Dynamics of the Eigen and the Crow-Kimura models for molecular evolution

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 78, Issue 4, 2008, Pages

  Saakian, David B ^a,b   Rozanova, Olga ^c   Akmetzhanov, Andrei ^d  

^a YEREVAN PHYSICS INSTITUTE   (Armenia)

^b INSTITUTE OF PHYSICS   (Taiwan)

^c MOSCOW STATE UNIVERSITY   (Russian Federation)

^d INSTITUTE FOR PROBLEMS IN MECHANICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; FUNCTION EVALUATION; HAMMING DISTANCE; MEATS; MOLECULAR BIOLOGY; PROBABILITY DENSITY FUNCTION;

ANALYTICAL RESULTS; DYNAMICAL PHASES; FITNESS FUNCTIONS; FITNESS LANDSCAPES; GENOME LENGTHS; GENOME SEQUENCES; HAMILTON; JACOBI METHODS; MOLECULAR EVOLUTIONS;

HEALTH;

EID: 54549111432     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.041908     Document Type: Article

References (28)

1. S. Wright, Genetics GENTAE 0016-6731 16, 97 (1931).
2. S. Wright, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.31.12.382 31, 382 (1945).
3. J. F. Crow and M. Kimura, An Introduction to Population Genetics Theory (Harper Row, New York, 1970).
4. E. Baake, M. Baake, and H. Wagner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.559 78, 559 (1997).
5. E. Baake and H. Wagner, Genet. Res. GENRA8 0016-6723 10.1017/ S0016672301005110 78, 93 (2001).
6. J. Hermisson, O. Redner, H. Wagner, and E. Baake, Theor Popul. Biol. ZZZZZZ 0040-5809 62, 9 (2002).
7. E. Baake and H. O. Georgii, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s00285-006-0039-5 54, 257 (2007).
8. M. Eigen, Naturwiss. NATWAY 0028-1042 10.1007/BF00623322 58, 465 (1971).
9. M. Eigen, J. McCaskill, and P. Schuster, Adv. Chem. Phys. ADCPAA 0065-2385 10.1002/9780470141243.ch4 75, 149 (1989).
10. L. S. Tsimring, H. Levine, and D. A. Kessler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.4440 76, 4440 (1996).
11. F. Bagnoli and M. Bezzi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3302 79, 3302 (1997).
12. U. Gerland and T. Hwa, J. Mol. Evol. JMEVAU 0022-2844 10.1007/s00239-002-2335-z 55, 386 (2002).
13. W. Peng, U. Gerland, T. Hwa, and H. Levine, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.088103 90, 088103 (2003).
14. D. B. Saakian and C. K. Hu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.021913 69, 021913 (2004).
15. D. B. Saakian and C. K. Hu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.046121 69, 046121 (2004).
16. D. B. Saakian, C. K. Hu, and H. Khachatryan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.041908 70, 041908 (2004).
17. I. M. Rouzine, J. Wakeley, and J. M. Coffin, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.242719299 100, 587 (2003).
18. D. B. Saakian, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-007-9334-9, 128 781 (2007).
19. K. Sato and K. Kaneko, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75. 061909 75, 061909 (2007).
20. H. Wagner, E. Baake, and T. Gerisch, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1023048711599 92, 1017 (1998).
21. C. J. Thompson and J. L. McBride, Math. Biosci. MABIAR 0025-5564 10.1016/0025-5564(74)90110-2 21, 127 (1974).
22. B. L. Jones, R. H. Enns, and R. S. Rangnekar, Bull. Math. Biol. BMTBAP 0092-8240 10.1016/S0092-8240(76)80040-7 38, 15 (1975).
23. L. C. Evans, Partial Differential Equations (American Mathematical Society, Providence, R. I., 1998).
24. A. Melikyan, Generalized Characteristics of First Order PDEs (Birkhäuser, Boston, 1998).
25. D. B. Saakian and C. K. Hu, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0504924103 103, 4935 (2006).
26. B. Drossel, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110041365 50, 209 (2001).
27. F. G. Carvalhaes and C. Goldman, e-print arXiv:q-bio.PE/0508026.
28. J. Hermisson, H. Wagner, and M. Baake, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1026577012763 102, 315 (2001).