Research question
To generate 2-D TorsionDrives of protein backbone dihedrals in dipeptides (2021-11-18-OpenFF-Protein-Dipeptide-2D-TorsionDrive), the heavy-atom dihedral angles of the amino acid sidechains (which were not driven in the TorsionDrive) were constrained to values corresponding to highly populated sidechain rotamers. These constraints prevent large sidechain rearrangements that lead to discontinuous jumps in the QM energy profile (2021-12-16 Meeting notes). There is concern that using CONstraints instead of REstraints may introduce artificially high energy barriers during the torsion scan.
Atomic gradients of constrained atoms
If constraints on non-driven dihedral angles introduce artificially high energy barriers, we would expect that the atoms in these constrained dihedrals would experience much larger forces after the QM optimizations at each grid point when these constraints are present. Below we compare the atomic gradients for the TRP-rotamer-2 record for a phi/psi 2-D TorsionDrive with constraints on sidechain dihedrals (OpenFF Protein Dipeptide 2D TorsionDrive v1.1) and without constraints on sidechain dihedrals (OpenFF Protein Dipeptide 2D TorsionDrive v1.0).
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The RMS force on non-constrained atoms is similar with and without constraints on sidechain dihedrals, and the RMS force on non-driven and not driven constrained atoms is 50 times higher with constraints on sidechain dihedrals than without.
Energy differences between TorsionDrives
We can also compare the QM energy profiles with and without constraints on sidechain dihedrals. First, we shift each energy profile by its own minimum energy so that the minimum energy is zero for both profiles. The minimum energy occurs at the same grid point for both profiles. Then, we compute an RMS error over grid points.
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With the weights defined using the shifted QM energies of the TorsionDrive without constraints on sidechain dihedrals, the weighted RMS error is 0.0779 kcal mol−1. Thus, the energy differences occur almost entirely in high energy regions which do not contribute to the ForceBalance objective function during torsion fitting.
Code to reproduce
The results in the table above can be reproduced with the following python code. Arguments are
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