Seminar in BioInformatics

1. Seminar in BioInformatics A Method for Biomolecular Structural Recognition and Docking Allowing Conformational Flexibility (1998) Bilha Sandak, Ruth Nussinov and Haim wolfson Presented by : Tzahi Sofer

2. Lecture Structure • Overview – the problem, general idea of • solutions, other approaches. • Problem definition. • Preview. • The algorithm. • Result Analysis, examples. • Summery and Discussion .

3. Problem Definition • The problem: generating binding modes • between two molecules (a ligand and a • receptor), also known as molecular • docking.

4. Overview • Solving this problem involves recognition of • molecular surfaces and depends on the 3-D • structures & flexibility of the molecules. • Our approach allows hinge motions to exist • in either the ligand or the receptor molecules, • of diverse size.

6. Overview (cont.) • We achieve this by adapting a technique from • computer vision & robotics (Wolfson, 1991). • Other docking techniques have enabled hinge • movements only in small ligands. Partial • flexibility in the receptor is enabled by few • of them (DesJarlais 1986, Leach & Kuntz 1992, • Rarey, “FlexX” 1996) • We apply the algorithm to cases of bound • and unbound complexes.

7. Preview • During the process of molecular association, • either of the participating molecules, may • undergo conformational changes.

8. ligand hinge receptor

9. Preview (cont.) • Rigid docking Vs. flexibile docking . • More then 6 degrees of freedom (3 rotation, • 3 translation, 1 relative). • By allowing flexibility in either the ligand or • the receptor, additional candidate inhibitors • may be obtained. • Simultaneous match of all parts of • the molecule.

10. Redefining the problem • So, the problem is: • “given a database of • known ligands, and a newly introduced • receptor, recover all ligands which exhibit • substantial partial surface match, without • colliding. If the ligands contain hinges, solve • the problem by recovering the ligand in a • plausible conformation, without having the • parts self-collide.”

11. Method Outcome • The output – transformations. • Verification- by docking bound structures. • Good binding modes are generated as well.

12. Key Questions • How do we find hinges? • What is the complexity advantage? • How to represent the model?

13. The Algorithm • Overview. • Phases – • Preprocessing. • Recognition. • Complexity analysis.

14. The Algorithm - Overview • Representing the surfaces as sets of interest • points – a non-trivial task. • Two major issues: • a precise representation. • execution time and memory consumption. • Recall the representation generated by • Lin and Nussinov(1996) . • There is also the sphere representetaion of • Kuntz(1982).

15. The Algorithm - Overview • here, “caps” for the receptor and “pits” for • the ligand. • Position the hinges in the model. • hinge locations are determained by either: • Comparing conformations of ligands • flexible alignment (FlexProt). • narrow regions in the molecule.

16. The Algorithm - PreProcessing • Represent the model as an “interest point” set • The hinge positions are picked as the origin of • 3-D frame, called the “ligand frame”. • Store the model in a look-up (hash) table: • creating “triplet frames” from triplets of • interest points. Why triplets? What is a frame?

17. Frames • An orthonormal 3-D frame. • Its basis is orthonormal. • Here, we compute the basis for each • invariant triangle. • Then, the transformation is computed from • the frame’s basis to the unit basis: • Translational vector. • Rotational transformation.

18. The Algorithm – PreProcessing (cont.) • the triplet triangle side lengths serves as an address to the hash table. • the information stored at each entry is the ligand’s id, part number, and the transformations between the ligand frame and the triplet frame.

19. PreProcessing Remarks • Multiple hinges = multiple trans’ (different ligand frames). • Min/Max distance constraints - robustness/ • reduced matchings.

20. The Algorithm – Recognition • Represent the target as an “interest point” set. • candidate models: • calculate triplet frames of the target. • compute the “candidate ligand frame” by applying the trans’ at that entry to the receptor (target) triplet frame. • the origins are the candidate hinge location.

21. The Algorithm – Recognition (cont.) • Choose only high scoring candidate solutions- • the hinge locations are inserted into a look up table. • we pick locations receiving votes from both sides connected to it. the hinge location is the translation from the original hinge position of the ligand to its new candidate location.

22. The Algorithm – Recognition (cont.) • Verify the conformations – • collision check ligand-receptor. • self collision check ligand-ligand. • done by applying the trans’ to the part’s atoms. • colliding criteria – 2 * van der Waals radii – threshold.

23. The Algorithm – optimizations & heuristics • min/max distance – dense regions heristic. • regular/rapid run – deviding the receptor’s • triplets set into 8 segments and 1 overlapping • segment (discarding triplets). • voting threshold .

24. The Algorithm – optimizations & heuristics (cont.) • prune/no prune – prunning trans’ in the • verification check. • collision check – only in the respective • segment. • contact percentage/distance/threshold - a • screen for the self collision check.

25. The Algorithm – Complexity • PreProcessing: • Im = N* (m/N)* ((m/N) –1)*((m/N) –2)/6 = O(m³ / 6N²) = O(m³) for N close to 1 where: Im - number of triplets. N – number of parts. m – number of interest points reduced by N² compared to the rigid model.

26. The Algorithm – Complexity(cont.) • An insertion to the hash table – O(1). • So, the preprocessing phase – O(m³). • Hash table manipulation: • B = (D / q)³ where: B - number of bins in the table. D – maxdist-mindist constraints q – resolution.

27. The Algorithm – Complexity(cont.) • R = Im / B. • where: • R – the avarage number of records • in an entry. • So, each look-up is O(R ), assuming • homongeneuse distribution.

28. The Algorithm – Complexity(cont.) • Recognition: • matching stage: • Cm = O(n³ * R) where: n - the number of interest points in the target R – the avarage access time to a look up table. For small bins – O(n³) , but there is a Trade off with accuracy.

29. The Algorithm – Complexity(cont.) • Verification stage: • Ccc = O( (m * n * f)/(8N)) • Cscc = O( (m * g) / (jump²) ) Complexity summery O(n³ + m³ + Ccc + Cscc) + Lin’s representation….

30. The Algorithm – Summery • Preprocessing: • Represent the model as an interest point Set. • position the hinges in the model. • store the model in a look up table. • Recognition: • Represent the target as an interest point Set. • Recover candidate model from the table. • Choose only high scoring solutions. • Verify by collision checks.

31. Experimental results • We investigate bound structures. • Thus, the “correct” solutions are those with • rotations and translations close to zero. • “best solution” = low RMSD. • Good-fitting predictive binding modes are • generated as well.

33. Examples • Docking MTX/DHFR • Motivation – MTX is an anticancer drug, preventing the replication of cells. • MTX – flexibile, hinge at C9 Atom. • DHFR – rigid. • bound case. Results

34. Examples (cont.) • Docking Maltose/MBP • Motivation – transportation of substrates between the inner and outer membrane of a bacteria. • Maltose – rigid (and small). • MBP – hinge at Cα atom of the GLU111. • unbound case. • Although small, all of the Maltose’s atomsare in contact with the receptor.

36. Summery • A method for docking a ligand into a • receptor, allowing hinge motion in either of • them. • A geometric analogy between the problems • of object matching in Computer Vision and • those of molecular binding. • No a-priory knowledge of the match.

37. Discussion • Advantages and attributes • More results compared to the rigid method. • 3-D to 3-D matching problem. • Full 3-D rotation during matching. • Large number of interest points. • Handling noisy samples. • Relatively low Complexity. • Diverse sized molecules. • Good predictive results. • Short execution times (under 1 min.)

38. Discussion (cont.) • Disadvantages • Not a good method for small parts. • Inconsistency. • No biological/chemical considerations.

39. Additional possible features • Inserting Chemical properties • considerations. • Allowing rotational bond movement only, • where full 3-D movement is not requiered. The end

40. Bibliography • Sandak, Nussinuv and Wolfson, • “A method for Biomolecular Structural • Recognition and Docking allowing • Conformational Flexiblity”, journal of • computational biology, vol. 5, 1998. • Shuo Liang Lin, Ruth Nussinov, Daniel • Fischer, Haim J. Wolfson, “A Geometry-base • Suite of Molecular Docking Processes, • Molecular surface representation by • sparse critical points” • Sandak, Nussinov and Wolfson, • “Flexible docking allowing induced fit”,1998.

41. Hinge position

42. ligand 3 4 5 (3,4,5) T1 (0,0,0) receptor T1 (1,2,3)

43. (ligand_part, hinge_location) (1,2,3) (1.1, 2.3, 3) (1, 2, 3.2)

44. Ligand(pits) Receptor(caps)

47. bound!

48. unbound