Principal component analysis on a torus: Theory and application to protein dynamics

Journal of Chemical Physics

Volumn 147, Issue 24, 2017, Pages

  Sittel, Florian ^a   Filk, Thomas ^a   Stock, Gerhard ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COVARIANCE MATRIX; DIHEDRAL ANGLE; FREE ENERGY; METADATA; MOLECULAR DYNAMICS; REACTION KINETICS; STATISTICS;

BIOMOLECULAR SYSTEM; DIMENSIONALITY REDUCTION METHOD; EIGEN DECOMPOSITION; FREE ENERGY LANDSCAPE; MOLECULAR DYNAMICS SIMULATIONS; PERIODIC BOUNDARIES; PRINCIPAL COMPONENTS; REACTION COORDINATES;

PRINCIPAL COMPONENT ANALYSIS;

ACTIN BINDING PROTEIN; PROTEIN; VILLIN;

CHEMICAL MODEL; CHEMISTRY; MOLECULAR DYNAMICS; PRINCIPAL COMPONENT ANALYSIS; PROTEIN SECONDARY STRUCTURE; THERMODYNAMICS;

MICROFILAMENT PROTEINS; MODELS, CHEMICAL; MOLECULAR DYNAMICS SIMULATION; PRINCIPAL COMPONENT ANALYSIS; PROTEIN STRUCTURE, SECONDARY; PROTEINS; THERMODYNAMICS;

EID: 85031046473     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4998259     Document Type: Article

References (51)

1. A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis (John Wiley & Sons, New York, 2001).
2. I. T. Jolliffe, Principal Component Analysis (Springer, New York, 2002).
3. P. Benner, V. Mehrmann, and D. C. Sorensen, Dimension Reduction of Large-Scale Systems (Springer, New York, 2005).
4. I. Borg and P. J. Groenen, Modern Multidimensional Scaling: Theory and Applications (Springer, New York, 2005).
5. J. A. Lee and M. Verleysen, Nonlinear Dimensionality Reduction (Springer, New York, 2007).
6. G. R. Bowman, V. S. Pande, and F. Noe, An Introduction to Markov State Models (Springer, Heidelberg, 2013).
7. M. A. Rohrdanz, W. Zheng, and C. Clementi, "Discovering mountain passes via torchlight: Methods for the definition of reaction coordinates and pathways in complex macromolecular reactions," Annu. Rev. Phys. Chem. 64, 295 (2013). 10.1146/annurev-physchem-040412-110006
8. O. F. Lange and H. Grubmüller, "Generalized correlation for biomolecular dynamics," Proteins: Struct., Funct., Bioinf. 62, 1053 (2006). 10.1002/prot.20784
9. G. Perez-Hernandez, F. Paul, T. Giorgino, G. De Fabritiis, and F. Noe, "Identification of slow molecular order parameters for Markov model construction," J. Chem. Phys. 139, 015102 (2013). 10.1063/1.4811489
10. A. Amadei, A. B. M. Linssen, and H. J. C. Berendsen, "Essential dynamics of proteins," Proteins: Struct., Funct., Genet. 17, 412 (1993). 10.1002/prot.340170408
11. B. L. de Groot, X. Daura, A. E. Mark, and H. Grubmüller, "Essential dynamics of reversible peptide folding: Memory-free conformational dynamics governed by internal hydrogen bonds," J. Mol. Biol. 309, 299 (2001). 10.1006/jmbi.2001.4655
12. G. Kurz, I. Gilitschenski, and U. D. Hanebeck, "Recursive nonlinear filtering for angular data based on circular distributions," in American Control Conference (ACC), 2013 (IEEE, 2013), pp. 5439-5445.
13. S. C. Lovell, I. W. Davis, W. B. Arendall, P. I. W. de Bakker, J. M. Word, M. G. Prisant, J. S. Richardson, and D. C. Richardson, "Structure validation by c α geometry: ø, ψ and c β deviation," Proteins: Struct., Funct., Bioinf. 50, 437 (2003). 10.1002/prot.10286
14. K. V. Mardia and P. E. Jupp, Directional Statistics (John Wiley & Sons, 2009).
15. D. M. D. van Aalten, B. L. de Groot, J. B. C. Finday, H. J. C. Berendsen, and A. Amadei, "A comparison of techniques for calculating protein essential dynamics," J. Comput. Chem. 18, 169 (1997). 10.1002/(sici)1096-987x(19970130)18:2<169::aid-jcc3>3.0.co;2-t
16. Y. Mu, P. H. Nguyen, and G. Stock, "Energy landscape of a small peptide revealed by dihedral angle principal component analysis," Proteins: Struct., Funct., Bioinf. 58, 45 (2005). 10.1002/prot.20310
17. A. Altis, P. H. Nguyen, R. Hegger, and G. Stock, "Dihedral angle principal component analysis of molecular dynamics simulations," J. Chem. Phys. 126, 244111 (2007). 10.1063/1.2746330
18. K. Sargsyan, J. Wright, and C. Lim, "GeoPCA: A new tool for multivariate analysis of dihedral angles based on principal component geodesics," Nucl. Acids Res. 40, e25 (2012). 10.1093/nar/gkr1069
19. K. Sargsyan, J. Wright, and C. Lim, "Corrigendum to GeoPCA: A new tool for multivariate analysis of dihedral angles based on principal component geodesics," Nucl. Acids Res. 43, 10571 (2015). 10.1093/nar/gkv1000
20. S. Huckemann and H. Ziezold, "Principal component analysis for Riemannian manifolds, with an application to triangular shape spaces," Adv. Appl. Prob. 38, 299 (2006). 10.1239/aap/1151337073
21. A. Nodehi, M. Golalizadeh, and A. Heydari, "Dihedral angles principal geodesic analysis using nonlinear statistics," J. Appl. Stat. 42, 1962 (2015). 10.1080/02664763.2015.1014892
22. B. Eltzner, S. Huckemann, and K. V. Mardia, "Torus principal component analysis with an application to RNA structures," e-print arXiv:1511.04993 (2015).
23. A. Altis, M. Otten, P. H. Nguyen, R. Hegger, and G. Stock, "Construction of the free energy landscape of biomolecules via dihedral angle principal component analysis," J. Chem. Phys. 128, 245102 (2008). 10.1063/1.2945165
24. L. Riccardi, P. H. Nguyen, and G. Stock, "Free energy landscape of an RNA hairpin constructed via dihedral angle principal component analysis," J. Phys. Chem. B 113, 16660 (2009). 10.1021/jp9076036
25. G. G. Maisuradze, A. Liwo, and H. A. Scheraga, "Principal component analysis for protein folding dynamics," J. Mol. Biol. 385, 312 (2009). 10.1016/j.jmb.2008.10.018
26. A. Jain, R. Hegger, and G. Stock, "Hidden complexity of protein energy landscape revealed by principal component analysis by parts," J. Phys. Chem. Lett. 1, 2769 (2010). 10.1021/jz101069e
27. D. A. Potoyan and G. A. Papoian, "Energy landscape analyses of disordered histone tails reveal special organization of their conformational dynamics," J. Am. Chem. Soc. 133, 7405 (2011). 10.1021/ja1111964
28. J. C. Miner, A. A. Chen, and A. E. García, "Free-energy landscape of a hyperstable RNA tetraloop," Proc. Natl. Acad. Sci. U. S. A. 113, 6665 (2016). 10.1073/pnas.1603154113
29. G. M. Hocky, J. L. Baker, M. J. Bradley, A. V. Sinitskiy, E. M. De La Cruz, and G. A. Voth, "Cations stiffen actin filaments by adhering a key structural element to adjacent subunits," J. Phys. Chem. B 120, 4558 (2016). 10.1021/acs.jpcb.6b02741
30. C. R. Watts, A. J. Gregory, C. P. Frisbie, and S. Lovas, "Structural properties of amyloid β(1-40) dimer explored by replica exchange molecular dynamics simulations," Proteins 85, 1024 (2017). 10.1002/prot.25270
31. S. Buchenberg, N. Schaudinnus, and G. Stock, "Hierarchical biomolecular dynamics: Picosecond hydrogen bonding regulates microsecond conformational transitions," J. Chem. Theory Comput. 11, 1330 (2015). 10.1021/ct501156t
32. S. Piana, K. Lindorff-Larsen, and D. E. Shaw, "Protein folding kinetics and thermodynamics from atomistic simulation," Proc. Natl. Acad. Sci. U. S. A. 109, 17845 (2012). 10.1073/pnas.1201811109
33. K. Pearson, "On lines and planes of closest fit to systems of points in space," Philos. Mag. 2, 559 (1901). 10.1080/14786440109462720
34. K. Hinsen, "Comment on 'Energy landscape of a small peptide revealed by dihedral angle principal component analysis,'" Proteins: Struct., Funct., Bioinf. 64, 795 (2006). 10.1002/prot.20900
35. Y. Mu, P. H. Nguyen, and G. Stock, "Reply to the comment on 'Energy landscape of a small peptide revealed by dihedral angle principal component analysis,'" Proteins: Struct., Funct., Bioinf. 64, 798 (2006). 10.1002/prot.21038
36. A. Jain and G. Stock, "Hierarchical folding free energy landscape of HP35 revealed by most probable path clustering," J. Phys. Chem. B 118, 7750 (2014). 10.1021/jp410398a
37. F. Sittel and G. Stock, "Robust density-based clustering to identify metastable conformational states of proteins," J. Chem. Theory Comput. 12, 2426 (2016). 10.1021/acs.jctc.5b01233
38. D. van der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark, and H. J. C. Berendsen, "Gromacs; fast, flexible and free," J. Comput. Chem. 26, 1701 (2005). 10.1002/jcc.20291
39. W. F. van Gunsteren, S. R. Billeter, A. A. Eising, P. H. Hünenberger, P. Krüger, A. E. Mark, W. R. P. Scott, and I. G. Tironi, Biomolecular Simulation: The GROMOS96 Manual and User Guide (Vdf Hochschulverlag AG an der ETH Zürich, Zürich, 1996).
40. I. G. Tironi and W. F. van Gunsteren, "A molecular dynamics simulation study of chloroform," Mol. Phys. 83, 381 (1994). 10.1080/00268979400101331
41. V. Hornak, R. Abel, A. Okur, B. Strockbine, A. Roitberg, and C. Simmerling, "Comparison of multiple Amber force fields and development of improved protein backbone parameters," Proteins: Struct., Funct., Bioinf. 65, 712 (2006). 10.1002/prot.21123
42. R. B. Best and G. Hummer, "Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides," J. Phys. Chem. B 113, 9004 (2009). 10.1021/jp901540t
43. K. Lindorff-Larsen, S. Piana, K. Palmo, P. Maragakis, J. L. Klepeis, R. O. Dror, and D. E. Shaw, "Improved side-chain torsion potentials for the Amber ff99sb protein force field," Proteins: Struct., Funct., Bioinf. 78, 1950 (2010). 10.1002/prot.22711
44. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. Klein, "Comparison of simple potential functions for simulating liquid water," J. Chem. Phys. 79, 926 (1983). 10.1063/1.445869
45. A. Jain and G. Stock, "Identifying metastable states of folding proteins," J. Chem. Theory Comput. 8, 3810 (2012). 10.1021/ct300077q
46. H. Frauenfelder, S. Sligar, and P. Wolynes, "The energy landscapes and motions of proteins," Science 254, 1598 (1991). 10.1126/science.1749933
47. J. N. Onuchic, Z. L. Schulten, and P. G. Wolynes, "Theory of protein folding: The energy landscape perspective," Annu. Rev. Phys. Chem. 48, 545 (1997). 10.1146/annurev.physchem.48.1.545
48. K. A. Dill and H. S. Chan, "From Levinthal to pathways to funnels: The 'new view' of protein folding kinetics," Nat. Struct. Biol. 4, 10 (1997). 10.1038/nsb0197-10
49. J.-H. Prinz, H. Wu, M. Sarich, B. Keller, M. Senne, M. Held, J. D. Chodera, C. Schütte, and F. Noe, "Markov models of molecular kinetics: Generation and validation," J. Chem. Phys. 134, 174105 (2011). 10.1063/1.3565032
50. D. Shukla, C. X. Hernández, J. K. Weber, and V. S. Pande, "Markov state models provide insights into dynamic modulation of protein function," Acc. Chem. Res. 48, 414 (2015). 10.1021/ar5002999
51. K. Sargsyan, Y. H. Hua, and C. Lim, "Clustangles: An open library for clustering angular data," J. Chem. Inf. Mod. 55, 1517 (2015). 10.1021/acs.jcim.5b00316