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There have been several efforts to smooth molecular dynamics trajectories so as to remove atomic thermal vibrations and make the overall articulation of the molecule more clear. Most such methods use dimension-reduction techniques, such as SVD, on the cartesian coordinates of the molecule. Methods operating in real-space, however, yield non-realistic animations, as bond lengths and angles are not preserved. We have been investigating how to do this in torsion angle space, with the goal of obtaining more natural-looking motions – as this would automatically preserve these quantities.
Traditional dimension-reduction techniques do not apply here, however, as the torsion angle space is not flat. We exploit recent advances on multiscale methods over Lie groups, but several challenges remain. These include the periodicity of the angle representation: changing a certain angle coordinate by 360 degrees gives a very different set of intermediate conformations. The right choice of angle is not obvious, especially in the early stages of folding, when angles change by relatively large amounts between consecutive frames. Also, guaranteeing no self-collisions in the smoothed trajectories is hard, as a small change in one of the bond angles, for instance, may create large displacements in distant parts of the molecule.