Bio-CAD

Bio-CAD

M. Ramanathan

Bio-CAD

Molecular surfaces

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Molecular surfaces

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Connolly surface

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Molecular surface representation

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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

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Mesh representation

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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.

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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).

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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)

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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)

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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.

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Diffusion distance (contd.)

Diffusion distance (DD) descriptor is compared to inner distance (ID) and Euclidean distance (ED).

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Inner and Euclidean distancesThe 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.

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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