1. Computational Methods for Protein Structure Prediction Ying Xu

2. Outline introduction to protein structures the problem of protein structure prediction why we can predict protein structure protein tertiary structure prediction –Ab initio folding –homology modeling protein threading

3. Protein and Structure >1MBN:_ MYOGLOBIN (154 AA) MVLSEGEWQLVLHVWAKVEADVAGHGQDILIRLFKSHPETLEKFDRFKHL KTEAEMKASEDLKKAGVTVLTALGAILKKKGHHEAELKPLAQSHATKHKI PIKYLEFISEAIIHVLHSRHPGNFGADAQGAMNKALELFRKDIAAKYKEL GYQG Protein sequence Protein structure Oxygen storage Protein function

4. Ball and stick spacefill

5. Protein Structure protein sequence folds into a “unique” shape (“structure”) that minimizes its free potential energy

6. Protein Structures Primary sequence Secondary structure MTYKLILNGKTKGETTTEAVDAATAEKVFQYANDNGVDGEWTYTE  -helix  -sheet anti-parallel parallel

7. Protein Structures Tertiary structure Quaternary structure

8. Protein Structures Protein structure –generally compact Soluble protein structure –individual domains are generally globular –they share various common characteristics, e.g. hydrophobic moment profile Membrane protein structure most of the amino acid sidechains of transmembrane segments are non-polar polar groups of the polypeptide backbone of transmembrane segments generally participate in hydrogen bonds

9. Protein Tertiary Structures Family: Clear evolutionary relationship, protein in the same family are homologous, sequence identity >=30%. Superfamily: Low sequence identity, probable common evolutionary origin. Fold: May not have a common evolutionary origin. Major structural similarity. Class: all- , all- ,  / ,  + , … http://scop.mrc-lmb.cam.ac.uk/scop/ SCOP 1.65 release: 2327 families, 1294 superfamilies, 800 folds SCOP: Structural Classification Of Proteins

10. Protein Tertiary Structures

11. Protein Structure Determination X-ray crystallography –most accurate –in vitro –need crystals proteins –~50K per structure NMR –accurate –in vivo –no need for crystals –limited to small proteins Cryo-EM –Imaging technology –Low-resolution

12. Protein Structure Prediction Problem: Given the amino acid sequence of a protein, what’s its 3-dimensional shape ? MVLSEGEWQLVLHVWAKVEADVAGHGQDILIRLFKSHPETLEKFDRFKHL KTEAEMKASEDLKKAGVTVLTALGAILKKKGHHEAELKPLAQSHATKHKI PIKYLEFISEAIIHVLHSRHPGNFGADAQGAMNKALELFRKDIAAKYKEL GYQG ? ……..

13. Why Protein Structure Prediction? Importance of protein structure –knowledge of the structure of a protein enable us to understand its function and functional mechanism –design better mutagenesis experiments –structure-based rational drug design Experimental methods for protein structure determination Pros: high resolution Cons: time-consuming and very expensive

14. Why Protein Structure Prediction? Big gap between the number of protein sequences and the number of protein structures –Uniprot/Swiss-prot, 283,454 protein sequences –Uniprot/TrEMBL, 4,864,587 gene sequences –PDB (Protein Data Bank), 48,385 protein structuresPDB (Protein Data Bank), Fundamental, unsolved, challenging problem

15. Why We Can Predict Structure In theory, a protein structure can solved computationally A protein folds into a 3D structure to minimizes its free potential energy –Anfinsen’s classic experiment on Ribonuclease A folding in the 1960’s –energy functions This problem can be formulated as an optimization problem –protein folding problem, or ab initio folding

16. Why We Can Predict Structure While there could be billions of billions of proteins in nature, the number of unique structural folds (shapes) might be small 90% of new structures submitted to PDB in the past three years have similar structural folds in PDB

17. Why We Can Predict Structure Theoretical studies suggest that the vast majority of the proteins in nature fall into not much more than 1000 structural folds This realization has fundamentally changed how protein structures can be predicted The structure prediction problem becomes for a protein sequence, find which of the structural folds the protein can fold into, plus possibly some structural refinement MTYKLILN …. NGVDGEWTYTE

18. Computational Methods for Protein Structure Prediction ab initio --use first principles to fold proteins --does not require templates --high computational complexity homology modeling --similar sequence  similar structures --practically very useful, need homologues protein threading --many proteins share the same structural fold --a folding problem becomes a fold recognition problem Need known protein structures

19. ab initio structure prediction An energy function to describe the protein obond energy obond angle energy odihedral angel energy ovan der Waals energy oelectrostatic energy Efficient and reliable algorithms to search the conformational space to minimize the function and obtain the structure.

20. ab initio structure prediction The problem is exceedingly difficult to solve –the search space is defined by psi/phi angles of backbone and side-chain positions –the search space is enormous even for small proteins! –the number of local minima increases exponentially of the number of residues Theoretically solvable but practically infeasible!

21. ROSETTA (Dave Baker’s Lab) Construct a library of small structure fragments, e.g. 9 AA Cut a target sequence to sequence fragments. For each sequence fragment, choose structural candidate fragments from the fragment library Assemble the fragment structures by Monte Carlo simulation The generated structures are grouped into clusters Clusters are ranked by their energy

22. Homology Modeling Observation : proteins with similar sequences tend to fold into similar structures. 1. Target sequence is aligned with the sequence of a known structure, they usually share sequence identity of 30% or higher 2. Superimpose target sequence onto the template, replacing equivalent side-chain atoms where necessary 3. Refine the model by minimizing an energy function. Programs: Modeller http://salilab.org/modeller/ Swiss-Model http://swissmodel.expasy.org//SWISS-MODEL.html

23. Protein Threading Basic premise Statistics from Protein Data Bank (~48,000 structures) Chances for a protein to have a native-like structural fold in PDB are quite good (estimated to be 60-70%) –Proteins with similar structural folds could be homologues or analogues The number of unique structural (domain) folds in nature is fairly small (possibly a few thousand) 90% of new structures submitted to PDB in the past three years have similar structural folds in PDB

24. Protein Threading The goal: find the “correct” sequence-structure alignment between a target sequence and its native-like fold in PDB Energy function – knowledge (or statistics) based rather than physics based –Should be able to distinguish correct structural folds from incorrect structural folds –Should be able to distinguish correct sequence-fold alignment from incorrect sequence-fold alignments MTYKLILN …. NGVDGEWTYTE

25. Protein Threading – four basic components Structure database Energy function Sequence-structure alignment algorithm Prediction reliability assessment

26. Protein Threading – structure database Build a template database

27. Protein Threading – structure database Non-redundant representatives through structure-structure and/or sequence-sequence comparison FSSP (http://www.bioinfo.biocenter.helsinki.fi:8080/dali/index.html) (Families of Structurally Similar Proteins) SCOP (http://scop.mrc-lmb.cam.ac.uk/scop/) PDB-Select (http://www.sander.embl-heidelberg.de/pdbsel/) Pisces (http://www.fccc.edu/research/labs/dunbrack/pisces/)

28. Protein Threading – energy function MTYKLILNGKTKGETTTEAVDAATAEKVFQYANDNGVDGEWTYTE how well a residue fits a structural environment: E_s how preferable to put two particular residues nearby: E_p alignment gap penalty: E_g total energy: E_p + E_s + E_g find a sequence-structure alignment to minimize the energy function

29. Protein Threading – energy function A singleton energy measures each residue’s preference in a specific structural environments –secondary structure –solvent accessibility Compare actual occurrence against its “expected value” by chance Where

30. Protein Threading – energy function A simple definition of structural environment –secondary structure: alpha-helix, beta-strand, loop –solvent accessibility: 0, 10, 20, …, 100% of accessibility –each combination of secondary structure and solvent accessibility level defines a structural environment E.g., (alpha-helix, 30%), (loop, 80%), … E_s: a scoring matrix of 30 structural environments by 20 amino acids –E.g., E_s ((loop, 30%), A) Singleton energy term

31. Protein Threading – energy function Helix SheetLoop Buried Inter Exposed Buried Inter Exposed Buried Inter Exposed ALA -0.578 -0.119 -0.160 0.010 0.583 0.921 0.023 0.218 0.368 ARG 0.997 -0.507 -0.488 1.267 -0.345 -0.580 0.930 -0.005 -0.032 ASN 0.819 0.090 -0.007 0.844 0.221 0.046 0.030 -0.322 -0.487 ASP 1.050 0.172 -0.426 1.145 0.322 0.061 0.308 -0.224 -0.541 CYS -0.360 0.333 1.831 -0.671 0.003 1.216 -0.690 -0.225 1.216 GLN 1.047 -0.294 -0.939 1.452 0.139 -0.555 1.326 0.486 -0.244 GLU 0.670 -0.313 -0.721 0.999 0.031 -0.494 0.845 0.248 -0.144 GLY 0.414 0.932 0.969 0.177 0.565 0.989 -0.562 -0.299 -0.601 HIS 0.479 -0.223 0.136 0.306 -0.343 -0.014 0.019 -0.285 0.051 ILE -0.551 0.087 1.248 -0.875 -0.182 0.500 -0.166 0.384 1.336 LEU -0.744 -0.218 0.940 -0.411 0.179 0.900 -0.205 0.169 1.217 LYS 1.863 -0.045 -0.865 2.109 -0.017 -0.901 1.925 0.474 -0.498 MET -0.641 -0.183 0.779 -0.269 0.197 0.658 -0.228 0.113 0.714 PHE -0.491 0.057 1.364 -0.649 -0.200 0.776 -0.375 -0.001 1.251 PRO 1.090 0.705 0.236 1.249 0.695 0.145 -0.412 -0.491 -0.641 SER 0.350 0.260 -0.020 0.303 0.058 -0.075 -0.173 -0.210 -0.228 THR 0.291 0.215 0.304 0.156 -0.382 -0.584 -0.012 -0.103 -0.125 TRP -0.379 -0.363 1.178 -0.270 -0.477 0.682 -0.220 -0.099 1.267 TYR -0.111 -0.292 0.942 -0.267 -0.691 0.292 -0.015 -0.176 0.946 VAL -0.374 0.236 1.144 -0.912 -0.334 0.089 -0.030 0.309 0.998

32. Protein Threading – energy function It measures the preference of a pair of amino acids to be close in 3D space. How close is close? –distance dependent –single cutoff –C , C , or centroid of the sidechain Observed occurrence of a pair compared with its “expected” occurrence Pair-wise interaction energy term

33. Protein Threading – energy function ALA -140 ARG 268 -18 ASN 105 -85 -435 ASP 217 -616 -417 17 CYS 330 67 106 278 -1923 GLN 27 -60 -200 67 191 -115 GLU 122 -564 -136 140 122 10 68 GLY 11 -80 -103 -267 88 -72 -31 -288 HIS 58 -263 61 -454 190 272 -368 74 -448 ILE -114 110 351 318 154 243 294 179 294 -326 LEU -182 263 358 370 238 25 255 237 200 -160 -278 LYS 123 310 -201 -564 246 -184 -667 95 54 194 178 122 MET -74 304 314 211 50 32 141 13 -7 -12 -106 301 -494 PHE -65 62 201 284 34 72 235 114 158 -96 -195 -17 -272 -206 PRO 174 -33 -212 -28 105 -81 -102 -73 -65 369 218 -46 35 -21 -210 SER 169 -80 -223 -299 7 -163 -212 -186 -133 206 272 -58 193 114 -162 -177 THR 58 60 -231 -203 372 -151 -211 -73 -239 109 225 -16 158 283 -98 -215 -210 TRP 51 -150 -18 104 52 -12 157 -69 -212 -18 81 29 -5 31 -432 129 95 -20 TYR 53 -132 53 268 62 -90 269 58 34 -163 -93 -312 -173 -5 -81 104 163 -95 -6 VAL -105 171 298 431 196 180 235 202 204 -232 -218 269 -50 -42 46 267 73 101 107 -324 ALA ARG ASN ASP CYS GLN GLU GLY HIS ILE LEU LYS MET PHE PRO SER THR TRP TYR VAL

34. Protein Threading – energy function w(k) = h + gk, k ≥ 1, w(0) = 0; Where h and g are constants. h: opening gap penalty g: extension gap penalty FDSK---THRGHR :.: :: ::: FESYWTCTH-GHR FDSK-T--HRGHR :.: : : ::: FESYWTCTH-GHR gap penalty term

35. Protein Threading – energy function Secondary structure prediction is mature and can achieve ~80% accuracy The performance of using probabilities of the predicted three secondary structure states (  -helices,  -strand, and loop) is better Secondary structure match energy

36. Threading Parameter Optimization The contribution of each term (weight). Based on threading performance on a training set (fold recognition and alignment accuracy). Different weight for different classes? (superfamily, fold) pair-wise may contribute more for fold level threading mutation/profile terms dominate in superfamily level threading Etotal =  s E singleton +  p E pairwise +  g E gap +  ss E ss

37. Protein Threading -- algorithm Considering only singleton energy + gap penalty Represent a structure a sequence of “structural environments” –(helix, 100%), (helix, 90%), ….. (strand, 0%) Align a sequence MACKLPV …. with a structural sequence (helix, 100%), (helix, 90%), ….. (strand, 0%)

38. Protein Threading – dynamic programming AAGG AACG | | | Two sequences: AACG and AAGG AACG A A G G 2 2 2 2 3 43 2 5 2 3 5 Step #1: calculating alignment matrix Rule: 1: initialization– fill the first row and column with matching scores 2: fill an empty cell based on scores of its left, upper and upper- left neighbors + the matching score of the current cell 3: chose the one giving the highest score

39. Protein Threading – dynamic programming AACG A A G G 2 2 2 2 3 43 2 5 2 3 5 Step #2: Tracing back to recover the alignment Rule: 1: start from the right- lower corner 2: trace back to left, upper or upper-left neighbor which gives the current cell’s score 3. Keep doing this until it cannot continue

40. Protein Threading – dynamic programming Steps: 1. Initialization: construct an (n+1) x (m+1) matrix F for two sequences of lengths n and m. 2. Matrix fill: for each cell in the matrix F, check all possible pathways back to the beginning of the sequence (allowing insertions and deletions) and give that cell the value of the maximum scoring. 3. Traceback: construct an alignment back from the last cell in the matrix (or the highest scoring) cell to give the highest scoring alignment.

41. Protein Threading -- dynamic programming (helix, 100%) (helix, 90%) (helix, 80%) (loop, 80%) M L V A

42. Protein Threading -- algorithm Considering all three energy terms Considering the pair-wise interaction energy makes the problem much more difficult to solve –dynamic programming algorithm does not work any more! There are other techniques that can be used to solve the problem

43. Protein Threading -- algorithm Dynamic programming Heuristic algorithms for pair-wise interactions –Frozen approximation algorithm (A. Godzik et al.) –Double dynamic programming (D. Jones et al.) –Monte carlo sampling (S.H. Bryant et al.) Rigorous algorithms for pair-wise interactions –Branch-and-bound (R.H. Lathrop and T.F. Smith) –Divide-and-conquer (Y. Xu et al.) --PROSPECT –Linear programming (J. Xu et al.) –RAPTOR –Tree decomposition (L. Cai et al.) Rigorous algorithm for treating backbone and side-chain simultaneously (Li et al.)

44. Fold Recognition MTYKLILNGKTKGETTTEAVDAATAEKVFQYANDNGVDGEWTYTE Score = -1500Score = -900Score = -1120Score = -720 Which one is the correct structural fold for the target sequence if any? The one with the highest score ?

45. Fold Recognition Template #1: AATTAATACATTAATATAATAAAATTACTGA Query sequence: AAAA Template #2: CGGTAGTACGTAGTGTTTAGTAGCTATGAA Better template? Which of these two sequences will have better chance to have a good match with the query sequence after randomly reshuffling them?

46. Fold Recognition Different template structures may have different background scores, making direct comparison of threading scores against different templates invalid Comparison of threading results should be made based on how standout the score is in its background score distribution rather than the threading scores directly

47. Fold Recognition Threading 100,000 sequences against a template structure provides the baseline information about the background scores of the template By locating where the threading score with a particular query sequence, one can decide how significant the score, and hence the threading result, is! Not significant significant

48. Fold Recognition Z-score = standard deviation score - average -- randomly shuffle the query sequence and calculate the alignment score

49. Fold Recognition Significance score versus prediction specificity/sensitivity Z-score

50. Fold Recognition Examine feature space of threading alignments: (singleton score, pair contact scores, secondary structure score, hydrophobic moment score,......) versus true/false fold recognition Separate true ones from false ones using support vector machine (SVM) false true -2000, -500, -35, -90,......, true -1000, -201, -11, -500,......, false -5020, -900, -20, -75,......, true -1050, -185, -18, -320,......, false......

51. Fold Recognition Each feature has somewhat different distributions in the true and false predictions E.g., hydrophobic moments (Hydrophobic moments of protein structures: spatially profiling the distribution, David Silverman, PNAS 2001 98: 4996-5001) is quite useful in distinguishing true from false threading predictions

52. Application Sequence preprocessing Protein sequence Remove signal peptide Membrane/soluble?? Domain prediction Database searching Find homolog in PDB? YES Homology modeling NO Fold recognition 3D structure Sequence profile generation Secondary structure Prediction Experimental data constraints

53. Challenging Issues Much improved energy functions for threading Considering side-chain information when doing protein threading Effective integration of fragment-based methods and threading techniques