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The evolution of the dynamic behaviors of beating rhythms from independent states to the formation of network is studied in biological experiment on two heterogeneous cells. The beating rhythms are independent and not synchronous when there is no coupling between two cells. With the enhancement of the coupling strength, the mean and maximum of absolute value of the phase difference drastically decrease in the beating rhythms of the two cells, from non-phase synchronization to phase synchronization, eventually not to full synchronization. Some of beatings become synchronous while others not synchronous for non-synchronization states while all beatings are synchronous for the phase synchronization state. With the increase of coupling strength, the times of synchronized beatings increases for the non-phase synchronization state, and time interval between the corresponding synchronous beatings of the two cells decreases to a low but non-zero value for the phase synchronization state. The results not only provide experimental demonstration of rhythm synchronization in a biological network, but also give changing regularity in the forming process of synchronous rhythm in the heterogeneous network.
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Keywords:
- biological network /
- synchronization /
- rhythm /
- heterogeneity
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[2] Steinmeta P N, Roy A, Fitzgerald P J 2000 Nature 404 187
[3] Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 2
[4] Pikovsky A, Rosenblum M, Kurth J 2001 Synchronization: A Universal Concept in Nonlinear Science (Cambridge: Cambridge University Press) p1
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[12] Soen Y, Cohen N, Lipson D, Braun E 1999 Phys. Rev. Lett. 82 3556
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[14] Liu H J, Liu Z Q, Gu H G, Yang M H, Li L, Ren W 2006 Acta Bio. Phys. Sin. 22 441 (in Chinese) [刘红菊, 刘志强, 古华光, 杨明浩, 李莉, 任维 2006 生物 22 441]
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[16] Zhang N, Zhang H M, Liu Z Q, Ding X L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 110501
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[18] Sato D, Xie L H, Sovari A A, Tran D X, Morita N, Xie F, Karagueuzian H, Garfinkel A, Weiss J N, Qu Z 2009 Proc. Natl. Acad. Sci. USA 106 2983
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[20] Yuan L, Liu Z Q, Zhang H M, Yang M H, Wei C L, Ding X L, Gu H G, Ren W 2011 Chin. Phys. B 20 020508
[21] Oyamada M, Kimura H, Oyamada Y, Miyamoto A, Ohshika H, Mori M 1994 Exp. Cell. Res. 212 351
[22] Jongsma H J, Masson-Pevet M, Tsjernina L 1987 Basic Res. Cardiol. 82 454
[23] Kimura H, Oyamada Y, Ohshika H, Mori M, Oyamda M 1995 Exp. Cell. Res. 220 348
[24] Cohen N, Soen Y, Braun E 1998 Physica A 249 600
[25] Yamauchi Y, Harada A, Kawahara K 2002 Biol. Cybern. 86 147
[26] Hachiro T, Kawahara K, Sato R, Yamauchi Y, Matsuyama D 2007 Bio. Systems 90 707
[27] Nakayama Y, Kawahara K, Yoneyama M, Hachiro T 2005 Biol. Rhythm Res. 36 317
[28] Dong S, Gu H G, Yuan L 2011 Acta Bio. Phys. Sin. 27 627 (in Chinese) [董珊, 古华光, 袁岚 2011 生物 27 627]
[29] Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I, Abarbane H D I 1998 Phys. Rev. Lett. 81 5692
[30] Norwood C R, Castaneda A R, Norwood W I 1980 J. Mol. Cell. Cardiol. 12 201
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[1] Gray C M, König P, Engel A K, Singer W 1989 Nature 338 334
[2] Steinmeta P N, Roy A, Fitzgerald P J 2000 Nature 404 187
[3] Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 2
[4] Pikovsky A, Rosenblum M, Kurth J 2001 Synchronization: A Universal Concept in Nonlinear Science (Cambridge: Cambridge University Press) p1
[5] Boyett M R, Honjo H, Kodama I 2000 Cardiovasc. Res. 47 658
[6] Li C 2001 Sino-Auricular Node (Beijing: Beijing Medical University Press) p1 (in Chinese) [李澈 2001 窦房结 (北京: 北京医科大学出版社) 第1页]
[7] Verheijck E E, Wilders R, Joyner R W, Golod D A, Kumar R, Jongsma H J, Bouman L N, van Ginneken A C 1998 J. Gen. Physiol. 111 95
[8] Kanakov O I, Osipov G V, Chan C K, Kurths J 2007 Chaos 17 015111
[9] Cai D, Lai Y C, Winslow R L 1993 Phys. Rev. Lett. 71 2501
[10] Cai D, Winslow R L, Noble D 1994 IEEE Trans. Biomed. Eng. 41 217
[11] Winslow R L, Cai D, Varghese A, Lai Y C 1995 Chaos Solitons Fractals 5 491
[12] Soen Y, Cohen N, Lipson D, Braun E 1999 Phys. Rev. Lett. 82 3556
[13] Yamauchi Y, Harada A, Kawahara K 2002 Biol. Cybern. 86 147
[14] Liu H J, Liu Z Q, Gu H G, Yang M H, Li L, Ren W 2006 Acta Bio. Phys. Sin. 22 441 (in Chinese) [刘红菊, 刘志强, 古华光, 杨明浩, 李莉, 任维 2006 生物 22 441]
[15] Lerma C, Krogh-Madsen T, Guevara M R, Glass L 2007 J. Stat. Phys. 128 347
[16] Zhang N, Zhang H M, Liu Z Q, Ding X L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 110501
[17] Kim M Y, Aguilar M, Hodge A, Vigmond E, Shrier A, Glass L 2009 Phys. Rev. Lett. 103 058101
[18] Sato D, Xie L H, Sovari A A, Tran D X, Morita N, Xie F, Karagueuzian H, Garfinkel A, Weiss J N, Qu Z 2009 Proc. Natl. Acad. Sci. USA 106 2983
[19] Petrov V S, Osipov G V, Kurths J 2010 Phys. Rev. E 82 026208
[20] Yuan L, Liu Z Q, Zhang H M, Yang M H, Wei C L, Ding X L, Gu H G, Ren W 2011 Chin. Phys. B 20 020508
[21] Oyamada M, Kimura H, Oyamada Y, Miyamoto A, Ohshika H, Mori M 1994 Exp. Cell. Res. 212 351
[22] Jongsma H J, Masson-Pevet M, Tsjernina L 1987 Basic Res. Cardiol. 82 454
[23] Kimura H, Oyamada Y, Ohshika H, Mori M, Oyamda M 1995 Exp. Cell. Res. 220 348
[24] Cohen N, Soen Y, Braun E 1998 Physica A 249 600
[25] Yamauchi Y, Harada A, Kawahara K 2002 Biol. Cybern. 86 147
[26] Hachiro T, Kawahara K, Sato R, Yamauchi Y, Matsuyama D 2007 Bio. Systems 90 707
[27] Nakayama Y, Kawahara K, Yoneyama M, Hachiro T 2005 Biol. Rhythm Res. 36 317
[28] Dong S, Gu H G, Yuan L 2011 Acta Bio. Phys. Sin. 27 627 (in Chinese) [董珊, 古华光, 袁岚 2011 生物 27 627]
[29] Elson R C, Selverston A I, Huerta R, Rulkov N F, Rabinovich M I, Abarbane H D I 1998 Phys. Rev. Lett. 81 5692
[30] Norwood C R, Castaneda A R, Norwood W I 1980 J. Mol. Cell. Cardiol. 12 201
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