Issue 63- Conformational Entropy Calculation

[ioanaapapa]

Summary

This PR addresses issues related to the calculation of the conformational entropy at the united atom and residue levels and resolves the differences between results obtained using the current implementation of the theory at the united atom level and the implementation from the previous release. Differences for each type of residue, prior the commit, with terminal residues being isolated, are shown in the figure below. This PR closes #63

Changes

Heavy atoms universe :

• A new MDAnalysis universe is created, containing only the heavy atoms in a residue and this universe now represents the data_container argument for the get_dihedrals and conformational_entropy functions. Previously, the functions called an MDAnalysis universe containing all atoms within a residue and iterated
  per heavy atom in residue - hence, all dihedrals that the heavy atoms were involved in were found and taken into account.

Impact

• Heavy atom-only dihedrals are now identified and taken into account for the conformational entropy calculation. Values obtained for aliphatic residues now match values obtained using the previous AEM implementation, as shown in the figure below.
  

• In the previous implementation, terminal residues each had an additional dihedral, as shown in the figure below. These dihedrals coincide with backbone dihedrals, which are now accounted for by the residue level calculation.

• Previous implementation seems to sometimes double count some turning points for aromatic side chains that are rigid, as seen in the figure below for a phenylalanine. However, the aromatic rings are flipped as a result of the rotation about a different bond, not as a result of these dihedral adopting a new conformation so these conformations shouldn't be taken into account. Therefore, entropy of residues with aromatic side chains was much higher sometimes - this should be fine in the current new implementation and explains the difference observed for aromatic side chains.

Possible future considerations

• Currently, the backbone entropy is estimated using the residue level calculation, which treats a whole residue as a bead and takes into account dihedrals consisting of four neighbouring residues. Backbone entropy could also be calculated using the phi and psi dihedrals, obtained using the corresponding MDAnalysis functions (https://userguide.mdanalysis.org/1.1.1/examples/analysis/structure/dihedrals.html). Results seem to be very close anyway.

[jimboid]

Code looks like it is matching the explainer in the PR. Very thorough analysis supporting this merger.

[skfegan]

I agree with James. The explanation makes sense and the code looks like what I would expect.

[harryswift01]

This looks like a very clean implementaion, thank you for going through so much detail in the PR comments its very nice to see, I'm happy to approve this.