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Differential evolution for protein folding optimization based on a three-dimensional AB off-lattice model

  • Borko BoškovićEmail author
  • Janez Brest
Original Paper

Abstract

This paper presents a differential evolution algorithm that is adapted for the protein folding optimization on a three-dimensional AB off-lattice model. The proposed algorithm is based on a self-adaptive differential evolution that improves the algorithm efficiency and reduces the number of control parameters. A mutation strategy for the fast convergence is used inside the algorithm. A temporal locality is used in order to speed up the algorithm convergence additionally and to find amino-acid conformations with the lowest free energy values. Within this mechanism a new vector is calculated when the trial vector is better than the corresponding vector from the population. This new vector is likely better than the trial vector and this accelerates convergence speed. Because of the fast convergence the algorithm has some chance to be trapped into the local optima. To mitigate this problem the algorithm includes reinitialization. The proposed algorithm was tested on amino-acid sequences that are used frequently in literature. The obtained results show that the proposed algorithm is superior to the algorithms from the literature and the obtained amino-acid sequences have significantly lower free energy values.

Graphical Abstract

Protein folding optimization on a three-dimensional AB off-lattice model using the differential evolution algorithm.

Keywords

Differential evolution Three-dimensional AB off-lattice model Protein folding optimization 

Notes

Acknowledgments

Our work was supported by the Slovenian Research Agency under Program P2-0041 (Computer Systems, Methodologies, and Intelligent Services).

Supplementary material

Folding simulation for 1AGT (AVI 2.50 MB)

Folding simulation for 2EWH (AVI 9.04 MB)

References

  1. 1.
    Bachmann M, Arkin H, Janke W (2005) Multicanonical study of coarse-grained off-lattice models for folding heteropolymers. Phys Rev E 71. doi: 10.1103/PhysRevE.71.031906
  2. 2.
    Bazzoli A, Tettamanzi AGB (2004) A Memetic Algorithm for Protein Structure Prediction in a 3D-Lattice HP Model. In: Raidl GR, Cagnoni S, Branke J, Corne DW, Drechsler R, Jin Y, Johnson CG, Machado P, Marchiori E, Rothlauf F, Smith GD, Squillero G (eds) Applications of Evolutionary Computing, Lecture Notes in Computer Science,. doi: 10.1007/978-3-540-24653-4_1, vol 3005. Springer, Berlin Heidelberg, pp 1–10
  3. 3.
    Bošković B, Brest J, Zamuda A, Greiner S, žumer V (2011) History Mechanism Supported Differential Evolution for Chess Evaluation Function Tuning. Soft Computing - A Fusion of Foundations, Methodologies and Applications 15:667–682. doi: 10.1007/s00500-010-0593-z Google Scholar
  4. 4.
    Brest J, Greiner S, Bošković B, Mernik M, žumer V (2006) Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems. IEEE Trans Evol Comput 10 (6):646–657. doi: 10.1109/TEVC.2006.872133 CrossRefGoogle Scholar
  5. 5.
    Chaves-González JM, Vega-Rodríguez MA, Granado-Criado JM (2013) A multiobjective swarm intelligence approach based on artificial bee colony for reliable {DNA} sequence design. Eng Appl Artif Intell 26 (9):2045–2057. doi: 10.1016/j.engappai.2013.04.011 CrossRefGoogle Scholar
  6. 6.
    Chen M, Huang WQ (2006) Heuristic algorithm for off-lattice protein folding problem. J Zhejiang Univ Sci B 7(1):7–12. doi: 10.1631/jzus.2006.B0007 CrossRefGoogle Scholar
  7. 7.
    Chen X, Lv M, Zhao L (2011) Zhang, X An Improved Particle Swarm Optimization for Protein Folding Prediction. International Journal of Information Engineering and Electronic Business 3(1):1–8CrossRefGoogle Scholar
  8. 8.
    Das S, Suganthan PN (2011) Differential Evolution: A Survey of the State-of-the-Art. IEEE Trans Evol Comput 15(1):4–31. doi: 10.1109/TEVC.2010.2059031 CrossRefGoogle Scholar
  9. 9.
    Denning PJ (2005) The Locality Principle. Commun ACM 48(7):19–24. doi: 10.1145/1070838.1070856 CrossRefGoogle Scholar
  10. 10.
    Dill KA, Ozkan SB, Weikl TR, Chodera JD, Voelz VA (2007) The protein folding problem: when will it be solved?. Curr Opin Struct Biol 17(3):342–346. doi: 10.1016/j.sbi.2007.06.001 CrossRefGoogle Scholar
  11. 11.
    Doğan B., Ölmez T (2015) Modified Off-lattice AB Model for Protein Folding Problem Using the Vortex Search Algorithm. International Journal of Machine Learning and Computing:5Google Scholar
  12. 12.
    Fraenkel AS (1993) Complexity of protein folding. Bull Math Biol 55 (6):1199 – 1210. doi: 10.1007/BF02460704 CrossRefGoogle Scholar
  13. 13.
    Glotić A, Zamuda A (2015) Short-term combined economic and emission hydrothermal optimization by surrogate differential evolution. Appl Energy 141:42–56. doi: 10.1016/j.apenergy.2014.12.020  10.1016/j.apenergy.2014.12.020 CrossRefGoogle Scholar
  14. 14.
    Hansmann UHE, Wille LT (2002) Global Optimization by Energy Landscape Paving. Phys Rev Lett 88:068,105. doi: 10.1103/PhysRevLett.88.068105  10.1103/PhysRevLett.88.068105 CrossRefGoogle Scholar
  15. 15.
    Hsu HP, Mehra V, Grassberger P (2003) Structure optimization in an off-lattice protein model. Phys Rev E 68. doi: 10.1103/PhysRevE.68.037703
  16. 16.
    Huang W, Liu J (2006) Structure optimization in a three-dimensional off-lattice protein model. Biopolymers 82(2):93–98. doi: 10.1002/bip.20400 CrossRefGoogle Scholar
  17. 17.
    Kim J, Straub JE, Keyes T (2007) Structure optimization and folding mechanisms of off-lattice protein models using statistical temperature molecular dynamics simulation: Statistical temperature annealing. Phys Rev E 76. doi: 10.1103/PhysRevE.76.011913
  18. 18.
    Kim SY, Lee SB, Lee J (2005) Structure optimization by conformational space annealing in an off-lattice protein model. Phys Rev E 72. doi: 10.1103/PhysRevE.72.011916
  19. 19.
    Lau KF, Dill KA (1989) A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules 22(10):3986–3997. doi: 10.1021/ma00200a030 CrossRefGoogle Scholar
  20. 20.
    Li B, Chiong R, Lin M (2015) A balance-evolution artificial bee colony algorithm for protein structure optimization based on a three-dimensional AB off-lattice model. Comput Biol Chem 54:1–12. doi: 10.1016/j.compbiolchem.2014.11.004 CrossRefGoogle Scholar
  21. 21.
    Li B, Li Y, Gong L (2014) Protein secondary structure optimization using an improved artificial bee colony algorithm based on AB off-lattice model. Eng Appl Artif Intell 27:70–79. doi: 10.1016/j.engappai.2013.06.010 CrossRefGoogle Scholar
  22. 22.
    Li B, Lin M, Liu Q, Li Y, Zhou C (2015) Protein folding optimization based on 3D off-lattice model via an improved artificial bee colony algorithm. J Mol Model 21(10):261. doi: 10.1007/s00894-015-2806-y CrossRefGoogle Scholar
  23. 23.
    Li B, Yao Y (2014) An edge-based optimization method for shape recognition using atomic potential function. Eng Appl Artif Intell 35:14–25. doi: 10.1016/j.engappai.2014.06.002 CrossRefGoogle Scholar
  24. 24.
    Li Y, Zhou C, Zheng X (2014) The Application of Artificial Bee Colony Algorithm in Protein Structure Prediction. In: Pan L, Paun G, Prez-Jimnez M, Song T (eds) Bio-Inspired Computing - Theories and Applications, Communications in Computer and Information Science. doi: 10.1007/978-3-662-45049-9_42, vol 472. Springer, Berlin Heidelberg, pp 255–258
  25. 25.
    Márquez-Chamorroa AE, Asencio-Cortésa G, Santiesteban-Tocab CE, Aguilar-Ruiza JS (2015) Soft Computing Methods for the Prediction of Protein Tertiary Structures: A Survey. Appl Soft Comput 35:398–410. doi: 10.1016/j.asoc.2015.06.024 CrossRefGoogle Scholar
  26. 26.
    Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33(1-2):61–106. doi: 10.1007/s10462-009-9137-2 CrossRefGoogle Scholar
  27. 27.
    Stillinger FH, Head-Gordon T (1995) Collective aspects of protein folding illustrated by a toy model. Phys Rev E 52:2872–2877. doi: 10.1103/PhysRevE.52.2872 CrossRefGoogle Scholar
  28. 28.
    Stillinger FH, Head-Gordon T, Hirshfeld CL (1993) Toy model for protein folding. Phys Rev E 48:1469–1477. doi: 10.1103/PhysRevE.48.1469  10.1103/PhysRevE.48.1469 CrossRefGoogle Scholar
  29. 29.
    Storn R., Price K (1995) Differential Evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces. Tech. Rep. TR-95-012, Berkeley CAGoogle Scholar
  30. 30.
    Storn R, Price K (1997) Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over continuous spaces. J Glob Optim 11(4):341–359CrossRefGoogle Scholar
  31. 31.
    Sun H, Luş H, Betti R (2013) Identification of structural models using a modified Artificial Bee Colony algorithm. Comput Struct 116:59–74. doi: 10.1016/j.compstruc.2012.10.017 CrossRefGoogle Scholar
  32. 32.
    Tanabe R, Fukunaga A (2014) Improving the search performance of SHADE using linear population size reduction. In: 2014 IEEE Congress on Evolutionary Computation (CEC2014), pp. 1658–1665. IEEEGoogle Scholar
  33. 33.
    Wang T, Zhang X (2009) 3D Protein Structure Prediction with Genetic Tabu Search Algorithm in Off-Lattice AB Model. In: Knowledge Acquisition and Modeling, 2009. KAM ’09. Second International Symposium on. doi: 10.1109/KAM.2009.2  10.1109/KAM.2009.2, vol 1, pp 43–46
  34. 34.
    Wang T, Zhang X (2011) A case study of 3D protein structure prediction with genetic algorithm and Tabu search. Wuhan University J Nat Sci 16(2):125–129. doi: 10.1007/s11859-011-0723-1 CrossRefGoogle Scholar
  35. 35.
    Wang Y, Guo G, Chen L (2013) Chaotic Artificial Bee Colony algorithm: A new approach to the problem of minimization of energy of the 3D protein structure. Mol Biol 47(6):894–900. doi: 10.1134/S0026893313060162 CrossRefGoogle Scholar
  36. 36.
    Wikipedia, The Free Encyclopedia: Locality of reference (2016) https://en.wikipedia.org/wiki/Locality_of_reference#Types_of_locality. [Online; accessed 01-January-2016]
  37. 37.
    Wong KC, Wu CH, Mok RKP, Peng C, Zhang Z (2012) Evolutionary multimodal optimization using the principle of locality. Inf Sci 194:138–170. doi: 10.1016/j.ins.2011.12.016 CrossRefGoogle Scholar
  38. 38.
    Zamuda A, Brest J (2014) Vectorized Procedural Models for Animated Trees Reconstruction using Differential Evolution. Inf Sci 278:1–21CrossRefGoogle Scholar
  39. 39.
    Zamuda A, Brest J, Bošković B, žumer V (2011) Differential Evolution for Parameterized Procedural Woody Plant Models Reconstruction. Appl Soft Comput 11:4904–4912. doi: 10.1016/j.asoc.2011.06.009 CrossRefGoogle Scholar
  40. 40.
    Zamuda A, Mlakar U (2015) Differential Evolution Control Parameters Study for Self-Adaptive Triangular Brushstrokes. Informatica - An International Journal of Computing and Informatics 39:105–113Google Scholar
  41. 41.
    Zamuda A, Sosa JDH (2014) Differential Evolution and Underwater Glider Path Planning Applied to the Short-Term Opportunistic Sampling of Dynamic Mesoscale Ocean Structures. Appl Soft Comput 24:95–108. doi: 10.1016/j.asoc.2014.06.048 CrossRefGoogle Scholar
  42. 42.
    Zhang X, Cheng W (2008) Protein 3D Structure Prediction by Improved Tabu Search in Off-Lattice AB Model. In: Bioinformatics and Biomedical Engineering, 2008. ICBBE 2008. The 2nd International Conference on. doi: 10.1109/ICBBE.2008.50, pp 184–187
  43. 43.
    Zhang X, Wang T, Luo H, Yang JY, Deng Y, Tang J, Yang MQ (2010) 3D Protein structure prediction with genetic tabu search algorithm. BMC Syst Biol 4:1–9. doi: 10.1186/1752-0509-4-S1-S6  10.1186/1752-0509-4-S1-S6 CrossRefGoogle Scholar
  44. 44.
    Zhou C, Hou C, Wei X, Zhang Q (2014) Improved hybrid optimization algorithm for 3D protein structure prediction. J Mol Model 20(7):2289. doi: 10.1007/s00894-014-2289-2 CrossRefGoogle Scholar
  45. 45.
    Zhou C, Hu T, Zhou S (2014) Protein Structure Prediction Based on Improved Multiple Populations and GA-PSO. In: Pan L, Paun G, Pérez-Jiménez M, Song T (eds) Bio-Inspired Computing - Theories and Applications, Communications in Computer and Information Science. doi: 10.1007/978-3-662-45049-9_105, vol 472. Springer, Berlin Heidelberg, pp 644–647

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering and Computer ScienceUniversity of MariborMariborSlovenia

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