A Dirichlet process mixture of hidden Markov models for protein structure prediction

Annals of Applied Statistics

Volumn 4, Issue 2, 2010, Pages 916-942

  Lennox, Kristin P ^a   Dahl, David B ^a   Vannucci, Marina ^b   Day, Ryan ^c   Tsai, Jerry W ^c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b RICE UNIVERSITY   (United States)

^c UNIVERSITY OF THE PACIFIC   (United States)

Author keywords

Bayesian nonparametrics; Density estimation; Dihedral angles; Protein structure prediction; Torsion angles; Von Mises distribution

Indexed keywords

EID: 79959282860     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/09-AOAS296     Document Type: Article

References (41)

1. Antoniak, C. E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2 1152-1174.
2. Baker, D. and Sali, A. (2001). Protein structure prediction and structural genomics. Science 294 93-96.
3. Beal, M. J., Ghahramani, Z. and Rasmussen, C. E. (2002). The infinite hidden Markov model. In Advances in Neural Information Processing Systems 14(Dietterich, T., Becker, S. and Ghahramani, Z., eds.) 504, 505, 508. MIT Press, Cambridge, MA.
4. Bernardo, J. M. and Smith, A. F. M. (1994). Bayesian Theory. Wiley, Chichester.
5. Bonneau, R. and Baker, D. (2001). Ab initio protein structure prediction: Progress and prospects. Annu. Rev. Biophys. Biomol. Struct. 30 173-189.
6. Boomsma, W., Mardia, K. V., Taylor, C. C., Ferkinghoff-Borg, J., Krogh, A. and Hamelryck, T. (2008). A generative, probabilistic model of local protein structure. Proc. Natl. Acad. Sci. USA 105 8932-8937.
7. Butterfoss, G. L., Richardson, J. S. and Hermans, J. (2005). Protein imperfections: Separating intrinsic from extrinsic variation of torsion angles. Acta Crystallogr. D Biol. Crystallogr. 61 88-98.
8. Chib, S. (1996). Calculating posterior distributions and modal estimates in Markov mixture models. J. Econometrics 75 79-97.
9. De Iorio, M., Müller, P., Rosner, G. L. and MacEachern, S. N. (2004). An ANOVA model for dependent random measures. J. Amer. Statist. Assoc. 99 205-215.
10. Dunson, D. B., Pillai, N. and Park, J.-H. (2007). Bayesian density regression. J. Roy. Statist. Soc. Ser. B Statist. Methodol. 69 163-183.
11. Edgar, R. C. (2004). MUSCLE: Multiple sequence alignment with high accuracy and high throughput. Nucleic Acids Res. 32 1792-1797.
12. Escobar, M. D. and West, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577-588.
13. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230.
14. Fitzkee, N. C., Fleming, P. J. and Rose, G. D. (2005). The protein coil library: A structural database of nonhelix, nonstrand fragments derived from the PDB. Proteins 58 852-854.
15. Gelfand, A. E., Kottas, A. and MacEachern, S. N. (2005). Bayesian nonparametric spatial modeling with Dirichlet process mixing. J. Amer. Statist. Assoc. 100 1021-1035.
16. Green, P. J. and Richardson, S. (2001). Modelling heterogeneity with and without the Dirichlet process. Scand. J. Statist. 28 355-375.
17. Griffin, J. E. and Steel, M. F. J. (2006). Order-based dependent Dirichlet processes. J. Amer. Statist. Assoc. 101 179-194.
18. Ho, B. K., Thomas, A. and Brasseur, R. (2003). Revisiting the Ramachandran plot: Hard-sphere repulsion, electrostatics, and h-bonding in the alpha-helix. Protein Sci. 12 2508-2522.
19. Kabsch, W. and Sander, C. (1983). Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 22 2577-2637.
20. Karplus, K., Sjolander, K., Barrett, C., Cline, M., Haussler, D., Hughey, R., Holm, L., Sander, C. and England, E. (1997). Predicting protein structure using hidden Markov models. Proteins: Structure, Function and Genetics29 134-139.
21. Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90773-795.
22. Kouranov, A., Xie, L., de la Cruz, J., Chen, L., Westbrook, J., Bourne, P. E. and Berman, H. M. (2006). The RCSB PDB information portal for structural genomics. Nucleic Acids Res. 34 D302-D305.
23. Lennox, K. P., Dahl, D. B., Vannucci, M. and Tsai, J. W. (2009a). Correction to density estimation for protein conformation angles using a bivariate von Mises distribution and Bayesian nonparametrics. J. Amer. Statist. Assoc.104 1728.
24. Lennox, K. P., Dahl, D. B., Vannucci, M. and Tsai, J. W. (2009b). Density estimation for protein conformation angles using a bivariate von Mises distribution and Bayesian nonparametrics. J. Amer. Statist. Assoc. 104586-596.
25. Lovell, S. C., Davis, I. W., Arendall, W. B. R., de Bakker, P. I., Word, J. M., Prisant, M. G., Richardson, J. S. and Richardson, D. C. (2003). Structure validation by Calpha geometry: Phi, Psi and Cbeta deviation. Proteins 50437-450.
26. MacEachern, S. N. (2000). Dependent Dirichlet processes. Technical report, Dept. Statistics, Ohio State Univ.
27. Mardia, K. V. (1975). Statistics of directional data (com: P371-392). J. Roy. Statist. Soc. Ser. B 37 349-371.
28. Mardia, K. V., Hughes, G., Taylor, C. C. and Singh, H. (2008). A multivariate von Mises distribution with applications to bioinformatics. Canadian J. Statist. 36 99-109.
29. Mardia, K. V., Taylor, C. C. and Subramaniam, G. K. (2007). Protein bioinformatics and mixtures of bivariate von Mises distributions for angular data. Biometrics 63 505-512.
30. McGuffin, L. J., Bryson, K. and Jones, T. D. (2000). The PSIPRED protein structure prediction server. Bioinformatics 16 404-405.
31. Michalsky, E., Goede, A. and Preissner, R. (2003). Loops in proteins (LIP)-a comprehensive loop database for homology modeling. Prot. Eng. 16 979-985.
32. Neal, R. M. (2000). Markov chain sampling methods for Dirichlet process mixture models. J. Comput. Graph. Statist. 9 249-265.
33. Osguthorpe, D. J. (2000). Ab initio protein folding. Curr. Opin. Struct. Biol. 10146-152.
34. Ramachandran, G. N., Ramakrishnan, C. and Sasisekharan, V. (1963). Stereochemistry of polypeptide chain configurations. Mol. Biol. 7 95-99.
35. Rivest, L. P. (1982). Some statistical methods for bivariate circular data. J. Roy. Statist. Soc. Ser. B 44 81-90.
36. Rodríguez, A., Dunson, D. B. and Gelfand, A. E. (2008). The nested Dirichlet process. J. Amer. Statist. Assoc. 103 1131-1144.
37. Scott, S. L. (2002). Bayesian methods for hidden Markov models: Recursive computing in the 21st century. J. Amer. Statist. Assoc. 97 337-351.
38. Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4 639-650.
39. Singh, H., Hnizdo, V. and Demchuk, E. (2002). Probabilistic model for two dependent circular variables. Biometrika 89 719-723.
40. Teh, Y. W., Jordan, M. I., Beal, M. J. and Blei, D. M. (2006). Hierarchical Dirichlet processes. J. Amer. Statist. Assoc. 101 1566-1581.
41. Xing, E. P. and Sohn, K. A. (2007). Hidden Markov Dirichlet process: Modeling genetic inference in open ancestral space. Bayesian Anal. 2 501-528.