Using normal mode analysis in teaching mathematical modeling to biology students
Mathematical Modelling of Natural Phenomena (2011)
- Volume: 6, Issue: 6, page 278-294
- ISSN: 0973-5348
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topKondrashov, D. A.. "Using normal mode analysis in teaching mathematical modeling to biology students." Mathematical Modelling of Natural Phenomena 6.6 (2011): 278-294. <http://eudml.org/doc/222280>.
@article{Kondrashov2011,
abstract = {Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning activities associated with building and understanding these models, ranging from analytical to computational. I provide a number of web resources where students can obtain structural data, perform calculations, and suggest research directions for independent projects. },
author = {Kondrashov, D. A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {mathematical modeling; elastic network models; normal mode analysis; curriculum development},
language = {eng},
month = {10},
number = {6},
pages = {278-294},
publisher = {EDP Sciences},
title = {Using normal mode analysis in teaching mathematical modeling to biology students},
url = {http://eudml.org/doc/222280},
volume = {6},
year = {2011},
}
TY - JOUR
AU - Kondrashov, D. A.
TI - Using normal mode analysis in teaching mathematical modeling to biology students
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/10//
PB - EDP Sciences
VL - 6
IS - 6
SP - 278
EP - 294
AB - Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning activities associated with building and understanding these models, ranging from analytical to computational. I provide a number of web resources where students can obtain structural data, perform calculations, and suggest research directions for independent projects.
LA - eng
KW - mathematical modeling; elastic network models; normal mode analysis; curriculum development
UR - http://eudml.org/doc/222280
ER -
References
top- A. Atilgan, S. Durell, R. Jernigan, M. Demirel, O. Keskin, and I. Bahar. Anisotropy of fluctuation dynamics of proteins with an elastic network model. Biophysical Journal, 80 (2001), 505–515.
- I. Bahar, A. R. Atilgan, and B. Erman. Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. Folding and Design, 2 (1997), 173–181.
- I. Bahar and A. Rader. Coarse-grained normal mode analysis in structural biology. Current Opinion in Structural Biology, 15 (2005), 586–592.
- Q. Cui and I. Bahar. Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems. Chapman and Hall/CRC, 1 ed., 2005.
- J. L. Dunn. A pictorial visualization of normal mode vibrations of the fullerene (C60) molecule in terms of vibrations of a hollow sphere. Journal of Chemical Education, 87 (2010), 819–822.
- D. A. Kondrashov, Q. Cui, and G. N. Phillips, Jr. Optimization and evaluation of a coarse-grained model of protein motion using X-Ray crystal data. Biophysical Journal, 91 (2006), 2760–2767.
- D. A. Kondrashov, A. W. Van Wynsberghe, R. M. Bannenl, Q. Cui, and G. N. Phillips, Jr.Protein structural variation in computational models and crystallographic data. Structure, 15 (2007), 169–177.
- W. G. Krebs, V. Alexandrov, C. A. Wilson, N. Echols, H. Yu, and M. Gerstein. Normal mode analysis of macromolecular motions in a database framework: Developing mode concentration as a useful classifying statistic. Proteins: Structure, Function, and Genetics, 48 (2002), 682–695.
- L. Orellana, M. Rueda, C. Ferrer-Costa, J. Lopez-Blanco, P. Chacon, and M. Orozco. Approaching elastic network models to molecular dynamics flexibility. Journal of Chemical Theory and Computation, 6 (2010), 2910–2923.
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical recipes: The art of scientific computing. Cambridge University Press, Cambridge, 3rd ed, 2007.
- K. Suhre and Y. Sanejouand. Elnemo: A normal mode web server for protein movement analysis and the generation of templates for molecular replacement. Nucleic Acids Research, 32 (2004), W610–W614.
- M. M. Tirion. Large-amplitude elastic motions in proteins from a single-parameter atomic analysis. Physical Review Letters, 77 (1996), 1905–1915.
- A. W. Van Wynsberghe and Q. Cui. Interpreting correlated motions using normal mode analysis. Structure, 14 (2006), 1647–1653.
- L. Yang and I. Bahar. Coupling between catalytic site and collective dynamics: A requirement for mechanochemical activity of enzymes. Structure, 13 (2005), 893–904.
- L. Yang, X. Liu, C. J. Jursa, M. Holliman, A. Rader, H. A. Karimi, and I. Bahar. iGNM: A database of protein functional motions based on gaussian network model. Bioinformatics, 21 (2005), 2978 –2987.
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