Effects of system size on population behavior

Yi Qi-Zhi; Du Yan; Zhou Tian-Shou

doi:10.7498/aps.62.118701

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:

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).

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Cited By

[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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Vol. 62, Issue 11 - 2013-06-05

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