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

An Ghysels UGent, Benjamin T Miller, Frank C, IV Pickard and Bernard R Brooks (2012) JOURNAL OF COMPUTATIONAL CHEMISTRY. 33(28). p.2250-2275
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
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
journal title
JOURNAL OF COMPUTATIONAL CHEMISTRY
J. Comput. Chem.
volume
33
issue
28
pages
2250 - 2275
Web of Science type
Article
Web of Science id
000309065400005
JCR category
CHEMISTRY, MULTIDISCIPLINARY
JCR impact factor
3.835 (2012)
JCR rank
34/150 (2012)
JCR quartile
1 (2012)
ISSN
0192-8651
DOI
10.1002/jcc.23076
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
3066364
handle
http://hdl.handle.net/1854/LU-3066364
date created
2012-12-06 10:36:38
date last changed
2012-12-06 11:36:13
@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},
  keyword      = {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://dx.doi.org/10.1002/jcc.23076},
  volume       = {33},
  year         = {2012},
}

Chicago
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.
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.
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.
MLA
Ghysels, An, Benjamin T Miller, Frank C Pickard IV, et al. “Comparing Normal Modes Across Different Models and Scales: Hessian Reduction Versus Coarse-graining.” JOURNAL OF COMPUTATIONAL CHEMISTRY 33.28 (2012): 2250–2275. Print.