Chandrajit Bajaj

Protein Protein Interaction

 Introduction | Representation | Function | Dynamic structure | Hierarchical model | Protein docking | Simulations | Meshing | Visualization

5. Hierarchical models and rendering

(See also dynamic shape representations)

The three dimensional structure and properties of molecules determine their functional behavior and interaction with other molecules. Since proteins are seen to be flexible, and have differing properties including fields at different configurations, a mere rigid body interaction simulation does not suffice. Hence, we need to perform simulations with flexible models.These models help in both calculations and visualization of protein docking in an adaptive manner. Bonds between different structures can be given different degrees and ranges of freedom, and this tree like structure lends itself to faster animation calculations than a full n body simulation. Hierarchical data structure to hold a protein which can be defined naturally in this manner. 

class GroupOfAtoms 
    GroupOfAtoms( );
    virtual ~GroupOfAtoms( );
    ExpandableArray<GroupOfAtoms> m_SubGroups;
    ExpandableArray<Atom> m_Atoms;
    ExpandableArray<Bond> m_Bonds;
The protein descriptions are parsed into the above recursive structure, with the following graph.

Hierarchical models are constructed from the new data structure in various ways for visualization. 

  • The union of balls representation has been extended to allow for a tree like representation, in which atoms are collapsed into larger primitives, preserving some error bounds.
  • Adaptive isocontouring and dynamic adaptive isocontour visualization are some of the tools developed for this purpose.
  • Hierarchical splatting softwares have been developed to render the functions in an adaptive manner.
  • A new data structure for representing Adaptive meshes has been presented.

C. Bajaj, V. Pascucci, R. Holt, A. Netravali.
Dynamic Maintenance and Visualization of Molecular Surfaces
Fourth issue in the special series of Discrete Applied Mathematics on Computational Molecular Biology

Sanner, M., and Olson, A.
Real-time surface reconstruction for moving molecular fragments.
Pacific Symposium on Biocomputing'97, 1996, R.Altman, A.Dunker, L.Hunter, and T.Klein, Eds., World Scientific Press, pp.~385-396.

Sanner, M., Olson, A., and Spehner, J.
Reduced surfaces: An efficient way to compute molecular surfaces.
Biopolymers 38, 1996, 305-320.

Lotan, I., Schwarzer, F., Halperin, D., and Latombe, J.C.
Efficient maintenance and self-collision testing for kinematic chains.
Proc. 18th ACM Symposium on Computational Geometry, 2002, pp.~43-52.

Halperin, D., Latombe, J.C., and Motwani, R.
Dynamic maintenance of kinematic structures. 
Robotic Motion and Manipulation, J.P. Laumond and M.Overmars, Eds. A. K. Peters, pp.~155-170.

Finn, P., Halperin, D., Kavraki, L., Latombe, J.C., Motwani, R., Shelton, C., and Venkatsubramanian, S.
Geometric manipulation of flexible ligands.
Applied Computational Geometry: Towards Geometric Engineering, M.C. Lin and D.Manocha, Eds., vol.~1148 of Lecture Notes Comput. Sci Springer-Verlag, 1996, pp.~67-78.