Moscow University Chemistry Bulletin

, Volume 74, Issue 5, pp 216–222 | Cite as

Long-Term Memory Effect in Spatial Series of Model Peptides Composed of Glycine and Alanine

  • V. Yu. GrigorevEmail author
  • L. D. Grigoreva


Spatial series based on the histograms of interatomic distances are investigated by the detrended fluctuation analysis and the rescaled range method. Model glycine and alanine peptides are used as the objects of the study. The influence of the monomer type, chain length, and conformation on the values of the Hurst coefficients is analyzed. Most of the spatial series studied are shown to exhibit persistent behavior, that is, to possess long-term memory.


peptides Hurst parameter DFA analysis R/S analysis 



The work was performed as part of state assignment 0090-2017-0020 for the Institute of Physiologically Active Compounds of the Russian Academy of Sciences for 2018.


The authors declare that they have no conflict of interest.


  1. 1.
    Zhang, X., Zeng, M., and Meng, Q., Phys. A(Amsterdam,Neth.), 2018, vol. 490, p. 513.Google Scholar
  2. 2.
    Li, H.-B., Yuen, K.H., Otto, F., Leung, P.K., Sridharan, T.K., Zhang, Q., Liu, H., Tang, Y.W., and Qiu, K., Nature, 2015, vol. 520, no. 7548, p. 518.CrossRefGoogle Scholar
  3. 3.
    Kong, Y.L., Muniandy, S.V., Sulaiman, K., and Fakir, M.S., Thin Solid Films, 2017, vol. 623, p. 147.CrossRefGoogle Scholar
  4. 4.
    Shang, J., Wang, Y., Chen, M., Dai, J., Zhou, X., Kuttner, J., Hilt, G., Shao, X., Gottfried, J.M., and Wu, K., Nat. Chem., 2015, vol. 7, p. 389.CrossRefGoogle Scholar
  5. 5.
    Lennon, F.E., Cianci, G.C., Cipriani, N.A., Hensing, T.A., Zhang, H.J., Chen, C.T., Murgu, S.D., Vokes, E.E., Vannier, M.W., and Salgia, R., Nat. Rev. Clin. Oncol., 2015, vol. 12, no. 11, p. 664.CrossRefGoogle Scholar
  6. 6.
    Burgunder, J., Pafčo, B., Petrželková, K.J., Modrý, D., Hashimoto, C., and MacIntosh, A.J.J., Anim. Behav., 2017, vol. 129, p. 257.CrossRefGoogle Scholar
  7. 7.
    Dong, Q., Wang, Y., and Li, P., Environ. Pollut., 2017, vol. 222, p. 444.CrossRefGoogle Scholar
  8. 8.
    Lahmiri, S. and Bekiros, S., Chaos, Solitons Fractals, 2018, vol. 106, p. 28.CrossRefGoogle Scholar
  9. 9.
    Kristoufek, L., Phys. A(Amsterdam,Neth.), 2018, vol. 503, p. 257.Google Scholar
  10. 10.
    Dai, M., Hou, J., and Ye, D., Phys. A(Amsterdam,Neth.), 2016, vol. 444, p. 722.Google Scholar
  11. 11.
    Oświȩcimka, P., Livi, L., and Drożdż, S., Commun. Nonlinear Sci. Numer. Simul., 2018, vol. 57, p. 231.CrossRefGoogle Scholar
  12. 12.
    Giuliani, A., Benigni, R., Zbilut, J.P., Webber, C.L., Jr., Sirabella, P., and Colosimo, A., Chem. Rev., 2002, vol. 102, no. 5, p. 1471.CrossRefGoogle Scholar
  13. 13.
    Huang, Y. and Xiao, Y., Chaos, Solitons Fractals, 2003, vol. 17, p. 895.CrossRefGoogle Scholar
  14. 14.
    Kanduc, D., Capone, G., Pesce Delfino, V., and Losa, G., Adv. Stud. Biol., 2010, vol. 2, nos. 1–4, p. 53.Google Scholar
  15. 15.
    Kornev, A.P. and Taylor, S.S., Biophys. J., 2017, vol. 112, no. 3, p. 194.CrossRefGoogle Scholar
  16. 16.
    Cracuin, D. and Isvoran, A., Rom. J. Phys., 2015, vol. 60, nos. 7–8, p. 1103.Google Scholar
  17. 17.
    Isvoran, A., Unipan, L., Cracuin, D., and Morariu, V., J. Serb. Chem. Soc., 2007, vol. 72, no. 4, p. 383.CrossRefGoogle Scholar
  18. 18.
    Feder, J., Fractals, New York: Plenum, 1988.CrossRefGoogle Scholar
  19. 19.
    Hypercube. Scholar
  20. 20.
    Peng, C.-K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., and Goldberger, A.L., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1994, vol. 49, no. 2, p. 1685.CrossRefGoogle Scholar
  21. 21.
    Eke, A., Herman, P., Kocsis, L., and Kozak, L.R., Physiol. Meas., 2002, vol. 23, p. R1.CrossRefGoogle Scholar
  22. 22.
    Bearcave. hurst/.Google Scholar
  23. 23.
    Forsythe, G.E., Malcolm, M.A., and Moler, C.B., Computer Methods for Mathematical Computations, New York: Prentice-Hall, 1977.Google Scholar
  24. 24.
    Schroeder, M., Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, New York: Freeman, 1991.Google Scholar
  25. 25.
    Grigorev, V.Yu. and Grigoreva, L.D., Moscow Univ. Chem. Bull. (Engl. Transl.), 2017, vol. 72, no. 3, p. 144.CrossRefGoogle Scholar
  26. 26.
    Cracuin, D., Isvoran, A., and Avram, N.M., Acta Phys. Pol., A, 2009, vol. 116, no. 4, p. 684.CrossRefGoogle Scholar
  27. 27.
    Talete. Scholar
  28. 28.
    Grigor’ev, V. and Raevskii, O., Russ J. Gen. Chem., 2011, vol. 81, no. 3, p. 449.CrossRefGoogle Scholar
  29. 29.
    Dimov, N., Osman, A., Mekenyan, O., and Papazova, D., Anal. Chim. Acta, 1994, vol. 298, no. 3, p. 303.CrossRefGoogle Scholar
  30. 30.
    Magnuson, V.R., Harriss, D.K., and Basak, S.C., in Chemical Applications of Topology and Graph Theory, King, R.B., Ed., New York: Elsevier, 1983.Google Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Institute of Physiologically Active Compounds, Russian Academy of SciencesChernogolovkaRussia
  2. 2.Department of Fundamental Physicochemical Engineering, Moscow State UniversityMoscowRussia

Personalised recommendations