Schwinger Boson formulation and solution of the Crow-Kimura and Eigen models of quasispecies theory

Journal of Statistical Physics

Volumn 125, Issue 4, 2006, Pages 975-1015

  Park, Jeong Man ^a,b   Deem, Michael W ^a  

^a RICE UNIVERSITY   (United States)

^b The Catholic University of Korea   (South Korea)

Author keywords

Eigen model; Finite; Genome; Paramuse model; Quasispecies theory; Spin coherent states

Indexed keywords

EID: 33845643098     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9190-z     Document Type: Article

References (16)

1. E. Baake, M. Baake and H. Wagner, Ising quantum chain is equivalent to a model of biological evolution. Phys. Rev. Lett. 78:559-562 (1997);
2. E. Baake, M. Baake and H. Wagner, Phys. Rev. Lett. 79:1782.
3. E. Baake, M. Baake and H. Wagner, Quantum mechanics versus classical probability in biological evolution. Phys. Rev. E 57:1191-1192 (1998).
4. R. B. Bapat and T. E. S. Raghavan, Nonnegative Matrices and Applications. Cambridge University Press, New York (1997).
5. R. Bürger, Mathematical properties of mutation-selection models. Genetica 102/103:279-298 (1998).
6. J. F. Crow and M. Kimura, An Introduction to Population Genetics Theory. Harper and Row, New York (1970).
7. M. Eigen, Self organization of matter and the evolution of biological macor molecules. Naturwissenschaften 58:465-523 (1971).
8. M. Eigen, J. McCaskill and P. Schuster, The molecular quasi-species. Adv. Chem. Phys. 75:149-263 (1989).
9. K. Jain and J. Krug, Adaptation in simple and complex fitness landscapes. In: H. R. U. Bastolla, M. Porto, and M. Vendruscolo (eds.) Structural approaches to sequence evolution: Molecules, networks and populations. Springer Verlag, Berlin (2005). Q-bio.PE/0508008.
10. I. Leuthäusser, An exact correspondence between Eigen's evolution model and a two-dimensional ising system. J. Chem. Phys. 84:1884-1885 (1986).
11. L. Peliti, Quasispecies evolution in general mean-field landscapes. Europhys. Lett. 57:745-751 (2002).
12. D. B. Saakian and C. K. Hu, Eigen model as a quantum spin chain: Exact dynamics. Phys. Rev. E 69:021-913 (2004).
13. D. B. Saakian and C. K. Hu, Solvable biological evolution model with a parallel mutation-selection scheme. Phys. Rev. E 69, 046-121 (2004).
14. D. B. Saakian, C. K. Hu and H. Khachatryan, Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme. Phys. Rev. E 70:041-908 (2004).
15. D. B. Saakian, E. Munoz, C. K. Hu and M. W. Deem, Quasispecies theory for multiple-peak fitness landscapes. Phys. Rev. E 73:041-913 (2006).
16. P. Tarazona, Error thresholds for molecular quasispecies as phase transitions: From simple landscapes to spin-glass models. Phys. Rev. A 45:6038-6050 (1992).