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

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Problem Definition Contact : Distance between two C α or C β atoms < 8Å short range: 6-12 AAs apart medium range: 12-24 AAs long range: >24 AAs apart 1J8B

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Existing Work Residue co-evolution method: mutual information (MI), PSICOV, Evfold N eeds 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 coupling if 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

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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

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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

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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, MI 2, MI 3, MI 4, equivalent to (1-MI), (1-MI) 2, (1-MI) 3, (1-MI) 4 (see http://arxiv.org/abs/1308.1975 for more details) http://arxiv.org/abs/1308.1975

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

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

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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

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Select Physically Feasible Contacts by Integer Linear Programming Maximize accumulative contact probability while minimize violation of physical constraints X i,j Indicate one contact between two residues i and j RrRr a relaxation variable of the r th soft constraint g(R) penalty for violation of physical constraints

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Soft Constraints 1 # contacts between two secondary structure segments is limited s1,s295%Max H,H512 H,E310 H,C411 E,H412 E,E913 E,C615 C,H312 C,E512 C,C620

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

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

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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

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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.

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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

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Accuracy w.r.t. #sequence homologs 1.M eff : #non-redundant sequence homologs of a protein 2.Divide the CASP10 targets into groups by M eff 3.Top L/10 predicted medium- and long-range contacts logM eff accuracy

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Results on CASP10 – Medium Range Overall accuracy on top L/5 predicted C β contacts: PhyCMAP 0.465, CMAPpro 0.370, PSICOV 0.316 CMAPpro PSICOV PhyCMAP

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Results on CASP10 – Long Range Overall accuracy on top L/5 predicted C β contacts: PhyCMAP: 0.373, CMAPpro: 0.313, PSICOV: 0.315 CMAPproPSICOV PhyCMAP

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

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

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

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Example: T0693-D2 Many sequence homologs Meff=2208 Upper triangles: native C β contacts Left lower triangle: PhyCMAP accuracy 0.744 Right lower triangle: Evfold accuracy 0.419

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

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Example: T0756-D1 Many sequence homologs Meff=1824 Upper triangles: native C β contacts Left lower triangle: PhyCMAP accuracy 0.944 Right lower triangle: Evfold accuracy 0.500

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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 C β accuracy on 130 proteins Meff ≤ 100

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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

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Protein contact Contact : Distance between two C α or C β 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

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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

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

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Integer Linear Programming Objective function: g(R): penalty for violation of physical constraints VariablesExplanations X i,j equal to 1 if there is a contact between two residues i and j. AP u,v equal to 1 if two beta-strands u and v form an anti-parallel beta-sheet. P u,v equal to 1 if two beta-strands u and v form a parallel beta-sheet. S u,v equal to 1 if two beta-strands u and v form a beta-sheet. T u,v equal to 1 if there is an alpha-bridge between two helices u and v. RrRr a non-negative integral relaxation variable of the r th soft constraint.

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

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

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

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Contribution of HPS and CMI features Average C β accuracy the 471 proteins with M eff >100

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Contribution of physical constraints Average C β accuracy on 130 proteins with Meff ≤ 100

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