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

(2012) JOURNAL OF COMPUTATIONAL CHEMISTRY. 33(28). p.2250-2275
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Abstract
Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse-graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the implosion of the all-atom (AA) Hessian to a coarse-grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass-weighting. The dimension-dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension-independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Go-like model, a canonical elastic network model, and a network model with intentionally unphysical force constants.
Keywords
normal mode analysis, chemical kinetics, NMA, effective Hessian, vibrational analysis, entropy, free energy, coarse-grained models, coarse-graining, kinetic tensor, elastic network model, heat capacity, CG, FREQUENCY NORMAL-MODES, ELASTIC NETWORK MODEL, MOLECULAR-DYNAMICS, HARMONIC-ANALYSIS, PROTEIN DYNAMICS, LARGE SYSTEMS, VIBRATIONAL ANALYSIS, SINGLE-PARAMETER, FORCE-FIELDS, MACROMOLECULES

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MLA
Ghysels, An, et al. “Comparing Normal Modes across Different Models and Scales: Hessian Reduction versus Coarse-Graining.” JOURNAL OF COMPUTATIONAL CHEMISTRY, vol. 33, no. 28, 2012, pp. 2250–75, doi:10.1002/jcc.23076.
APA
Ghysels, A., Miller, B. T., Pickard, F. C., IV, & Brooks, B. R. (2012). Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining. JOURNAL OF COMPUTATIONAL CHEMISTRY, 33(28), 2250–2275. https://doi.org/10.1002/jcc.23076
Chicago author-date
Ghysels, An, Benjamin T Miller, Frank C Pickard IV, and Bernard R Brooks. 2012. “Comparing Normal Modes across Different Models and Scales: Hessian Reduction versus Coarse-Graining.” JOURNAL OF COMPUTATIONAL CHEMISTRY 33 (28): 2250–75. https://doi.org/10.1002/jcc.23076.
Chicago author-date (all authors)
Ghysels, An, Benjamin T Miller, Frank C Pickard IV, and Bernard R Brooks. 2012. “Comparing Normal Modes across Different Models and Scales: Hessian Reduction versus Coarse-Graining.” JOURNAL OF COMPUTATIONAL CHEMISTRY 33 (28): 2250–2275. doi:10.1002/jcc.23076.
Vancouver
1.
Ghysels A, Miller BT, Pickard FC IV, Brooks BR. Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining. JOURNAL OF COMPUTATIONAL CHEMISTRY. 2012;33(28):2250–75.
IEEE
[1]
A. Ghysels, B. T. Miller, F. C. Pickard IV, and B. R. Brooks, “Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining,” JOURNAL OF COMPUTATIONAL CHEMISTRY, vol. 33, no. 28, pp. 2250–2275, 2012.
@article{3066364,
  abstract     = {{Dimension reduction is often necessary when attempting to reach longer length and time scales in molecular simulations. It is realized by constraining degrees of freedom or by coarse-graining the system. When evaluating the accuracy of a dimensional reduction, there is a practical challenge: the models yield vectors with different lengths, making a comparison by calculating their dot product impossible. This article investigates mapping procedures for normal mode analysis. We first review a horizontal mapping procedure for the reduced Hessian techniques, which projects out degrees of freedom. We then design a vertical mapping procedure for the implosion of the all-atom (AA) Hessian to a coarse-grained scale that is based upon vibrational subsystem analysis. This latter method derives both effective force constants and an effective kinetic tensor. Next, a series of metrics is presented for comparison across different scales, where special attention is given to proper mass-weighting. The dimension-dependent metrics, which require prior mapping for proper evaluation, are frequencies, overlap of normal mode vectors, probability similarity, Hessian similarity, collectivity of modes, and thermal fluctuations. The dimension-independent metrics are shape derivatives, elastic modulus, vibrational free energy differences, heat capacity, and projection on a predefined basis set. The power of these metrics to distinguish between reasonable and unreasonable models is tested on a toy alpha helix system and a globular protein; both are represented at several scales: the AA scale, a Go-like model, a canonical elastic network model, and a network model with intentionally unphysical force constants.}},
  author       = {{Ghysels, An and Miller, Benjamin T and Pickard, Frank C, IV and Brooks, Bernard R}},
  issn         = {{0192-8651}},
  journal      = {{JOURNAL OF COMPUTATIONAL CHEMISTRY}},
  keywords     = {{normal mode analysis,chemical kinetics,NMA,effective Hessian,vibrational analysis,entropy,free energy,coarse-grained models,coarse-graining,kinetic tensor,elastic network model,heat capacity,CG,FREQUENCY NORMAL-MODES,ELASTIC NETWORK MODEL,MOLECULAR-DYNAMICS,HARMONIC-ANALYSIS,PROTEIN DYNAMICS,LARGE SYSTEMS,VIBRATIONAL ANALYSIS,SINGLE-PARAMETER,FORCE-FIELDS,MACROMOLECULES}},
  language     = {{eng}},
  number       = {{28}},
  pages        = {{2250--2275}},
  title        = {{Comparing normal modes across different models and scales: Hessian reduction versus coarse-graining}},
  url          = {{http://doi.org/10.1002/jcc.23076}},
  volume       = {{33}},
  year         = {{2012}},
}

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