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Bio-CAD

Bio-CAD. M. Ramanathan. Molecular surfaces. Molecular surfaces. Connolly surface. Molecular surface representation. Union of partial spheres and tori. Geometric Model of Molecule. Molecular surface = Reentrant Surface + Contact Surface. Molecule Surface Visualization.

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Bio-CAD

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  1. Bio-CAD M. Ramanathan Bio-CAD

  2. Molecular surfaces Bio-CAD

  3. Molecular surfaces Bio-CAD

  4. Connolly surface Bio-CAD

  5. Bio-CAD

  6. Molecular surface representation Bio-CAD

  7. Union of partial spheres and tori Bio-CAD

  8. Geometric Model of Molecule Molecular surface = Reentrant Surface + Contact Surface

  9. Molecule Surface Visualization Connolly,Science (83)

  10. Rolling blend Link blend Type of blending surface Probe Probe

  11. Example – Blending surface

  12. Area of molecular surface Area of molecular surface = Area of link blend + Area of rolling blend + Area of contact Surface

  13. Voronoi diagram for circles

  14. VD(S) – Sphere set

  15. Detection of link blend

  16. Docking in a Pocket

  17. Distances between atom groups • between the closest atoms from both groups • these two atoms define a Voronoi face on the separation surface • distances between centers • average : 6.33 • maximum : 41.69 • minimum : 2.58 • distances between surfaces • average : 4.56 • maximum : 39.87 • minimum : 0.94

  18. Mesh representation Bio-CAD

  19. Segmenting molecular model (a) A simple height function with two maxima surrounded by multiple local minima and its Morse–Smale complex. (b) Combinatorial structure of the Morse–Smale complex in a planar illustration. Bio-CAD

  20. Segmentation results (a) The atomic density function: Darker regions correspond to protrusions and lighter regions correspond to cavities. Simplified triangulations and their segmentations are shown in (b), (c), and (d). Bio-CAD

  21. Protein structure The 3D protein structure of Human Insulin Receptor — Tyrosine Kinase Domain (1IRK): the folded sequence of amino acids (a) and a ribbon diagram (b) showing -helices (green spirals) and -sheets (blue arrows). The amino acids in these secondary structure elements are colored accordingly in (a) Bio-CAD

  22. Helix correspondence as shape matching the inputs are the 1D amino-acid sequence of the protein (a), where -helices are highlighted in green, and the 3D volume obtained by cryoEM (b), where possible locations of -helices have been detected (c). The method computes the correspondence between the two sets of helixes (e) by matching the 1D sequence with a skeleton representation of the volume (d) Bio-CAD

  23. Diffusion distance Given a molecular shape, sampling (red points), calculating inner distances green line segments) between all sample point pairs, computing diffusion distances based on diffusion maps, and building the descriptor (blue histogram). Input shape is the volumetric data. Bio-CAD

  24. Diffusion distance (contd.) Diffusion distance (DD) descriptor is compared to inner distance (ID) and Euclidean distance (ED). Bio-CAD

  25. Inner and Euclidean distances The red dashed line denotes the inner distance (ID), which is the shortest path within the shape boundary. The black bold line denotes the Euclidean distance (ED). ED does not have the property of deformation invariant in contrast to the ID. Bio-CAD

  26. References • Vijay Natarajan, YusuWang, Peer-TimoBremer,ValerioPascucci d, Bernd Hamann, Segmenting Molecular Surfaces, Computer-Aided Geometric Design, 23, 2006, pp. 495-509 • SasakthiAbeysinghea, Tao Jua,, Matthew L. Bakerb, WahChiu, Shape modeling and matching in identifying 3D protein structures, Computer-Aided Design, 40, 2008, pp 708-720 • Yu-ShenLiu, QiLi, Guo-Qin Zheng, KarthikRamani, William Benjamin, Using diffusion distances for flexible molecular shape comparison, BMC Bioinformatics, 2010. • www.cs.princeton.edu/courses/archive/fall07/cos597A/lectures/surfaces.pdf • biogeometry.duke.edu/meetings/ITR/04jun12/presentations/kim.ppt Bio-CAD

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