1 / 36

Alignment of Flexible Molecular Structures

Alignment of Flexible Molecular Structures. Motivation. Proteins are flexible. One would like to align proteins modulo the flexibility. Hinge and sh ear protein domain motions (Gerstein, Lesk , Chotia). Conformational flexibility in drugs. Problem definition. Flexible Geometric Hashing.

reece-bruce
Download Presentation

Alignment of Flexible Molecular Structures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Alignment of Flexible Molecular Structures

  2. Motivation • Proteins are flexible. One would like to align proteins modulo the flexibility. • Hinge and shear protein domain motions (Gerstein, Lesk , Chotia). • Conformational flexibility in drugs.

  3. Problem definition

  4. Flexible Geometric Hashing • Exploit the fact that neighboring parts share the joint - accumulate mutual information at the joint. • Achieve complexity of the same order of magnitude as in rigid alignment.

  5. Flexible protein alignment without prior hinge knowledge FlexProt - algorithm • detects automatically flexibility regions, • exploits amino acid sequence order.

  6. Motivation

  7. Geometric Representation 3-D Curve {vi}, i=1…n

  8. Experimental Results

  9. Experimental Results

  10. FlexProt Algorithm • Input:two protein molecules A and B, each being represented by the sequence of the 3-D coordinates of its Caatoms. • Task:largest flexible alignment by decomposing the two molecules into a minimal number of rigid fragment pairs having similar 3-D structure.

  11. FlexProt Main Steps Detection of Congruent Rigid Fragment Pairs Joining Rigid Fragment Pairs Rigid Structural Comparison Clustering (removing ins/dels)

  12. Congruent Rigid Fragment Pair Structural Similarity Matrix

  13. k+l-1 k t+l-1 t Fragkt(l) = vk…vi ...vk+l-1 wt…wj…wt+l-1 RMSD (Fragkt(l) ) < e Detection of Congruent Rigid Fragment Pairs i-1 i+1 i j-1 j+1 j vi-1vivi+1 wj-1 wjwj+1

  14. RMSD( P ) RMSD( PUQ ) in O(1) time NOT O( |P|+|Q| ) RMSD( Q ) RMSD Computation Vi…...Vi+l Wj...…Wj+l Vk…...Vk+m Wt...…Wt+m P= Q= PU Q

  15. FlexProt Main Steps Detection of Congruent Rigid Fragment Pairs Joining Rigid Fragment Pairs Rigid Structural Comparison Clustering (removing ins/dels)

  16. How to Join Rigid Fragment Pairs ?

  17. Graph Representation Graph Node Graph Edge

  18. Graph Representation • The fragments are in ascending order. • The gaps (ins/dels) are limited. • Allow some overlapping. W a b +Size of the rigid fragment pair (node b) - Gaps (ins/dels) - Overlapping Penalties

  19. W_k W_m W_n W_t W_i Graph Representation • DAG (directed acyclic graph)

  20. Optimal Solution ? W_k W_m W_n W_t W_i • “All Shortest Paths” • O(|E|*|V|+|V|2) (for DAG) • “Single-source shortest paths” • O(|E|+|V|)

  21. FlexProt Main Steps Detection of Congruent Rigid Fragment Pairs Joining Rigid Fragment Pairs Rigid Structural Comparison Clustering (removing ins/dels)

  22. Clustering (removing ins/dels) T1 T2 If joining two fragment pairs gives small RMSD (T1 ~ T2) then put them into one cluster.

  23. FlexProt Main Steps Detection of Congruent Rigid Fragment Pairs Joining Rigid Fragment Pairs Rigid Structural Comparison Clustering (removing ins/dels)

  24. Correspondence Problem

  25. Molecular Surface Representation Applications to docking

  26. Motivation • Prediction of biomolecular recognition. • Detection of drug binding ‘cavities’. • Molecular Graphics.

  27. 1. Solvent Accessible Surface – SAS2. Connolly Surface

  28. Connolly’s MS algorithm • A ‘water’ probe ball (1.4-1.8 A diameter) is rolled over the van der Waals surface. • Smoothes the surface and bridges narrow ‘inaccessible’ crevices.

  29. Connolly’s MS algorithm - cont. • Convex, concave and saddle patches according to the no. of contact points between the surface atoms and the probe ball. • Outputs points+normals according to the • required sampling density (e.g. 10 pts/A2).

  30. Example - the surface of crambin

  31. Critical points based on Connolly rep. (Lin, Wolfson, Nussinov) • Define a single point+normal for each patch. • Convex-caps, concave-pits, saddle - belt.

  32. Critical point definition

  33. Connolly => Shou Lin

  34. Solid Angle local extrema hole knob

  35. Chymotrypsin surface colored by solid angle (yellow-convex, blue-concave)

More Related