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Building a Coarse-Grained Model Based on the Mori-Zwanzig Formalism

Published online by Cambridge University Press:  24 February 2015

Hee Sun Lee ,
Surl-Hee Ahn  and
Eric F. Darve
Hee Sun Lee
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
Surl-Hee Ahn
Affiliation:
Department of Chemistry, Stanford University, Stanford, CA 94305, U.S.A.
Eric F. Darve
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, U.S.A. Institute for Computational and Mathematical Engineering, Jen-Hsun Huang Engineering Center, Stanford University, Stanford, CA 94305, U.S.A.
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Abstract

We present a novel method to build a coarse-grained (CG) model based on the Mori-Zwanzig (MZ) formalism that reproduces kinetics. Our approach leads to the computation of a generalized Langevin equation (GLE), which includes the memory kernel and the fluctuation that are consistent with brute force molecular dynamics (MD) simulations. Our CG model based on the MZ formalism successfully reproduces kinetics, i.e. the distribution of first passage times (FPT) and velocity autocorrelation functions (VACF), for alanine dipeptide. In addition, we show that the memory part of the CG model of GLE is essential to reproduce kinetics. In other words, the Markovian model fails to reproduce brute force MD results, whereas the GLE model succeeds.

Keywords

kineticssimulationbiological
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1753: Symposium NN – Mathematical and Computational Aspects of Materials Science , 2015 , mrsf14-1753-nn09-03
Copyright
Copyright © Materials Research Society 2015 

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References

REFERENCES

Schlick, T., Molecular Modeling and Simulation: An Interdisciplinary Guide, Vol. 21, (Springer, 2010) pp. 507–508.CrossRefGoogle Scholar
Hoogerbrugge, P.J., Koelman, J.M.V.A., EPL (Europhys. Lett.) 19.3, 155 (1992).CrossRefGoogle Scholar
Zwanzig, R., Phys. Rev. 124.4, 983 (1961).CrossRefGoogle Scholar
Mori, H., Progr. Theoret. Phys. 33.3, 423–455 (1965).CrossRefGoogle Scholar
Zwanzig, R., Nonequilibrium Statistical Mechanics, (Oxford University Press, 2001) pp. 18–21.Google Scholar
Zwanzig, R., J. Statist. Phys. 9.3, 215–220 (1973).CrossRefGoogle Scholar
Chorin, A.J., Hald, O.H. and Kupferman, R., Proc. Natl. Acad. Sci. USA 97.7, 2968–2973 (2000).CrossRefGoogle Scholar
Chorin, A.J., Hald, O.H. and Kupferman, R., Physica. D: Nonlinear Phenomena 166.3, 239–257 (2002).CrossRefGoogle Scholar
Ceriotti, M., Bussi, G., and Parrinello, M., J. Chem. Theory Comput. 6.4, 1170–1180 (2010).CrossRefGoogle Scholar
Morrone, J.A., Markland, T.E., Ceriotti, M., and Berne, B.J., J. Chem. Phys. 134.1, 014103 (2011).CrossRefGoogle Scholar
Jorgensen, W.L., Maxwell, D.S., and Tirado-Rives, J., J. Am. Chem. Soc. 118.45, 11225–11236 (1996).CrossRefGoogle Scholar
Kaminski, G.A., Friesner, R.A., Tirado-Rives, J., and Jorgensen, W.L., J. Phys. Chem. B 105.28, 6474–6487 (2001).CrossRefGoogle Scholar
Wu, Y., Tepper, H.L., and Voth, G.A., J. Chem. Phys. 124.2, 024503 (2006).CrossRefGoogle Scholar
Darve, E. and Pohorille, A., J. Chem. Phys. 115.20, 9169–9183 (2001).CrossRefGoogle Scholar
Bracewell, R.N. and Bracewell, R.N, The Fourier transform and its applications, Vol. 31999, (New York: McGraw-Hill, 1986) pp. 465.Google Scholar
Staszewski, W.J., Sound Vib, J.. 203.2, 283–305 (1997).Google Scholar
Izvekov, S. and Voth, G.A.., J. Chem. Phys. 125.15, 151101 (2006).CrossRefGoogle Scholar
Markutsya, S. and Lamm, M.H.. J. Chem. Phys. 141.17 174107 (2014).CrossRefGoogle Scholar