PyCPR – a python-based implementation of the Conjugate Peak Refinement (CPR) algorithm for finding transition state structures

  • Florian J. Gisdon
  • Martin Culka
  • G. Matthias Ullmann
Original Paper

Abstract

Conjugate peak refinement (CPR) is a powerful and robust method to search transition states on a molecular potential energy surface. Nevertheless, the method was to the best of our knowledge so far only implemented in CHARMM. In this paper, we present PyCPR, a new Python-based implementation of the CPR algorithm within the pDynamo framework. We provide a detailed description of the theory underlying our implementation and discuss the different parts of the implementation. The method is applied to two different problems. First, we illustrate the method by analyzing the gauche to anti-periplanar transition of butane using a semiempirical QM method. Second, we reanalyze the mechanism of a glycyl-radical enzyme, namely of 4-hydroxyphenylacetate decarboxylase (HPD) using QM/MM calculations. In the end, we suggest a strategy how to use our implementation of the CPR algorithm. The integration of PyCPR into the framework pDynamo allows the combination of CPR with the large variety of methods implemented in pDynamo. PyCPR can be used in combination with quantum mechanical and molecular mechanical methods (and hybrid methods) implemented directly in pDynamo, but also in combination with external programs such as ORCA using pDynamo as interface. PyCPR is distributed as free, open source software and can be downloaded from http://www.bisb.uni-bayreuth.de/index.php?page=downloads.

Graphical Abstract

PyCPR is a search tool for finding saddle points on the potential energy landscape of a molecular system.

Keywords

Potential energy surface Saddle point Transition state search Minimum energy path Reaction mechanism pDynamo 

References

  1. 1.
    Aleksandrov A, Field MJ (2012) A hybrid elastic band string algorithm for studies of enzymatic reactions. Phys Chem Chem Phys 14:12,544–12,553CrossRefGoogle Scholar
  2. 2.
    Allinger NL, Fermann JT, Allen WD, Schaefer IIIHF (1997) The torsional conformations of butane: Definitive energetics from ab initio methods. J Chem Phys 106:5143–5150CrossRefGoogle Scholar
  3. 3.
    Beale EML (1972) A derivation of conjugate gradients. In: Lootsma FA (ed) Numerical methods for nonlinear optimization. Academic Press, London, pp 39–43Google Scholar
  4. 4.
    Becke A (1993) Density functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648–5652CrossRefGoogle Scholar
  5. 5.
    Bernardi RC, Melo MCR, Schulten K (2015) Enhanced sampling techniques in molecular dynamics simulations of biological systems. Biochim Biophys Acta 1850:872–877CrossRefGoogle Scholar
  6. 6.
    Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4:187–217CrossRefGoogle Scholar
  7. 7.
    Cerjan CJ (1981) On finding transition states. J Chem Phys 75:2800CrossRefGoogle Scholar
  8. 8.
    Czerminski R, Elber R (1990) Self-avoiding walk between two fixed points as a tool to calculate reaction paths in large molecular systems. Int J Quantum Chem 38:167–185CrossRefGoogle Scholar
  9. 9.
    EW, Ren W, Vanden-Eijnden E (2002) String method for the study of rare events. Phys Rev B 66:052,301Google Scholar
  10. 10.
    Elber R, Karplus M (1987) Multiple conformational states of proteins: a molecular dynamics analysis of myoglobin. Science 235:318–321CrossRefGoogle Scholar
  11. 11.
    Feliks M, Martins BM, Ullmann GM (2013) Catalytic mechanism of the glycyl radical enzyme 4-hydroxyphenylacetate decarboxylase from continuum electrostatic and QC/MM calculations. J Am Chem Soc 135:14,574–14,585CrossRefGoogle Scholar
  12. 12.
    Field MJ (2008) The pdynamo program for molecular simulations using hybrid quantum chemical and molecular mechanical potentials. J Chem Theory Comput 4:1151–1161CrossRefGoogle Scholar
  13. 13.
    Fischer S (2003) TReK: A program for trajectory refinement and kinematics. In: CHARMM c40b1 documentation. https://www.charmm.org/charmm/documentation/by-version/c40b1/params/doc/trek/ [Accessed: 2016-06-02]
  14. 14.
    Fischer S, Karplus M (1992) Conjugate peak refinement: an algorithm for finding reaction paths and accurate transition states in systems with many degrees of freedom. Chem Phys Lett 194:252–261CrossRefGoogle Scholar
  15. 15.
    Fletcher R, Reeves CM (1964) Function minimization by conjugate gradients. Comput J 7:149–154CrossRefGoogle Scholar
  16. 16.
    Galván IF, Field MJ (2008) Improving the efficiency of the NEB reaction path finding algorithm. J Comput Chem 29:139– 143CrossRefGoogle Scholar
  17. 17.
    Gilbert JC, Nocedal J (1992) Global convergence properties of conjugate gradient methods for optimization. SIAM J Optim 2:21–42CrossRefGoogle Scholar
  18. 18.
    Hehre WJ, Ditchfield R, Pople J (1972) Self-consistent molecular orbital methods. XII. Further extensions of gaussian-type basis sets for use in molecular orbital studies of organic molecules. J Chem Phys 56:2257–2261CrossRefGoogle Scholar
  19. 19.
    Henkelman G, Uberuaga BP, Jónsson H (2000) A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J Chem Phys 113:9901–9904CrossRefGoogle Scholar
  20. 20.
    Herrebout WA, van der Veken BJ, Wang A, Durig JR (1995) Enthalpy difference between conformers of n-butane and the potential function governing conformational interchange. J Phys Chem 99:578–585CrossRefGoogle Scholar
  21. 21.
    Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49:409– 436CrossRefGoogle Scholar
  22. 22.
    Hu X, Yang W (2010) Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function. J Chem Phys 132:1–7Google Scholar
  23. 23.
    Imhof P, Fischer S, Smith JC (2009) Catalytic mechanism of DNA backbone cleavage by the restriction enzyme EcoRV: A quantum mechanical/molecular mechanical analysis. Biochemistry 48:9061–9075CrossRefGoogle Scholar
  24. 24.
    Jonsson H, Mills G, Jacobsen KW (1998) Nudged elastic band method for finding minimum energy paths of transition. In: BJ Berne GC, Coker DF (eds) Classical and quantum dynamics in condensed phase simulations, world scientific, chap 16, pp 385–404Google Scholar
  25. 25.
    Leach AR (2003) Molecular modelling – principles and applications, 2nd edn. Pearson Education LtdGoogle Scholar
  26. 26.
    MacKerell AD, Bashford D, Dunbrack RL, Evanseck JD, Field MJ, Fischer S, Gao J, Guo H, Ha S, Joseph-McCarthy D, Kuchnir L, Kuczera K, Lau FTK, Mattos C, Michnick S, Ngo T, Nguyen DT, Prodhom B, Reiher WE, Roux B, Schlenkrich M, Smith JC, Stote R, Straub J, Watanabe M, Wiórkiewicz-Kuczera J, Yin D, Karplus M (1998) All-atom empirical potential for molecular modeling and dynamics studies of proteins. J Phys Chem B 102:3586–3616CrossRefGoogle Scholar
  27. 27.
    Madhumalar A, Smith DJ, Verma C (2008) Stability of the core domain of p53: Insights from computer simulations. BMC Bioinformatics 9 Suppl 1:S17CrossRefGoogle Scholar
  28. 28.
    Martins BM, Blaser M, Feliks M, Ullmann GM, Buckel W, Selmer T (2011) Structural basis for a kolbe-type decarboxylation catalyzed by a glycyl radical enzyme. J Am Chem Soc 133:14,666–14,674CrossRefGoogle Scholar
  29. 29.
    Mixcoha E, Garcia-Viloca M, Lluch JM, González-Lafont A (2012) Theoretical analysis of the catalytic mechanism of helicobacter pylori glutamate racemase. J Phys Chem B 116:12,406–12,414CrossRefGoogle Scholar
  30. 30.
    Moré JJ, Thuente DJ (1994) Line search algorithms with guaranteed sufficient decrease. ACM T Math Softw 20:286–307CrossRefGoogle Scholar
  31. 31.
    Neese F (2012) The ORCA program system. Wiley Interdiscip Rev Comput Mol Sci 2:73–78CrossRefGoogle Scholar
  32. 32.
    Noé F, Ille F, Smith JC, Fischer S (2005) Automated computation of low-energy pathways for complex rearrangements in proteins: Application to the conformational switch of Ras p21. Proteins 59:534–544CrossRefGoogle Scholar
  33. 33.
    Peng T, Larkin JD, Brooks BR (2012) Reaction path optimization and sampling methods and their applications for rare events. In: Pahlavani MR (ed) Some applications of quantum mechanics, intech, pp 27–66Google Scholar
  34. 34.
    Peters B, Heyden A, Bell AT, Chakraborty A (2004) A growing string method for determining transition states: Comparison to the nudged elastic band and string methods. J Chem Phys 120:7877–7886CrossRefGoogle Scholar
  35. 35.
    Polak E, Ribiere G (1969) Note sur la convergence de methods de directions conjugues. ESAIM: Math Model Num 3:35–43Google Scholar
  36. 36.
    Polyak BT (1969) The conjugate gradient method in extremal problems. USSR Comp Math Math + 9:807–821Google Scholar
  37. 37.
    Powell MJD (1986) Convergence properties of algorithms for nonlinear optimization. SIAM Rev 28(4):487–500CrossRefGoogle Scholar
  38. 38.
    Raghavachari K (1984) Rotational potential surface for alkanes: Basis set and electron correlation effects on the conformations of nbutane. J Chem Phys 81:1383–1388CrossRefGoogle Scholar
  39. 39.
    Rocha BG, Freire RO, Simas AM, Stewart JJP (2006) RM1: A reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I. J Comput Chem 27:1101–1111CrossRefGoogle Scholar
  40. 40.
    Rodríguez A, Oliva C, González M (2010) A comparative QM/MM study of the reaction mechanism of the Hepatitis C virus NS3/NS4A protease with the three main natural substrates NS5A/5B, NS4B/5A and NS4A/4B. Phys Chem Chem Phys 12:8001–8015CrossRefGoogle Scholar
  41. 41.
    Selvaraj B, Buckel W, Golding BT, Ullmann GM, Martins BM (2016) Structure and function of 4-hydroxyphenylacetate decarboxylase and its cognate activating enzyme. J Mol Microb Biotech 26:76–91CrossRefGoogle Scholar
  42. 42.
    Sinclair JE, Fletcher R (1974) A new method of saddle-point location for the calculation of defect migration energies. J Phys C Solid State 7:864–870CrossRefGoogle Scholar
  43. 43.
    Smith GD, Jaffe RL (1996) Quantum chemistry study of conformational energies and rotational energy barriers in n-alkanes. J Phys Chem 100:18,718–18,724CrossRefGoogle Scholar
  44. 44.
    Spiwok V, Šučur Z, Hošek P (2014) Enhanced sampling techniques in biomolecular simulations. Biotechnol Adv 33:1130–1140CrossRefGoogle Scholar
  45. 45.
    Sylvester JJ (1852) A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares. Philos Mag 4:138–142Google Scholar
  46. 46.
    Zheng M, Xu D (2013) Catalytic mechanism of hyaluronate lyase from streptococcus pneumonia [corrected]: Quantum mechanical/molecular mechanical and density functional theory studies. J Phys Chem B 117:10,161–10,172CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Computational BiochemistryUniversity of BayreuthBayreuthGermany

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