Geodesic
Analysis of torsion angles between helical axes in pairs of helices in protein molecules
Matematičeskaâ biologiâ i bioinformatika, Tome 13 (2018), pp. t17-t28.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this study, an analysis of distribution of the torsion angles $\Omega$ between helical axes in pairs of connected helices found in known proteins has been performed. The database for helical pairs was compiled using the Protein Data Bank taking into account the definite rules suggested earlier. The database was analyzed in order to elaborate its classification and find out novel structural features in helix packing. The database was subdivided into three subsets according to criterion of crossing helix projections on the parallel planes passing through the axes of the helices. It was shown that helical pairs not having crossing projections are distributed along whole range of angles $\Omega$, although there are two maxima at $\Omega=0^\circ$ and $\Omega=180^\circ$. Most of helical pairs of this subset are pairs formed by $\alpha$-helices and $3_{10}$- helices. It is shown that the distribution of all the helical pairs having the crossing helix projections has a maximum at $20^\circ \Omega 25^\circ$. In this subset, most helical pairs are formed by $\alpha$-helices. The distribution of only $\alpha$-helical pairs having crossing axes projections has three maxima, at $-50^\circ \Omega -25^\circ$, $20^\circ \Omega 25^\circ$, and $70^\circ \Omega 110^\circ$. 
@article{MBB_2018_13_a1,
     author = {D. A. Tikhonov and L. I. Kulikova and A. V. Efimov},
     title = {Analysis of torsion angles between helical axes in pairs of helices in protein molecules},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {t17--t28},
     publisher = {mathdoc},
     volume = {13},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MBB_2018_13_a1/}
}
TY  - JOUR
AU  - D. A. Tikhonov
AU  - L. I. Kulikova
AU  - A. V. Efimov
TI  - Analysis of torsion angles between helical axes in pairs of helices in protein molecules
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2018
SP  - t17
EP  - t28
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2018_13_a1/
LA  - en
ID  - MBB_2018_13_a1
ER  - 
%0 Journal Article
%A D. A. Tikhonov
%A L. I. Kulikova
%A A. V. Efimov
%T Analysis of torsion angles between helical axes in pairs of helices in protein molecules
%J Matematičeskaâ biologiâ i bioinformatika
%D 2018
%P t17-t28
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2018_13_a1/
%G en
%F MBB_2018_13_a1
D. A. Tikhonov; L. I. Kulikova; A. V. Efimov. Analysis of torsion angles between helical axes in pairs of helices in protein molecules. Matematičeskaâ biologiâ i bioinformatika, Tome 13 (2018), pp. t17-t28. http://geodesic.mathdoc.fr/item/MBB_2018_13_a1/

[1] Tikhonov D.A., Kulikova L.I., Efimov A.V., “Statistical analysis of the internal distances of helical pairs in protein molecules”, Mathematical Biology and Bioinformatics, 11:2 (2016), 170–190 (in Russ.) <ext-link ext-link-type='doi' href='http://dx.doi.org/10.17537/2016.11.170'>http://dx.doi.org/10.17537/2016.11.170</ext-link>

[2] Tikhonov D.A., Kulikova L.I., Efimov A.V., “The study of interhelical angles in the structural motifs formed by two helices”, Mathematical Biology and Bioinformatics, 12:1 (2017), 83–101 (in Russ.) <ext-link ext-link-type='doi' href='http://dx.doi.org/10.17537/2017.12.83'>http://dx.doi.org/10.17537/2017.12.83</ext-link>

[3] Berman H. M., Westbrook J., Feng Z., Gilliland G., Bhat T. N., Weissig H., Shindyalov I. N., Bourne P. E., “The Protein Data Bank”, Nucleic Acids Research, 28 (2000), 235–242 <ext-link ext-link-type='doi' href='https://doi.org/10.1093/nar/28.1.235'>10.1093/nar/28.1.235</ext-link>

[4] Crick F. H. C., “The Packing of a-helices: simple coiled-coils”, Acta Crystallographica, 6 (1953), 689–697 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0365110X53001964'>10.1107/S0365110X53001964</ext-link>

[5] Lee H. S., Choi J., Yoon S., “QHELIX: A Computational tool for the improved measurement of inter-helical angles in proteins”, Protein, 26 (2007), 556–561 <ext-link ext-link-type='doi' href='http://dx.doi.org/10.1007/s10930-007-9097-9'>http://dx.doi.org/10.1007/s10930-007-9097-9</ext-link>

[6] Walther D., Eisenhaber F., Argos P., “Principles of helix-helix packing in proteins: the helical lattice superposition model”, Molecular Biology, 255 (1996), 536–553 <ext-link ext-link-type='doi' href='https://doi.org/10.1006/jmbi.1996.0044'>10.1006/jmbi.1996.0044</ext-link>

[7] Chothia C., Levitt M., Richardson D., “Structure of proteins: packing of $\alpha$-helices and pleated sheets”, Proc. Natl. Acad. Sci., 74 (1977), 4130–4134 <ext-link ext-link-type='doi' href='https://doi.org/10.1073/pnas.74.10.4130'>10.1073/pnas.74.10.4130</ext-link>

[8] Chothia C., Levitt M., Richardson D., “Helix to helix packing in proteins”, Molecular Biology, 145 (1981), 215–250 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/0022-2836(81)90341-7'>10.1016/0022-2836(81)90341-7</ext-link>

[9] Levitt M., Chothia C., “Structural patterns in globular proteins”, Nature, 261 (1976), 552–558 <ext-link ext-link-type='doi' href='https://doi.org/10.1038/261552a0'>10.1038/261552a0</ext-link>

[10] Efimov A. V., “Standard structures in proteins”, Prog. Biophys. Molec. Biol., 60 (1993), 201–239 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/0079-6107(93)90015-C'>10.1016/0079-6107(93)90015-C</ext-link>

[11] 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 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.bbrc.2010.05.136'>10.1016/j.bbrc.2010.05.136</ext-link>

[12] 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 <ext-link ext-link-type='doi' href='https://doi.org/10.1007/978-1-62703-065-6_11'>10.1007/978-1-62703-065-6_11</ext-link>

[13] Brazhnikov E. V., Efimov A. V., “Structure of $\alpha$-$\alpha$-hairpins with short connections in globular proteins”, Molecular Biology, 35:1 (2001), 89–97 <ext-link ext-link-type='doi' href='https://doi.org/10.1023/A:1004859003221'>10.1023/A:1004859003221</ext-link>

[14] Kabsch W., Sander C., “Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features”, Biopolymers, 22:12 (1983), 2577–2637 <ext-link ext-link-type='doi' href='https://doi.org/10.1002/bip.360221211'>10.1002/bip.360221211</ext-link>

[15] Kabsch W., “A solution for the best rotation to relate two sets of vectors”, Acta Crystallographica, 32 (1976), 922–923 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0567739476001873'>10.1107/S0567739476001873</ext-link>

[16] Kabsch W., “A discussion of the solution for the best rotation to relate two sets of vectors”, Acta Crystallographica, 34 (1978), 827–828 <ext-link ext-link-type='doi' href='https://doi.org/10.1107/S0567739478001680'>10.1107/S0567739478001680</ext-link>

[17] Legland D., MatGeom: Matlab geometry toolbox for 2D/3D geometric computing, (accessed 11.05.2017) <ext-link ext-link-type='uri' href='http://github.com/dlegland/matGeom'>http://github.com/dlegland/matGeom</ext-link>

[18] Calhoun J. R., Kono H., Lahr S., Wang W., DeGrado W. F., Saven J. G., “Computational design and characterization of a monomeric helical dinuclear metalloprotein”, Journal of Molecular Biology, 334:5 (2003), 1101–1115 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.jmb.2003.10.004'>10.1016/j.jmb.2003.10.004</ext-link>

[19] Calhoun J. R., Nastri F., Maglio O., Pavone V., Lombardi A., DeGrado W. F., “Artificial diiron proteins: From structure to function”, Peptide Science, 80:2–3 (2005), 264–278 <ext-link ext-link-type='doi' href='https://doi.org/10.1002/bip.20230'>10.1002/bip.20230</ext-link>

[20] Chino M., Maglio O., Nastri F., Pavone V., DeGrado W. F., Lombardi A., “Artificial diiron enzymes with a de novo designed four-helix bundle structure”, European Journal of Inorganic Chemistry, 2015, 3371–3390 <ext-link ext-link-type='doi' href='http://dx.doi.org/10.1002/ejic.201500470'>http://dx.doi.org/10.1002/ejic.201500470</ext-link>

[21] Chino M., Leone L., Maglio O., Lombardi A., “Designing Covalently Linked Heterodimeric Four-Helix Bundles”, Methods in Enzymology, 580, 2016, 471–499 <ext-link ext-link-type='doi' href='http://dx.doi.org/10.1016/bs.mie.2016.05.036'>http://dx.doi.org/10.1016/bs.mie.2016.05.036</ext-link>

[22] Trovato A., Seno F., “A new perspective on analysis of helix-helix packing preferences in globular proteins”, Proteins: Structure, Function, Bioinformatics, 55 (2004), 1014–1022 <ext-link ext-link-type='doi' href='https://doi.org/10.1002/prot.20083'>10.1002/prot.20083</ext-link>