Recursiveness, switching, and fluctuations in a replicating catalytic network

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

Volumn 68, Issue 3 1, 2003, Pages 319091-319095

  Kaneko, Kunihiko ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CATALYST ACTIVITY; COMPUTER SIMULATION; MOLECULES; PHASE TRANSITIONS; PROBABILITY;

CATALYTIC NETWORKS; LOCALIZED PATTERNS;

CATALYSIS;

EID: 0242578195     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. See, e.g., D. Segré and D. Lancet, EMBO Rep. 1, 217 (2000), and papers cited therein.
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13. ij show qualitatively same behaviors.
14. We use a stochastic approach, since discreteness in molecule numbers is sometimes found to be important; Y. Togashi and K. Kaneko, Phys. Rev. Lett. 86, 2459 (2001); see also B. Hess and A.S. Mikhailov, Science 264, 223 (1994); J. Theor. Biol. 176, 181 (1995).
15. We use a stochastic approach, since discreteness in molecule numbers is sometimes found to be important; Y. Togashi and K. Kaneko, Phys. Rev. Lett. 86, 2459 (2001); see also B. Hess and A.S. Mikhailov, Science 264, 223 (1994); J. Theor. Biol. 176, 181 (1995).
16. We use a stochastic approach, since discreteness in molecule numbers is sometimes found to be important; Y. Togashi and K. Kaneko, Phys. Rev. Lett. 86, 2459 (2001); see also B. Hess and A.S. Mikhailov, Science 264, 223 (1994); J. Theor. Biol. 176, 181 (1995).
17. The results do not depend on at what stage of the molecule numbers (between N/2 and N) the cell state is observed.
18. The behavior discussed here hardly depends on the choice of initial chemical compositions.
19. This number does not depend on N,k,ρ,μ, although with the decrease of μ and ρ, there is a tendency of its decrease toward 3, the minimal number for a hypercycle here.
20. -1.
21. See K. Kaneko and T. Yomo, J. Theor. Biol. 214, 563 (2002) for relevance of minority molecules to heredity.
22. As such this equation diverges with time, but here, the cell divides into two before the divergence becomes significant. The finiteness of the total number N means that the asymptotic distribution as N→∞ is not available, but the argument on the distribution form is valid as long as N is sufficiently large.
23. A. S. Mikhailov and V. Calenbuhr, From Cells to Societies (Springer, New York, 2002); D. Sornette, Critical Phenomena in Natural Science (Springer, New York, 2002).
24. A. S. Mikhailov and V. Calenbuhr, From Cells to Societies (Springer, New York, 2002); D. Sornette, Critical Phenomena in Natural Science (Springer, New York, 2002).
25. For some networks, the distributions may sometimes be intermediate between log-normal and Gaussian, and even have double peaks.
26. V. Shivashnakar et al. (private communication); see also W.J. Blake et al., Nature (London) 422, 633 (2003).
27. V. Shivashnakar et al. (private communication); see also W.J. Blake et al., Nature (London) 422, 633 (2003).
28. C. Furusawa et al. (unpublished).
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