Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
   
 
 
 
Previous Article
Optimal replica exchange method combined with Tsallis weight sampling
A unified framework integrating the generalized ensemble sampling associated with the Tsallis weight [C. Tsallis, J. Stat. Phys. 52, 479 (1988)] and the replica exchange method (REM) has been proposed...
Next Article
Perturbative total energy evaluation in self-consistent field Iterations: Tests on molecular systems
The corrected Hohenberg–Kohn–Sham and corrected Harris total energy functionals recently proposed [B. Zhou and Y. A. Wang, J. Chem. Phys. 128, 084101 (2008)] have been generalized to the H...

Topological methods for exploring low-density states in biomolecular folding pathways

J. Chem. Phys. 130, 144115 (2009); doi:10.1063/1.3103496

Published 14 April 2009

You are not logged in to this journal. Log in

Yuan Yao,1 Jian Sun,2 Xuhui Huang,3 Gregory R. Bowman,4 Gurjeet Singh,1 Michael Lesnick,5 Leonidas J. Guibas,2 Vijay S. Pande,6 and Gunnar Carlsson1
1Department of Mathematics, Stanford University, Stanford, California 94305, USA
2Department of Computer Science, Stanford University, Stanford, California 94305, USA
3Department of Bioengineering, Stanford University, Stanford, California 94305, USA
4Biophysics Program, Stanford University, Stanford, California 94305, USA
5Insititute of Computational and Mathematical Engineering. Stanford University, Stanford, California 94305, USA
6Department of Chemistry, Stanford University, Stanford, California 94305, USA
Characterization of transient intermediate or transition states is crucial for the description of biomolecular folding pathways, which is, however, difficult in both experiments and computer simulations. Such transient states are typically of low population in simulation samples. Even for simple systems such as RNA hairpins, recently there are mounting debates over the existence of multiple intermediate states. In this paper, we develop a computational approach to explore the relatively low populated transition or intermediate states in biomolecular folding pathways, based on a topological data analysis tool, MAPPER, with simulation data from large-scale distributed computing. The method is inspired by the classical Morse theory in mathematics which characterizes the topology of high-dimensional shapes via some functional level sets. In this paper we exploit a conditional density filter which enables us to focus on the structures on pathways, followed by clustering analysis on its level sets, which helps separate low populated intermediates from high populated folded/unfolded structures. A successful application of this method is given on a motivating example, a RNA hairpin with GCAA tetraloop, where we are able to provide structural evidence from computer simulations on the multiple intermediate states and exhibit different pictures about unfolding and refolding pathways. The method is effective in dealing with high degree of heterogeneity in distribution, capturing structural features in multiple pathways, and being less sensitive to the distance metric than nonlinear dimensionality reduction or geometric embedding methods. The methodology described in this paper admits various implementations or extensions to incorporate more information and adapt to different settings, which thus provides a systematic tool to explore the low-density intermediate states in complex biomolecular folding systems. ©2009 American Institute of Physics
History: Received 5 January 2009; accepted 3 March 2009; published 14 April 2009
Permalink: http://link.aip.org/link/?JCPSA6/130/144115/1
BUY THIS ARTICLE   (US$28)
Download HTML Download Sectioned HTML Download PDF (370 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 87.15.R-
    Biochemical reactions and kinetics
  • 36.20.Hb
    Macromolecular configuration (bonds, dimensions)
  • 34.20.-b
    Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions
  • YEAR: 2009

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (27)
View in Separate Window/Tab
For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. J. D. Chodera, N. Singhal, V. S. Pande, K. A. Dill, and W. C. Swope, J. Chem. Phys. 126, 155101 (2007).
  2. J. Tenenbaum, V. de Silva, and J. Langford, Science 290, 2319 (2000).
  3. S. T. Roweis and L. K. Saul, Science 290, 2323 (2000).
  4. M. Belkin and P. Niyogi, Neural Comput. 15, 1373 (2003).
  5. D. Donoho and C. Grimes, Proc. Natl. Acad. Sci. U.S.A. 100, 5591 (2003).
  6. R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler, F. Warner, and S. W. Zucker, Proc. Natl. Acad. Sci. U.S.A. 102, 7426 (2005).
  7. P. W. Jones, M. Maggioni, and R. Schul, Proc. Natl. Acad. Sci. U.S.A. 105, 1803 (2008).
  8. P. Das, M. Moll, H. Stamati, L. E. Kavraki, and C. Clementi, Proc. Natl. Acad. Sci. U.S.A. 103, 9885 (2006).
  9. P. Barbano, M. Spivak, M. Flajolet, A. C. Nairn, P. Greengard, and L. Greengard, Proc. Natl. Acad. Sci. U.S.A. 104, 19169 (2007).
  10. J. Milnor, Morse Theory (Princeton University Press, Princeton, NJ, 1963).
  11. G. Singh, F. Mémoli, and G. Carlsson, Eurographics Symposium on Point-Based Graphics, 2007 (unpublished).
  12. O. M. Becker and M. Karplus, J. Chem. Phys. 106, 1495 (1997).
  13. H. Ma, C. Wan, A. Wu, and A. H. Zewail, Proc. Natl. Acad. Sci. U.S.A. 104, 712 (2007).
  14. G. R. Bowman, X. Huang, Y. Yao, J. Sun, G. Carlsson, L. J. Guibas, and V. S. Pande, J. Am. Chem. Soc.103, 9676 (2008).
  15. S. Smale, Ann. Math. 74, 391 (1961).
  16. G. Reeb, Comptes Rendus Acad. Science Paris 222, 847 (1946).
  17. M. van Kreveld, R. van Oostrum, C. Bajaj, V. Pascucci, and D. Schikore, Proceedings of the 13th Annual ACM Symposium on Computational Geometry, 1997 (unpublished), pp. 212–220.
  18. J. A. Hartigan, J. Am. Stat. Assoc. 76, 388 (1981).
  19. W. Stuetzle, J. Classif., 20, 25 (2003).
  20. Q. Zhou and W. -H. Wong, The Annals of Applied Statistics 2, 1307 (2008).
  21. P. Niyogi, S. Smale, and S. Weinberger, Discrete and Computational Geometry39, 419 (2008).
  22. J. Liu, Monte Carlo Strategies in Scientific Computing (Springer, New York, 2004).
  23. B. W. Silverman, Density Estimation for Statistics and Data Analysis (Chapman and Hall, London/CRC, Boca Raton, FL, 1986).
  24. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning (Springer-Verlag, Berlin, 2001).
  25. C. Ding and H. Zha, Spectral Clustering, Ordering and Ranking–Statistical Learning with Matrix Factorizations (Springer, New York, 2007).
  26. X. Huang, G. R. Bowman, and V. S. Pande, J. Chem. Phys.128, 205106 (2008).
  27. M. Menger, F. Eckstein, and D. Porschke, Biochemistry 39, 4500 (2000).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics