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M. Ramanathan
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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
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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
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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
triangulations
and 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 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.
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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 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.
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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/surfac
es.pdf
• biogeometry.duke.edu/meetings/ITR/04jun12/presentations/kim.ppt
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