Visualization of AD tetrahedra with large thresholds in TrpRS chains.

Downloads

• Download the KIN file with all tetrahedra visualization options -- vectors, volumes, spheres and solids (trpRS18chn.kin, 25MB). Warning: it can take quite a while for Mage to load this file! A version is available with only spheres (trpRSspheres.kin,2.6MB), which should load faster.
• More information about the Kinemage 3D visualization format is here, and the Mage program for various platforms may be downloaded here.
• Download the 3 original PDB files here ( 1D2R, 1MB2, 1MAW).



Background and Tutorial


Click here for a general context about almost-Delaunay tetrahedra and their other uses in the analysis of protein structure.

This kinemage compares the AD tetrahedra across 18 different copies of the same structure, the TrpRS monomer from PDB structures 1D2R (chains 1-6), 1MB2 (7-12) and 1MAW (13-18) that have 6 copies each of this structure. AD tetrahedra were computed for the 18 chains individually, with epsilon cutoff being 2.0 and edges over 12 A being pruned. All the chains had the same sequence numbering, so that tetrahedra with the same indices across all the chains corresponded to the same four neighboring residues. The chains were then structurally aligned using code for RMSD minimization, for ease of display superposition and visual comparison of corresponding tetrahedra across the chains. The chains are displayed by joining the Calphas (deadwhite color), side-chain Centroids (purple), and links from each Calpha to the corresponding centroid ("magenta" which is actually a shade of blue).

The tetrahedra across all the chains are classified into groups based on how many of them are Delaunay:

• all D means all the chains have a tetrahedron as Delaunay,
• 1/3rd D means between 1/3 and 2/3rd of the chains have a tetrahedron Delaunay (the others have it AD with some threshold less than the cutoff used for AD computation.)
• 2/3rd D means over 2/3rd but not all the chains have a tetrahedron Delaunay

Note that tetrahedra with less than 1/3rd of the chains Delaunay are deemed to not denote structural neighbors, and are discarded.

Within the 1/3rd D and 2/3rd D groups, tetrahedra are also classified into groups based on the maximum threshold over all chains being compared. This classification is into threshold brackets, currently 5: 0-0.01, 0.01-0.1, 0.1-0.5, 0.5-1.0, 1.0-2.0. Thus there are a total of 11 groups, and one can toggle between them with "animate" or switch a few of them on. NOTE: to keep this kinemage as small as possible and since they don't reveal a lot of information except by their absence, the "all D" group was not included in this kinemage.

Our interest would be in the first two threshold brackets to look at the significance of small changes in "a few" of the chains (2/3rd D) or "quite a few" chains (1/3rd D). The last two brackets on the other hand correspond to large changes (perhaps hinges), and could be looked at in the same two cases. The middle group corresponds to moderate changes.

To help make some sense of the clutter, I would suggest to use the "spheres" display option (instead of or along with the default "volumes"). The spheres at the centroids of tetrahedra serve as ID markers, identifying the four residues and the chain that the tetrahedron comes from, as well as the exact value of its threshold. Also, there are "master buttons" that help pinpoint parts of the comparison:

• groups like 2/3rd D and 1/3rd D
• individual chains (C1..C18)
• Calphas/Centroids (only one should be checked!)
• thresholds of individual tetrahedra in these groups (not the max across all chains): Delaunay, AD e0.01, AD e0.10, AD e0.50, AD e1.00, AD e2.00. These help zero in on the tetrahedra with thresholds of interest, eg. blocking out Delaunay.



Observations  

Below are some screen shots from my Kinemage vizualization of Almost-Delaunay Tetrahedra in 18 chains of TrpRS (6 each from PDB files 1D2R, 1MB2 and 1MAW). Chains are aligned, and only tetrahedra with high ε in some chain are shown, as spheres at the centroid of the four neighboring residue C-αs or sidechain centroids. Click on each image to see a larger Mage screen shot.

C-alphas, Delaunay in 1/3-2/3rd of the chains	C-alphas, Delaunay in over 2/3rd of the chains
SC centroids, Delaunay in 1/3-2/3rd of the chains	SC centroids, Delaunay in over 2/3rd of the chains




A comparison of the 4 views shown above is instructive and depicts our observations about the connection of almost-Delaunay tetrahedra with hinges and conformational changes. We look at the 1/3rd D and 2/3rd D groups for Calphas and SC Centroids. In each case, only groups with at least one chain having a high threshold (more than 0.1 or 0.5A) tetrahedron are considered, since it signifies a significant change in nearest neighbors in a significant number of chains. Then, the "Delaunay" and for the Centroid case, the 0-0.01 and 0.01-0.1 groups are also turned off so we can see clearly the regions with deviations.

After above-mentioned filtering, we observe a concentration of AD tetrahedra in and around regions where alignment is poor, signifying conformational change.

• For C-alphas, 1/3rd D, residues 178-183 and nearby residues 20-21 form one cluster of tetrahedra, and 106-118 form another cluster.
• For C-alphas, 2/3rd D, we see interesting behavior. {20,181,244,247} is a single tetrahedron that is different in 3 chains, 3, 9 and 15, which correspond to chain C of all three PDB files. This indicates some difference in conformation in this region that. At the other end tetrahedra from residues 106-118 form a cluster, and each tetrahedron with a high threshold occurs either in either 5 or all 6 of chains 1-6, with very similar values of threshold in all the cases. Thus we conclude that chains 1-6 differ significantly from the other chains in this region and are topologically very similar to each other. We also conclude that the categories of 1/3rd D and 2/3rd D need to be adjusted, since there is a significant number of tetrahedra on the borderline, that are non-Delaunay in 5 or 6 of the chains.
• For sidechain centroids, 1/3rd D, the regions of neighbor differences are slighly more widespread than for the Calphas. We see clusters of high-threshold tetrahedra connecting residues 180-184 with 230-232 and 240-243; residues 175-182 with each other as well as 20-26; and finally, residues 106-122 among themselves.
• For sidechain centroids, 2/3rd D, the clusters again shrink drastically, into {107-108-110-122}, {109-111-112-113}, and a few isolated tetrahedra joining residues 20-25 with 175-183. These are concentrated in chains 2-7 and 13-15, and miss the regions of most drastic conformational change, settling on peripheral regions. This fact again undermines the importance of this group and suggests a merger with the 1/3rd D group or a change in group boundaries.

Recall that the AD tetrahedra were computed for the 18 unaligned chains. Thus the ability to determine regions of conformational change by intersecting and clustering these tetrahedra across the chains based on the maximum threshold and number that are not Delaunay is significant.



Conclusions   AD tetrahedra can help us compare similar potein structures and highlight the similarities and differences, including hinge regions or regions of conformational change or motion. The tetrahedra that are Delaunay in a significant number of individual chains, while being AD with a high threshold (>0.5) in some others, are seen to be clustered around the 2 regions of greatest conformational change in TrpRS, which strengthens the above argument. Further tests are necessary to quantify this argument and yield a way of identifying the hinge residues robustly from AD data.



Project Members  

Deepak Bandyopadhyay Graduate Student UNC Chapel Hill debug at cs.unc.edu

Alexander Tropsha Professor and Director, Laboratory of Molecular Modeling, School of Pharmacy, UNC Chapel Hill alex_tropsha at unc.edu

Charles W. Carter, Jr. Professor of Biochemistry and Biophysics, School of Medicine, UNC Chapel Hill carter at med.unc.edu

Jack Snoeyink Professor of Computer Science UNC Chapel Hill snoeyink at cs.unc.edu