Coherence, collective rhythm, and phase difference distribution in populations of stochastic genetic oscillators with cellular communication

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

Volumn 78, Issue 3, 2008, Pages

  Yuan, Zhanjiang ^a   Zhang, Jiajun ^a   Zhou, Tianshou ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CELLULAR RADIO SYSTEMS; CHEMICAL REACTIONS; DEFORMATION; GRAFTING (CHEMICAL); POPULATION STATISTICS; RELAXATION OSCILLATORS; RESONANCE; STOCHASTIC PROGRAMMING; SYNTHESIS (CHEMICAL);

CELL NUMBERS; CELLULAR COMMUNICATION; PHASE DIFFERENCE DISTRIBUTION;

CYTOLOGY;

EID: 51549107579     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.031901     Document Type: Article

References (64)

1. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Science SCIEAS 0036-8075 10.1126/science.298.5594.824 298, 824 (2002).
2. R. Milo, S. Itzkovitz, N. Kashtan, R. Levitt, S. Shen-Orr, I. Ayzenshtat, M. Sheffer, and U. Alon, Science SCIEAS 0036-8075 10.1126/science.1089167 303, 1538 (2004).
3. N. Maheshri and E. K. O'Shea, Annu. Rev. Biophys. Biomol. Struct. ABBSE4 1056-8700 10.1146/annurev.biophys.36.040306.132705 36, 413 (2007).
4. J. R. Chabot, J. M. Pedraza, P. Luitel, and A. van Oudenaarden, Nature (London) NATUAS 0028-0836 450, 1249 (2007).
5. A. Goldbeter, Nature (London) NATUAS 0028-0836 10.1038/nature01259 420, 238 (2002).
6. M. B. Elowitz and S. Leibler, Nature (London) NATUAS 0028-0836 10.1038/35002125 403, 335 (2000).
7. M. R. Atkinson, M. A. Savageau, J. T. Myers, and A. J. Ninfa, Cell CELLB5 0092-8674 10.1016/S0092-8674(03)00346-5 113, 597 (2003).
8. E. Fung, W. W. Wong, J. K. Suen, T. Bulter, Sun-gu Lee, and J. C. Liao, Nature (London) NATUAS 0028-0836 10.1038/nature03508 435, 118 (2005).
9. D. Bell-Pedersen, V. M. Cassone, D. J. Earnest, S. S. Golden, P. E. Hardin, T. L. Thomas, and M. J. Zoran, Nat. Rev. Genet. NRGAAM 1471-0056 10.1038/nrg1633 6, 544 (2005).
10. J. R. Pomerening, S. Y. Kim, and J. E. Ferrell, Cell CELLB5 0092-8674 10.1016/j.cell.2005.06.016 122, 565 (2005).
11. J. Keener and J. Sneyd, Mathematical Physiology (Springer-Verlag, New York, 1998).
12. L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.223 70, 223 (1998).
13. B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2003.10.015 392, 321 (2004).
14. F. Sagués, J. M. Sancho, and J. García-Ojalvo, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.79.829 79, 829 (2007).
15. Hu Gang, T. Ditzinger, C. Z. Ning, and H. Haken, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.807 71, 807 (1993).
16. A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.775 78, 775 (1997).
17. C. B. Muratov, E. V. Eijnden, and W. E, Physica D PDNPDT 0167-2789 10.1016/j.physd.2005.07.014 210, 227 (2005).
18. R. E. Lee DeVille, E. Van den-Eijnden, and C. B. Muratov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.031105 72, 031105 (2005).
19. C. B. Muratov, E. V. Eijnden, and W. E, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0607433104 104, 702 (2007).
20. G. M. Süel, J. García-Ojalvo, L. M. Liberman, and M. B. Elowitz, Nature (London) NATUAS 0028-0836 10.1038/nature04588 440, 545 (2007).
21. H. Maamar, A. Raj, and D. Dubnau, Science SCIEAS 0036-8075 317, 526 (2007).
22. D. Schultz, E. Ben Jacob, J. N. Onuchic, and P. G. Wolynes, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0707965104 104, 17582 (2007).
23. J. M. Vilar, H. Y. Kueh, N. Barkai, and S. Leibler, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.092133899 99, 5988 (2002).
24. M. Scott, T. Hwa, and B. Ingalls, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0610468104 104, 7402 (2007).
25. D. McMillen, N. Kopell, J. Hasty, and J. J. Collins, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.022642299 99, 679 (2002).
26. J. García-Ojalvo, M. B. Elowitz, and S. H. Strogatz, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0307095101 101, 10955 (2004).
27. T. S. Zhou, L. N. Chen, and K. Aihara, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.178103 95, 178103 (2005).
28. E. Ullner, A. Zaikin, E. I. Volkov, and J. García-Ojalvo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.148103 99, 148103 (2007).
29. I. Leyva, I. Sendina-Nadal, J. A. Almendral, and M. A. F. Sanjuán, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.056112 74, 056112 (2006).
30. P.-J. Kim, T.-W. Ko, H. Jeong, and H.-T. Moon, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.065201 70, 065201 (R) (2004).
31. A. T. Winfree, The Geometry of Biological Time (Springer, Berlin, 1980).
32. A. S. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization-A Unified Approach to Nonlinear Science (Cambridge University Press, Cambridge, 2001).
33. J. Hasty, F. Isaacs, M. Dolnik, D. McMillen, and J. J. Collins, Chaos CHAOEH 1054-1500 10.1063/1.1345702 11, 207 (2001).
34. J. Hasty, J. Pradines, M. Dolnik, and J. J. Collins, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.040411297 97, 2075 (2000).
35. M. Kaern, T. C. Elston, W. J. Blake, and J. J. Collins, Nat. Rev. Genet. NRGAAM 1471-0056 10.1038/nrg1615 6, 451 (2005).
36. J. M. Raser and E. K. O'Shea, Science SCIEAS 0036-8075 10.1126/science.1105891 309, 2010 (2005).
37. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 3rd ed. (Springer-Verlag, Berlin 1985).
38. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
39. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992).
40. A. Kuznetsov, M. Kaern, and N. Kopell, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139903436029 65, 392 (2004).
41. T. S. Zhou, J. J. Zhang, Z. J. Yuan, and A. L. Xu, PLoS ONE ZZZZZZ 1932-6203 2, e231 (2007).
42. J. Rinzel and G. B. Ermentrout, in Analysis of Neural Excitability and Oscillations, Methods in Neuronal Modeling, edited by, C. Koch, and, I. Segev, (MIT, Cambridge, MA, 1989).
43. E. M. Izhikevich, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127400000840 10, 1171 (2000).
44. R. Guantes and J. F. Poyatos, PLOS Comput. Biol. ZZZZZZ 1553-734X 2, 3:e30 (2006).
45. M. I. Freidlin, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1004827921214 103, 283 (2000).
46. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer-Verlag, Berlin, 1984).
47. B. Hu and C. S. Zhou, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61. R1001 61, R1001 (2000).
48. C. S. Zhou, J. Kurths, and B. Hu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.098101 87, 098101 (2001).
49. Y. Shinohara, T. Kanamaru, H. Suzuki, T. Horita, and K. Aihara, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.051906 65, 051906 (2002).
50. O. Kwon, H.-H. Jo, and H.-T. Moon, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.066121 72, 066121 (2005).
51. B. S. Kerner and V. V. Osipov, Usp. Fiz. Nauk UFNAAG 0042-1294 160, 1 (1990).
52. D. Ruwisch, M. Bode, D. Volkov, and E. Volkov, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127499001437 9, 1969 (1999).
53. V. K. Vanag, L. F. Yang, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, Nature (London) NATUAS 0028-0836 10.1038/35019038 406, 389 (2000).
54. K. Wiesenfeld, C. Bracikowski, G. James, and R. Roy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65.1749 65, 1749 (1990).
55. K. Yoshikawa, N. Oyama, M. Shoji, and S. Nakata, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.16593 59, 137 (1991).
56. H. Meinhardt, Models of Biological Pattern Formation (Academic Press, London, 1982).
57. A. J. Koch and H. Meinhardt, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.66.1481 66, 1481 (1994).
58. C. S. Zhou and J. Kurths, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.040101 65, 040101 (R) (2002).
59. C. E. Shannon, Bell Syst. Tech. J. BSTJAN 0005-8580 27, 379 (1948);
60. C. E. Shannon, Bell Syst. Tech. J. BSTJAN 0005-8580 27, 623 (1948).
61. G. Balazsi, A. Cornell-Bell, A. B. Neiman, and F. Moss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.041912 64, 041912 (2001).
62. L. C. Yu, Y. Chen, and P. Zhang, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2007-00278-0 59, 249 (2007).
63. E. I. Volkov and M. N. Stolyarov, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(91)90162-2 159, 61 (1991).
64. J. J. Zhang, Z. J. Yuan, J. W. Wang, and T. S. Zhou, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.77.021101 77, 021101 (2008).