Zhiyong Wang and Jinbo Xu Toyota Technological Institute at Chicago

1. PhyCMAP: Predicting protein contact map using evolutionary and physical constraints by integer programming Zhiyong Wang and JinboXu Toyota Technological Institute at Chicago Web server at http://raptorx.uchicago.edu See http://arxiv.org/abs/1308.1975 for an extended version

2. Problem Definition Contact : Distance between two Cα or Cβ atoms < 8Å 1J8B short range: 6-12 AAs apart medium range: 12-24 AAs long range: >24 AAs apart

3. Existing Work Residue co-evolution method: mutual information (MI), PSICOV, Evfold • Needs a large number of homologous sequences • PSICOV and Evfold better than MI since they differentiate direct and indirect residue couplings(Residues A and C indirect couplingif it is due to direct A-B and B-C couplings) • PSICOV and Evfold also enforce sparsity Supervised learning method: NNcon, SVMcon, CMAPpro • Mutual information, sequence profile and others • Predicts contacts one by one, ignoring their correlation • Do not differentiate direct and indirect residue couplings First-principle method: Astro-Fold • No evolutionary information • Minimize contact potential • Enforce physical feasibility including sparsity

4. Our Method: PhyCMAP 1. Focus on proteins with few sequence homologs • proteins with many sequence homologs very likely have similar templates in PDB 2. Integrate by machine learning • seq profile, residue co-evolution and non-evolutionary info • (implicitly) differentiate direct and indirect residue couplings through feature engineering 3. Enforce physical constraints, which imply sparsity

5. Info used by Random Forests • Evolution info from a single protein family • sequence profile • co-evolution: 2 types of mutual information (MI) • Non-evolution info from the whole structure space: residue contact potential • Mixed info from the above 2 sources • homologous pairwise contact score • EPAD: context-specific evolutionary-based distance-dependent statistical potential • amino acid physic-chemical properties

6. Mutual Information 1. Contrastive Mutual Information (CMI): remove local background by measuring the MI difference of one pair with its neighbors. 2. Chaining effect of residue couplings: MI, MI2, MI3,MI4, equivalent to (1-MI), (1-MI)2, (1-MI)3, (1-MI)4(see http://arxiv.org/abs/1308.1975 for more details)

7. CMI Example: 1J8B • Upper triangle: mutual information • Lower triangle: contrastive mutual information • Blue boxes: native contacts

8. Homologous Pairwise Contact Score Probability of a residue pair forming a contact between 2 secondary structures. PSbeta (a, b): prob of two AAs a and b forming a beta contact PShelix (a, b): prob of two AAs a and b forming a helix contact H: the set of sequence homologs in a multiple seq alignment

9. Training Random Forests • Training dataset • Chosen before CASP10 started • 900 non-redundant protein structures • <25% sequence identity • All contacts and 20% of non-contacts • Model parameters • Number of features: 300 • Number of trees: 500 • 5 fold cross validation

10. Select Physically Feasible Contacts by Integer Linear Programming Maximize accumulative contact probability while minimize violation of physical constraints

11. Soft Constraints 1 # contacts between two secondary structure segments is limited

12. Soft Constraints 2 Upper and lower bounds for #contacts between two beta strands

13. Soft Constraints 3 Statistics shows that only 3.4% of loop segments that have a contact between the start and end residues.

14. Hard Constraints 1 • For parallel contacts between two β strands, the contacts of neighboring residue pairs should satisfy the following constraints • For anti-parallel contacts

15. Hard Constraints 2 1) One residue cannot form contacts with both j and j+2 when j and j+2 are in the same alpha helix 2) One beta-strand can form beta-sheets with up to 2 other beta-strands.

16. Test Datasets • CASP10: 123 proteins • 36 are “hard”, i.e., no similar templates in PDB • low sequence identity (<25%) among them • low seq id with the training data, which were chosen before CASP10 started • Set600: 601 proteins • share <25% seq ID with the training proteins • each has ≥50 AAs and an X-ray structure with resolution <1.9Å • each has ≥5 AAs with predicted secondary structure being alpha-helix or beta-strand

17. Accuracy w.r.t. #sequence homologs • Meff: #non-redundant sequence homologs of a protein • Divide the CASP10 targets into groups by Meff • Top L/10 predicted medium- and long-range contacts accuracy logMeff

18. Results on CASP10 – Medium Range Overall accuracy on top L/5 predicted Cβ contacts: PhyCMAP 0.465, CMAPpro0.370, PSICOV 0.316 PhyCMAP PhyCMAP PSICOV CMAPpro

19. Results on CASP10 – Long Range Overall accuracy on top L/5 predicted Cβcontacts: PhyCMAP: 0.373, CMAPpro: 0.313, PSICOV: 0.315 PhyCMAP PhyCMAP CMAPpro PSICOV

20. Results on 36 hard CASP10 targets accuracy on top L/5 medium and long-range Cβ contacts: PhyCMAP: 0.363, CMAPpro: 0.308, PSICOV: 0.180 PhyCMAP PhyCMAP CMAPpro PSICOV

21. Results on Set600 with few homologs (Meff ≤ 100) top L/5 predicted medium and long Cβcontacts: PhyCMAP: 0.345, CMAPpro: 0.287, PSICOV: 0.059 PhyCMAP PhyCMAP PSICOV CMAPpro

22. Example: T0677-D2 Dozens of sequence homologs Meff=31 Upper triangle: native Cβcontacts Left lower triangle: PhyCMAP accuracy 0.357 Right lower triangle: Evfold accuracy ~0 Note contacts between alpha helices are not continuous

23. Example: T0693-D2 Many sequence homologs Meff=2208 Upper triangles: native Cβcontacts Left lower triangle: PhyCMAPaccuracy 0.744 Right lower triangle: Evfold accuracy 0.419

24. Example: T0701-D1 Many sequence homologs Meff=3300 Upper triangle: native Cβ contacts Left lower triangle: PhyCMAP accuracy 0.794 Right lower triangle: Evfold accuracy 0.444

25. Example: T0756-D1 Many sequence homologs Meff=1824 Upper triangles: native Cβcontacts Left lower triangle: PhyCMAP accuracy 0.944 Right lower triangle: Evfold accuracy 0.500

26. Summary • Combining seq profile, residue co-evolution, non-evolutionary info can result in good accuracy even for proteins with 10--100 non-redundant seq homologs • Physical constraints are helpful for proteins with few sequence homologs Cβaccuracy on 130 proteins Meff ≤ 100

27. Acknowledgements • Student: Zhiyong Wang • Funding • NIH R01GM0897532 • NSF CAREER award • Alfred P. Sloan Research Fellowship • Computational resources • University of Chicago Beagle team • TeraGrid Web server at http://raptorx.uchicago.edu

28. Protein contact Contact : Distance between two Cα or Cβ atoms < 8Å; or Distance between the closest atoms of 2 residues. 1J8B short range: 6-12 AAs apart medium range: 12-24 AAs long range: >24 AAs apart

29. Why contact prediction? • Contacts describe spatial and functional relationship of residues • Contains key information for 3D structure • Useful for protein structure prediction • Used for protein structure alignment and classification

30. Contrastive Mutual Information Contrastive Mutual Information (CMI) removes local background, by measuring the MI difference between one pair of residues and neighboring pairs.

31. Integer Linear Programming • Objective function: • g(R): penalty for violation of physical constraints

32. Hard Constraints 3 One beta-strand can form beta-sheets with up to 2 other beta-strands.

33. Global constraints • Antiparallel and parallel contacts • A residue contact implies a segment-wise contact • Put a limit of total number of contacts • kis the number of top contacts we want to predict.

34. Results on Set600 with many sequence homologs (Meff > 100) top L/5 predicted medium and long Cβcontacts: PhyCMAP: 0.611, CMAPpro: 0.515, PSICOV: 0.569 PhyCMAP PhyCMAP CMAPpro PSICOV

35. Contribution of HPS and CMI features Average Cβaccuracy the 471 proteins with Meff>100

36. Contribution of physical constraints Average Cβaccuracy on 130 proteins with Meff ≤ 100