Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining.

Area of Science:

• Computational Chemistry
• Molecular Dynamics
• Statistical Mechanics

Background:

• Dimension reduction is crucial for simulating molecular systems at longer length and time scales.
• Comparing models at different scales is challenging due to vector length discrepancies, hindering direct dot product analysis.

Purpose of the Study:

• To investigate and develop mapping procedures for normal mode analysis in dimensionally reduced molecular models.
• To introduce a suite of metrics for evaluating the accuracy and consistency of these reduced models.

Main Methods:

• Reviewed horizontal mapping for reduced Hessian techniques.
• Designed a vertical mapping procedure for coarse-graining all-atom Hessians using vibrational subsystem analysis.
• Developed dimension-dependent and independent metrics, emphasizing mass-weighting.

Main Results:

• The vertical mapping procedure effectively derives effective force constants and kinetic tensors.
• Tested metrics on toy and globular protein systems across various scales (all-atom, Gō-like, elastic network models).
• Demonstrated the ability of metrics to differentiate physically reasonable from unreasonable models.

Conclusions:

• The developed mapping procedures and metrics provide a robust framework for assessing dimensionally reduced molecular models.
• Accurate comparison across different simulation scales is now feasible, advancing molecular simulation accuracy.