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The colored noise induced switch in the gene transcriptional regulatory system is investigated. The approximate Fokker-Planck equation is obtained based on the Novikov theorem and the Fox approach. The explicit expressions of the steady state probability distribution, the mean value, and the mean first passage time are derived. After the numerical computations, these results show that the TF-A monomer concentration switches from the off position to the on position with the self-correlation time of the multiplicative noise increasing. The TF-A monomer concentration switches from the on position to the off position with the self-correlation time of the additive noise increasing. With the two kinds of the self-correlation time increasing, the mean first passage time becomes large, namely, the TF-A monomer concentration switch becomes difficult. The theoretical predictions are found to be in basic agreement with numerical results.
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Keywords:
- colored noises /
- gene transcriptional regulatory system /
- switch
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[1] Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Press) (in Chinese ) [胡岗 1994 随机力与非线性系统 (上海: 上海科技教育出版社)]
[2] Landa P S, McClintock P V E 2000 Phys. Rep. 323 1
[3] Gammaitoni L, Hänggi P, Jung P, Marchesoni M 1998 Rev. Mod. Phys. 70 223
[4] Li J H 2002 Phys. Rev. E 66 031104
[5] Ning L J, Xu W 2007 Acta Phys. Sin. 56 1944 (in Chinese ) [宁丽娟, 徐伟 2007 物理学报 56 1944]
[6] Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[7] Castro F, Sáchez A D, Wio H S 1995 Phys. Rev. Lett. 75 1691
[8] Cao L, Wu D J, Ke S Z 1995 Phys. Rev. E 52 3228
[9] Jia Y, Li J R 1996 Phys. Rev. E 53 5764
[10] Luo X Q, Zhu S Q 2001 Acta Phys. Sin. 51 0977 (in Chinese ) [罗晓琴, 朱士群 2001 物理学报 51 0977]
[11] Wang C J, Chen S B, Mei D C 2006 Chin. Phys. 15 1435
[12] Ai B Q,Wang X J , Liu G T, Liu L G 2003 Phys. Rev. E 67 022903
[13] Mei D C , Xie G Z, Zhang L 2004 Eur. Phys. J. B 41 107
[14] Wang C J, Wei Q, Mei D C 2007 Modern Phys. Lett. B 21 789
[15] Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375 (in Chinese) [王参军, 魏群, 郑宝兵, 梅冬成 2008 物理学报 57 1375]
[16] Dubkov A A, Agudov N V, Spagnolo B 2004 Phys. Rev. E 69 061103
[17] Jia Z L 2008 Chin. Phys. Lett. 25 1209
[18] Agudov N V, Spagnolo B 2001 Phys. Rev. E 64 035102
[19] Zhu S 1993 Phys. Rev. A 47 2405
[20] Zhang L Y, Cao L, Wu D J 2002 Acta Phys. Sin. 52 1174 (in Chinese) [张良英, 曹力, 吴大进 2002 物理学报 52 1174]
[21] Spagnolo B, Valenti D, Fiasconaro A 2004 arXiv:q-bio. PE/0403004 and references
[22] Vilar J M G, Solé R V 1998 Phys. Rev. Lett. 80 4099
[23] Zhong W R, Shao Y Z, He Z H 2006 Chin. Phys. Lett. 23 742
[24] Nie L R, Mei D C 2007 Eur. Phys. Lett. 79 20005
[25] Paulsson J 2004 Nature 427 415
[26] Raser J M, O’Shea Erin K 2005 Science 309 2010
[27] Smolen P, Baxter D A, Byrne J H 1998 Am. J. Physiol. 274 C531
[28] Smolen P, Baxter D A, Byrne J H 1999 Am. J. Physiol. 277 C777
[29] Liu Q, Jia Y 2004 Phys. Rev. E 70 041907.
[30] Wang C J, Mei D C 2008 Acta Phys. Sin. 57 3983 (in Chinese ) [王参军, 梅冬成 2008 物理学报 57 3983]
[31] Wang J Y, Zhu C L, Jia Y, Li J R 2006 Chin. Phys. Lett. 23 1398
[32] Wang C J 2010 Chin. Phys. B 19 030503
[33] Liu X M, Xie H Z, Liu L G, Li Z B 2009 Physica A 388 392
[34] Zeng C H, Xie C W 2008 Chin. Phys. Lett. 25 1587
[35] Liang G Y, Cao L, Wu D J 2004 Physica A 335 371
[36] Mei D C, Xie G Z, Cao L, Wu D J 1999 Phys. Rev. E 59 3880
[37] Masoliver J, West B J, Lindenbergerg K 1987 Phys. Rev. A 35 3086
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