Combining stochastic and deterministic approaches within high efficiency molecular simulations

Bruno Escribano; Elena Akhmatskaya; Jon Mujika

Open Mathematics (2013)

  • Volume: 11, Issue: 4, page 787-799
  • ISSN: 2391-5455

Abstract

top
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.

How to cite

top

Bruno Escribano, Elena Akhmatskaya, and Jon Mujika. "Combining stochastic and deterministic approaches within high efficiency molecular simulations." Open Mathematics 11.4 (2013): 787-799. <http://eudml.org/doc/269667>.

@article{BrunoEscribano2013,
abstract = {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.},
author = {Bruno Escribano, Elena Akhmatskaya, Jon Mujika},
journal = {Open Mathematics},
keywords = {Hybrid Monte Carlo; Shadow Hamiltonian; Molecular dynamics; hybrid Monte Carlo; shadow Hamiltonian; molecular dynamics},
language = {eng},
number = {4},
pages = {787-799},
title = {Combining stochastic and deterministic approaches within high efficiency molecular simulations},
url = {http://eudml.org/doc/269667},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Bruno Escribano
AU - Elena Akhmatskaya
AU - Jon Mujika
TI - Combining stochastic and deterministic approaches within high efficiency molecular simulations
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 787
EP - 799
AB - 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.
LA - eng
KW - Hybrid Monte Carlo; Shadow Hamiltonian; Molecular dynamics; hybrid Monte Carlo; shadow Hamiltonian; molecular dynamics
UR - http://eudml.org/doc/269667
ER -

References

top
  1. [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. [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 Zbl1161.65302
  3. [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 Zbl1161.65302
  4. [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 Zbl1148.82316
  5. [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. [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. [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. [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. [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. [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 Zbl0994.65135
  11. [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. [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. [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. [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 Zbl1115.65383
  15. [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. [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 Zbl0969.81639
  17. [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. [18] Liu J.S., Monte Carlo Strategies in Scientific Computing, Springer Ser. Statist., Springer, New York, 2001 Zbl0991.65001
  19. [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. [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. [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. [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. [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 Zbl1002.65135
  24. [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. [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. [26] GROMACS Programmer’s Guide, available at http://www.gromacs.org/Developer_Zone/Programming_Guide/Programmer 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.