Bio-CAD M. Ramanathan Bio-CAD Molecular surfaces Bio-CAD Molecular surfaces Bio-CAD Connolly surface Bio-CAD Bio-CAD Molecular surface representation Bio-CAD Union of partial spheres and tori Bio-CAD Geometric Model of Molecule Reentrant Surface Contact Surface Accessible Surface Atom Probe (Solvent) Molecular surface = Reentrant Surface + Contact Surface Molecule Surface Visualization Connolly, Science (83) Type of blending surface Rolling blend Link blend Probe Probe Example – Blending surface Area of molecular surface Area of molecular surface = Area of link blend + Area of rolling blend + Area of contact Surface Voronoi diagram for circles p1 p2 p4 p3 p6 p5 VD(S) – Sphere set Detection of link blend Docking in a Pocket 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 Mesh representation Bio-CAD 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 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 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 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 representationBio-CAD of the volume (d) 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 Diffusion distance (contd.) Diffusion distance (DD) descriptor is compared to inner distance (ID) and Euclidean distance (ED). Bio-CAD 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 References • Vijay Natarajan , Yusu Wang, Peer-Timo Bremer,Valerio Pascucci d, Bernd Hamann, Segmenting Molecular Surfaces, Computer-Aided Geometric Design, 23, 2006, pp. 495-509 • Sasakthi Abeysinghea, Tao Jua,, Matthew L. Bakerb, Wah Chiu, Shape modeling and matching in identifying 3D protein structures, Computer-Aided Design, 40, 2008, pp 708-720 • Yu-Shen Liu, Qi Li, Guo-Qin Zheng, Karthik Ramani, William Benjamin, Using diffusion distances for flexible molecular shape comparison, BMC Bioinformatics, 2010. • www.cs.princeton.edu/courses/archive/fall07/cos597A/lectures/surfac es.pdf • biogeometry.duke.edu/meetings/ITR/04jun12/presentations/kim.ppt Bio-CAD