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Quantitative Criteria of Chirality in Hierarchical Protein Structures

  • MOLECULAR BIOPHYSICS
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Abstract

Based on the theory of the formation of sign-alternating hierarchical structures in macromolecular systems, a quantitative approach was developed to assess the chirality sign of individual levels in hierarchical protein structures. Quantitative estimates are necessary for modeling the folding of proteins and their function as molecular machines. Mutual attraction between the α-carbon atoms of amino acids is a sufficient condition for characterizing the level in the hierarchical structure and determining the chirality sign of protein blocks. A quantitative estimate of the twist in helical (secondary) and superhelical (tertiary) structures is provided by the absolute value of the sum of vector cross products. The sign of the scalar product of the direction vector to the vector of the sum of vector products indicates the direction of the twist. Chiral maps were constructed for the secondary and tertiary structures of several proteins. The reliability of the maps was confirmed by analyzing the respective real structures.

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REFERENCES

  1. B. Alberts, D. Bray, J. Lewis, et al., Molecuar Biology of the Cell, 2nd ed. (Garland Scim New York, 1989; Mir, Moscow, 1994), Vol. 1.

  2. V. A. Tverdislov, A. E. Sidorova, and L. V. Iakovenko, Biophysics (Moscow) 57 (1), 146 (2012).

    Google Scholar 

  3. V. A. Tverdislov, Biophysics (Moscow) 58 (1), 128 (2013).

    Article  Google Scholar 

  4. V. A. Tverdislov, E. V. Malyshko, S. A. Il’chenko, et al., Biophysics (Moscow) 62 (3), 331 (2017).

    Article  Google Scholar 

  5. P. A. Guye, Comptes Rendus Acad. Sci. 110, 714 (1890).

    Google Scholar 

  6. P. A. Guye, Comptes Rendus Acad. Sci. 116, 1451 (1893).

    Google Scholar 

  7. P. A. Guye and L. Chavanne, Comptes Rendus Acad. Sci. 116, 1454 (1893).

    Google Scholar 

  8. M. Petitjean, Entropy 5 (3), 271 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  9. E. Ruch and A. Schönhofer, Theor. Chim. Acta 10 (2), 91 (1968).

    Article  Google Scholar 

  10. M. Randic, J. Am. Chem. Soc. 97 (23), 6609 (1975).

    Article  Google Scholar 

  11. M. Randic, Chemometr. Intell. Lab. Syst. 10, 213 (1991).

    Article  Google Scholar 

  12. X. L. Peng, K.-T. Fang, Q.-N. Hu, Y.-Z. Liang, Molecules 9 (12), 1089 (2004).

    Article  Google Scholar 

  13. G. Rücker and C. Rücker, J. Chem. Inf. Comput. Sci. 39 (5), 788 (1999).

  14. Y. Du, Y. Liang, B. Li, and Ch. Xu, J. Chem. Inf. Comput. Sci. 42 (5), 993 (2002).

    Article  Google Scholar 

  15. D. Yaffe and Y. Cohen, J. Chem. Inf. Comput. Sci. 41 (2), 463 (2001).

    Article  Google Scholar 

  16. E. S. Goll and P. C. Jurs, J. Chem. Inf. Comput. Sci. 39 (6), 1081 (1999).

    Article  Google Scholar 

  17. H. E. McClelland and P. C. Jurs, J. Chem. Inf. Comput. Sci. 40 (4), 967 (2000).

    Article  Google Scholar 

  18. J. A. Dean, Lange’s Handbook of Chemistry (McGraw-Hill, New York, 1998).

    Google Scholar 

  19. A. R. Katritzky, S. Sild, and M. Karelson, J. Chem. Inf. Comput. Sci. 38 (5), 840 (1998).

    Article  Google Scholar 

  20. B. E. Turner, C. L. Costello, and P. C. Jurs, J. Chem. Inf. Comput. Sci. 38 (4), 639 (1998).

    Article  Google Scholar 

  21. M. Randic and M. Razinger, J. Chem. Inf. Comput. Sci. 36 (3), 429 (1996).

    Article  Google Scholar 

  22. T. Zhao, Q. Zhang, H. Long, and L. Xu, PLoS One 9 (7) (2014). https://doi.org/10.1371/journal.pone.0102043

  23. M. Randic, J. Chem. Inf. Comput. Sci. 41 (3), 639 (2001).

    Article  Google Scholar 

  24. A. B. Buda, T. A. der Heyde, and K. Mislow, Angew. Chem. Int. Ed. 31 (8), 989 (1992).

    Article  Google Scholar 

  25. A. Rassat, Comptes Rendus Acad. Sci., Ser. B 299 (2), 53 (1984).

    Google Scholar 

  26. F. Hausdorff, Grundzüge der Mengenlehre (von Veit, Leipzig, 1914; ONTI, Moscow, 1937).

  27. P. G. Mezey, THEOCHEM 455 (2–3), 183 (1998).

  28. G. Gilat and L. S. Schulman, Chem. Phys. Lett. 121 (1–2), 13 (1985).

  29. H. Zabrodsky, S. Peleg, and D. Avnir, J. Am. Chem. Soc. 114 (20), 7843 (1992).

    Article  Google Scholar 

  30. H. Zabrodsky, S. Peleg, and D. Avnir, J. Am. Chem. Soc. 115 (18), 8278 (1993).

    Article  Google Scholar 

  31. M. Pinsky, C. Dryzun, D. Casanova, et al., J. Comput. Chem. 29 (16), 2712 (2008). https://doi.org/10.1002/jcc.20990

    Article  Google Scholar 

  32. V. E. Kuz’min, I. B. Stel’makh, M. B. Bekker, and D. V. Pozigun, J. Phys. Org. Chem. 5 (6), 295 (1992).

    Article  Google Scholar 

  33. L. A. Kutulya, V. E. Kuz’min, I. B. Stel’mach, et al., J. Phys. Org. Chem. 5 (6), 308 (1992).

    Article  Google Scholar 

  34. S. E. Alikhanidi and V. E. Kuz’min, Zh. Struct. Khim. 41 (4), 795 (2000).

    Google Scholar 

  35. V. M. Markov, V. A. Potemkin, and A. V. Belik, Zh. Struct. Khim. 42 (1), 91 (2001).

    Google Scholar 

  36. P. M. Zorkii and N. N. Afonina, Symmetry of Molecular and Crystals (Moscow State Univ., Moscow, 1979) [in Russian].

    Google Scholar 

  37. A. V. Belik and V. A. Potemkin, Zh. Struct. Khim. 66 (1), 140 (1992).

    Google Scholar 

  38. P. W. Fowler, Symmetry Cult. Sci. 16 (4), 321 (2005).

    Google Scholar 

  39. A. V. Luzanov, V. V. Ivanov, and R. M. Minyaev, Zh. Struct. Khim. 39 (2), 319 (1998).

    Google Scholar 

  40. A. V. Luzanov and D. Nerukh, Funct. Mater. 12 (1), 55 (2005).

    Google Scholar 

  41. A. V. Luzanov and D. Nerukh, J. Math. Chem. 41 (4), 417 (2007).

    Article  MathSciNet  Google Scholar 

  42. A. V. Luzanov, Funct. Mater. 22 (3), 355 (2015).

    Article  Google Scholar 

  43. S. Janssens, P. Bultinck, A. Borgoo, et al., J. Phys. Chem. A 114 (1), 640 (2010). https://doi.org/10.1021/jp9081883

    Article  Google Scholar 

  44. Sh. R. Buxton and S. M. Roberts, Guide to Organic Stereochemistry: From Methane to Macromolecules (Prentice Hall, 1997; Mir, Moscow, 2015).

  45. G. Raos, Macromol. Theor. Simul. 11 (7), 739 (2002).

    Article  Google Scholar 

  46. M. Petitjean, The Mathematical Theory of Chirality. http://petitjeanmichel.free.fr/itoweb.petitjean.html. Cited April 10, 2018.

  47. M. Petitjean, J. Math. Phys. 43 (8), 4147 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  48. G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan, J. Mol. Biol. 7 (1), 95 (1963).

    Article  Google Scholar 

  49. C. R. Cantor and P. R. Schimmel, Biophysical Chemistry (Freeman, San Francisco, 1980; Mir, Moscow, 1984), Vol. 2.

  50. D. A. Brant and P. R. Schimmel, Proc. Natl. Acad. Sci. U.S.A. 58, 428 (1967).

    Article  ADS  Google Scholar 

  51. A. V. Finkelstein and O. B. Ptitsyn, Protein Physics (KDU, Moscow, 2002; Academic, New York, 2002).

  52. Yu. A. Ovchinnikov, Bioorganic Chemistry (Prosveshchenie, Moscow, 1987) [in Russian].

  53. A. R. Kotov, A. E. Sidorova, V. A. Tverdislov, and M. N. Ustini, Uch. Zap. Fiz. Fakyl’t. Mosk. Gos. Univ. 1 830 701 (3), 1 (2018).

    Google Scholar 

  54. The Protein Data Bank. http://www.rcsb.org. Cited April 10, 2018.

  55. W. Kabsch and C. Sander, Biopolymers 22 (12), 2577 (1983).

    Article  Google Scholar 

  56. C. Chothia, J. Mol. Biol. 75, 295 (1973).

    Article  Google Scholar 

  57. http://www.wwpdb.org/documentation/file-format.

  58. G. E. Schulz and R. H. Schirmer, Principles of Protein Structure (Springer, 1979; Mir, Moscow, 1982).

Download references

COMPLIANCE WITH ETHICAL STANDARDS

The authors declare that they have no conflict of interest. This article does not contain any studies involving animals or human participants performed by any of the authors.

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Authors and Affiliations

  1. Department of Physics, Moscow State University, 119991, Moscow, Russia

    A. E. Sidorova, E. V. Malyshko, A. R. Kotov & V. A. Tverdislov

  2. Institute of Mathematical Problems of Biology, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 142290, Pushchino, Moscow oblast, Russia

    M. N. Ustinin

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  1. A. E. Sidorova
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  2. E. V. Malyshko
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  3. A. R. Kotov
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  4. V. A. Tverdislov
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Correspondence to A. E. Sidorova.

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Translated by T. Tkacheva

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Sidorova, A.E., Malyshko, E.V., Kotov, A.R. et al. Quantitative Criteria of Chirality in Hierarchical Protein Structures. BIOPHYSICS 64, 155–166 (2019). https://doi.org/10.1134/S0006350919020167

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