Quaternion-based Characterization of Protein <i>α</i> Helix_Journal of Biomedical Engineering

Authors：

 XUYonghong , CHUZefei

Institute of Biomedical Engineering, Yanshan University, Qinhuangdao 066004, China;

Corresponding author：

XUYonghong, Email: xyh@ysu.edu.cn

Keywords：

quaternion; protein; secondary structure; α helix

DOI：

10.7507/1001-5515.20160028

Video：

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Abstract Full text Figures/Tables Video References Cited by

This paper proposes a method based on quaternion for characterization α helix of proteins. The method defines the parameter called Quaternion Helix Axis Spherical Distance (QHASD) on the basis of mapping protein Cα frames′ helical axis onto a unit sphere, and uses QHASD to characterize the α helix of the protein secondary structure. Application of this method has been verified based on the PDBselect database, with an α helix characterization accuracy of 91.7%. This method possesses significant advantages of high detection accuracy, low computation and clear geometric significance.

Citation： XUYonghong, CHUZefei. Quaternion-based Characterization of Protein α Helix. Journal of Biomedical Engineering, 2016, 33(1): 155-160. doi: 10.7507/1001-5515.20160028 Copy

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6.	QUINE J R. Helix parameters and protein structure using quaternions[J]. Journal of Molecular Structure: THEOCHEM, 1999, 460(1-3): 53-66.
7.	COUTSIAS E A, SEOK C, DILL K A. Using quaternions to calculate RMSD[J]. J Comput Chem, 2004, 25(15): 1849-1857.
8.	KNELLER G R, CALLIGARI P. Efficient characterization of protein secondary structure in terms of screw motions[J]. Acta Crystallogr D Biol Crystallogr, 2006, 62(3): 302-311.
9.	HANSON R M, KOHLER D, BRAUN S G. Quaternion-based definition of protein secondary structure straightness and its relationship to Ramachandran angles[J]. Proteins, 2011, 79(7): 2172-2180.
10.	HANSON A J, THAKUR S. Quaternion maps of global protein structure[J]. J Mol Graph Model, 2012, 38: 256-278.
11.	白凤兰,姚玉华,孙立波.RNA二级结构的6-D表示及相似性分析[J].黑龙江大学自然科学学报,2006,23(1):81-86.
12.	刘俊峰.三维转动的四元数表述[J].大学物理,2004,23(4):39-43, 62.
13.	RAMACHANDRAN G N, RAMAKRISHNAN C, SASISEKHARAN V. Stereochemistry of polypeptide chain configurations[J]. J Mol Biol, 1963, 7(1): 95-99.
14.	KABSCH W, SANDER C. Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features[J]. Biopolymers, 1983, 22(12): 2577-2637.
15.	ANDERSEN C A F, PALMER A G, BRUNAK S, et al. Continuum secondary structure captures protein flexibility[J]. Structure, 2002, 10(2): 175-184.
16.	MARTIN J, LETELLIER G, MARIN A, et al. Protein secondary structure assignment revisited: a detailed analysis of different assignment methods[J]. BMC Struct Biol, 2005, 5(1): 17.
17.	MAJUMDAR I, KRISHNA S S, GRISHIN N V. PALSSE: A program to delineate linear secondary structural elements from protein structures[J]. BMC Bioinformatics, 2005, 6(1): 202.
18.	LABESSE G, COLLOC′H N, POTHIER J, et al. P-SEA: a new efficient assignment of secondary structure from C α trace of proteins[J]. Comput Appl Biosci, 1997, 13(3): 291-295.
19.	TAYLOR W R. Defining linear segments in protein structure[J]. J Mol Biol, 2001, 310(5): 1135-1150.
20.	FRISHMAN D, ARGOS P. Knowledge-based protein secondary structure assignment[J]. Proteins, 1995, 23(4): 566-579.
21.	KING S M, JOHNSON W C. Assigning secondary structure from protein coordinate data[J]. Proteins, 1999, 35(3): 313-320.

1. 孙啸,陆祖宏,谢建明.生物信息学基础[M].北京:清华大学出版社, 2005: 42-106.
2. KARNEY C F F. Quaternions in molecular modeling[J]. J Mol Graph Model, 2007, 25(5): 595-60.
3. WASNIK I, SAWLEKAR R, KAZI F, et al. Dual quaternion applications to bioinformatics for kinematical analysis of Protein Backbone[C]// 2013 International Conference on Advances in Computing, Communications and Informatics (ICACCI). Mysore: 2013: 2043-2048.
4. HANSON A J. Visualizing quaternions[M]. New York: Elsevier, 2006.
5. SRINIVASAN R, GEETHA V, SEETHARAMAN J, et al. A unique or essentially unique single parametric characterisation of biopolymeric structures[J]. Journal of Biomolecular Structure and Dynamics, 1993, 11(3): 583-596.
6. QUINE J R. Helix parameters and protein structure using quaternions[J]. Journal of Molecular Structure: THEOCHEM, 1999, 460(1-3): 53-66.
7. COUTSIAS E A, SEOK C, DILL K A. Using quaternions to calculate RMSD[J]. J Comput Chem, 2004, 25(15): 1849-1857.
8. KNELLER G R, CALLIGARI P. Efficient characterization of protein secondary structure in terms of screw motions[J]. Acta Crystallogr D Biol Crystallogr, 2006, 62(3): 302-311.
9. HANSON R M, KOHLER D, BRAUN S G. Quaternion-based definition of protein secondary structure straightness and its relationship to Ramachandran angles[J]. Proteins, 2011, 79(7): 2172-2180.
10. HANSON A J, THAKUR S. Quaternion maps of global protein structure[J]. J Mol Graph Model, 2012, 38: 256-278.
11. 白凤兰,姚玉华,孙立波.RNA二级结构的6-D表示及相似性分析[J].黑龙江大学自然科学学报,2006,23(1):81-86.
12. 刘俊峰.三维转动的四元数表述[J].大学物理,2004,23(4):39-43, 62.
13. RAMACHANDRAN G N, RAMAKRISHNAN C, SASISEKHARAN V. Stereochemistry of polypeptide chain configurations[J]. J Mol Biol, 1963, 7(1): 95-99.
14. KABSCH W, SANDER C. Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features[J]. Biopolymers, 1983, 22(12): 2577-2637.
15. ANDERSEN C A F, PALMER A G, BRUNAK S, et al. Continuum secondary structure captures protein flexibility[J]. Structure, 2002, 10(2): 175-184.
16. MARTIN J, LETELLIER G, MARIN A, et al. Protein secondary structure assignment revisited: a detailed analysis of different assignment methods[J]. BMC Struct Biol, 2005, 5(1): 17.
17. MAJUMDAR I, KRISHNA S S, GRISHIN N V. PALSSE: A program to delineate linear secondary structural elements from protein structures[J]. BMC Bioinformatics, 2005, 6(1): 202.
18. LABESSE G, COLLOC′H N, POTHIER J, et al. P-SEA: a new efficient assignment of secondary structure from C α trace of proteins[J]. Comput Appl Biosci, 1997, 13(3): 291-295.
19. TAYLOR W R. Defining linear segments in protein structure[J]. J Mol Biol, 2001, 310(5): 1135-1150.
20. FRISHMAN D, ARGOS P. Knowledge-based protein secondary structure assignment[J]. Proteins, 1995, 23(4): 566-579.
21. KING S M, JOHNSON W C. Assigning secondary structure from protein coordinate data[J]. Proteins, 1999, 35(3): 313-320.

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