu, Jaime Carbonell Vanathi Gopalakrishnan (U Pitt), Peter Weigele (MIT) Language Technologies Institute School of Computer Science Carnegie Mellon University IJCAI-2007 – Hyderabad, India

2. Nobelprize.org DSCTFTTAAAAKAGKAKAG Protein sequence + Protein function Protein structure Snapshot of Cell Biology

3. Example Protein Structures Triple beta-spiral fold in Adenovirus Fiber Shaft Adenovirus Fibre Shaft Virus Capsid

4. 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

5. Seq 1: APA FSVSPA … SGACGPECAESG Seq 2 : DSCTFT…TAAAAKAGKAKCSTITL 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

6. 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] Fail to capture the structure properties and long-range dependencies 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

7. 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

8. Our Solution: Conditional Graphical Models Local dependency Long-range dependency • Outputs Y = {M, {Wi} }, where Wi = {pi, qi, si} • Feature definition • Node feature • Local interaction feature • Long-range interaction feature

9. Joint Labels 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

10. Linked Segmentation CRF (II) • Classification: • Training : learn the model parametersλ • 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

11. 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] withFour 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

12. 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

13. Features for Protein Fold Recognition

14. Tertiary Fold Recognition: β-Helix fold • Histogram and ranks for known β-helices against PDB-minus dataset 5 Chain graph model reduces the real running time of SCRFs model by around 50 times

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

16. 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!

17. Experiment Results: Fold Recognition Triple beta-spirals Double barrel-trimer

18. Triple beta-spirals Four states: B1, B2, T1 and T2 Correct Alignment: B1: i – o B2: a - h Predicted Alignment B1 B2 Experiment Results: Alignment Prediction

19. 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

20. 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

22. 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)