Why do four different triangles share one TSR key?
Ubiquitin (PDB 1UBQ), chain A, computed with the protein Cα method of BioTSR 1.0.0. Four different triangles in it have the same key, 17637781. Choose one, rotate the structure, and see what changes and what stays the same.
With the picture focused: arrow keys rotate, plus and minus zoom, 1 to 4 choose a triangle, R resets the view.
A key keeps only three things: the three vertex labels, which bin the triangle’s angle θ falls in, and which bin its longest edge falls in. Exact positions and lengths are not part of it, so different triangles whose values land in the same bins get the same key.
- Residues
- Val 70, Ile 44, Leu 8 triangle 1
- TSR angle θ
- 43.25°
- Longest edge (maxDist)
- 11.96 Åbetween Ile 44 and Leu 8
- Vertex labels (residue codes)
- Val 20 · Ile 10 · Leu 8
- θ class
- class 11: 42.64° ≤ θ < 45.17°
- Distance class
- class 5: 11.00 Å ≤ maxDist < 14.00 Å
θ is the angle between the base (the first two vertices in BioTSR’s order, highest label first) and the line from the base’s midpoint to the third vertex, folded into 0–90°. In the picture the dashed line is that median and the bold edge is the longest edge.
The four triangles
All four have the vertex labels Val 20, Ile 10 and Leu 8, θ in class 11 and maxDist in class 5, so all four get key 17637781, and the .keys file gives that key a frequency of 4. Their positions in the chain and their exact angles and lengths differ.
| # | Residues (BioTSR’s order) | θ | θ class | maxDist | Longest edge | Distance class |
|---|---|---|---|---|---|---|
| 1 | Val 70 · Ile 44 · Leu 8 | 43.25° | 11 | 11.96 Å | Ile 44 – Leu 8 | 5 |
| 2 | Val 5 · Ile 61 · Leu 56 | 43.67° | 11 | 13.22 Å | Val 5 – Leu 56 | 5 |
| 3 | Val 17 · Ile 61 · Leu 15 | 44.38° | 11 | 13.11 Å | Ile 61 – Leu 15 | 5 |
| 4 | Val 70 · Ile 36 · Leu 71 | 44.03° | 11 | 11.02 Å | Val 70 – Ile 36 | 5 |
Values from the four rows of 1UBQ_A_protein.triplets with this key and the .keys row that counts them, written by biotsr run --method protein --pdb 1UBQ.pdb --chain A with BioTSR 1.0.0. Coordinates: Cα atoms of PDB entry 1UBQ, the copy BioTSR 1.0.0 was tested with. Triangle 1 is the one followed in the worked example; the others follow in the order the file lists them.
Next
- Your first 10 minutes with BioTSR: compute these four triangles yourself, in a notebook.
- The worked example on Understand TSR: how labels, θ and maxDist become the key.
- Learn BioTSR: this lesson and the notebook together.