Molecular Surface Abstraction

1. Greg Cipriano Advised by Michael Gleicher and George N. Phillips Jr. Molecular Surface Abstraction

2. Structural Biology: form influences function • Standard metaphor: Lock and key • Proteins and their ligands have complementary • Shape • Charge • Hydrophobicity

3. A functional surface... too much detail Hard to visualize. Hard to compute with. (2POR)‏

4. What we're up to... • Creating tools for structural biology. • Molecular surface abstraction for: • Visualization • Functional surface analysis

5. VisualizingMolecular Surface Abstractions

6. How scientists currently look at molecular surfaces • Salient features: • Solvent-excluded interface • Charge field • Binding partners (in yellow)‏

7. Our surface abstraction • Simplified • Geometry • Surface fields Decals applied at important features Ligands were here.

8. The molecular surface Here's the geometric surface How is it made?

9. Molecular surfaces

10. Confusing surface detail Catalytic Antibody (1F3D)‏ Rendered with PyMol

11. How do biologists deal with complicated things? Confusing stick-and-ball model Clearer ribbon representation.

12. How do they do the same things with surfaces? ... they don't.

13. Prior art: QuteMol Stylized shading helps convey shape

14. Our method: abstraction Simplifies both geometry and surface fields (e.g. charge).

15. How to convey additional information We can now show interesting regions as decals applied directly to the surface. Why? Smooth surfaces are easier to parameterize.

16. How we can use decals Peaks and bowls

17. How we can use decals Predicted Ligand Binding Sites

18. How we can use decals Ligand Shadows

19. Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. Build surface patches and apply a decal for each patch

20. Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. Build surface patches and apply a decal for each patch

21. Diffusing surface fields Starting with a triangulated surface: • Edges in blue • Vertices at points where • edges meet

22. Diffusing surface fields Starting with a triangulated surface: We sample scalar fields onto each vertex:

23. Diffusing surface fields Starting with a triangulated surface: We sample scalar fields onto each vertex: And apply our filter to smooth out them, preserving large regions of uniform value.

24. Smoothing Standard Gaussian smoothing tends to destroy region boundaries: Weights pixel neighbors by distance when averaging.

25. Bilateral filtering A bilateral filter* smooths an image by taking into account both distance and value difference when averaging neighboring pixels. * C. Tomasi and R.Manduchi. Bilateral filtering for gray and color images. In ICCV, pages 839–846, 1998.

26. Bilateral filtering A bilateral filter* smooths an image by taking into account both distance and value difference when averaging neighboring pixels. ...producing a smooth result while still retaining sharp edges.

27. Bilateral filtering We do the same thing, but on a irregular graph: Here's one vertex, and its immediate neighbors

28. Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. Build surface patches and apply a decal for each patch

29. Smoothing the mesh Taubin* (lamda/mu) smoothing: simple and fast * G. Taubin. A signal processing approach to fair surface design. In Proceedings of SIGGRAPH 95, pages 351–358.

30. The trouble with smoothing... Taubin* (lamda/mu) smoothing: simple and fast Resulting mesh still has high-curvature regions!

31. A quick digression: what is curvature? In 2D, defined by an osculating circle tangent to a given point.

32. A quick digression: what is curvature? In 3D, it's now defined by radial planes, going through a point P and its normal, N. For us, curvature = maximum over all planes So for us, high curvature = pointy in some direction

33. High-curvature (pointy) regions

34. Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. Build surface patches and apply a decal for each patch

35. Further abstraction Select a user-defined percentage of vertices with highest curvature. Grow region about each point. Remove, by edge-contraction, all but a few vertices in each region, proceeding from center outward.

36. Final smooth mesh Original Completely smooth With Decals

37. Abstraction in 4 steps Our method: 1. Diffuse surface fields 2. Smooth mesh 3. Identify and remove remaining high-curvature regions 4. Build surface patches and apply a decal for each patch

38. Building surface patches We highlight interesting regions using surface patches. Just a few of them: Ligand Shadows Predicted Binding Sites

39. Parameterization Maps a piece of the surface to a plane

40. Parameterization

41. Adding decals – what we do We parameterize the surface with Discrete Exponential Maps* Advantages: Local, Fast Starts at center point, progresses outward over surface. * R. Schmidt, C. Grimm, and B.Wyvill. Interactive decal compositing with discrete exponential maps. ACM Transactions on Graphics, 25(3):603–613, 2006.

42. Decals representing points of interest 'H' stickers represent potential hydrogen-bonding sites

43. Surface patch construction

44. Surface patch construction

45. Surface patch smoothing

46. Surface patch smoothing

47. Surface patch smoothing Before After

48. Examples (1AI5)‏

49. Examples (1BMA)‏

50. Examples (1ANK)‏