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Protein Structural Prediction

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  1. Protein Structural Prediction

  2. Structure Determines Function The Protein Folding Problem • What determines structure? • Energy • Kinematics • How can we determine structure? • Experimental methods • Computational predictions

  3. Protein Structure Prediction • ab initio • Use just first principles: energy, geometry, and kinematics • Homology • Find the best match to a database of sequences with known 3D-structure • Threading • Meta-servers and other methods

  4. Threading • Threading is the golden mean between homology-based prediction and molecular modeling (?) MTYKLILN …. NGVDGEWTYTE Main difference between homology-based prediction and threading: Threading uses the structure to compute energy function during alignment

  5. Threading – Overview • Build a structural template database • Define a sequence–structure energy function • Apply a threading algorithm to query sequence • Perform local refinement of secondary structure • Report best resulting structural model

  6. Threading Search Space Protein Sequence X Protein Structure Y MTYKLILNGKTKGETTTEAVDAATAEKVFQYANDNGVDGEWTYTE

  7. Threading – Template Database • FSSP, SCOP, CATH • Remove pairs of proteins with highly similar structures • Efficiency • Statistical skew in favor of large families

  8. Threading – Energy Function MTYKLILNGKTKGETTTEAVDAATAEKVFQYANDNGVDGEWTYTE how well a residue fits a structural environment: Es how preferable to put two particular residues nearby: Ep how often a residue mutates to the template residue: Em alignment gap penalty: Eg compatibility with local secondary structure prediction: Ess total energy:wmEm + wsEs + wpEp + wgEg + wssEss

  9. Threading – Formulation • Contact graph captures amino acid interactions • Cores represent important local structure units • No gaps within each core x y z u Ci v Cj x y z C1 C2 C3 C4 u v a λ0 t1a λ1 t4a λ4 λ3 λ2 t3a t2a

  10. Threading – Formulation CMG = (v, )

  11. Threading – Formulation From Lathrop & Smith

  12. Threading Search Space Protein Sequence X Protein Structure Y How Hard is Threading? MTYKLILNGKTKGETTTEAVDAATAEKVFQYANDNGVDGEWTYTE CORES

  13. 1 7 2 6 3 4 5 How Hard is Threading? • At least as hard as MAX-CUT MAX-CUT: Given graph G = (V, E), find a cut (S, T) of V with maximum number of edges between S and T. The Bad News: APX-complete even when each node has at most B edges (where B>2)

  14. 1 7 2 6 3 4 5 Reduction of MAX-CUT to Threading • |V| cores, each core i has length 1 and corresponds to vi • Let Ep(0,1) = 1: every edge labeled 0-1 or 1-0 gets a score of 1 • Then, size of cut = threading score 0101 01 01 010101 v1 v2 v3 v4 v5 v6 v7 Sequence consists of |V| 01-pairs

  15. Threading with Branch & Bound • Set of solutions can be partitioned into subsets (branch) • Upper limit on a subset’s solution can be computed fast (bound) Branch & Bound • Select subset with best possible bound • Subdivide it, and compute a bound for each subset

  16. Threading with Branch & Bound • Key to this algorithm is tradeoff on lower bound • efficient • tight

  17. Threading with Integer Programming maximize z = 6x+5y Linear function Subject to Linear Program Integer Program 3x+y ≤ 11 -x+2y ≤ 5 x, y ≥ 0 Linear constraints Integral constraints (nonlinear) x, y  {0, 1} RAPTOR: integer programming-based threading perhaps the best protein threading system

  18. Threading with Integer Programming x(i,k) denotes that core i is aligned to sequence position k y(i,k,j,l) denotes that core i is aligned to position k and core j is aligned to position l D(i) all positions where core i can be aligned to R(i, j, k) set of possible alignments of core j, given that core i aligns to position k corei (headi, taili, lengthi = taili – headi + 1)

  19. Threading with Integer Programming Cores are aligned in order Each y variable is 1 if and only if its two x variables are 1 – x and y represent exactly the same threading Each core has only one alignment position

  20. Energy Function is Linear • Sequence substitution score • Fitness of aa in each position (example, hydrophobicity) • Agreement with secondary structure prediction • Pairwise interaction between two cores • Gap between two successive cores

  21. LP Relaxation and (again) Branch & Bound • Relax the integral constraint, to x(i,j), y(i,k,j,l)  0 • Solve the LP using a standard method (RAPTOR uses IBM’s OSL) • If resulting solution is integral, done • Else, select one non-integral variable (heuristically), and generate two subproblems by setting it to 0, and 1 -- use Branch & Bound In practice, in RAPTOR only 1% of the instances in the test database required step 4; almost all solutions are integral !!!

  22. CAFASP GOAL The goal of CAFASP is to evaluate the performance of fully automatic structure prediction servers available to the community. In contrast to the normal CASP procedure, CAFASP aims to answer the question of how well servers do without any intervention of experts, i.e. how well ANY user using only automated methods can predict protein structure. CAFASP assesses the performance of methods without the user intervention allowed in CASP.

  23. Performance Evaluation in CAFASP3 Servers with name in italic are meta servers MaxSub score ranges from 0 to 1 Therefore, maximum total score is 30 (, released in December, 2002.)

  24. One structure where RAPTOR did best Red: true structure Blue: correct part of prediction Green: wrong part of prediction • Target Size:144 • Super-imposable size within 5A: 118 • RMSD:1.9

  25. Some more results by other programs

  26. Some more results by other programs

  27. Some more results by other programs

  28. Structural Motifs beta helix beta barrel beta trefoil

  29. Structural Motif Recognition • Secondary Structure Prediction • Find the  helices,  sheets, loops in a protein sequence • Given an amino acid residue sequence, does it fold as a • Coiled Coil? •  helix? •  barrel? • Zinc finger? • Intermediate goals towards folding • Useful information about the function of a protein • More amenable to sequence analysis, than full fold prediction

  30. Structural Motif Recognition • Collect a database of known motifs and corresponding amino acid subsequences • Devise a method/model to “match” a new sequence to existing motif database • Verify computationally on a test set (divide database into training and testing subsets) • Verify in lab

  31. Structural Motif Recognition Methods • Alignment • Neural Nets • Hidden Markov Models • Threading • Profile-based Methods • Other Statistical Methods

  32. Predicting Coiled Coils

  33. Predicting Coiled Coils • NewCoils: multiply probs of frequencies in each coiled coil position

  34. Predicting Coiled Coils • PairCoil: multiply pairwise probs of spatially neighboring positions • Use a sliding window of length 28 • Perfect score separation between true and false examples (false = non-coil-coil  helices) • Berger et al. PNAS 1995

  35. Predicting  helices • Helix composed of three parallel  sheets • Very few solved structures, very different from one another • Absent in eukaryotes! • Probably evolved subsequent to prok/euk split

  36. Predicting  helices • Only available program: BetaWrap • The rungs subproblem Given the location of a T2 turn of one rung, find location of T2 turn of next rung • Distribution of turn lengths • Bonus/penalty for stacked pairs in the parallel strands • Discard if highly charged residues in the inward-point positions of  strand • From a rung to multiple rungs • Find multiple initial B2-T2-B3 rungs • Use sequence template based on hydrophobicity to find many candidate rungs • Find “optimal wrap” by DP + heuristic score, based on 5 consistent rungs • Completing the parse • Find B1 strands by locally optimizing their location

  37. Predicting  helices • BetaWrap gives scores that separate true from false  helices Bradley et al. PNAS 2001

  38. Predicting  trefoils Similar idea – use a combination of domain-specific expert knowledge with statistics WRAP-AND-PACK WRAP: Search for antiparallel  strands to “wrap” a cap PACK: Place the side chains in the interior of the wrapped  strands

  39. Predicting Secondary Structure • Given amino acid sequence, classify positions into  helices,  strands, or loops • In general, harder than protein motif identification • Best methods rely on Neural Networks • Similarly good separation can be achieved by SVMs PSIPRED • Given a sequence x, generate profile using PSI-BLAST • Pass the profile to a pre-trained NN • Output classification:  helix /  strand / loops

  40. PSIPRED Profile M • Training & Testing • Start with database of determined folds (<1.87 Ao) • Remove redundancy: any pair of proteins with high similarity (found by PSI-BLAST) – 187 remaining proteins • 3-fold cross validation • ~76% classification accuracy

  41. PSIPRED server PSIPRED PREDICTION RESULTS Conf: Confidence (0=low, 9=high) Pred: Predicted secondary structure (H=helix, E=strand, C=coil) AA: Target sequence # PSIPRED HFORMAT (PSIPRED V2.3 by David Jones) Conf: 998888872100111210012112359 Pred: CCCCCCCCCCCHHHHHHHHCCCCCCCC AA: PTYPTYPTXXXXXXXXXXXXTEETEET PSIPRED PREDICTION RESULTS Conf: Confidence (0=low, 9=high) Pred: Predicted secondary structure (H=helix, E=strand, C=coil) AA: Target sequence # PSIPRED HFORMAT (PSIPRED V2.3 by David Jones) Conf: 91025687432236422336410232027743223653334679 Pred: CCCCCCCCCCCCCCCCCCCCCCCEEEECCCCCCCCCCCCCCCCC AA: THISISAPRXTEINSEQXENCETHISISAPRXTEINSEQXENCE PSIPRED PREDICTION RESULTS Conf: Confidence (0=low, 9=high) Pred: Predicted secondary structure (H=helix, E=strand, C=coil) AA: Target sequence # PSIPRED HFORMAT (PSIPRED V2.3 by David Jones) Conf: 9888788777656877765688766579 Pred: CCCCCCCCCCCCCCCCCCCCCCCCCCCC AA: PEPTIDEPEPTIDEPEPTIDEPEPTIDE Conf: Confidence (0=low, 9=high) Pred: Predicted secondary structure (H=helix, E=strand, C=coil) AA: Target sequence # PSIPRED HFORMAT (PSIPRED V2.3 by David Jones) Conf: 988888600148777777885001487777778842003789 Pred: CCCCCCCCEECCCCCCCCCCCCEECCCCCCCCCCCCCCCCCC AA: PPEEPPTTIIDDEEPPEEPPTTIIDDEEPPEEPPTTIIDDEE

  42. TRILOGY: Sequence–Structure Patterns • Identify short sequence–structure patterns 3 amino acids • Find statistically significant ones (hypergeometric distribution) • Correct for multiple trials • These patterns may have structural or functional importance • Pseq: R1xa-bR2xc-dR3 • Pstr: 3 C– C distances, & 3 C – C vectors • Start with short patterns of 3 amino acids {V, I, L, M}, {F, Y, W}, {D, E}, {K, R, H}, {N, Q}, {S, T}, {A, G, S} • Extend to longer patterns Bradley et al. PNAS 99:8500-8505, 2002


  44. TRILOGY: Extension Glue together two 3-aa patterns that overlap in 2 amino acids P-score = i:Mpat,…,min(Mseq, Mstr)C(Mseq, i) C(T – Mseq, Mstr – i) C(T, Mstr)-1

  45. TRILOGY: Longer Patterns -- unit found in three proteins with the TIM-barrel fold NAD/RAD binding motif found in several folds Type-II  turn between unpaired  strands Helix-hairpin-helix DNA-binding motif A -hairpin connected with a crossover to a third -strand Three strands of an anti-parallel -sheet A fold with repeated aligned -sheets Four Cysteines forming 4 S-S disulfide bonds

  46. Small Libraries of Structural Fragments for Representing Protein Structures

  47. protein sequence fragment library … Fragment Libraries For Structure Modeling predicted structure known structures

  48. f Small Libraries of Protein Fragments Kolodny, Koehl, Guibas, Levitt, JMB 2002 Goal: Small “alphabet” of protein structural fragments that can be used to represent any structure • Generate fragments from known proteins • Cluster fragments to identify common structural motifs • Test library accuracy on proteins not in the initial set

  49. f Small Libraries of Protein Fragments Dataset: 200 unique protein domains with most reliable & distinct structures from SCOP • 36,397 residues • Divide each protein domain into consecutive fragments beginning at random initial position Library: Four sets of backbone fragments • 4, 5, 6, and 7-residue long fragments • Cluster the resulting small structures into k clusters using cRMS, and applying k-means clustering with simulated annealing • Cluster with k-means • Iteratively break & join clusters with simulated annealing to optimize total variance Σ(x – μ)2

  50. Evaluating the Quality of a Library • Test set of 145 highly reliable protein structures (Park & Levitt) • Protein structures broken into set of overlapping fragments of length f • Find for each protein fragment the most similar fragment in the library (cRMS) Local Fit: Average cRMS value over all fragments in all proteins in the test set Global Fit: Find “best” composition of structure out of overlapping fragments • Complexity is O(|Library|N) • Greedy approach extends the C best structures so far from pos’n 1 to N