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

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

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

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

8. hinge ligand receptor

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

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

11. Method Outcome The output – transformations. The output – transformations. Verification- by docking bound structures. Verification- by docking bound structures. Good binding modes are generated as well. 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. Overview. Phases – Phases –  Preprocessing.  Recognition. Complexity analysis. Complexity analysis.

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

15. The Algorithm - Overview here, “caps” for the receptor and “pits” for here, “caps” for the receptor and “pits” for the ligand. the ligand. Position the hinges in the model. Position the hinges in the model. hinge locations are determained by either: 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 Represent the model as an “interest point” set The hinge positions are picked as the origin of The hinge positions are picked as the origin of 3-D frame, called the “ligand frame”. 3-D frame, called the “ligand frame”. Store the model in a look-up (hash) table: Store the model in a look-up (hash) table:  creating “triplet frames” from triplets of interest points. interest points. Why triplets? What is a frame?

17. Frames An orthonormal 3-D frame. An orthonormal 3-D frame. Its basis is orthonormal. Its basis is orthonormal. Here, we compute the basis for each Here, we compute the basis for each invariant triangle. invariant triangle. Then, the transformation is computed from Then, the transformation is computed from the frame’s basis to the unit basis: 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. an address to the hash table.  the information stored at each entry is the ligand’s id, part number, and the ligand’s id, part number, and the transformations between the ligand frame transformations between the ligand frame and the triplet frame. and the triplet frame.

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

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

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

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

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

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

25. The Algorithm – Complexity PreProcessing: PreProcessing:  Im = N* (m/N)* ((m/N) –1)*((m/N) –2)/6 = O(m³ / 6N²) = O(m³) = O(m³ / 6N²) = O(m³) for N close to 1 for N close to 1where: Im - number of triplets. Im - number of triplets. N – number of parts. N – number of parts. m – number of interest points 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). An insertion to the hash table – O(1). So, the preprocessing phase – O(m³). So, the preprocessing phase – O(m³). Hash table manipulation: 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. R = Im / B.where: R – the avarage number of records R – the avarage number of records in an entry. in an entry. So, each look-up is O(R ), assuming So, each look-up is O(R ), assuming homongeneuse distribution. homongeneuse distribution.

28. The Algorithm – Complexity (cont.) Recognition: Recognition:  matching stage:  Cm = O(n³ * R) where: where: n - the number of interest points n - the number of interest points in the target R – the avarage access time to a 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: Preprocessing:  Represent the model as an interest point Set.  position the hinges in the model.  store the model in a look up table. Recognition: 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. We investigate bound structures. Thus, the “correct” solutions are those with Thus, the “correct” solutions are those with rotations and translations close to zero. rotations and translations close to zero. “best solution” = low RMSD. “best solution” = low RMSD. Good-fitting predictive binding modes are Good-fitting predictive binding modes are generated as well. generated as well.

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

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

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

37. Discussion Advantages and attributesAdvantages 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.) DisadvantagesDisadvantages  Not a good method for small parts.  Inconsistency.  No biological/chemical considerations.

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

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

41. Hinge position

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

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

44. Ligand(pits) Receptor (caps)

47. bound!

48. unbound

56. Connolly ’ s molecular surface Probe spheres are rained upon the atoms from all directions, stopping just before a collision. Set the probe ball in all possible locations of the molecule. The intersection point between the probe ball and the atoms defines a point on the molecular surface. In three dimensions this produces a grid.

57. Connolly ’ s molecular surface Probe balls van der Waals atoms

58. Connolly ’ s molecular surface Probe balls Contact surface reentrant surface van der Waals atoms Contact surface + reentrant surface = molecular surface

59. Connolly ’ s molecular surface

60. Connolly ’ s representation Face – an atomic size unit of Connolly’s surface Convex face – the part of an atom’s van der Waal’s surface which the probe ball can touch. Concave face – the part of the probe ball surface which is bordered by three atoms. Saddle face – the part of the surface between two atoms.

61. Connolly ’ s representation Convex face Concaveface Concave face Saddle face

62. Connolly ’ s molecular surface This representation has the ability to visualize the shape complementarity at interfaces. It has become popular for protein recognition problems. But need more concise representation….

63. Critical points creation – basic terms The representation is a set of critical points, obtained by projecting the gravity center of a Connolly face onto the surface. Cap – a point on a convex face Pit – a point on a concave face Belt – a point on a saddle- shaped face Dense MS surface (Connolly) Sparse surface

64. A sparse set of critical points Dense MS surface (Connolly)Sparse surface