Skip to main content
SpringerLink
Log in

A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation

  • Original Paper
  • Published:
Journal of Molecular Modeling Aims and scope Submit manuscript

Abstract

Main chain torsions of alanine dipeptide are parameterized into coupled 2-dimensional Fourier expansions based on quantum mechanical (QM) calculations at M06 2X/aug-cc-pvtz//HF/6-31G** level. Solvation effect is considered by employing polarizable continuum model. Utilization of the M06 2X functional leads to precise potential energy surface that is comparable to or even better than MP2 level, but with much less computational demand. Parameterization of the 2D expansions is against the full main chain torsion space instead of just a few low energy conformations. This procedure is similar to that for the development of AMBER03 force field, except unique weighting factor was assigned to all the grid points. To avoid inconsistency between quantum mechanical calculations and molecular modeling, the model peptide is further optimized at molecular mechanics level with main chain dihedral angles fixed before the calculation of the conformational energy on molecular mechanical level at each grid point, during which generalized Born model is employed. Difference in solvation models at quantum mechanics and molecular mechanics levels makes this parameterization procedure less straightforward. All force field parameters other than main chain torsions are taken from existing AMBER force field. With this new main chain torsion terms, we have studied the main chain dihedral distributions of ALA dipeptide and pentapeptide in aqueous solution. The results demonstrate that 2D main chain torsion is effective in delineating the energy variation associated with rotations along main chain dihedrals. This work is an implication for the necessity of more accurate description of main chain torsions in the future development of ab initio force field and it also raises a challenge to the development of quantum mechanical methods, especially the quantum mechanical solvation models.

A coupled two-dimensional main chain torsional potential for protein dynamics

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Duan Y, Wu C, Chowdhury S, Lee MC, Xiong G, Zhang W, Yang R, Cieplak P, Luo R, Lee T, Caldwell J, Wang J, Kollman P (2003) J Comput Chem 24:1999–2012

    Article  CAS  Google Scholar 

  2. MacKerell AD Jr et al. (1998) J Phys Chem B 102:3586–3616

    Article  CAS  Google Scholar 

  3. Kaminski GA, Friesner RA, Tirado-Rives J, Jorgensen WL (2001) J Phys Chem B 105:6474–6487

    Article  CAS  Google Scholar 

  4. Oostenbrink C, Villa A, Mark AE, Van Gunsteren WF (2004) J Comput Chem 25:1656–1676

    Article  CAS  Google Scholar 

  5. Bixon M, Lifson S (1967) Tetrahedron 23:769–784

    Article  CAS  Google Scholar 

  6. Li D-W, Brüschweiler R (2010) Angew Chem Int Edit 49:6778–6780

    Article  CAS  Google Scholar 

  7. Best RB, Hummer G (2009) J Phys Chem B 113:9004–9015

    Article  CAS  Google Scholar 

  8. Nerenberg PS, Head-Gordon T (2011) J Chem Theor Comput 7:1220–1230

    Article  CAS  Google Scholar 

  9. Lindorff-Larsen K, Piana S, Palmo K, Maragakis P, Klepeis JL, Dror RO, Shaw DE (2010) Proteins 78:1950–1958

    CAS  Google Scholar 

  10. Jorgensen WL, Tirado-Rives J (2005) Proc Natl Acad Sci USA 102:6665–6670

    Article  CAS  Google Scholar 

  11. Mackerell AD (2004) J Comput Chem 25:1584–1604

    Article  CAS  Google Scholar 

  12. Ponder JW, Case DA (2003) Protein simulations. Academic, New York 66:27–85

  13. Freddolino PL, Park S, Roux B, Schulten K (2009) Biophys J 96:3772–3780

    Article  CAS  Google Scholar 

  14. Okur A, Strockbine B, Hornak V, Simmerling CJ (2003) J Comput Chem 24:21–31

    Article  CAS  Google Scholar 

  15. Garcia AE, Sanbonmatsu KY (2002) Proc Natl Acad Sci USA 99:2782–2787

    Article  CAS  Google Scholar 

  16. Kamiya N, Higo J, Nakamura H (2002) Protein Sci 11:2297–2307

    Article  CAS  Google Scholar 

  17. Higo J, Ito N, Kuroda M, Ono S, Nakajima N, Nakamura H (2001) Protein Sci 10:1160–1171

    Article  CAS  Google Scholar 

  18. Ono S, Nakajima N, Higo J, Nakamura HJ (2000) J Comput Chem 21:748–762

    Article  CAS  Google Scholar 

  19. Wang L, Duan Y, Shortle R, Imperiali B, Kollman PA (1999) Protein Sci 8:1292–1304

    Article  CAS  Google Scholar 

  20. Best RB, Buchete N-V, Hummer G (2008) Biophys J 95:L07–L09

    Article  CAS  Google Scholar 

  21. Simmerling C, Strockbine B, Roitberg AE (2002) J Am Chem Soc 124:11258–11259

    Article  CAS  Google Scholar 

  22. Hornak V, Abel R, Okur A, Strockbine B, Roitberg A, Simmerling C (2006) Proteins 65:712–725

    Article  CAS  Google Scholar 

  23. MacKerell AD, Feig M, Brooks CL (2004) J Am Chem Soc 126:698–699

    Article  CAS  Google Scholar 

  24. Mackerell AD, Feig M, Brooks CL (2004) J Comput Chem 25:1400–1415

    Article  CAS  Google Scholar 

  25. Wang Z-X, Zhang W, Wu C, Lei H, Cieplak P, Duan Y (2006) J Comput Chem 27:781–790

    Article  CAS  Google Scholar 

  26. Sakae Y, Okamoto Y (2010) Mol Simulat 36:138–158

    Article  CAS  Google Scholar 

  27. Sorin EJ, Pande VS (2005) Biophys J 88:2472–2493

    Article  CAS  Google Scholar 

  28. Piana S, Lindorff-Larsen K, Shaw DE (2011) Biophys J 100:L47–L49

    Article  CAS  Google Scholar 

  29. Kamiya N, Watanabe YS, Ono S, Higo J (2005) Chem Phys Lett 401:312–317

    Article  CAS  Google Scholar 

  30. Iwaoka M, Tomoda S (2003) J Comput Chem 24:1192–1200

    Article  CAS  Google Scholar 

  31. Zaman MH, Shen M-Y, Berry RS, Freed KF, Sosnick TR (2003) J Mol Biol 331:693–711

    Article  CAS  Google Scholar 

  32. Liu ZW, Ensing B, Moore PB (2011) J Chem Theor Comput 7:402–419

    Article  CAS  Google Scholar 

  33. Buck M, Bouguet-Bonnet S, Pastor RW, MacKerell AD (2006) Biophys J 90:L36–L38

    Article  CAS  Google Scholar 

  34. Sakae Y, Okamoto Y (2006) J Phys Soc Jpn 75:054802

    Article  Google Scholar 

  35. Case DA et al. (2010) AMBER 11. University of California, San Francisco

  36. Head-Gordon M, Pople JA, Frisch MJ (1988) Chem Phys Lett 153:503–506

    Article  CAS  Google Scholar 

  37. Scuseria GE, Janssen CL, Schaefer HF III (1988) J Chem Phys 89:7382–7387

    Article  CAS  Google Scholar 

  38. Zhao Y, Truhlar DG (2007) Theor Chem Accounts 120:215–241

    Article  Google Scholar 

  39. Zhao Y, Truhlar DG (2008) Accounts Chem Res 41:157–167

    Article  CAS  Google Scholar 

  40. Tomasi J, Mennucci B, Cancès E (1999) J Mol Struct (Theochem) 464:211–226

    Article  CAS  Google Scholar 

  41. Tomasi J, Mennucci B, Cammi R (2005) Chem Rev 105:2999–3094

    Article  CAS  Google Scholar 

  42. Frisch MJ et al. (2010) Gaussian 09, revision B.01. Gaussian, Inc, Wallingford

    Google Scholar 

  43. Tsui V, Case DA (2000) Biopolymers 56:275–291

    Article  CAS  Google Scholar 

  44. Cao Z, Lin Z, Wang J, Liu H (2009) J Comput Chem 30:645–660

    Article  CAS  Google Scholar 

  45. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1986) Numerical recipes. Cambridge University Press, Cambridge, UK

    Google Scholar 

  46. Blondel A, Karplus M (1996) J Comput Chem 17:1132–1141

    Article  CAS  Google Scholar 

  47. Sugita Y, Okamoto Y (1999) Chem Phys Lett 314:141–151

    Article  CAS  Google Scholar 

  48. Onufriev A, Bashford D, Case DA (2004) Proteins 55:383–394

    Article  CAS  Google Scholar 

  49. Mongan J, Simmerling C, McCammon JA, Case DA, Onufriev A (2007) J Chem Theor Comput 3:156–169

    Article  CAS  Google Scholar 

  50. Jorgensen WL, Candrasekhar J, Madura JD, Impey RW, Klein ML (1983) J Chem Phys 79:926–935

    Article  CAS  Google Scholar 

  51. Kumar S, Rosenberg JM, Bouzida D, Swendsen RH, Kollman PA (1992) J Comput Chem 13:1011–1021

    Article  CAS  Google Scholar 

  52. Chodera JD, Swope WC, Pitera JW, Seok C, Dill KA (2007) J Chem Theor Comput 3:26–41

    Article  CAS  Google Scholar 

  53. Kim YS, Wang JP, Hochstrasser RM (2005) J Phys Chem B 109:7511–7521

    Article  CAS  Google Scholar 

  54. Grdadolnik J, Golic Grdadolnik S, Avbelj F (2008) J Phys Chem B 112:2712–2718

    Article  CAS  Google Scholar 

  55. Mukhopadhyay P, Zuber G, Beratan DN (2008) Biophys J 95:5574–5586

    Article  CAS  Google Scholar 

  56. Schweitzer-Stenner R, Measey T, Kakalis L, Jordan F, Pizzanelli S, Forte C, Griebenow K (2007) Biochemistry 46:1587–1596

    Article  CAS  Google Scholar 

  57. Mehta MA, Fry EA, Eddy MT, Dedeo MT, Anagnost AE, Long JR (2004) J Phys Chem B 108:2777–2780

    Article  CAS  Google Scholar 

  58. Beachy MD, Chasman D, Murphy RB, Halgren TA, Friesner RA (1997) J Am Chem Soc 119:5908–5920

    Article  CAS  Google Scholar 

  59. Smith PE (1999) J Chem Phys 111:5568–5579

    Article  CAS  Google Scholar 

  60. Vargas R, Garza J, Hay BP, Dixon DA (2002) J Phys Chem A 106:3213–3218

    Article  CAS  Google Scholar 

  61. Hu H, Elstner M, Hermans J (2003) Proteins 50:451–463

    Article  CAS  Google Scholar 

  62. Wang Z-X, Duan Y (2004) J Comput Chem 25:1699–1716

    Article  CAS  Google Scholar 

  63. Kwac K, Lee K-K, Han JB, Oh K-I, Cho M (2008) J Chem Phys 128:105106

    Article  Google Scholar 

  64. de Seabra GM, Walker RC, Roitberg AE (2009) J Phys Chem A 113:11938–11948

    Article  CAS  Google Scholar 

  65. Gaigeot M-P (2009) J Phys Chem B 113:10059–10062

    Article  CAS  Google Scholar 

  66. Mu YG, Kosov DS, Stock G (2003) J Phys Chem B 107:5064–5073

    Article  CAS  Google Scholar 

  67. Graf J, Nguyen PH, Stock G, Schwalbe H (2007) J Am Chem Soc 129:1179–1189

    Article  CAS  Google Scholar 

  68. Woutersen S, Pfister R, Hamm P, Mu YG, Kosov DS, Stock G (2002) J Chem Phys 117:6833–6840

    Article  CAS  Google Scholar 

  69. Avbelj F, Grdadolnik SG, Grdadolnik J, Baldwin RL (2006) Proc Natl Acad Sci USA 103:1272–1277

    Article  CAS  Google Scholar 

  70. Hu J-S, Bax A (1997) J Am Chem Soc 119:6360–6368

    Article  CAS  Google Scholar 

  71. Case DA, Scheurer C, Brüschweiler R (2000) J Am Chem Soc 122:10390–10397

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 10974054, 20933002, 21173082 and 31200545), the Shanghai PuJiang Program (09PJ1404000), and the Shanghai Rising-Star Program (Grant No. 11QA1402000). We thank Supercomputer Center of East China Normal University for CPU time support.

Author information

Authors and Affiliations

  1. Center for Laser and Computational Biophysics, State Key Laboratory of Precision Spectroscopy and Department of Physics and Institute of Theoretical and Computational Science, East China Normal University, Shanghai, 200062, China

    Yongxiu Li, Ya Gao, Xiao He, Ye Mei & John Z. H. Zhang

  2. Department of Chemistry, New York University, New York, NY, 10003, USA

    Xuqiang Zhang, Xingyu Wang & John Z. H. Zhang

  3. Institutes for Advanced Interdisciplinary Research, East China Normal University, Shanghai, 200062, China

    Lirong Mou

  4. College of Physics and Electronics, Shandong Normal University, Jinan, 250014, China

    LiLi Duan

Authors
  1. Yongxiu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ya Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xuqiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xingyu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lirong Mou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. LiLi Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Xiao He
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Ye Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. John Z. H. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xiao He, Ye Mei or John Z. H. Zhang.

Additional information

Yongxiu Li and Ya Gao contributed equally to this work

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Y., Gao, Y., Zhang, X. et al. A coupled two-dimensional main chain torsional potential for protein dynamics: generation and implementation. J Mol Model 19, 3647–3657 (2013). https://doi.org/10.1007/s00894-013-1879-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00894-013-1879-8

Keywords

Search

Navigation