6. Contributions and Results

Contour Spectrum Analysis

Contour spectrum analysis computes quantitative signature functions. The horizontal axis spans the scalar values a. Computation and Plot of a set of signatures (length, area, gradient …) as functions of the scalar value a. Vertical axis spans normalized ranges of each signature. White vertical white bars mark current selected isovalues.

Topological Analysis and Quantitative Tools (TAQT)

TAQT computes topological properties of scalar data such as Betti numbers and contour trees. Contour tree tells us the number of components per isocontour which isocontours merge together or split while modifying the isovalue.

Morse Complex

Here is an example of Morse complex of electron density.

Critical points with linking curves.

The gradual increase of the field opacity allows to better understand its spatial distribution of path connected components.

HyperVolume Exploration Tools

HyperVolume Exploration Tools is a High Dimensional Scalar Field Exploration software. Consider the molecular interaction energy between a receptor and a ligand. Assuming rough axial symmetry of the ligand, this is a scalar field SF defined on a five-dimensional configuration space (three translational degrees of freedom and two rotational degrees of freedom). RED = attraction BLUE = repulsion GREEN = free configuration 5-dimensional scalar field given by the interaction energy between a small ligand and a large receptor (three translational degrees of freedom and two rotational degrees of freedom). The axis of one degree of freedom is much longer than the others to highlight the relevance of such rotation. From the top picture it is clear that low or high angles (large red spots) are more favorable for the docking of the two molecules. Removing all colors but red as in the bottom figure you can also see how the two large regions are connected by a narrow tunnel.

Hodgkin Similarity Index Analysis for 242 Protein Chains by UPGMA

“Family tree” of electrostatic similarity generated by UPGMA algorithm; colors: cholinesterase-like proteins (red), enolase-like proteins (green), ferritin-like proteins (gold), kinases (blue), superoxide dismutases (magenta).
Matrix of similariy indices for all 242 protein chain pairs. Axes labeled by chain ID and colored as in A. Matrix colors range from red (similarity index 0) to purple (similarity index 1).	Subset of matrix in B for kinases

Biological Database Results

Preliminary classification results

4 Main Classes

1. Cholinesterase-like proteins
2. Enolase-like proteins
3. kinases
   (1AD5A and 1AD5B are sub-chains in 1AD5)
   sub chain also can be compared with other protein.
4. Superoxide dismutases

Distance values represent the relative difference between proteins within each class. For example, if we choose 2ACE as the query, and select a distance value of 0.08, we get the molecules 1FSS, 2ACE and 1ACL, all of which belong to the same class.

Within these distance PDB database return the same class PDB

The PDB Files: Grouped by Class Description