PAE and pCMAP order of residues pair definition

[St3451]

Issue
The PAE is not a symmetric matrix, for a pair of residue (i, j), the PAE matrix includes the predicted error of i when the structure is aligned to j. Now, the problem is that we are not sure if the order of residues is the one just mentioned above and, therefore, j and j could be flipped. In fact, we did implemented the calculation of the probability of contact map matrix (pc) assuming the opposite, i.e., pc(i, j) = probability of j to be in contact with i, considering pae(i, j) as the error of j when the structure is aligned to i.

https://github.com/bbglab/clustering_3d/blob/93600fb275ab9f0b049bc37e8945e432dddfa60b/scripts/datasets/prob_contact_maps.py#L130-L168

Potential solution
We should first check what is the real order for the relationship between each pair of residues in the PAE object. If pae(i, j) represents the error of j when the structure is aligned to i, then our calculation is correct. If it is the other way around, we should flip the residues in our code.

Probably, swapping the residues in the PAE matrix in line 166 could be enough:

m[i, j] = get_prob_contact(pae[j, i], d, distance)

Disclaimer
It is important to note that while the PAE matrix is indeed not symmetric, the difference between (i, j) and (j, i) is marginal. This asymmetry has a negligible impact on the 3D clustering analysis and does not significantly affect the overall results.

[St3451]

@koszulordie