Application of local rules and cellular automata in representing protein translation and enhancing protein folding approximation

  • Alia Madain
  • Abdel Latif Abu Dalhoum
  • Azzam Sleit
Regular Paper
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Abstract

It is self-evident that the coarse-grained view of transcription and protein translation is a result of certain computations. Although there is no single definition of the term “computation,” protein translation can be implemented over mathematical models of computers. Protein folding, however, is a combinatorial problem; it is still unknown whether a fast, accurate, and optimal folding algorithm exists. The discovery of near-optimal folds depends on approximation algorithms and heuristic searches. The hydrophobic–hydrophilic (HP) model is a simplified representation of some of the realities of protein structure. Despite the simplified representation, the folding problem in the HP model was proven to be NP-complete. We use simple and local rules to model translation and folding of proteins. Local rules imply that at a certain level of abstraction an entity can move from a state to another based on its state and information collected from its neighborhood. Also, the rules are simple in a sense that they do not require complicated computation. We use one-dimensional cellular automata to describe translation of mRNA into protein. Cellular automata are discrete models of computation that use local interactions to produce a global behavior of some sort. We will also discuss how local rules can improve approximation algorithms of protein folding and give an example of a CA that accept a certain family of strings to achieve half H–H contacts.

Keywords

Protein translation Protein folding Cellular automata HP model 

Notes

Acknowledgements

We would like to thank Dr. Khair Eddin Sabri, Dr. Loai Alnemer, and Dr. Rawan Ghnemat for their suggestions and comments that greatly improved the content of this manuscript.

References

  1. 1.
    Abu Dalhoum, L.A., Madain, A., Hiary, H.: Digital image scrambling based on elementary cellular automata. Multimed. Tools Appl. 75(24), 17019–17034 (2016).  https://doi.org/10.1007/s11042-015-2972-z CrossRefGoogle Scholar
  2. 2.
    Aleksic, Z.: Artificial life: growing complex systems. In: Bossomaier, T.R.J., Green, D.G. (eds.) Complex Systems, pp. 91–126. Cambridge University Press, Cambridge (2000). (Cambridge Books Online)CrossRefGoogle Scholar
  3. 3.
    Anfinsen, C.B.: Principles that govern the folding of protein chains. Science 181(4096), 223–230 (1973)CrossRefGoogle Scholar
  4. 4.
    Berger, B., Leighton, T.: Protein folding in the hydrophobic–hydrophilic (HP) is NP-complete. In: Proceedings of the Second Annual International Conference on Computational Molecular Biology, RECOMB ’98, pp. 30–39. ACM, New York (1998)Google Scholar
  5. 5.
    Bokovi, B., Brest, J.: Genetic algorithm with advanced mechanisms applied to the protein structure prediction in a hydrophobic-polar model and cubic lattice. Appl. Soft Comput. 45(Supplement C), 61–70 (2016)Google Scholar
  6. 6.
    Burks, C., Farmer, D.: Towards modeling DNA sequences as automata. Phys. D 10(1–2), 157–167 (1984)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Cook, M.: Universality in elementary cellular automata. Complex Syst. 15, 1–40 (2004)MathSciNetMATHGoogle Scholar
  8. 8.
    Crescenzi, P., Goldman, D., Papadimitriou, C., Piccolboni, A., Yannakakis, M.: On the complexity of protein folding (abstract). In: Proceedings of the Second Annual International Conference on Computational Molecular Biology, RECOMB ’98, pp. 61–62. ACM, New York (1998)Google Scholar
  9. 9.
    Crick, F.: On protein synthesis. Symp. Soc. Exp. Biol. 12, 138–163 (1958)Google Scholar
  10. 10.
    Crick, F.: Central dogma of molecular biology. Nature 227(5258), 561–563 (1970)CrossRefGoogle Scholar
  11. 11.
    de Sales, J.A., Martins, M.L., Stariolo, D.A.: Cellular automata model for gene networks. Phys. Rev. E 55, 3262–3270 (1997)CrossRefGoogle Scholar
  12. 12.
    Diao, Y., Ma, D., Wen, Z., Yin, J., Xiang, J., Li, M.: Using pseudo amino acid composition to predict transmembrane regions in protein: cellular automata and lempel-ziv complexity. Amino Acids 34(1), 111–117 (2008)CrossRefGoogle Scholar
  13. 13.
    Dill, K.A.: Theory for the folding and stability of globular proteins. Biochemistry 24(6), 1501–1509 (1985)CrossRefGoogle Scholar
  14. 14.
    Dill, K.A., Bromberg, S., Yue, K., Chan, H.S., Ftebig, K.M., Yee, D.P., Thomas, P.D.: Principles of protein folding a perspective from simple exact models. Protein Sci. 4(4), 561–602 (1995)CrossRefGoogle Scholar
  15. 15.
    Drabo, H.K.: Formalization of transcription and translation processes by Turing machines. Master’s thesis, Morgan State University (2015)Google Scholar
  16. 16.
    Gardner, M.: Mathematical games: the fantastic combinations of John Conway’s new solitaire game “life”. Sci. Am. 223, 120–123 (1970)CrossRefGoogle Scholar
  17. 17.
    Gianni, S., Jemth, P.: Protein folding: vexing debates on a fundamental problem. Biophys. Chem. 212, 17–21 (2016)CrossRefGoogle Scholar
  18. 18.
    Gibson, M., Mjolsness, E.: Computational modeling of genetic and biochemical networks, vol. 8, chap. In: Bower, J. M., Bolouri, H. (eds.) Modeling the Activity of Single Genes, pp. 3–48. MIT Press, Cambridge MA (2001)Google Scholar
  19. 19.
    Günther, F., Möbius, A., Schreiber, M.: Structure optimisation by thermal cycling for the hydrophobic-polar lattice model of protein folding. Eur. Phys. J. Spec. Top. 226(4), 639–649 (2017)CrossRefGoogle Scholar
  20. 20.
    Haralick, R.M., Shanmugam, K., Dinstein, I.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973)CrossRefGoogle Scholar
  21. 21.
    Hart, W.E., Istrail, S.: Fast protein folding in the hydrophobichydrophilic model within three-eighths of optimal. J. Comput. Biol. 3(1), 53–96 (1996)CrossRefGoogle Scholar
  22. 22.
    Hu, M.K.: Visual pattern recognition by moment invariants. IRE Trans. Inf. Theory 8(2), 179–187 (1962)CrossRefMATHGoogle Scholar
  23. 23.
    Kaushik, A.C., Sahi, S.: Biological complexity: ant colony meta-heuristic optimization algorithm for protein folding. Neural Comput. Appl. 28(11), 3385–3391 (2017)CrossRefGoogle Scholar
  24. 24.
    Kier, L.B., Seybold, P.G., Cheng, C.K.: Cellular Automata, pp. 9–38. Springer, Dordrecht (2005)Google Scholar
  25. 25.
    Koehl, P.: Protein Structure Classification, pp. 1–55. Wiley, New York (2006)Google Scholar
  26. 26.
    Lau, K.F., Dill, K.A.: A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules 22(10), 3986–3997 (1989)CrossRefGoogle Scholar
  27. 27.
    Levinthal, C.: How to fold graciously. In: Debrunnder, J.T.P., Munck, E. (eds.) Mossbauer Spectroscopy in Biological Systems: Proceedings of a Meeting Held at Allerton House, Monticello, Ill, pp. 22–24. University of Illinois Press (1969)Google Scholar
  28. 28.
    Llanes, A., Vélez, C., Sánchez, A.M., Pérez-Sánchez, H., Cecilia, J.M.: Parallel Ant Colony Optimization for the HP Protein Folding Problem, pp. 615–626. Springer, New York (2016)Google Scholar
  29. 29.
    Lopes, H.S., Bitello, R.: A differential evolution approach for protein folding using a lattice model. J. Comput. Sci. Technol. 22(6), 904–908 (2007)CrossRefGoogle Scholar
  30. 30.
    Lopes, H.S.: Evolutionary algorithms for the protein folding problem: A review and current trends. In: Smolinski, T.G., Milanova, M.G., Hassanien, A.E. (eds.) Computational intelligence in biomedicine and bioinformatics. Studies in computational intelligence, vol. 151, pp. 297–315. Springer, Berlin, Heidelberg (2008)Google Scholar
  31. 31.
    Madain, A., Abu Dalhoum, A.L., Hiary, H., Ortega, A., Alfonseca, M.: Audio scrambling technique based on cellular automata. Multimed. Tools Appl. 71(3), 1803–1822 (2014)CrossRefGoogle Scholar
  32. 32.
    Madain, A., Abu Dalhoum, A.L., Sleit, A.: Computational modeling of proteins based on cellular automata. Int. J. Adv. Comput. Sci. Appl. 7(7), 491–498 (2016)Google Scholar
  33. 33.
    Madain, A., Abu Dalhoum, A.L., Sleit, A.: Potentials and challenges of building computational models of proteins based on cellular automata. Int. J. Comput. Sci. Inf. Secur. 14(9), 1–6 (2016)Google Scholar
  34. 34.
    Madain, A., Abu Dalhoum, A.L., Sleit, A.: Protein folding in the two-dimensional hydrophobic polar model based on cellular automata and local rules. Int. J. Comput. Sci. Netw. Secur. 16(9), 48–54 (2016)Google Scholar
  35. 35.
    Mauri, G., Pavesi, G.: Approximation algorithms for string folding problems. In: Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics, TCS ’00, pp. 45–58. Springer, London (2000)Google Scholar
  36. 36.
    Mizas, C., Sirakoulis, G., Mardiris, V., Karafyllidis, I., Glykos, N., Sandaltzopoulos, R.: Reconstruction of DNA sequences using genetic algorithms and cellular automata: Towards mutation prediction? Biosystems 92(1), 61–68 (2008)CrossRefGoogle Scholar
  37. 37.
    Newman, A.: A new algorithm for protein folding in the HP model. In: Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’02, pp. 876–884. Society for Industrial and Applied Mathematics, Philadelphia (2002)Google Scholar
  38. 38.
    Nishio, H.: How does the neighborhood affect the global behavior of cellular automata? In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) Cellular Automata. Lecture Notes in Computer Science, vol. 4173, pp. 122–130. Springer, Berlin (2006)CrossRefGoogle Scholar
  39. 39.
    Paterson, M., Przytycka, T.: On the complexity of string folding. Discrete Appl. Math. 71(1), 217–230 (1996)MathSciNetCrossRefMATHGoogle Scholar
  40. 40.
    Santos, J., Villot, P., Dieguez, M.: Cellular automata for modeling protein folding using the hp model. In: Evolutionary Computation (CEC), 2013 IEEE Congress, pp. 1586–1593 (2013)Google Scholar
  41. 41.
    Santos, J., Villot, P., Diéguez, M.: Emergent protein folding modeled with evolved neural cellular automata using the 3d HP model. J. Comput. Biol. 21(11), 823–845 (2014)CrossRefGoogle Scholar
  42. 42.
    Sarkar, P.: A brief history of cellular automata. ACM Comput. Surv. 32(1), 80–107 (2000)CrossRefGoogle Scholar
  43. 43.
    Sirakoulis, G., Karafyllidis, I., Mizas, C., Mardiris, V., Thanailakis, A., Tsalides, P.: A cellular automaton model for the study of dna sequence evolution. Comput. Biol. Med. 33(5), 439–453 (2003)CrossRefGoogle Scholar
  44. 44.
    Takata, D., Isokawa, T., Matsui, N., Peper, F.: Modeling chemical reactions in protein synthesis by a Brownian cellular automaton. In: 2013 First International Symposium on Computing and Networking, pp. 527–532 (2013)Google Scholar
  45. 45.
    Unger, R., Moult, J.: Genetic algorithms for protein folding simulations. J. Mol. Biol. 231(1), 75–81 (1993)CrossRefGoogle Scholar
  46. 46.
    Wang, S., Wu, L., Huo, Y., Wu, X., Wang, H., Zhang, Y.: Predict Two-Dimensional Protein Folding Based on Hydrophobic-Polar Lattice Model and Chaotic Clonal Genetic Algorithm, pp. 10–17. Springer, New York (2016)Google Scholar
  47. 47.
    Wooley, J.C., Lin., H.S.: Computational modeling and simulation as enablers for biological discovery. In: Catalyzing Inquiry at the Interface of Computing and Biology, pp. 117–202. National Academies Press (US), Washington (2005)Google Scholar
  48. 48.
    Xiao, X., Ling, W.: Using cellular automata images to predict protein structural classes. In: Bioinformatics and Biomedical Engineering, 2007. ICBBE 2007. The 1st International Conference, pp. 346–349 (2007)Google Scholar
  49. 49.
    Xiao, X., Shao, S., Ding, Y., Huang, Z., Chou, K.C.: Using cellular automata images and pseudo amino acid composition to predict protein subcellular location. Amino Acids 30(1), 49–54 (2006)CrossRefGoogle Scholar
  50. 50.
    Xiao, X., Wang, P., Chou, K.C.: GPCR-CA: a cellular automaton image approach for predicting g-protein-coupled receptor functional classes. J. Comput. Chem. 30(9), 1414–1423 (2008)CrossRefGoogle Scholar
  51. 51.
    Xiao, X., Wang, P., Chou, K.C.: Predicting protein structural classes with pseudo amino acid composition: an approach using geometric moments of cellular automaton image. J. Theor. Biol. 254(3), 691–696 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alia Madain
    • 1
  • Abdel Latif Abu Dalhoum
    • 1
  • Azzam Sleit
    • 1
  1. 1.Department of Computer Science, King Abdulla II School for Information TechnologyThe University of JordanAmmanJordan

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