An analytic study of the phase transition line in local sequence alignment with gaps

Discrete Applied Mathematics

Volumn 104, Issue 1-3, 2000, Pages 113-142

  Bundschuh, R ^a   Hwa, T ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

First passage percolation; Longest common subsequence; Phase transition; Sequence alignment

Indexed keywords

EID: 0009074821     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(00)00188-8     Document Type: Article

References (34)

1. Alexander K.S. The rate of convergence of the mean length of the longest common subsequence. Ann. Appl. Probab. 4:1994;1074-1082.
2. Altschul S.F., Gish W., Miller W., Myers E.W., Lipman D.J. Basic local alignment search tool. J. Mol. Biol. 215:1990;403-410.
3. Arratia R., Morris P., Waterman M.S. Stochastic scrabbles: a law of large numbers for sequence matching with scores. J. Appl. Probab. 25:1988;106-119.
4. Arratia R., Waterman M.S. A phase transition for the score in matching random sequences allowing deletions. Ann. Appl. Probab. 4:1994;200-225.
5. Boutet de Monvel J. Extensive simulations for longest common subsequences. European Phys. J. B. 7:1999;293-308.
6. R. Bundschuh, High precision simulations of the longest common subsequence problem, in preparation.
7. R. Bundschuh, T. Hwa, in preparation.
8. Chvátal V., Sankoff D. Longest common subsequences of two random sequences. J. Appl. Probab. 12:1975;306-315.
9. V. Dančík, Expected length of longest common subsequences, Ph.D. Thesis, University of Warwick (1994) .
10. V. Dančík, M. Paterson, Upper bounds for expected length of a longest common subsequence of two random sequences STACS94, Lecture Notes in Computer Science, Vol. 775, Springer, Berlin, 1994, pp. 669-678.
11. Deken J. Some limit results for longest common subsequences. Discrete Math. 26:1979;17-31.
12. Dembo A., Karlin S. Strong limit theorems of empirical functionals for large exceedances of partial sums of iid variables. Ann. Probab. 19:1991;1737-1755.
13. Doolittle R.F. Methods in Enzymology, Vol. 266. 1996;Academic Press, San Diego.
14. Drasdo D., Hwa T., Lässig M. DNA sequence alignment and critical phenomena. Mater. Res. Soc. Symp. Proc. 263:1997;75-80.
15. Drasdo D., Hwa T., Lässig M. Scaling laws and similarity detection in sequence alignment with gaps. Glasgow J.et al. Proceedings of the sixth International Conference on Intelligent Systems for Molecular Biology. 1998;52-58 AAAI Press, Menlo Park.
16. Hwa T., Lässig M. Similarity detection and localization. Phys. Rev. Lett. 76:1996;2591-2594.
17. Hwa T., Lässig M. Optimal detection of sequence similarity by local alignment. Israil S.et al. Proceedings of the Second Annual International Conference on Computational Molecular Biology. 1998;109-116 ACM Press, New York.
18. Karlin S., Altschul S.F. Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes. Proc. Natl. Acad. Sci. USA. 87:1990;2264-2268.
19. Karlin S., Altschul S.F. Applications and statistics for multiple high-scoring segments in molecular sequences. Proc. Natl. Acad. Sci. USA. 90:1993;5873-5877.
20. Karlin S., Dembo A. Limit distributions of maximal segmental score among Markov-dependent partial sums. Adv. Appl. Probab. 24:1992;113-140.
21. H. Kesten, Aspects of first-passage percolation, Ecole d'Eté de Probabilités de Saint Flour XIV, Lecture Notes in Mathematics, Vol. 1180, Springer, Berlin, 1986, pp. 125-264.
22. Krug J., Spohn H. Kinetic Roughening of Growing Surfaces. Godreche C. Solids Far From Equilibrium: Growth, Morphology, and Defects. 1991;479 Cambridge University Press, Cambridge.
23. Lipman D.J., Pearson W.R. Rapid and sensitive protein similarity searches. Science. 227:1985;1435-1441.
24. Needleman S.B., Wunsch C.D. A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 48:1970;443-453.
25. R. Olsen, T. Hwa, M. Lässig, Optimizing Smith-Waterman Alignments, Proceedings of the Fourth Pacific Symposium on Biocomputing, 1998, to appear.
26. M. Paterson, V. Dančík, Longest common subsequences, Proceedings of the 19th international Symposium of Mathematical Foundations of Computer Science 1994, MFSC'94, Springer, Berlin, 1994, pp. 127-142.
27. Pearson W.R., Lipman D.J. Improved tools for biological sequence comparison. Proc. Natl. Acad. Sci. USA. 85:1988;2444-2448.
28. Smith T.F., Waterman M.S. Comparison of biosequences. Adv. Appl. Math. 2:1981;482-489.
29. Steele J.M. An Efron-Stein inequality for nonsymmetric statistics. Ann. Statist. 14:1986;753-758.
30. Steele J.M. Probability Theory and Combinatorial Optimization. 1997;SIAM, Philadelphia.
31. Waterman M.S. Waterman M.S. Mathematical Methods for DNA Sequences. 1989;CRC Press, Boca Raton, FL.
32. Waterman M.S. Introduction to Computational Biology. 1994;Chapman & Hall, London.
33. Waterman M.S. Estimating statistical significance of Sequence alignments. Philos. Trans. Roy. Soc. London B. 344:1994;383-390.
34. Waterman M.S., Gordon L., Arratia R. Phase transitions in sequence matches and nucleic acid structure. Proc. Natl. Acad. Sci. USA. 84:1987;1239-1243.