bio-cad m. ramanathan bio-cad. molecular surfaces bio-cad
TRANSCRIPT
Bio-CAD
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
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
Probe
Probe
Rolling blend
Link blend
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
p3p4
p5
p6
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
Bio-CAD
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 triangulationsand 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 representation of the volume (d)
Bio-CAD
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/surfaces.pdf
• biogeometry.duke.edu/meetings/ITR/04jun12/presentations/kim.ppt