Statistical analysis of the internal distances of helical pairs in protein molecules

D. A. Tikhonov ; L. I. Kulikova ; A. V. Efimov

Matematičeskaâ biologiâ i bioinformatika, Tome 11 (2016) no. 2, pp. 170-190.

Résumé

The statistical analysis of interhelical distances in pairs of connected $\alpha$-helices found in known proteins has been performed. In accordance with the certain rules, a database of the pairs found in the Protein Data Bank has been compiled. This set was subdivided into three subsets according to criterion of crossing helix projections on the parallel plane passing through the axis of the helix. It was shown that the distribution of distances between the pairs of helices whose projections are not crossed has a more long-range nature than those whose projections are overlapped. Using the regression analysis the nature of distributions is investigated. In particular, it is shown that the distributions of interhelical distances in the subset of pairs of helices without intersections belong to the gamma distributions. It is also shown that the subset of the pairs with crossing projections have a smaller ratio of the minimal distance between the helical axes to the interplanar distance that is contrast to the set without crossing projections. It was concluded that the helical pairs with crossing projections are additionally stabilized by internal interactions.

Bibliographie

[1] Efimov A. V., “Standard structures in proteins”, Prog. Biophys. Molec. Biol., 60 (1993), 201–239 | DOI

[2] Gordeev A. B., Kargatov A. M., Efimov A. V., “PCBOST: Protein classification based on structural trees”, Biochemical and Biophysical Research Communications, 397 (2010), 470–471 | DOI

[3] Efimov A. V., “Super-secondary structures and modeling of protein folds”, Methods in Molecular Biology, 932, ed. Kister A. E., Humana Press, Clifton, 2013, 177–189 | DOI

[4] Brazhnikov E. V., Efimov A. V., “Structure of $\alpha$-$\alpha$-hairpins with short connections in globular proteins”, Molecular Biology, 35:1 (2001), 89–97 | DOI

[5] Efimov A. V., “$\mathrm{L}$-obraznaya struktura iz dvukh $\alpha$-spiralei s ostatkom prolina mezhdu nimi”, Molekulyarnaya biologiya, 26 (1992), 1370–1376

[6] Efimov A. V., “Novaya supervtorichnaya struktura belkov: $\alpha$-$\alpha$-ugolok”, Molekulyarnaya biologiya, 18 (1984), 1524–1537

[7] Finkelshtein A. V., Fizika belkovykh molekul, ANO «Izhevskii institut kompyuternykh issledovanii», M.–Izhevsk, 2014, 424 pp.

[8] Ptitsyn O. B., Filkenshtein A. V., “Problemy predskazaniya struktury belka”, Itogi nauki i tekhniki. Seriya «Molekulyarnaya biologiya», 15, ed. Volkenshtein M. D., VINITI, M., 1979, 6–41 | Zbl

[9] Shults G. E., Shirmer R. Kh., Printsipy strukturnoi organizatsii belkov, Mir, M., 1982, 354 pp.

[10] Miller S., Janin J., Lesk A. M., Chothia C., “Interior and surfage of monomeric proteins”, J. Molecular Biology, 196 (1987), 641–656 | DOI

[11] Creighton T. E., Proteins, 2-nd edn., W.H. Freeman Co, N.Y., 1991

[12] Stepanov V. M., Molekulyarnaya biologiya. Struktura i funktsii belkov, Vysshaya shkola, M., 1996, 336 pp.

[13] Finkelshtein A. V., “Elektrostaticheskie vzaimodeistviya zaryazhennykh grupp v vodnoi srede i ikh vliyanie na obrazovanie vtorichnykh struktur polipeptidnoi tsepi”, Molekulyarnaya biologiya, 11 (1970), 811–819

[14] Fersht A., Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding, W.H. Freeman Co, N.Y., 1999

[15] Lim V. I., “Structural principles of the globular organization of protein chains. A stereochemical theory of globular protein secondary structure”, J. Molecular Biology, 88 (1974), 857–872 | DOI

[16] Lim V. I., “Algorithm for prediction of $\alpha$-helices and $\beta$-structural regions in globular proteins”, J. Molecular Biology, 88 (1974), 873–894 | DOI

[17] Wierenga R. K., Terpstra P., Hol W. G. S., “Prediction of the occurrence of the ADP-binding $\beta\alpha\beta$-fold in proteins, using an amino acid sequence fingerprint”, J. Molecular Biology, 187 (1986), 101–107 | DOI

[18] Rudnev V. R., Pankratov A. N., Kulikova L. I., Dedus F. F., Tikhonov D. A., Efimov A. V., “Raspoznavanie i analiz ustoichivosti strukturnykh motivov tipa $\alpha$-$\alpha$-ugolok v globulyarnykh belkakh”, Matematicheskaya biologiya i bioinformatika, 8:2 (2013), 398–406 | DOI

[19] Rudnev V. R., Pankratov A. N., Kulikova L. I., Dedus F. F., Tikhonov D. A., Efimov A. V., “Konformatsionnyi analiz strukturnykh motivov tipa $\alpha$-$\alpha$-ugolok v vychislitelnom eksperimente molekulyarnoi dinamiki”, Matematicheskaya biologiya i bioinformatika, 9:2 (2014), 575–584 | DOI

[20] Dedus F. F., Kulikova L. I., Pankratov A. N., Tetuev R. K., Klassicheskie ortogonalnye bazisy v zadachakh analiticheskogo opisaniya i obrabotki informatsionnykh signalov, Uchebnoe posobie, Izdatelskii otdel VMiK MGU, M., 2004, 147 pp.

[21] Pankratov A. N., Gorchakov M. A., Dedus F. F., Dolotova N. S., Kulikova L. I., Makhortykh S. A., Nazipova N. N., Novikova D. A., Olshevets M. M., Pyatkov M. I., Rudnev V. R., Tetuev R. K., Filippov V. V., “Spectral Analysis for identification and visualization of repeats in genetic sequences”, Pattern Recognition and Image Analysis, 19:4 (2009), 687–692 | DOI

[22] Tsai F. C., Sherman J. C., “Circular dichroism analysis of a synthetic peptide corresponding to the $\alpha,\alpha$-corner motif of hemoglobin”, Biochemical and Biophysical Research Communications, 196:1 (1993), 435–439 | DOI

[23] Kabsch W., Sander C., “Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features”, Biopolymers, 22:12 (1983), 2577–2637 | DOI

[24] Kabsch W., “A solution for the best rotation to relate two sets of vectors”, Acta Crystallographica, 32 (1976), 922–923 | DOI

[25] Kabsch W., “A discussion of the solution for the best rotation to relate two sets of vectors”, Acta Crystallographica, 34 (1978), 827–828 | DOI

[26] Legland D., MatGeom: Matlab geometry toolbox for 2D/3D geometric computing, (data obrascheniya: 11.03.2016) http://github.com/dlegland/matGeom

[27] Holland P. W., Welsch R. E., “Robust regression using iteratively reweighted least-squares”, Communications in Statistic — Theory and Methods, 6:9 (1977), 813–827 | DOI