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基因转录调控系统中的色噪声诱导转化研究

王参军

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基因转录调控系统中的色噪声诱导转化研究

王参军

Colored noise induced switch in the gene transcriptional regulatory system

Wang Can-Jun
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  • 研究了基因转录调控系统中的色噪声诱导蛋白质浓度转换现象. 据Novikov定理和Fox近似方法得到相应的Fokker-Planck方程, 给出稳态概率分布函数、蛋白质浓度平均值及其平均首通时间的近似表达式, 分析了噪声的自关联时间对稳态概率、平均值和平均首通时间的影响. 研究表明, 分解率的噪声的自关联时间引起蛋白质的浓度经历了关开的转换; 合成率的噪声的自关联时间引起蛋白质的浓度经历了开关转换. 然而, 随着两种自关联时间的增大, 平均首通时间增大, 即蛋白质浓度之间的转换变得困难. 数值模拟结果与理论预测基本符合.
    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.
    • 基金项目: 国家自然科学基金(批准号: 11047146, 10865006)、陕西省自然科学基金(批准号: 2010JQ1014)、陕西省教育厅自然科学基金(批准号: 09JK331)和宝鸡文理学院重点科研项目(批准号: ZK0954)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11047146, 10865006), the Science Foundation of the Education Bureau of Shaanxi Province of China (Grant No. 09JK331), the Natural Science Foundation of Shaanxi Province of China (Grant No. 2010JQ1014), and the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK0954).
    [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

  • [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

计量
  • 文章访问数:  2663
  • PDF下载量:  414
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-02-25
  • 修回日期:  2011-04-11
  • 刊出日期:  2012-01-05

基因转录调控系统中的色噪声诱导转化研究

  • 1. 宝鸡文理学院非线性研究所, 宝鸡 721007
    基金项目: 

    国家自然科学基金(批准号: 11047146, 10865006)、陕西省自然科学基金(批准号: 2010JQ1014)、陕西省教育厅自然科学基金(批准号: 09JK331)和宝鸡文理学院重点科研项目(批准号: ZK0954)资助的课题.

摘要: 研究了基因转录调控系统中的色噪声诱导蛋白质浓度转换现象. 据Novikov定理和Fox近似方法得到相应的Fokker-Planck方程, 给出稳态概率分布函数、蛋白质浓度平均值及其平均首通时间的近似表达式, 分析了噪声的自关联时间对稳态概率、平均值和平均首通时间的影响. 研究表明, 分解率的噪声的自关联时间引起蛋白质的浓度经历了关开的转换; 合成率的噪声的自关联时间引起蛋白质的浓度经历了开关转换. 然而, 随着两种自关联时间的增大, 平均首通时间增大, 即蛋白质浓度之间的转换变得困难. 数值模拟结果与理论预测基本符合.

English Abstract

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