Generalized Shadow Hybrid Monte Carlo (GSHMC) is a method for molecular simulations that rigorously alternates Monte Carlo sampling from a canonical ensemble with integration of trajectories using Molecular Dynamics (MD). While conventional hybrid Monte Carlo methods completely re-sample particle’s velocities between MD trajectories, our method suggests a partial velocity update procedure which keeps a part of the dynamic information throughout the simulation. We use shadow (modified) Hamiltonians, the asymptotic expansions in powers of the discretization parameter corresponding to timestep, which are conserved by symplectic integrators to higher accuracy than true Hamiltonians. We present the implementation of this method into the highly efficient MD code GROMACS and demonstrate its performance and accuracy on computationally expensive systems like proteins in comparison with the molecular dynamics techniques already available in GROMACS. We take advantage of the state-of-the-art algorithms adopted in the code, leading to an optimal implementation of the method. Our implementation introduces virtually no overhead and can accurately recreate complex biological processes, including rare event dynamics, saving much computational time compared with the conventional simulation methods.
@article{bwmeta1.element.doi-10_2478_s11533-012-0164-x,
author = {Bruno Escribano and Elena Akhmatskaya and Jon Mujika},
title = {Combining stochastic and deterministic approaches within high efficiency molecular simulations},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {787-799},
zbl = {1264.82077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0164-x}
}
Bruno Escribano; Elena Akhmatskaya; Jon Mujika. Combining stochastic and deterministic approaches within high efficiency molecular simulations. Open Mathematics, Tome 11 (2013) pp. 787-799. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0164-x/
[1] Aisen P., Transferrin, the transferrin receptor, and the uptake of iron by cells, In: Metal Ions in Biological Systems, 35, Marcel Dekker, New York, 1998, 585–631
[2] Akhmatskaya E., Bou-Rabee N., Reich S., A comparison of generalized hybrid Monte Carlo methods without momentum flip, J. Comput. Phys., 2009, 228(6), 2256–2265 http://dx.doi.org/10.1016/j.jcp.2008.12.014 | Zbl 1161.65302
[3] Akhmatskaya E., Bou-Rabee N., Reich S., Erratum to ”A comparison of generalized hybrid Monte Carlo methods with and without momentum flip” [J. Comput. Phys. 228 (2009) 2256–2265], J. Comput. Phys., 2009, 228(19), 7492–7496 http://dx.doi.org/10.1016/j.jcp.2009.06.039 | Zbl 1161.65302
[4] Akhmatskaya E., Reich S., GSHMC: An efficient method for molecular simulation, J. Comput. Phys., 2008, 227(10), 4934–4954 http://dx.doi.org/10.1016/j.jcp.2008.01.023 | Zbl 1148.82316
[5] Bussi G., Donadio D., Parrinello M., Canonical sampling through velocity rescaling, J. Chem. Phys., 2007, 126(1), #014101 http://dx.doi.org/10.1063/1.2408420
[6] Darden T., York D., Pedersen L., Particle mesh Ewald: An N-log(N) method for Ewald sums in large systems, J. Chem. Phys., 1993, 98(12), 10089–10092 http://dx.doi.org/10.1063/1.464397
[7] Duane S., Kennedy A.D., Pendleton B.J., Roweth D., Hybrid Monte Carlo, Phys. Lett. B, 1987, 195, 216–222 http://dx.doi.org/10.1016/0370-2693(87)91197-X
[8] Essmann U., Perera L., Berkowitz M.L., Darden T., Lee H., Pedersen L.G., A smooth particle mesh Ewald potential method, J. Chem. Phys., 1995, 103(19), 8577–8593 http://dx.doi.org/10.1063/1.470117
[9] Jorgensen W.L., Chandrasekhar J., Madura J.D., Impey R.W., Klein M.L., Comparison of simple potential functions for simulating liquid water, J. Chem. Phys., 1983, 79(2), 926–935 http://dx.doi.org/10.1063/1.445869
[10] Hairer E., Lubich C., Wanner G., Geometric Numerical Integration, Springer Ser. Comput. Math., 31, Springer, Berlin-Heidelberg, 2002 http://dx.doi.org/10.1007/978-3-662-05018-7 | Zbl 0994.65135
[11] Hess B., Bekker H., Berendsen H.J.C. Fraaije J.G.E.M., LINCS: A linear constraint solver for molecular simulations, J. Comput. Chem., 1997, 18(12), 1463–1472 http://dx.doi.org/10.1002/(SICI)1096-987X(199709)18:12<1463::AID-JCC4>3.0.CO;2-H
[12] Hess B., Kutzner C., van der Spoel D., Lindahl E., GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation, J. Chem. Theory Comput., 2008, 4(3), 435–447 http://dx.doi.org/10.1021/ct700301q
[13] Horowitz A.M., A generalized guided Monte Carlo algorithm, Phys. Lett. B, 1991, 268(2), 247–252 http://dx.doi.org/10.1016/0370-2693(91)90812-5
[14] Izaguirre J.A., Hampton S.S., Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules, J. Comput. Phys., 2004, 200(2), 581–604 http://dx.doi.org/10.1016/j.jcp.2004.04.016 | Zbl 1115.65383
[15] Kennedy A.D., Pendleton B., Acceptances and autocorrelations in hybrid Monte Carlo, Nuclear Phys. B - Proceedings Supplements, 1991, 20, 118–121 http://dx.doi.org/10.1016/0920-5632(91)90893-J
[16] Kennedy A.D., Pedlenton B., Cost of the generalised hybrid Monte Carlo algorithm for free field theory, Nuclear Phys. B, 2001, 607(3), 456–510 http://dx.doi.org/10.1016/S0550-3213(01)00129-8 | Zbl 0969.81639
[17] Klausner R.D., Ashwell G., van Renswoude J., Harford J.B., Bridges K.R., Binding of apotransferrin to K562 cells¶ explanation of the transferrin cycle, Proc. Natl. Acad. Sci. USA, 1983, 80(8), 2263–2266 http://dx.doi.org/10.1073/pnas.80.8.2263
[18] Liu J.S., Monte Carlo Strategies in Scientific Computing, Springer Ser. Statist., Springer, New York, 2001 | Zbl 0991.65001
[19] MacGillivray R.T., Moore S.A., Chen J., Anderson B.F., Baker H., Luo Y., Bewley M., Smith C.A., Murphy M.E., Wang Y., Mason A.B., Woodworth R.C., Brayer G.D., Baker E.N., Two high-resolution crystal structures of the recombinant N-lobe of human transferrin reveal a structural change implicated in iron release, Biochemistry, 1998, 37(22), 7919–7928 http://dx.doi.org/10.1021/bi980355j
[20] MacKerell A.D., Bashford D., Bellott E.M., Dunbrack R.L., Evanseck J.D., Field M.J., Fischer S., Gao J., Guo H., Ha S., Joseph-McCarthy D., Kuchnir L., Kuczera K., Lau F.T.K., Mattos C., Michnick S., Ngo T., Nguyen D.T., Prodhom B., Reiher W.E., Roux B., Schlenkrich M., Smith J.C., Stote R., Straub J., Watanabe M., Wiórkiewicz-Kuczera J., Yin D., Karplus M., All-atom empirical potential for molecular modeling and dynamics studies of proteins, The Journal of Physical Chemistry B, 1998, 102(18), 3586–3616 http://dx.doi.org/10.1021/jp973084f
[21] Mujika J.I., Escribano B., Akhmatskaya E., Ugalde J.M., Lopez X., Molecular dynamics simulations of iron- and aluminum-loaded serum transferrin: protonation of Tyr188 is necessary to prompt the metal release, Biochemistry, 2012, 51(35), 7017–7027 http://dx.doi.org/10.1021/bi300584p
[22] Rinaldo D., Field M.J., A computational study of the open and closed forms of the N-lobe human serum transferrin apoprotein, Biophys. J., 2003, 85(6), 3485–3501 http://dx.doi.org/10.1016/S0006-3495(03)74769-9
[23] Skeel R.D., Hardy D.J., Practical construction of modified Hamiltonians, SIAM J. Comput., 2001, 23(4), 1172–1188 http://dx.doi.org/10.1137/S106482750138318X | Zbl 1002.65135
[24] Sweet C.R., Hampton S.S., Skeel R.D., Izaguirre J.A., A separable shadow Hamiltonian hybrid Monte Carlo method, J. Chem. Phys., 2009, 131(17), #174106 http://dx.doi.org/10.1063/1.3253687
[25] Wee C.L., Sansom M.S., Reich S., Akhmatskaya E., Improved sampling for simulations of interfacial membrane proteins: application of generalized shadow hybrid Monte Carlo to a peptide toxin/bilayer system, The Journal of Physical Chemistry B, 2008, 112(18), 5710–5717 http://dx.doi.org/10.1021/jp076712u
[26] GROMACS Programmer’s Guide, available at http://www.gromacs.org/Developer_Zone/Programming_Guide/Programmer