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Transition Path Sampling with Quantum/Classical Mechanics for Reaction Rates

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Molecular Modeling of Proteins

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1215))

Abstract

Predicting rates of biochemical reactions through molecular simulations poses a particular challenge for two reasons. First, the process involves bond formation and/or cleavage and thus requires a quantum mechanical (QM) treatment of the reaction center, which can be combined with a more efficient molecular mechanical (MM) description for the remainder of the system, resulting in a QM/MM approach. Second, reaction time scales are typically many orders of magnitude larger than the (sub-)nanosecond scale accessible by QM/MM simulations. Transition path sampling (TPS) allows to efficiently sample the space of dynamic trajectories from the reactant to the product state without an additional biasing potential. We outline here the application of TPS and QM/MM to calculate rates for biochemical reactions, by means of a simple toy system. In a step-by-step protocol, we specifically refer to our implementation within the MD suite Gromacs, which we have made available to the research community, and include practical advice on the choice of parameters.

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References

  1. Lane TJ, Bowman GR, Beauchamp K et al (2011) Markov state model reveals folding and functional dynamics in ultra-long MD trajectories. J Am Chem Soc 133:18413–18419

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  2. Bowman GR, Pande VS (2010) Protein folded states are kinetic hubs. Proc Natl Acad Sci U S A 107:10890–10895

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  3. van der Spoel D, Seibert MM (2006) Protein folding kinetics and thermodynamics from atomistic simulations. Phys Rev Lett 96:238102

    Article  PubMed  Google Scholar 

  4. Best RB, Hummer G (2006) Diffusive model of protein folding dynamics with Kramers turnover in rate. Phys Rev Lett 96:228104

    Article  PubMed  Google Scholar 

  5. Popa I, FernĂ¡ndez JM, Garcia-Manyes S (2011) Direct quantification of the attempt frequency determining the mechanical unfolding of ubiquitin protein. J Biol Chem 286:31072–31079

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  6. Dellago C, Bolhuis PG, Csajka FS et al (1998) Transition path sampling and the calculation of rate constants. J Chem Phys 108:1964

    Article  CAS  Google Scholar 

  7. Dellago C, Bolhuis PG, Chandler D (1998) Efficient transition path sampling: application to Lennard-Jones cluster rearrangements. J Chem Phys 108:9236

    Article  CAS  Google Scholar 

  8. Quaytman SL, Schwartz SD (2007) Reaction coordinate of an enzymatic reaction revealed by transition path sampling. Proc Natl Acad Sci U S A 104:12253–12258

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  9. Saen-Oon S, Quaytman-Machleder S, Schramm VL et al (2008) Atomic detail of chemical transformation at the transition state of an enzymatic reaction. Proc Natl Acad Sci U S A 105:16543–16548

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  10. Li W, Gräter F (2010) Atomistic evidence of how force dynamically regulates thiol/disulfide exchange. J Am Chem Soc 132:16790–16795

    Article  PubMed  CAS  Google Scholar 

  11. Xia F, Bronowska AK, Cheng S et al (2011) Base-catalyzed peptide hydrolysis is insensitive to mechanical stress. J Phys Chem B 115:10126–10132

    Article  PubMed  CAS  Google Scholar 

  12. van der Kamp MW, Mulholland AJ (2013) Combined quantum mechanics/molecular mechanics (QM/MM) methods in computational enzymology. Biochemistry 52:2708–2728

    Article  PubMed  Google Scholar 

  13. Steinbrecher T, Elstner M (2013) QM and QM/MM simulations of proteins. In: Monticelli L, Salonen E (eds) Biomolecular simulations. Humana Press, New York, pp 91–124

    Chapter  Google Scholar 

  14. Groenhof G (2013) Introduction to QM/MM simulations. In: Monticelli L, Salonen E (eds) Biomolecular simulations. Humana Press, New York, pp 43–66

    Chapter  Google Scholar 

  15. Hess B, Kutzner C, Van Der Spoel D et al (2008) GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theory Comput 4:435–447

    Article  CAS  Google Scholar 

  16. Bolhuis PG, Dellago C, Chandler D (1998) Sampling ensembles of deterministic transition pathways. Faraday Discuss 110:421–436

    Article  CAS  Google Scholar 

  17. Dellago C, Bolhuis PG, Chandler D (1999) On the calculation of reaction rate constants in the transition path ensemble. J Chem Phys 110:6617

    Article  CAS  Google Scholar 

  18. Dellago C, Bolhuis PG, Geissler PL (2002) Transition path sampling. Adv Chem Phys 123:1–78

    CAS  Google Scholar 

  19. Metropolis N, Rosenbluth AW, Rosenbluth MN et al (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087

    Article  CAS  Google Scholar 

  20. Chandler D (1978) Statistical mechanics of isomerization dynamics in liquids and the transition state approximation. J Chem Phys 68:2959

    Article  CAS  Google Scholar 

  21. Lindahl EL (2008) Molecular dynamics simulations. In: Kukol A (ed) Molecular modeling of proteins. Humana Press, Totowa, NJ, pp 3–23

    Chapter  Google Scholar 

  22. Bolhuis PG, Chandler D, Dellago C et al (2002) Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu Rev Phys Chem 53:291–318

    Article  PubMed  CAS  Google Scholar 

  23. Jolliffe I (2005) Principal component analysis. Wiley Online Library

    Google Scholar 

  24. Dellago C, Bolhuis PG, Geissler PL (2006) Transition path sampling methods. In: Computer simulations in condensed matter systems: from materials to chemical biology, vol 1. Springer, Berlin, pp 349–391

    Google Scholar 

  25. Bolhuis PG (2003) Transition-path sampling of β-hairpin folding. Proc Natl Acad Sci U S A 100:12129–12134

    Article  PubMed  CAS  PubMed Central  Google Scholar 

  26. Hu J, Ma A, Dinner AR (2006) Bias annealing: a method for obtaining transition paths de novo. J Chem Phys 125:114101

    Article  PubMed  Google Scholar 

  27. GrubmĂ¼ller H (1995) Predicting slow structural transitions in macromolecular systems: conformational flooding. Phys Rev E 52:2893

    Article  Google Scholar 

  28. Laio A, Gervasio FL (2008) Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep Prog Phys 71:126601

    Article  Google Scholar 

  29. Crehuet R, Field MJ (2007) A transition path sampling study of the reaction catalyzed by the enzyme chorismate mutase. J Phys Chem B 111:5708–5718

    Article  PubMed  CAS  Google Scholar 

  30. Ma A, Dinner AR (2005) Automatic method for identifying reaction coordinates in complex systems. J Phys Chem B 109:6769–6779

    Article  PubMed  CAS  Google Scholar 

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Acknowledgment

We are grateful to the Klaus Tschira Foundation for financial support.

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Authors and Affiliations

  1. Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, Heidelberg, 69118, Germany

    Frauke Gräter

  2. Department of Bioengineering, University of Illinois at Chicago, 835 S Wolcott St, W100 CSN, Chicago, IL, 60612, USA

    Wenjin Li

Authors
  1. Frauke Gräter
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  2. Wenjin Li
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Corresponding author

Correspondence to Frauke Gräter .

Editor information

Editors and Affiliations

  1. University of Hertfordshire, Hatfield, Hertfordshire, United Kingdom

    Andreas Kukol

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Gräter, F., Li, W. (2015). Transition Path Sampling with Quantum/Classical Mechanics for Reaction Rates. In: Kukol, A. (eds) Molecular Modeling of Proteins. Methods in Molecular Biology, vol 1215. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-1465-4_2

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  • DOI: https://doi.org/10.1007/978-1-4939-1465-4_2

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  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-1464-7

  • Online ISBN: 978-1-4939-1465-4

  • eBook Packages: Springer Protocols

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