Abstract
Superpositioning of atoms in an ensemble of biomolecules is a common task in a variety of fields in structural biology. Although several automated tools exist based on previously established methods, manual operations to define the atoms in the ordered regions are usually preferred. The task is difficult and lacks output efficiency for multi-core proteins having complicated folding topology. The new method presented here can systematically and quantitatively achieve the identification of ordered cores even for molecules containing multiple cores linked with flexible loops. In contrast to established methods, this method treats the variance of inter-atomic distances in an ensemble as information content using a non-linear (NL) function, and then subjects it to multi-dimensional scaling (MDS) to embed the row vectors in the inter-atomic distance variance matrix into a lower dimensional matrix. The plots of the identified atom groups in a one or two-dimensional map enables users to visually and intuitively infer well-ordered atoms in an ensemble, as well as to automatically identify them by the standard clustering methods. The performance of the NL-MDS method has been examined for number of structure ensembles studied by nuclear magnetic resonance, demonstrating that the method can be more suitable for structural analysis of multi-core proteins in comparison to previously established methods.
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Abbreviations
- IVM:
-
Inter-atomic distance variance matrix
- NL-MDS:
-
Non-linear multi-dimensional scaling
References
Coutsias EA, Seok C, Dill KA (2004) Using quaternions to calculate RMSD. J Comput Chem 25(15):1849–1857
Diamond R (1995) Coordinate-based cluster analysis. Acta Crystallogr D Biol Crystallogr 51(Pt 2):127–135
Havel TF, Kuntz ID, Crippen GM (1983) The theory and practice of distance geometry. Bull Math Biol 45(5):665–720
Hirsch M, Habeck M (2008) Mixture models for protein structure ensembles. Bioinformatics 24(19):2184–2192
Kabsch W, Sander C (1983) Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 22(12):2577–2637
Kainosho M, Torizawa T, Iwashita Y, Terauchi T, Mei Ono A, Güntert P (2006) Optimal isotope labelling for NMR protein structure determinations. Nature 440(7080):52–57
Kelley LA, Gardner SP, Sutcliffe MJ (1996) An automated approach for clustering an ensemble of NMR-derived protein structures into conformationally related subfamilies. Protein Eng 9(11):1063–1065
Kelley LA, Gardner SP, Sutcliffe MJ (1997) An automated approach for defining core atoms and domains in an ensemble of NMR-derived protein structures. Protein Eng 10(6):737–741
Kirchner DK, Güntert P (2011) Objective identification of residue ranges for the superposition of protein structures. BMC Bioinformatics 12(170):1471–2105
Koradi R, Billeter M, Wüthrich K (1996) MOLMOL: a program for display and analysis of macromolecular structures. J Mol Graph 14(1):51–55
Mechelke M, Habeck M (2010) Robust probabilistic superposition and comparison of protein structures. BMC Bioinformatics 11:363
Nabuurs SB, Spronk CA, Krieger E, Maassen H, Vriend G, Vuister GW (2003) Quantitative evaluation of experimental NMR restraints. J Am Chem Soc 125(39):12026–12034
Nilges M, Clore M, Gronenborn A (1987) A simple method for delineating well-defined and variable regions in protein structures determined from interproton distance data. Bioinformatics 219(1):11–16
Schneider TR (2000) Objective comparison of protein structures: error-scaled difference distance matrices. Acta Crystallogr D Biol Crystallogr 56(Pt 6):714–721
Snyder DA, Montelione GT (2005) Clustering algorithms for identifying core atom sets and for assessing the precision of protein structure ensembles. Proteins 59:673–686
Acknowledgments
I would like to thank Prof. Toshimichi Fujiwara, Prof. Junichi Higo (Institute for Protein Research, University Osaka, Japan) and Prof. Daron M. Standley (Immunology Frontier Research Center, University Osaka, Japan) for helpful discussions. Dr. David A. Snyder and Prof. Gaetano T. Montelione, and Prof. Peter Güntert are greatly acknowledged for kindly providing their respective programs FindCore and Cyrange. I also acknowledge Mr. Bikash Ranjan Shahoo for proofreading the manuscript. This work was supported by National Bioscience Database Center (NBDC) in Japan Science and Technology Agency (JST) and also by JSPS KAKENHI Grant Number 80272160.
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Kobayashi, N. A robust method for quantitative identification of ordered cores in an ensemble of biomolecular structures by non-linear multi-dimensional scaling using inter-atomic distance variance matrix. J Biomol NMR 58, 61–67 (2014). https://doi.org/10.1007/s10858-013-9805-z
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DOI: https://doi.org/10.1007/s10858-013-9805-z