系统规模对群体行为的效果

易奇志; 杜焰; 周天寿

doi:10.7498/aps.62.118701

摘要

影响细胞群体行为的因素是多种多样的, 除了以前研究的细胞通讯方式和环境因素外, 还与现有文献没有或很少研究的细胞数目(即系统规模)有关. 本文研究了系统规模对一类合成多细胞通讯系统的聚类行为的影响. 在该系统中, 单个系统是由压制振动子和基于延迟的松弛振子整合而成的振子, 而振子之间通过群体感应机制相互耦合. 通过分岔分析和数值模拟发现: 细胞数目的增加不仅可以改变平衡态聚类稳定性区间的大小并诱导新的聚类行为, 而且有利于扩大平衡态聚类的吸引域, 表明细胞分化可能与系统规模有密切关系; 细胞数目的增加还可以极大地丰富平衡态聚类和振动聚类的表现形式和共存方式, 为生物体对环境的适应性提供了良好的基础. 我们的结果不仅扩充了耦合系统的动力学行为, 也为理解多细胞现象奠定了基础.

关键词:

Abstract

There are many factors to influence the population behavior of cells. Except for the ways of cellular communication and the cellular environment, Which have been considered in the previous studies, the number of cells (or system size) that has been little considered before is also an important factor. This article investigates effects of system size on clustering behavior in a synthetic multicellular system, where individual oscillators are an integration of repressilator and hysteresis-based oscillators and are coupled through a quorum-sensing mechanism. By bifurcation analysis and numerical simulation, we find that increasing the cell number not only can change the size of the stability interval of steady state clusters and induce new clustering behaviors, but also benefits the enlargement of the attraction basin of steady state clusters, implying that cell differentiation may be closely related to the system size. In addition, such an increase can greatly extend the kinds and coexisting modes of steady state and oscillatory clusters, which would provide a good basis for the adaptability of organisms to the environment. Our results have extended the connotation of dynamics of coupled systems and also may be the foundation for understanding multicellular phenomena.

Keywords:

作者及机构信息

1.
江西师范大学数学与信息科学学院, 南昌 330022;

2.
江西师范大学化学与化工学院, 南昌 330022;

3.
中山大学数学与计算科学学院, 广州 510275

基金项目: 国家自然科学基金(批准号: 91230204, 30973980)、中山大学广东省计算科学重点实验室开放基金 (批准号: 20120611)、江西省教育厅科学技术研究项目(批准号: GJJ13218)、江西师范大学科研计划(批准号: 3092)和江西师范大学博士启动基金(批准号: 4166)资助的课题.

Authors and contacts

1.
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;

2.
College of Chemistry and Chemical Engineering, Jiangxi Normal University, Nanchang 330022, China;

3.
School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 91230204, 30973980), the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University, China (Grant No. 20120611), the Scientific Research Project of Department of Education of Jiangxi Province (Grant No. GJJ13218), the Scientific Research Program of Jiangxi Normal University, China (Grant No. 3092), and the Doctoral Initial Foundation of Jiangxi Normal University, China (Grant No. 4166).

参考文献

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[15]	Yi Q Z, Zhang J J, Yuan Z J, Zhou T S 2010 Eur. Phys. J. B 75 365
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[19]	Koseska A, Volkov E, Kurths J 2007 Phys. Rev. E 75 031916
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[21]	Yi Q Z, Zhou T S 2011 Phys. Rev. E 83 051907
[22]	Gurdon J, Lemaire P, Kato K 1993 Cell 75 831
[23]	Shimuta K, Nakajo N, Uto K, Hayano Y, Okazaki K, Sagata N 2002 EMBO J. 21 3694
[24]	Okuda K 1993 Physica D (Amsterdam) 63 424
[25]	Golomb D, Hansel D, Shraiman B, Sompolinsky H 1992 Phys. Rev. A 45 3516
[26]	Taylor A F, Kapetanopoulos P, Whitaker B J, Toth R, Bull L, Tinsley M R 2008 Phys. Rev. Lett. 100 214101
[27]	Kuramoto Y 1984 Chemical oscillations, waves and turbulence (Berlin: Springer-Verlag)
[28]	Tabata T, Takei Y 2004 Development 131 703
[29]	Zhou T S, Zhang J J, Yuan Z J, Chen L N 2008 Chaos 18 037126
[30]	Ermentrout B 2002 Simulating, analyzing and animating dynamical systems: A guide to Xppaut for researchers and students (software, environment and tools) 1st ed. (Philadephia, PA: SIAM Press)
[31]	Krupa M, Popovic N, Kopell N, Rotstein H G 2008 Chaos 18 015106
[32]	Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[33]	Zhou T S, Chen L N, Aihara K 2005 Phys. Rev. Lett. 95 178103
[34]	Koseska A, Volkov E, Kurths J 2009 EuroPhys. Lett. 85 28002
[35]	Koseska A, Volkov E, Kurths J 2010 Chaos 20 023132
[36]	Smolen P, Baxter D A, Byrne J H 2002 Biophys. J. 83 2349
[37]	Song H, Smolen P, Av-Ron E, Douglas D A, Byrne J H 2007 Biophys. J. 92 3407
[38]	Potapov I, Volkov E, Kuznetsov A 2011 Phys. Rev. E 83 031901

施引文献

[1]	Nakajima A, Kaneko K 2008 J. Theor. Biol. 253 779
[2]	Kaneno K, Yomo T 1994 Physica D 75 89
[3]	Kaneko K, Yomo T 1997 B. Math. Biol. 59 139
[4]	Wang J W, Chen A M, Zhang J J, Yuan Z J, Zhou T S 2009 Chin. Phys. B 18 1294
[5]	Wang B H, Lu Q S, Lv S J, Lang X F 2009 Chin. Phys. B 18 872
[6]	Greenwald I, Rubin G M 1992 Cell 68 271
[7]	Armour C, Garson K, McBurney M W 1999 Exp. Cell Res. 251 79
[8]	Garcia-Ojalvo J, Elowitz M B, Strogatz S H 2004 Proc. Natl. Acad. Sci. U.S.A. 101 10955
[9]	Blair S S 2007 Annu. Rev. Cell Dev. Biol. 23 293
[10]	Fields R D, Burnstock G 2006 Nat. Rev. Neurosci. 7 423
[11]	Scherrer R, Shull V 1986 Can. J. Microbiol. 32 607
[12]	Ben-Jacob E, Cohen I, Shochet O, Tenenbaum A, Czirok A, Vicsek T 1995 Phys. Rev. Lett. 75 2899
[13]	Basu S, Gerchman Y, Collins C H, Arnold F H, Weiss R 2005 Nature 434 1130
[14]	Zhang J J, Yuan Z J, Zhou T S 2009 Phys. Rev. E 79 041903
[15]	Yi Q Z, Zhang J J, Yuan Z J, Zhou T S 2010 Eur. Phys. J. B 75 365
[16]	McMillen D, Kopell N, Hasty J, Collins J 2002 Proc. Natl. Acad. Sci. U.S.A. 99 679
[17]	Ullner E, Koseska A, Kurths J, Volkov E, Kantz H, García-Ojalvo J 2008 Phys. Rev. E 78 031904
[18]	Ullner E, Zaikin A, Volkov E I, García-Ojalvo J 2007 Phys. Rev. Lett. 99 148103
[19]	Koseska A, Volkov E, Kurths J 2007 Phys. Rev. E 75 031916
[20]	Koseska A, Ullner E, Volkov E, Kurths J, García-Ojalvo J 2010 J. Theor. Biol. 263 189
[21]	Yi Q Z, Zhou T S 2011 Phys. Rev. E 83 051907
[22]	Gurdon J, Lemaire P, Kato K 1993 Cell 75 831
[23]	Shimuta K, Nakajo N, Uto K, Hayano Y, Okazaki K, Sagata N 2002 EMBO J. 21 3694
[24]	Okuda K 1993 Physica D (Amsterdam) 63 424
[25]	Golomb D, Hansel D, Shraiman B, Sompolinsky H 1992 Phys. Rev. A 45 3516
[26]	Taylor A F, Kapetanopoulos P, Whitaker B J, Toth R, Bull L, Tinsley M R 2008 Phys. Rev. Lett. 100 214101
[27]	Kuramoto Y 1984 Chemical oscillations, waves and turbulence (Berlin: Springer-Verlag)
[28]	Tabata T, Takei Y 2004 Development 131 703
[29]	Zhou T S, Zhang J J, Yuan Z J, Chen L N 2008 Chaos 18 037126
[30]	Ermentrout B 2002 Simulating, analyzing and animating dynamical systems: A guide to Xppaut for researchers and students (software, environment and tools) 1st ed. (Philadephia, PA: SIAM Press)
[31]	Krupa M, Popovic N, Kopell N, Rotstein H G 2008 Chaos 18 015106
[32]	Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[33]	Zhou T S, Chen L N, Aihara K 2005 Phys. Rev. Lett. 95 178103
[34]	Koseska A, Volkov E, Kurths J 2009 EuroPhys. Lett. 85 28002
[35]	Koseska A, Volkov E, Kurths J 2010 Chaos 20 023132
[36]	Smolen P, Baxter D A, Byrne J H 2002 Biophys. J. 83 2349
[37]	Song H, Smolen P, Av-Ron E, Douglas D A, Byrne J H 2007 Biophys. J. 92 3407
[38]	Potapov I, Volkov E, Kuznetsov A 2011 Phys. Rev. E 83 031901

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