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

(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:
http://hdl.handle.net/1854/LU-3066364

- author
- An Ghysels UGent, Benjamin T Miller, Frank C, IV Pickard and Bernard R Brooks
- organization
- year
- 2012
- 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.