Advertisement

Correction of diffusion calculations when using two types of non-rectangular simulation boxes in molecular simulations

  • Ting Cao
  • Xiangfei Ji
  • Jinpeng Wu
  • Shiju Zhang
  • Xiaofeng YangEmail author
Original Paper
  • 39 Downloads

Abstract

Although simulation boxes used in molecular dynamics are normally chosen to be cubic or rectangular, two other cell shapes that are very familiar to crystallographers—the truncated octahedron and the rhombic dodecahedron—could also be used because they are also space-filling cells. Due to their spherical nature, these boxes have been intentionally applied in simulations of biomolecular solutions and liquid structures. Indeed, due to the advantages of running many molecular dynamic codes in parallel, simulations based on these non-rectangular boxes have been growing in popularity in recent years. In this work, the effects of using these two types of boxes on diffusion are explored for the first time, and an appropriate correction formula is derived theoretically within the framework of hydrodynamics. In addition, the range of validity for the correction formula is evaluated by performing molecular dynamic simulations on argon at three different densities.

Keywords

Truncated octahedron Rhombic dodecahedron Diffusion coefficient Periodic boundary conditions 

Notes

References

  1. 1.
    Allen MP, Tildesley DJ (1989) Computer simulation of liquids. Clarendon, Oxford, p 26Google Scholar
  2. 2.
    van der Spoel D, Lindahl E, Hess B, van Buuren AR, Apol E, Meulenhoff PJ, Tieleman DP, Sijbers ALTM, Feenstra KA, van Drunen R, Berendsen HJC (2010) Gromacs user manual, version 4.5.6, p 13. www.gromacs.org
  3. 3.
    Papavasileiou KD, Avramopoulos GL, Papadopoulos MG (2017) Computational investigation of fullerene–DNA interactions: implications of fullerene’s size and functionalization on DNA structure and binding energetics. J Mol Graph Model 74:177–192Google Scholar
  4. 4.
    Xun SN, Jiang F, Wu YD (2016) Intrinsically disordered regions stabilize the helical form of the C-terminal domain of RfaH: a molecular dynamics study. Bioorg Med Chem 24:4970–4977Google Scholar
  5. 5.
    Maganti L, Grandhb P, Ghoshal N (2016) Integration of ligand and structure based approaches for identification of novel MbtI inhibitors in Mycobacterium tuberculosis and molecular dynamics simulation studies. J Mol Graph Model 70:14–22Google Scholar
  6. 6.
    Tarus B, Nguyen PH, Berthoumieu O, Faller P, Doig AJ, Derreumaux P (2015) Molecular structure of the NQTrp inhibitor with the Alzheimer Ab1-28 monomer. Eur J Med Chem 91:43–50CrossRefGoogle Scholar
  7. 7.
    Zhou M, Du K, Ji PJ, Feng W (2012) Molecular mechanism of the interactions between inhibitory tripeptides and angiotensin-converting enzyme. Biophys Chem 168:60–66CrossRefGoogle Scholar
  8. 8.
    Han S (2008) Force field parameters for S-nitrosocysteine and molecular dynamics simulations of S-nitrosated thioredoxin. Biochem Biophys Res Commun 377:612–616CrossRefGoogle Scholar
  9. 9.
    Farhi A, Singh B (2017) A novel method for calculating relative free energy of similar molecules in two environments. Comput Phys Commun 212:132–145CrossRefGoogle Scholar
  10. 10.
    Hirano A, Maruyama T, Shiraki K, Arakawa T, Kameda T (2017) A study of the small-molecule system used to investigate the effect of arginine on antibody elution in hydrophobic charge-induction chromatography. Protein Expr Purif 129:44–52CrossRefGoogle Scholar
  11. 11.
    Rogers DM (2016) Overcoming the minimum image constraint using the closest point search. J Mol Graph Model 68:197–205CrossRefGoogle Scholar
  12. 12.
    Ghadari R, Alavi FS, Zahedi M (2015) Evaluation of the effect of the chiral centers of Taxol on binding to β-tubulin: a docking and molecular dynamics simulation study. Comput Biol Chem 56:33–40CrossRefGoogle Scholar
  13. 13.
    Tekin ED (2014) Odd–even effect in the potential energy of the self-assembled peptide amphiphiles. Chem Phys Lett 614:204–206CrossRefGoogle Scholar
  14. 14.
    Gupta M, Chauhan R, Prasad Y, Wadhwa G, Jain CK (2016) Protein–protein interaction and molecular dynamics analysis for identification of novel inhibitors in Burkholderia cepacia GG4. Comput Biol Chem 65:80–90Google Scholar
  15. 15.
    Ngo ST, Truong DT, Tam NM, Nguyen MT (2017) EGCG inhibits the oligomerization of amyloid beta (16-22) hexamer: theoretical studies. J Mol Graph Model 76:1–10CrossRefGoogle Scholar
  16. 16.
    Luo MH, Wang H, Zou Y, Zhang SP, Xiao JH, Jiang GD, Zhang YH, Lai YS (2016) Identification of phenoxyacetamide derivatives as novel dot1L inhibitors via docking screening and molecular dynamics. Simulation 68:128–139Google Scholar
  17. 17.
    Hess B, Van der Spoel D, Lindahl E (2008) GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theory Comput 4:435–447Google Scholar
  18. 18.
    Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1–19 http://lammps.sandia.gov CrossRefGoogle Scholar
  19. 19.
    Kale L, Skeel R, Bhandarkar M, Brunner R, Gursoy A, Krawetz N et al (1999) NAMD2: greater scalability for parallel molecular dynamics. J Comput Phys 151:283–312 http://www.ks.uiuc.edu/Research/namd/ CrossRefGoogle Scholar
  20. 20.
    Mackerell AD, Bashford D, Bellott M, Dunbrack RL, Evanseck JD et al (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102:3586–3616 https://www.charmm.org/ CrossRefGoogle Scholar
  21. 21.
    Dünweg B, Kremer K (1993) Molecular dynamics simulation of a polymer chain in solution. J Chem Phys 99:6983–6997CrossRefGoogle Scholar
  22. 22.
    Yeh IC, Hummer G (2004) System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions. J Phys Chem B 108:15873–15879CrossRefGoogle Scholar
  23. 23.
    Yang XF, Zhang H, Li L, Ji XF (2017) Corrections of the periodic boundary conditions with rectangular simulation boxes on the diffusion coefficient, general aspects. Mol Simul 43:1423–1429CrossRefGoogle Scholar
  24. 24.
    Kikugawa G, Ando S, Suzuki J, Naruke Y, Nakano T, Ohara T (2015) Effect of the computational domain size and shape on the self-diffusion coefficient in a Lennard-Jones liquid. J Chem Phys 142:024503CrossRefGoogle Scholar
  25. 25.
    Kikugawa G, Nakano T, Ohara T (2015) Hydrodynamic consideration of the finite size effect on the self-diffusion coefficient in a periodic rectangular parallelepiped system. J Chem Phys 143:0245071–0245078CrossRefGoogle Scholar
  26. 26.
    Moultos OA, Zhang Y, Tsimpanogiannis IN, Economou IG, Maginn E (2016) System-size correction for self-diffusion coefficients calculated from molecular dynamics simulations: the case of CO2, n-alkanes, and poly(ethylene glycol) dimethyl ethers. J Chem Phys 145:074109Google Scholar
  27. 27.
    Simonnin P, Noetinger B, Nieto-Draghi C, Marry V, Rotenberg B (2017) Diffusion under confinement: hydrodynamic finite-size effect in simulation. J Chem Theory Comput 13:2881–2889CrossRefGoogle Scholar
  28. 28.
    Jamali SH, Wolff L, Becker TM, Bardow A, Vlugt TJH, Moultos OA (2018) Finite-size effect of binary mutual diffusion coefficients from molecular dynamics. J Chem Theory Comput 14:2667–2677Google Scholar
  29. 29.
    Stearn AE, Irish EM, Eyring H (1940) A theory of diffusion in liquids. J Phys Chem 44:981–995CrossRefGoogle Scholar
  30. 30.
    Mccall DW, Douglass DC (1967) Diffusion in binary solutions. J Phys Chem 71:987–997CrossRefGoogle Scholar
  31. 31.
    Hasimoto H (1959) On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J Fluid Mech 5:317–328Google Scholar
  32. 32.
    Nijboer BRA, De Wette FW (1957) On the calculation of lattice sums. Physica 23:309–321CrossRefGoogle Scholar
  33. 33.
    Yamakawa H (1970) Transport properties of polymer chains in dilute solution: hydrodynamic interaction. J Chem Phys 53:436–443CrossRefGoogle Scholar
  34. 34.
    Lide DR (2005) CRC handbook of chemistry and physics, 86th edn. CRC, Boca Raton, p 1209Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsNorth University of ChinaTaiyuanChina
  2. 2.School of Chemistry and Chemical EngineeringShanxi UniversityTaiyuanChina

Personalised recommendations