Skip to main content
SpringerLink
Log in

Tensor Train Global Optimization: Application to Docking in the Configuration Space with a Large Number of Dimensions

  • Conference paper
  • First Online:
Supercomputing (RuSCDays 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 793))

Included in the following conference series:

Abstract

The novel docking algorithm is presented and it is applied to the docking problem with flexible ligand and moveable protein atoms. The energy of the protein-ligand complex is calculated in the frame of the MMFF94 force field in vacuum. The conformation space of the system coordinates is formed by translations and rotations of the ligand as a whole, by the ligand torsions and also by Cartesian coordinates of the selected target protein atoms. The algorithm is realized in the novel parallel docking SOL-P program and results of its performance for a set of 30 protein-ligand complexes are presented. It is shown that mobility of the protein atoms improves docking positioning accuracy. The SOL-P program is able to perform docking of a flexible ligand into the active site of the target protein with several dozen of protein moveable atoms – up to 157 degrees of freedom.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Sliwoski, G., Kothiwale, S., Meiler, J., Lowe, E.W.: Computational Methods in Drug Discovery. Pharmacol. Rev. 66, 334–395 (2014). https://doi.org/10.1124/pr.112.007336

    Article  Google Scholar 

  2. Sadovnichii, V.A., Sulimov, V.B.: Supercomputing technologies in medicine. In: Voevodin, V.V., Sadovnichii, V.A., Savin, G.I. (eds.) Supercomputing Technologies in Science, Education, and Industry, pp. 16–23. Moscow University Publishing (2009). (in Russian)

    Google Scholar 

  3. Mobley, D.L., Dill, K.A.: Binding of small-molecule ligands to proteins: “what you see” is not always “what you get”. Structure 17(4), 489–498 (2009). https://doi.org/10.1016/j.str.2009.02.010

    Article  Google Scholar 

  4. Sulimov, A.V., Kutov, D.C., Oferkin, I.V., Katkova, E.V., Sulimov, V.B.: Application of the docking program SOL for CSAR benchmark. J. Chem. Inf. Model. 53(8), 1946–1956 (2013). https://doi.org/10.1021/ci400094h

    Article  Google Scholar 

  5. Antunes, D.A., Devaurs, D., Kavraki, L.E.: Understanding the challenges of protein flexibility in drug design. Expert Opin. Drug Discov. 10(12), 1301–1313 (2015). https://doi.org/10.1517/17460441.2015.1094458

    Article  Google Scholar 

  6. Chen, W., Gilson, M.K., Webb, S.P., Potter, M.J.: Modeling protein-ligand binding by mining minima. J. Chem. Theor. Comput. 6(11), 3540–3557 (2010)

    Article  Google Scholar 

  7. Oferkin, I.V., Katkova, E.V., Sulimov, A.V., Kutov, D.C., Sobolev, S.I., Voevodin, V.V., Sulimov, V.B.: Evaluation of docking target functions by the comprehensive investigation of protein-ligand energy minima. Adv. Bioinf. 2015, 12 (2015). https://doi.org/10.1155/2015/126858. Article ID 126858

    Article  Google Scholar 

  8. Oferkin, I.V., Zheltkov, D.A., Tyrtyshnikov, E.E., Sulimov, A.V., Kutov, D.C.: Evaluation of the docking algorithm based on tensor train global optimization. Bull. South Ural State Univ. Ser. Math. Model. Program. Comput. Softw. 8(4), 83–99 (2015). https://doi.org/10.14529/mmp150407

    MATH  Google Scholar 

  9. Sulimov, A.V., Kutov, D.C., Katkova, E.V., Sulimov, V.B.: Combined docking with classical force field and quantum chemical semiempirical method PM7. Adv. Bioinf. 2017, 6 (2017). https://doi.org/10.1155/2017/7167691. Article ID 7167691

    Article  Google Scholar 

  10. Pecina, A., Meier, R., Fanfrlík, J., Lepšík, M., Řezáč, J., Hobza, P., Baldauf, C.: The SQM/COSMO filter: reliable native pose identification based on the quantum-mechanical description of protein-ligand interactions and implicit COSMO solvation. Chem. Commun. 52, 3312–3315 (2016)

    Article  Google Scholar 

  11. Zheltkov, D.A., Oferkin, I.V., Katkova, E.V., Sulimov, A.V., Sulimov, V.B.: TTDock: docking method based on tensor train. Vychislitelnie metody i programmirovanie (Numer. Meth. Program.) 14, 279–291 (2013). (in Russian). http://num-meth.srcc.msu.ru/english/zhurnal/tom_2013/v14r131.html. Accessed 10 April 2017

    Google Scholar 

  12. Sulimov, A., Zheltkov, D., Oferkin, I., Kutov, D., Tyrtyshnikov, E.: Novel gridless program SOL-P for flexible ligand docking with moveable protein atoms. In: 21st EuroQSAR Where Molecular Simulations Meet Drug Discovery. Aptuit Conference Center, Verona Italy, Abstract book, OC15, p. 52, 4–8 September 2016. www.euroqsar2016.org

  13. Sulimov, A.V., Zheltkov, D.A., Oferkin, I.V., Kutov, D.C., Katkova, E.V., Tyrtyshnikov, E.E., Sulimov, V.B.: Evaluation of the novel algorithm of flexible ligand docking with moveable target protein atoms. Comput. Struct. Biotechnol. J. 15, 275–285 (2017). https://doi.org/10.1016/j.csbj.2017.02.004

    Article  MATH  Google Scholar 

  14. Halgren, T.A.: Merck molecular force field. I. basis, form, scope, parameterization and performance of MMFF94. J. Comput. Chem. 17, 490–519 (1996)

    Article  Google Scholar 

  15. Sinauridze, E.I., Romanov, A.N., Gribkova, I.V., Kondakova, O.A., Surov, S.S.: New synthetic thrombin inhibitors: molecular design and experimental verification. PLoS ONE 6(5), e19969 (2011). https://doi.org/10.1371/journal.pone.0019969

    Article  Google Scholar 

  16. Oseledets, I.V., Tyrtyshnikov, E.E.: Breaking the curse of dimensionality, or how to use SVD in many dimensions. SIAM J. Sci. Comput. 31(5), 3744–3759 (2009). https://doi.org/10.1137/090748330

    Article  MATH  MathSciNet  Google Scholar 

  17. Oseledets, I.V.: Tensor-train decomposition. SIAM J. Sci. Comput. 33(5), 2295–2317 (2011). https://doi.org/10.1137/090752286

    Article  MATH  MathSciNet  Google Scholar 

  18. Oseledets, I.V., Tyrtyshnikov, E.E.: TT-Cross approximation for multidimensional arrays. Linear Algebra Appl. 432(1), 70–88 (2010). https://doi.org/10.1016/j.laa.2009.07.024

    Article  MATH  MathSciNet  Google Scholar 

  19. Goreinov, S.A., Tyrtyshnikov, E.E., Zamarashkin, N.L.: Pseudo-skeleton approximations of matrices. Rep. Russ. Acad. Sci. 342(2), 151–152 (1995). https://doi.org/10.1016/S0024-3795(96)00301-1

    MATH  MathSciNet  Google Scholar 

  20. Goreinov, S.A., Tyrtyshnikov, E.E., Zamarashkin, N.L.: A theory of pseudo-skeleton approximations. Linear Algebra Appl. 261, 1–21 (1997). https://doi.org/10.1016/S0024-3795(96)00301-1

    Article  MATH  MathSciNet  Google Scholar 

  21. Tyrtyshnikov, E.E.: Incomplete cross approximation in the mosaic-skeleton method. Computing 64(4), 367–380 (2000). https://doi.org/10.1007/s006070070031

    Article  MATH  MathSciNet  Google Scholar 

  22. Goreinov, S.A., Tyrtyshnikov, E.E.: The maximal-volume concept in approximation by low-rank matrices. Contemp. Math. 208, 47–51 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  23. Goreinov, S.A., Oseledets, I.V., Savostyanov, D.V., Tyrtyshnikov, E.E., Zamarashkin, N.L.: How to find a good submatrix. Research Report 8-10, ICM HKBU, Kowloon Tong, Hong Kong (2008). https://doi.org/10.1142/9789812836021_0015

  24. Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  25. Rowan, T.: Functional stability analysis of numerical algorithms. Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin (1990)

    Google Scholar 

  26. Steven, G.J.: The NLopt nonlinear-optimization package. http://ab-initio.mit.edu/nlopt

  27. Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5), 1190–1208 (1995). https://doi.org/10.1137/0916069

    Article  MATH  MathSciNet  Google Scholar 

  28. Zhu, C., Byrd, R.H., Lu, P., Nocedal, J.: Algorithm 778: L-BFGS-B: fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Softw. 23(4), 550–560 (1997). https://doi.org/10.1145/279232.279236

    Article  MATH  MathSciNet  Google Scholar 

  29. Berman, H.M., Westbrook, J., Feng, Z.: The protein data bank. Nucleic Acids Res. 28(1), 235–242 (2000). http://www.rcsb.org/pdb/home/home.do

    Article  Google Scholar 

  30. Zheltkov, D.A., Tyrtyshnikov, E.E.: Parallel Implementation of Matrix Cross Method. Vychislitelnye metody i programmirovanie (Numer. Meth. Program.) 16, 369–375 (2015). (in Russian)

    Google Scholar 

  31. MSU Supercomputers: Lomonosov-2. http://hpc.msu.ru/?q=node/159. Accessed 30 May 2017

  32. Sadovnichy, V.A., Tikhonravov, A.V., Voevodin, V.V., Opanasenko, V.: “Lomonosov”: supercomputing at Moscow State University. In: Contemporary High Performance Computing: From Petascale toward Exascale, pp. 283–307. CRC Press (2013)

    Google Scholar 

Download references

Acknowledgements

The work was financially supported by the Russian Science Foundation, Agreement no. 15-11-00025.

Author information

Authors and Affiliations

  1. Dimonta, Ltd., Moscow, 117186, Russia

    A. V. Sulimov, I. V. Oferkin, D. C. Kutov, E. V. Katkova & V. B. Sulimov

  2. Research Computer Center, Lomonosov Moscow State University, Moscow, 119992, Russia

    A. V. Sulimov, D. C. Kutov, E. V. Katkova, E. E. Tyrtyshnikov & V. B. Sulimov

  3. Institute of Numerical Mathematics of Russian Academy of Sciences, Moscow, 119333, Russia

    D. A. Zheltkov & E. E. Tyrtyshnikov

  4. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow, 119992, Russia

    E. E. Tyrtyshnikov

  5. Siedlce University of Natural Sciences and Humanities, Siedlce, woj. Mazowieckie, Poland

    E. E. Tyrtyshnikov

Authors
  1. A. V. Sulimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Zheltkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. V. Oferkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. C. Kutov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. E. V. Katkova
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. E. E. Tyrtyshnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. V. B. Sulimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. B. Sulimov .

Editor information

Editors and Affiliations

  1. Research Computing Center (RCC), Moscow State University, Moscow, Russia

    Vladimir Voevodin

  2. Moscow State University, Moscow, Russia

    Sergey Sobolev

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sulimov, A.V. et al. (2017). Tensor Train Global Optimization: Application to Docking in the Configuration Space with a Large Number of Dimensions. In: Voevodin, V., Sobolev, S. (eds) Supercomputing. RuSCDays 2017. Communications in Computer and Information Science, vol 793. Springer, Cham. https://doi.org/10.1007/978-3-319-71255-0_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-71255-0_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71254-3

  • Online ISBN: 978-3-319-71255-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation