Protein Structure Similarity

1. Protein Structure Similarity

2. Secondary Structure Elements: a helices, b strands/sheets, & loops

3. NMR spectrometry Structure Prediction/Determination • Computational tools • Homology, threading • Molecular dynamics • Experimental tools X-ray crystallography

4. Protein Structure Determination (1) • X-ray diffraction crystallography

5. Protein Structure Determination (2) • Nuclear magnetic resonance spectroscopy

6. Protein Data Bank 1990  250 new structures 1999  2500 new structures 2000  >20,000 structures total 2004  ~30,000 structures total

7. Protein Data Bank Only about 10% of structures have been determined for known protein sequences  Protein Structure Initiative (PSI) 1990  250 new structures 1999  2500 new structures 2000  >20,000 structures total 2004  ~30,000 structures total

8. Structure Similarity • Refers to how well (or poorly) 3D folded structures of proteins can be aligned • Expected to reflect functional similarities (interaction with other molecules) Proteins in the TIM barrel fold family

9. Alignment of 1xis and 1nar (TIM-Barrels) ribbon format Sayle, R. RasMol. A protein visualization tool. http://www.umass.edu/microbio/rasmol/index2.htm. 1xis 1nar backbone format Alignment computed by DALI ahelix axes

10. Structure Similarity • Refers to how well (or poorly) 3D folded structures of proteins can be aligned • Is expected to reflect functional similarities (interaction with other molecules) • 2000: ~ 20,000 structures in PDB ~ 4,000 different folds (1:5 ratio)

13. Structure Similarity • Refers to how well (or poorly) 3D folded structures of proteins can be aligned • Is expected to reflect functional similarities (interaction with other molecules) • 2000: ~ 20,000 structures in PDB ~ 4,000 different folds (1:5 ratio) • Three possible reasons: - evolution, - physical constraints (e.g., few ways to maximize hydrophobic interactions), - limits in techniques used for structure determination • Given a new structure, the probability is high that it is similar to an existing one

14. sequencesimilarity Why Comparing Protein Folded Structures? • Low sequence similarity may yield very similar structures • Sometimes high sequence similarity yields different structures Sequence Structure Function

15. Alignment of 1xis and 1nar (TIM-Barrels) 1xis and 1nar have only 7% sequenceidentity, but approximately 70% of the residues are structurally similar

16. sequencesimilarity structuresimilarity Why Comparing Protein Folded Structures? • Low sequence similarity may yield very similar structures • Sometimes high sequence similarity yields different structures • Structure comparison is expected to provide more pertinent information about functional (dis-)similarity among proteins, especially with non-evolutionary relationships or non-detectable evolutionary relationships Sequence Structure Function

17. Ill-Posed Problem Multiple Terminology • (Dis-)similarity analysis • Structure comparison • Alignment, superposition, matching • Classification • Applications • Definitions and issues • Methods

18. A Few Web Sites • Protein Data Bank (PDB):http://www.rcsb.org/pdb/ • Protein classification: • SCOP:http://scop.berkeley.edu/ • CATHhttp://www.biochem.ucl.ac.uk/bsm/cath/ • Protein alignment: • DALI:http://www.ebi.ac.uk/dali/ • LOCK:http://motif.stanford.edu/lock2/

19. Application #1: Find Global Similarities Among Protein Structures • Given two protein structures, find the largest similar substructures • For example, a substructure is a subset of Ca atoms or a subset of secondary structure elements in each molecule • Several possible similarity measures • Variants: 1-to-1, 1-to-many, many-to-many (PDB) • Must be automatic (and fast)

20. Application #2: Classify Proteins • Many proteins, but relatively few distinct fold families [Chotia, 1992; Holm and Sander, 1996; Brenner et al. 1997] • Hierarchical classification • Insight into functions and structure stabilization • Basis for homology and threading • Manual classification  SCOP [Murzin et al., 1995]

21. Application #2: Classify Proteins Class: Similar secondary structure content • Many proteins, but relatively few distinct fold families [Chotia, 1992; Holm and Sander, 1996; Brenner et al. 1997] • Hierarchical classification • Insight into functions and structure stabilization • Basis for homology and threading • Manual classification  SCOP [Murzin et al., 1995] • Increasing size of PDB  Automatic classifiers: CATH [Orengo et al., 1997]; Pclass [Singh et al.]; FSSP [Holm and Sander] Fold: SSE’s in similar arrangement Family: Clear evolutionary relationship

22. Manuel vs. Automatic Classification

23. Application #3: Find Motif in Protein Structure • Given a protein structure and a motif (e.g., a small collection of atoms corresponding to a binding site) • Find whether the motif matches a substructure of the protein • Variant: One motif against many proteins Active sites of 1PIP and 5PAD. Only 3 amino-acids participate in the motif

24. Application #4: Find Pharmacophore • Given: • Small collection (5-10) of small flexible ligands with similar activity (hence, assumed to bind at same protein site) • Low-energy conformations (several dozens to few 100’s) for each ligand • Find substructure (pharmacophore) that occurs in at least one conformation of each ligand • Key problem in drug design when binding site is unknown

25. 1TLP 4TMN 5TMN 6TMN The 4 ligands overlappedwith their pharmacophorematched Clusters of low-energy conformations of 1TLP Application #4: Find Pharmacophore Inhibitors of thermolysin

26. Application #5: Search for Ligands Containing a Pharmacophore • Given: • Database containing several 100,000, or more, small ligands • A pharmacophore P • Find all ligands that have a low-energy conformation containing P • Data mining of pharmaceutical databases (lead generation) S.M. LaValle, P.W. Finn, L.E. Kavraki, and J.C. Latombe. A Randomized Kinematics-Based Approach to Pharmacophore-Constrained Conformational Search and Database Screening. J. of Computational Chemistry, 21(9):731-747, July 2000

27. Applications • Definitions and issues • Methods

28. 3D Molecular Structure • Collection of (possibly typed) atoms or groups of atoms in some given 3D relative placement • The placement of a group of atoms is defined by the position of a reference point (e.g., the center of an atom) and the orientation of a reference direction • The type can be the atom ID, the amino-acid ID, etc…

29. Matching of Structures Two structures A and B match iff: • Correspondence:There is a one-to-one map between their elements • Alignment:There exists a rigid-body transform T such that the RMSD between the elements in A and those in T(B) is less than some threshold e.

30. Complete Match

31. But a complete match is rarely possible: • The molecules have different sizes • Their shapes are only locally similar Alignment of 3adk and 1gky Both matching and non-matching secondary structure elements

32. Partial Match • Notion of support σ of the match: the match is between σ(A) and σ(B) •  Dual problem: - What is the support? - What is the transform? • Often several (many) possible supports • Small supports  motifs

33. Mathematical Relative g f s ||f - g||2 Over which support?

34. Mathematical Relative g f s ||f - g||2 Over which support?

35. Multiple Partial Matches

36. A A σ(B) B B σ(A) Gap Distributed Support

37. A A B B What is Best? Should gaps be penalized?

38. A B What About This? Sequence along backbone is not preserved

39.  Similarity measure is unlikely to satisfy triangular inequality for partial match

40. Scoring Issues • Trade-off between size of σ and RMSD • How should gaps be counted? • Is there a “quality” of the correspondence? [The correspondence may, or may not, satisfy type and/or backbone sequence preferences] • Should accessible surface be given more importance? •  Similarity measure may be different from the inverse of RSMD (though no consensus on best measure!) • But RMSD is computationally very convenient!

41. Gap penalty Examples RMSD dissimilarity measure  emphasizes differences  smaller support STRUCTAL’s similarity measure emphasizes similarities  larger support

42. Comparison of Similarity Measures A.C.M. May. Toward more meaningful hierarchical classification of amino acids scoring functions. Protein Engineering, 12:707-712, 1999reviews 37 protein structure similarity measures The difficulty of defining a similarity score is probably due to the facts that structure comparison is an ill-posed problem and has multiple solutions

43. Bottom Line Finding an optimal partial match is NP-hard: No fast algorithm is guaranteed to give an optimal answer for any given measure [Godzik, 1996]  Heuristic/approximate algorithms  Probably not a single solution, but application- dependent solutions  But there exist general algorithmic principles

44. Computational Questions Given a (dis)similarity measure and two proteins, compute the best match: • Which support? • Which correspondence? • Which alignment transform?

45. Applications • Definitions and issues • Methods

46. Find Global Similarities Among Protein Structures • Input:Two sets of features (atoms or groups of atoms) {a1,…,an} and {b1,…,bm} belonging to two different proteins A and B • Output:- Maximal correspondence set C of pairs (ai,bj), where all ai and all bj are distinct- Alignment transform T such that the RMSD of the pairs (ai,T(bj)) is less than a given e • Several possible outputs Variant of the Largest Common Point Set problem[Akutsu and Halldorsson, 1994]

47. Possible Correspondence Constraints • Typed features:(ai,bj) is a possible correspondence pair iff Type(ai) = Type(bj) • Ordered features:(ai,bj) and (ai’,bj’), where i’>i, are possible correspondence pairs iff j’>j[E.g., sequence along backbone]

48. Some Existing Software Ca atoms: • DALI [Holm and Sander, 1993] • STRUCTAL [Gerstein and Levitt, 1996] • MINAREA [Falicov and Cohen, 1996] • CE [Shindyalov and Bourne, 1998] • ProtDex [Aung,Fu and Tan, 2003] Secondary structure elements and Ca atoms: • VAST [Gibrat et al., 1996] • LOCK [Singh and Brutlag, 1996] • 3dSEARCH [Singh and Brutlag, 1999]

49. RMSD ≠ Similarity But matches and RMSD’s are not exactly what we need In general, we need to computea similarity measure of the form maxT S(A,T(B))where S is more complex than RMSD Two-step approach: 1. Compute best matches using RMSD 2. Adjust transform to maximize similarity measure

50. Computation of Best Matches Two “simultaneous” subproblems • Find maximal correspondence set C • Find alignment transform T Chicken-and-egg issue: • Each subproblem is relatively simple: • If we knew C, we could compute T • If we knew T, we could get C by proximity • But the combination is hard !!!