Journal of Computer-Aided Molecular Design

, Volume 32, Issue 2, pp 363–374 | Cite as

Congestion game scheduling for virtual drug screening optimization

  • Natalia NikitinaEmail author
  • Evgeny Ivashko
  • Andrei Tchernykh


In virtual drug screening, the chemical diversity of hits is an important factor, along with their predicted activity. Moreover, interim results are of interest for directing the further research, and their diversity is also desirable. In this paper, we consider a problem of obtaining a diverse set of virtual screening hits in a short time. To this end, we propose a mathematical model of task scheduling for virtual drug screening in high-performance computational systems as a congestion game between computational nodes to find the equilibrium solutions for best balancing the number of interim hits with their chemical diversity. The model considers the heterogeneous environment with workload uncertainty, processing time uncertainty, and limited knowledge about the input dataset structure. We perform computational experiments and evaluate the performance of the developed approach considering organic molecules database GDB-9. The used set of molecules is rich enough to demonstrate the feasibility and practicability of proposed solutions. We compare the algorithm with two known heuristics used in practice and observe that game-based scheduling outperforms them by the hit discovery rate and chemical diversity at earlier steps. Based on these results, we use a social utility metric for assessing the efficiency of our equilibrium solutions and show that they reach greatest values.


Drug discovery Virtual drug screening High-performance computing High-throughput computing Desktop grid Game theory Congestion game 



This work is partially supported by the Russian Fund for Basic Research under Grant Nos. 16-07-00622, 15-29-07974 and 16-51-55006, and CONACYT (Consejo Nacional de Ciencia y Tecnología, México) under Grant No. 178415.


  1. 1.
    Pharmaceutical Research and Manufacturers of America (PhRMA). 2016 Biopharmaceutical Industry Profile (2016) Accessed 21 November 2017
  2. 2.
    Bleicher K et al (2003) Hit and lead generation: beyond high-throughput screening. Nat Rev Drug Discov 2:369–378CrossRefGoogle Scholar
  3. 3.
    Bielska E et al (2011) Virtual screening strategies in drug design—methods and applications. BioTechnol 92(3):249–264CrossRefGoogle Scholar
  4. 4.
    Sosič I et al (2016) Nonpeptidic selective inhibitors of the chymotrypsin-like (β5 i) subunit of the immunoproteasome. Angew Chem Int Ed 55(19):5745–5748CrossRefGoogle Scholar
  5. 5.
    Cavasotto CN, Palomba D (2015) Expanding the horizons of G protein-coupled receptor structure-based ligand discovery and optimization using homology models. Chem Commun 51(71):13576–13594CrossRefGoogle Scholar
  6. 6.
    Leung CH et al (2011) A natural product-like inhibitor of NEDD8-activating enzyme. Chem Commun 47(9):2511–2513CrossRefGoogle Scholar
  7. 7.
    Bohacek RS, McMartin C, Guida WC (1996) The art and practice of structure-based drug design: a molecular modeling perspective. Med Res Rev 16(1):3–50CrossRefGoogle Scholar
  8. 8.
    Irwin J et al (2012) ZINC: a fee tool to discover chemistry for biology. J Chem Inf Model 52:1757–1768CrossRefGoogle Scholar
  9. 9.
    Bento AP et al (2014) The ChEMBL bioactivity database: an update. Nucleic Acids Res 42:1083–1090CrossRefGoogle Scholar
  10. 10.
    Pence HE, Williams A (2010) ChemSpider: an online chemical information resource. J Chem Educ 87(11):1123–1124CrossRefGoogle Scholar
  11. 11.
    Bolton EE et al (2008). In: Wheeler RA, Spellmeyer DC (eds) Annual reports in computational chemistry, vol 4, pp 217–241Google Scholar
  12. 12.
    Ruddigkeit L et al (2012) Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17. J Chem Inf Model 52:2864–2875CrossRefGoogle Scholar
  13. 13.
    Liu T et al (2016) Applying high performance computing in drug discovery and molecular simulation. Natl Sci Rev 3(1):49–63CrossRefGoogle Scholar
  14. 14.
    Tchernykh A et al (2015) Towards understanding uncertainty in cloud computing resource provisioning. Proced Comput Sci 51:1772–1781CrossRefGoogle Scholar
  15. 15.
    Muegge I, Oloffa S (2006) Advances in virtual screening. Drug Discov Today Technol 3(4):405 411CrossRefGoogle Scholar
  16. 16.
    Wale N, Karypis G (2007) Methods for effective virtual screening and scaffold-hopping in chemical compounds. Comput Syst Bioinform Conf 6:403 416Google Scholar
  17. 17.
    Krüger DM, Evers A (2010) Comparison of structure- and ligand-based virtual screening protocols considering hit list complementarity and enrichment factors. ChemMedChem 5(1):148 158Google Scholar
  18. 18.
    Tanrikulu Y, Krüger B, Proschak E (2013) The holistic integration of virtual screening in drug discovery. Drug Discov Today 18(7/8):358 364Google Scholar
  19. 19.
    Lionta E et al (2014) Structure-based virtual screening for drug discovery: principles, applications and recent advances. Curr Top Med Chem 14:1923 1938CrossRefGoogle Scholar
  20. 20.
    Harper G, Pickett SD, Green DV (2004) Design of a compound screening collection for use in high throughput screening. Comb Chem High Throughput Screen 7(1):63–70CrossRefGoogle Scholar
  21. 21.
    Harris CJ et al The design and application of target-focused compound libraries. Comb Chem High Throughput Screen 14:521 531Google Scholar
  22. 22.
    Böhm M (2011) In: Sotriffer C (ed) Virtual screening: principles, challenges, and practical guidelines, Wiley, WeinheimGoogle Scholar
  23. 23.
    Leach AR, Gillet VJ (2007) An introduction to chemoinformatics. Springer, New YorkCrossRefGoogle Scholar
  24. 24.
    Rupakheti CR et al (2015) Strategy to discover diverse optimal molecules in the small molecule universe. J Chem Inf Model 55:529 – 537CrossRefGoogle Scholar
  25. 25.
    Rupakheti CR (2015) Property biased-diversity guided explorations of chemical spaces. PhD dissertation, Duke UniversityGoogle Scholar
  26. 26.
    Irwin J, Shoichet BK (2016) Docking screens for novel ligands conferring new biology. J Med Chem 59(9):4103–4120CrossRefGoogle Scholar
  27. 27.
    World Community Grid. Accessed 21 Nov 2017
  28. 28.
    Patterson DE et al (1996) Neighborhood behavior: a useful concept for validation of “molecular diversity” descriptors. J Med Chem 39:3049–3059CrossRefGoogle Scholar
  29. 29.
    Willet P, Barnard JM, Downs GM (1998) Chemical similarity searching. J Chem Inf Comput Sci 38(6):983–996Google Scholar
  30. 30.
    Hann MM, Leach AR, Harper G (2001) Molecular complexity and its impact on the probability of finding leads for drug discovery. J Chem Inf Comput Sci 41:856 864CrossRefGoogle Scholar
  31. 31.
    Rosenthal R (1973) A class of games possessing pure-strategy Nash equilibria. Int J Game Theory 2(1):65 67CrossRefGoogle Scholar
  32. 32.
    Milchtaich I (1996) Congestion games with player-specific payoff functions. Games Econ Behav 13:111–124CrossRefGoogle Scholar
  33. 33.
    Ieong S et al (2005) Fast and compact: a simple class of congestion games. In: AIII proceedings 1–6Google Scholar
  34. 34.
    Gairing M, Klimm M (2013) Congestion games with player-specific costs revisited. International symposium on algorithmic game theory. Springer, BerlinGoogle Scholar
  35. 35.
    Blum LC, Reymond J-L (2009) 970 Million druglike small molecules for virtual screening in the chemical universe database GDB-13. J Am Chem Soc 131(25):8732–8733CrossRefGoogle Scholar
  36. 36.
    O’Boyle NM et al (2011) Open Babel: an open chemical toolbox. J Cheminform 3(1):33CrossRefGoogle Scholar
  37. 37.
    Nikitina N, Ivashko E, Tchernykh A (2017) Congestion game scheduling implementation for high-throughput virtual drug screening using BOINC-based desktop grid. 14th international conference on parallel computing 2017. LNCS 10421, pp 480–491Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute of Applied Mathematical Research, Karelian Research CenterRussian Academy of SciencesPetrozavodskRussia
  2. 2.Computer Science DepartmentCICESE Research CenterEnsenadaMexico

Personalised recommendations