细胞内钙离子螺旋波动力学研究
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摘要
钙离子(Ca~(2+))是细胞内最重要的信使之一。它不仅参与细胞内的信号传输,而且在细胞间的协同中起着重要作用。大量的实验研究表明,细胞钙离子浓度的动力学涵盖了从细胞内局域随机释放(如钙火花spark),到单细胞全局钙离子振荡或波的传播,再到多细胞体系的钙离子波等不同的层次,钙离子螺旋波(spiral wave)是其中一种非常新奇的钙离子浓度斑图。为了解释钙离子浓度的动力学行为,理论生物学家们提出了不同的数学模型。
细胞内的一些重要的参数,比如IP_3浓度等,是实验上可控的,研究这些可控因素对螺旋波的影响有利于进一步的认识细胞钙离子的交换机制,以及细胞内信息的传递过程,而且,钙离子螺旋波的控制也为人工介入钙离子信号提供了途径。鉴于此,本文从理论上对于影响细胞内钙离子螺旋波的各种可控因素,以及钙离子螺旋波的控制做了较为深入的研究。本文的主要工作包括以下几个方面:
第一,基于空间扩展的Tang-Othmer模型,研究了IP_3浓度对细胞内钙离子螺旋波的影响。结果发现: (1)随着IP_3浓度的变化,钙离子螺旋波周期呈现出非单调的变化过程,这些变化过程与细胞内钙离子螺旋波的稳定性及失稳过程相对应; (2)随着IP_3浓度的变化,螺旋波波头动力学经历了复杂的变化过程,这些变化过程可以用来描述螺旋波稳定性的变化,并且所得到的螺旋波波头动力学与其它可激发系统(比如Belousov-Zhabotinsky reaction)具有相似性; (3)基于以上结果,直观上提出了通过实验控制IP_3浓度来控制螺旋波的方法; (4)与前人实验研究的对比说明,本研究所得到的结果是可以被具体实验方案验证的。
第二,基于空间扩展的Tang-Othmer模型,研究了弱电场控制下的细胞内钙离子螺旋波,并以螺旋波波头动力学来描述螺旋波的控制过程。结果发现:(1)在直流弱电场的作用下,螺旋波的波头沿直线漂移; (2)在交流弱电场的作用下,出现了所谓的倍频共振漂移,也就是当电场的频率为螺旋波频率的两倍时,螺旋波的波头沿直线漂移; (3)所得到的数值结果,能够用近似方法给予理论解释。
第三,基于Bugrim等提出的考虑钙离子交换位点的离散随机分布的钙离子时空模型,研究了钙离子交换位点的离散随机分布对钙离子螺旋波的影响。研究发现: (1)考虑了交换位点的离散随机分布,才能在合理的参数范围内形成稳定的钙离子螺旋波,反之,则不能形成螺旋波; (2)交换位点随机分布模型能模拟钙离子螺旋波的自然形成过程; (3)由这种空间随机模型所得到的数值结果,与实验事实相吻合。
Ca~(2+) is one of the most important messengers. It transmits intracellular signals and takes part in intercellular coordination. The kinetics of the Ca~(2+) concentration involves a transition from locally stochastic release (e.g. Ca~(2+) spark) to intracellular global oscillations and waves, even waves spreading across cells. Ca~(2+) spiral wave is one of the most intriguing Ca~(2+) pattern. In order to explain the dynamics of Ca~(2+) concentration found in experiments, a number of mathematical models are presented.
Many important factors in the cell, for example IP_3 concentration, are experimentallycontrollable. Investigating the effect of these controllable factors on Ca~(2+) spiral waves can help us understanding the mechanism of Ca~(2+) exchanging in the cell, and Ca~(2+) signalling. Thus, in this thesis, we have studied the factors effecting the Ca~(2+) spiral waves and the control of Ca~(2+) spiral waves. The main works are as follow:
First, based on a spatial extended Tang-Othmer Ca~(2+) model, the dependence of spiral dynamics on IP_3 concentration is studied. we find: (i)The period of Ca~(2+) spiral wave changes un-monotonously with IP_3 concentration, and the increasing of periods corresponds to instability of spiral waves. (ii)Changing IP_3 concentration, the spiral dynamics undergoes fruitful transitions between rigidly rotating and meanderingspiral waves. The transitions are similar to that found in other systems (e.g. BZ reactions). (iii) Understanding the IP_3-dependent Ca~(2+) spiral dynamics, intuitively, some methods of controlling spirals through the control of IP_3 concentrationare introduced. (iv) Our results are experimentally accessable.
Then, Based on previous work in BZ reaction, the electric fields are used to control Ca~(2+) spiral waves, and the controlling effects are exhibited by spiral tips. we find: (i) Under the influence of dc electric field, the spiral tip gradually drifts from center to edge of the system along a straight line; (ii) When the applied electric field is periodic, the system resonates at a frequencyω= 2ω_0 and the spiral tip drift along a straight line; (iii) These numerical results can be explained by an analytical method based on the weak deformation approximation.
Finally, based on the model presented by Bugrim et. al., we have studied the effect of spatially discrete and random distribution of sites for Ca~(2+) releasing onCa~(2+) spiral waves. It is found that: (i) Only when the random distributions are considered, the spiral waves can be observed in reasonable parameters, vise verse, no spiral waves can be observed; (ii) the model considering random distribution of ion channel clusters can simulation the naturally initiation of Ca~(2+) spiral wave; (iii) when the random distributions are considered, the numerical results accord to experiments.
细胞内的一些重要的参数,比如IP_3浓度等,是实验上可控的,研究这些可控因素对螺旋波的影响有利于进一步的认识细胞钙离子的交换机制,以及细胞内信息的传递过程,而且,钙离子螺旋波的控制也为人工介入钙离子信号提供了途径。鉴于此,本文从理论上对于影响细胞内钙离子螺旋波的各种可控因素,以及钙离子螺旋波的控制做了较为深入的研究。本文的主要工作包括以下几个方面:
第一,基于空间扩展的Tang-Othmer模型,研究了IP_3浓度对细胞内钙离子螺旋波的影响。结果发现: (1)随着IP_3浓度的变化,钙离子螺旋波周期呈现出非单调的变化过程,这些变化过程与细胞内钙离子螺旋波的稳定性及失稳过程相对应; (2)随着IP_3浓度的变化,螺旋波波头动力学经历了复杂的变化过程,这些变化过程可以用来描述螺旋波稳定性的变化,并且所得到的螺旋波波头动力学与其它可激发系统(比如Belousov-Zhabotinsky reaction)具有相似性; (3)基于以上结果,直观上提出了通过实验控制IP_3浓度来控制螺旋波的方法; (4)与前人实验研究的对比说明,本研究所得到的结果是可以被具体实验方案验证的。
第二,基于空间扩展的Tang-Othmer模型,研究了弱电场控制下的细胞内钙离子螺旋波,并以螺旋波波头动力学来描述螺旋波的控制过程。结果发现:(1)在直流弱电场的作用下,螺旋波的波头沿直线漂移; (2)在交流弱电场的作用下,出现了所谓的倍频共振漂移,也就是当电场的频率为螺旋波频率的两倍时,螺旋波的波头沿直线漂移; (3)所得到的数值结果,能够用近似方法给予理论解释。
第三,基于Bugrim等提出的考虑钙离子交换位点的离散随机分布的钙离子时空模型,研究了钙离子交换位点的离散随机分布对钙离子螺旋波的影响。研究发现: (1)考虑了交换位点的离散随机分布,才能在合理的参数范围内形成稳定的钙离子螺旋波,反之,则不能形成螺旋波; (2)交换位点随机分布模型能模拟钙离子螺旋波的自然形成过程; (3)由这种空间随机模型所得到的数值结果,与实验事实相吻合。
Ca~(2+) is one of the most important messengers. It transmits intracellular signals and takes part in intercellular coordination. The kinetics of the Ca~(2+) concentration involves a transition from locally stochastic release (e.g. Ca~(2+) spark) to intracellular global oscillations and waves, even waves spreading across cells. Ca~(2+) spiral wave is one of the most intriguing Ca~(2+) pattern. In order to explain the dynamics of Ca~(2+) concentration found in experiments, a number of mathematical models are presented.
Many important factors in the cell, for example IP_3 concentration, are experimentallycontrollable. Investigating the effect of these controllable factors on Ca~(2+) spiral waves can help us understanding the mechanism of Ca~(2+) exchanging in the cell, and Ca~(2+) signalling. Thus, in this thesis, we have studied the factors effecting the Ca~(2+) spiral waves and the control of Ca~(2+) spiral waves. The main works are as follow:
First, based on a spatial extended Tang-Othmer Ca~(2+) model, the dependence of spiral dynamics on IP_3 concentration is studied. we find: (i)The period of Ca~(2+) spiral wave changes un-monotonously with IP_3 concentration, and the increasing of periods corresponds to instability of spiral waves. (ii)Changing IP_3 concentration, the spiral dynamics undergoes fruitful transitions between rigidly rotating and meanderingspiral waves. The transitions are similar to that found in other systems (e.g. BZ reactions). (iii) Understanding the IP_3-dependent Ca~(2+) spiral dynamics, intuitively, some methods of controlling spirals through the control of IP_3 concentrationare introduced. (iv) Our results are experimentally accessable.
Then, Based on previous work in BZ reaction, the electric fields are used to control Ca~(2+) spiral waves, and the controlling effects are exhibited by spiral tips. we find: (i) Under the influence of dc electric field, the spiral tip gradually drifts from center to edge of the system along a straight line; (ii) When the applied electric field is periodic, the system resonates at a frequencyω= 2ω_0 and the spiral tip drift along a straight line; (iii) These numerical results can be explained by an analytical method based on the weak deformation approximation.
Finally, based on the model presented by Bugrim et. al., we have studied the effect of spatially discrete and random distribution of sites for Ca~(2+) releasing onCa~(2+) spiral waves. It is found that: (i) Only when the random distributions are considered, the spiral waves can be observed in reasonable parameters, vise verse, no spiral waves can be observed; (ii) the model considering random distribution of ion channel clusters can simulation the naturally initiation of Ca~(2+) spiral wave; (iii) when the random distributions are considered, the numerical results accord to experiments.
引文
[1]M.J.Berridge,M.D.Bootman,and P.Lipp,Calcium-a life and death signal,Nature,395,645(1998).
[2]R.E.Dolmetsch,K.Xu,and R.S.Lewis,Calcium oscillations increase the efficiency and specificity of gene expression,Nature,392,933(1998).
[3]V.A.Golovina,and M.P.Blaustein,Spatially and Functionally Distinct Ca~(2+) Stores in Sarcoplasmic and Endoplasmic Reticulum,Science,275,1643(1997).
[4]A.H.Cornell-Bell,S.M.Finkbeiner,M.S.Cooper,and S.J.Smith,Glutamate induces calcium waves in cultured astrocytes:long-range glial signaling,Science,247,470(1990).
[5]C.A.Swanson,A.P.Arkin,and J.Ross,An endogenous calcium oscillator may control early embryonic division,Proc.Natl.Acad.Sci.,94,1194(1997).
[6]G.Majno,and I.Joris,Apoptosis,oncosis,and necrosis.An overview of cell death,Am.J.Pathol.,146,3(1995).
[7]R.Jacob,J.E.Merritt,T.J.Hallam,and T.R.Rink,Repetitive spikes in cytoplasmic calcium evoked by histamine in human endothelial cells,Nature,335,40-45(1988).
[8]T.Capiod,J.Noel,L.Combettes,and M.Claret,Cyclic AMP-evoked oscillations of intracellular[Ca~(2+)]in guinea-pig hepatocytes,Biochem.J.,275,277—280(1991).
[9]P.Shen,and R.Larter,Chaos in intracellular Ca~(2+) oscillations in a new model for non-excitable cells,Cell calcium,17,225-232(1995).
[10]M.Falcke,Reading the patterns in living cells — the physics of Ca~(2+) signaling,Adv.Phys.53,255(2004).
[11]X.P.Sun,N.Callamaras,J.S.Marchant,and I.Parker,A continuum of Ins P_3-mediated elementary Ca2+ signalling events in Xenopus oocytes,J.Physiol.,509(1),67(1998).
[12]J.W.Shuai,and P.Jung,Optimal Intracellular Calcium Signaling,Phys.Rev.Lett.,88,68102(2002).
[13]N.Callamaras,J.S.Marchant,X.P.Sun,and I.Parker,Activation and co-ordination of InsP_3-mediated elementary Ca~(2+) events during global Ca~(2+) signals in Xenopus oocytes, J. Physiol., 509(1), 81-91(1998).
[14] D. Thomas, P. Lipp, M. J. Berridge, and M. D. Bootman, Hormone-evoked elementary Ca~(2+) signals are not stereotypic, but reflect activation of different size channle clusters and variable recruitment of channels within a cluster, J. Biol. Chem.,273(42), 27130-27136(1998).
[15] D.D.Mak,S.Mcbride,V.Raghuram,Y.Yue,S.K.Joseph,and J. K. Foskett,Single-channel properties in endoplasmic reticulum membrane of recombinant type 3 inositol trisphosphate receptor, J. Gen. Physiol., 115, 241-255(2000).
[16] D. D. Mak, and J. K. Foskett, Effects of divalent cations on single-channel conduction properties of Xenopus IP_3 receptor, Am. J. Physiol., 275(Cell. Physiol. 44),C179-C188(1998).
[17] K. R. Porter, A. Claude, and E. F. Fullam, A Study of Tissue Culture Cells by Electron Microscopy: Methods and Preliminary Observations, J. Exp. Med., 81,233-246(1945).
[18] G. Magnus, and J. Keizer, Minimal model of beta-cell mitochondrial Ca~(2+) handling,Am. J. Physiol., 273, C717-C733(1997).
[19] G. Magnus, and J. Keizer, Model of beta-cell mitochondrial calcium handling and electrical activity, I. Cytoplasmic variables, Am. J. Physiol., 274,C1158-C1173(1998).
[20] G. Magnus, and J. Keizer, Model of beta-cell mitochondrial calcium handling and electrical activity, Ⅱ. Mitochondrial variables, Am. J. Physiol., 274,C1174-C1184(1998).
[21] T. E. Gunter, and D. R. Pfeiffer, Mechanisms by which mitochondria transport calcium, Am. J. Physiol., 258, C755-C786(1990).
[22] T. E. Gunter, L. Buntinas, G. Sparagna, R. Eliseev, and K. Gunter, Mitochondrial calcium transport: mechanisms and functions, Cell Calcium, 28(5/6),285-296(2000).
[23] 詹璇,对胰腺β细胞电活性调控机制的研究及其动力学分析,华中师范大学博士学位论文,2007.
[24] R. Sudbrak, J. Brown, C. Dobson-Stone, Simon Carter, et. al., Hailey-Hailey disease is caused by mutations in ATP2C1 encoding a novel Ca~(2+) pump, Hum. Mol. Genet., 9,1131-1140(2000).
[25] 刘洪国,朱广友,赵子琴,阴茎海绵体平滑肌钙信号通路研究进展,中国男科学杂志,19,63-65(2005).
[26] P. Pinton,T.Pozzan,and R.Rizzuto,The Golgi apparatus is an inositol 1,4,5-trisphosphate-sensitive Ca~(2+) store, with functional properties distinct from those of the endoplasmic reticulum, Embo J., 17, 5298-5308(1998).
[27] L. Santella, and E. Carafoli,Calcium signaling in the cell nucleus, FASEB J., 11,1091-1109(1997).
[28] S. Hatta, J. Sakamoto, and Y. Horio, Ion channels and diseases, Med. Electron Microsc., 35, 117-126(2002).
[29] 张宗明,裘法祖,离子通道与疾病,世界华人消化杂志,1:13(5),585-587(2005March).
[30] 高菁华,汤浩,钙通道的分类和几种主要钙通道的功能,日本医学介绍,26(5),232-235(2005).
[31] T. Quinna, M. Molloya, A. Smytha and A. W. Baird, Capacitative calcium entry in guinea pig gallbladder smooth muscle in vitro, Life Sci.,74(13),1659-1669(2004).
[32] F. V. Abeele, L. Lemonnier, S. Th(?)bault, et. al., Two Types of Store-operated Ca~(2+) Channels with Different Activation Modes and Molecular Origin in LNCaP Human Prostate Cancer Epithelial Cells, J. Biol. Chem., 279, 30326-30337(2004).
[33] M. S. Islam, The ryanodine receptor calcium channel of β cells: molecular regulation and physiological significance, Diabetes 51,1299-1308(2002).
[34] C. Franzini-Armstrong, and F. Protasi, Ryanodine receptors of striated muscles: a complex channel capable of multiple interactions,Physiol. Rev.,77,699-729(1997).
[35] J. Tang, Y. Jia, J. Ma, and M. Yi, Numerical study of IP_3-dependent Ca~(2+) spiral waves in xenopus oocytes, Europhys. Lett. 83, 68001(2008).
[36] J. Tang, J. Ma, M. Yi, and Y. Jia, Numerical study of IP_3-induced Ca~(2+) spiral pattern evolution, Chin. Phys. B 2008 accepted.
[37] J. Tang, Y. Jia, J. Ma, and M. Yi, Theoretical study on the drift of Ca~(2+) spiral waves controlled by electric field, Commun. Theor. Phys., 2008 accepted.
[38] C. W. Taylor, P. C. A. da Fonseca, and E. P. Morris, IP_3 receptors: the search for structure, Trends Biochem. Sci., 29, 210-219(2004).
[39] P. C. A. da Fonseca et al., Domain organisation of the type 1 inositol 1,4,5- trisphosphate receptor as revealed by single-particle analysis, Proc.Natl. Acad.Sci. U. S. A.,100,3936-3941(2003).
[40] I. Bosanac, J.R. Alattia, and T.K. Mal, et. al., Structure of the inositol 1,4,5-trisphosphate receptor binding core in complex with its ligand, Nature 420,696-701(2002).
[41] K. Hamada, A. Terauchi, and K. Mikoshiba,Three-dimensional rearrangements within inositol 1,4,5-trisphosphate receptor by calcium, J. Biol. Chem., 278,52881-52889(2003).
[42] I. I. Serysheva, D.J. Bare, and S. J. Ludtke, et. al., Structure of the type 1 inositol 1,4,5-trisphosphate receptor revealed by cryomicroscopy, J. Biol. Chem., 278,21319-21322(2003).
[43] C. D. Ferris, R. L. Huganir, S. Supattapone, and S. H. Snyder, Purified inositol 1,4,5-trisphosphate receptor mediates calcium flux in reconstituted lipid vesicles,Nature(London), 342, 87-89(1989).
[44] T. Meyer, T. Wensel, and L. Stryer, Kinetics of calcium channel opening by inositol 1, 4, 5-trisphosphate, Biochemistry, 29, 32-37(1990).
[45] J. Watras, I. Bezprozvanny and B.E. Ehrlich, Inositol 1,4,5-trisphosphate-gated channels in cerebellum: presence of multiple conductance states, J. Neurosci., 11,3239-3245(1991).
[46] 刘燕平,沈韫芳,韩凤霞,医学细胞生物学,中南大学出版社(2001)
[47] 寿天德,现代生物学导论,中国科学技术大学出版社(1998)
[48] A. Atri, J. Amundson, D. Clapham, and J. Sneyd, A Single-Pool Model for Intracellular Calcium Oscillations and Waves in the Xenopus laevis Oocyte, Biophys. J.,65, 1727-1739(1993).
[49] B. J. Roth, S. V. Yagodin, L. Holtzclaw, and J. T. Russell, A mathematical model of agonist-induced propagation of calcium waves in astrocytes, Cell Calcium, 17,53-64(1995).
[50] J. Sneyd, J. Keizer, and M. J. Sanderson, Mechanisms of calcium oscillations and waves: a quantitative analysis, FASEB J., 9, 1463-1472(1995).
[51] G. W. De Young, and J. Keizer, A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca~(2+) concentration, Proc. Natl. Acad. Sci. USA, 89, 9895(1992).
[52] Y. X. Li, and J. Rinzel, Equations for InsP_3 receptor-mediated [Ca~(2+)]_i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism, J. Theor.Biol. 166, 461-473(1994).
[53] A. Lebeau, D. I. Yule, G. E. Groblewski, and J. Sneyd, Agonistdependent phos-phorylation of the inositol 1,4,5-trisphosphate receptor-a possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells, J. Gen. Physiol.,113,851-871(1999).
[54] J. Sneyd, A. Lebeau, and D. I. Yule, Traveling waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis, Physica D, 145, 158-179(2000).
[55] J. Sneyd, and J. F. Dufour, A dynamic model of the type-2 inositol trisphosphate receptor, Proc.Nat. Acad. Sci. USA, 99(4), 2398-2403(2002).
[56] A. P. Dawson, E. J. A. Lea, and F. Irvine, Kinetic model of the inositol trisphosphate receptor that shows both steady-state and quantal patterns of Ca~(2+) release from intracellular stores, Biochem.J.,370,621-629(2003).
[57] S. Swillens, L. Combettes, and P. Champeil, Transient inositol 1,4,5-trisphosphate-induced Ca~(2+) release: a model based on regulatory Ca_(2+)-binding sites along the permeation pathway, Proc. Nat. Acad. Sci. USA, 91,10074-10078(1994).
[58] R. Somogyi, and J. W. Stucki, Hormone-induced calcium oscillations in liver cells can be explained by a simple one pool model, J. Biol. Chem., 266,11068-11077(1991).
[59] G. Dupont, and A. Goldbeter, One-pool model for Ca~(2+) oscillations involving Ca~(2+) and inositol 1,4,5-trisphosphate as co-agonists for Ca~(2+) release, Cell Calcium, 14,311-322(1993).
[60] J. Sneyd, An introduction to mathematical modeling in physiology, cell biology and immunology, volume 59 of Proceedings of symposia in applied mathematics, AMS short course lecture notes, Chapter, Calcium excitability; the dynamics of calcium oscillations and waves, American Mathematical Society, (2002).
[61] T. A. Rooney, E. J. Sass, and A. P. Thomas, Characterization of cytosolic calcium oscillations induced by phenylephrine and vasopressin in single fura-2-loaded hep- atocytes,J.Biol.Chem.,264,17131-17141(1989).
[62]M.J.Berridge,and A.Galione,Cytosolic calcium oscillators,FASEB J.,2,3074-3082(1988).
[63]A.Goldbeter(ed.),Cell to Cell Signalling:From Experiments to Theoretical Models,Academic Press,London(1989).
[64]A.Goldbeter,G.Dupont,and M.J.Berridge,Minimal model for signal induced Ca~(2+) oscillations and for their frequency encoding through protein phosphorylation,Proc.Nat.Acad.Sci.USA,87,1461-1465(1990).
[65]G.Dupont,and A.Goldbeter,Theoretical insights into the origin of signal induced Ca~(2+) oscillations,449-459.In Goldbeter,(1989).
[66]Y.Tang,and H.G.Othmer,A model of calcium dynamics in cardiac myocytes based on the kinetics of ryanodine—sensitive calcium channels,Biophys.J.,67,2223-42235(1994).
[67]Y.Tang,and J.Stephenson,Calcium dynamics and homeostasis in a mathematical model of the principal cell of the cortical collecting tubule,J.Gen.Physiol.,107,207-230(1996).
[68]Y.Tang,J.Stephenson,and H.Othmer,Simplification and analysis of models of calcium dynamics based on IP~3—sensitive calcium channel kinetics,Biophys.J.,70,246-263(1996).
[69]M.Falcke,J.L.Hudson,P.Camacho,and J.D.Lechleiter,Impact of Mitochondrial Ca~(2+) Cycling on Pattern Formation and Stability,Biophys.J.,77,37-44(1999).
[70]M.Falcke,Y.Li,J.D.Lechleiter,and P.Camacho,Modeling the dependence of the period of intracellular Ca~(2+) waves on SERCA expression,85,1474-1481(2003).
[71]M.Falcke,Deterministic and stochastic models of intracellular Ca~(2+) waves,New J.Phys.,596.1-96.28(2003).
[72]M Falcke,M.Or—Guil,and M.Bar,Dispersion gap and localized spiral waves in a model for intracellular Ca~(2+) dynamics,Phys.Rev.Lett.,84 4753-6(2000).
[73]G.Dupont,and S.Swillens,Quantal Release,Incremental Detection,and Long—Period Ca2+ Oscillations in a Model Based on Regulatory Ca2+-Binding Sites Along the Permeation Pathway,Biophys.J.,71,1714-1722(1996).
[74]G.DuPont,and C.Erneux,Simulations of the effects of inositol 1,4,5—trisphosphate 3-kinase and 5-phosphatase activities on Ca~(2+) oscillations, Cell Calcium, 22(5),321-331(1997).
[75] G. Dupont, L. Combettes, and L. Leybaert, Calcium Dynamics: Spatio-Temporal Organization from the Subcellular to the Organ Level, Int. Rev. Cytol., 261,193(2007).
[76] K. Hirose, S. Kadowski, M. Tanabe, H. Takeshima, and M. Iino, Spatiotemporal dynamics of inositol 1,4,5-trisphosphate that underlies complex mobilization patterns,Science, 284, 1527-1530(1999).
[77] M. Nash, K. Young, R. Challis, and S. Nahorski, Single-cell imaging of graded Ins (1,4,5)P_3 production following G-protein-coupled-receptor activation, Biochem.J. 356, 137-142(2001).
[78] M. Nash, K. Young, R. Challis, and S. Nahorski, Receptor-specific messenger oscillations, Nature, 413, 381-382(2001).
[79] K. Young, M. Nash, R. Challis, and S. Nahorski, Role of Ca~(2+) feedback on single cell inositol 1,4,5-trisphosphate oscillations mediated by G-protein-coupled receptors,J. Biol.Chem., 278, 20753-20760(2003).
[80] C. Erneux, and K. Takazawa, Intracellular control of inositol phosphates by their metabolizing enzymes, Trends Pharnuzcol. Sci., 12, 174-176(1991).
[81] S. Shears, Metabolism of inositol phosphates. Adv. Second Messenger Phosphoprotein Res., 26, 63-90(1992).
[82] A. Hughes, and J. J. Putney, Inositol phosphate formation and its relationship to calcium signaling, Env. Health Perspect., 84, 141-147(1990).
[83] R. Irvine, Inositol lipids in cell signalling, Curr. Opin. Cell Biol. 4, 212-219(1992).
[84] R. Wilcox, and R. Nahorski, Does Ins( 1,3,4,5)P, play a role in Ca~(2+) signaling? In: Liscovitch M. (Ed.) Signal-activated phospholipases, R. G. Landes Co.,189-212(1994).
[85] G. Bird, and J. J. Putney, Effects of inositol 1,3,4,5-tetrakisphosphate on inositol trisphosphate-activated Ca~(2+) signaling in mouse lacrimal acinar cells, J. Biol.Chem., 271, 6766-6770(1996).
[86] K. Choi, H. Kim, S. Lee, et al., Molecular cloning and expression of a complementary DNA for inositol 1,4,5-trisphosphate 3- kinase, Science, 248, 64-66(1990).
[87] K. Takazawa, J. Vandekerckhove, J. E. Dumont, and C. Emeux, Cloning and expression in Escherichia coli of a rat brain cDNA encoding a Ca~(2+)/calmodulin-sensitive inositol 1,4,5-trisphosphate 3-kinase, Biochem. J., 272, 107-112(1990).
[88] K. Takazawa, J. Perret, J. Dumont, and C. Erneux, Molecular cloning and expression of a human brain inositol 1,4,5-trisphosphate 3-kinase. Biochem. Biophys. Res.Commun., 174, 529-535(1991).
[89] K. Takazawa, J. Perret, J. Dumont, and C. Erneux, Molecular cloning and expression of a new putative inositol 1,4,5-trisphosphate 3-kinase, Biochem. J., 261,483-488(1991).
[90] B. Verjans, F. De Smedt, R. Lecocq, V. Vanweyenberg, C. Moreau, and C. Erneux,Cloning and expression in Escherickia coli of a dog thyroid cDNA encoding a novel inositol 1,4,5-phosphate 5-phosphatase, Biochem. J., 300, 85-90(1994).
[91] C. Emeux, M. Lemos, B. Verjans, P. Vanderhaegen, A. Delvaux, and J. E.Dumont, Soluble and particulate Ins-1,4,5-P,/Ins-1,3,4,5-P, 5-phosphatase in bovine brain, Eur. J. Biochem., 181, 317-322(1989).
[92] B. Verjans, R. Lecocq, C. Moreau, and C. Emeux, Purification of bovine brain inositol 1,4,5-trisphosphate 5-phosphatase, Eur. J. Biochem., 204, 1083-1087(1992).
[93] K. Laxminarayan, M. Matzaris, C. Speed, and C. Mitchell, Purification and characterization of a 43-kDa membrane-associated inositol polyphosphate 5-phosphatase from human placenta, J. Biol. Chem., 268, 4968-4974(1993).
[94] E. B. Ridgway, J. C. Gilkey, and L. F. Jaffe, Free calcium increases explosively in activating medaka eggs, Proc. Natl Acad. Sci. USA, 74 623-7(1977).
[95] R. A. Fontanilla, and R. Nuccitelli, Characterization of the sperm-induced calcium wave in Xenopus eggs using confocal microscopy, Biophys. J., 75, 2079-87(1998).
[96] J. D. Lechleiter, L. M. John, and P. Camacho, Ca~(2+) wave dispersion and spiral wave entrainment in Xenopus laevis oocytes overexpressing Ca~(2+) ATPases, J. Biophys.Chem., 72 123-9(1998).
[97] J. D. Lechleiter, S. Girard, E. Peralta, and D. Clapham, Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes, Science, 252, 123-6(1991).
[98] H. M. Nathanson, A. D. Burgstahler, and M. B. Fallon Multistep mechanism of polarized Ca~(2+) wave patterns in hepatocytes, Am. J. Physiol., 267, G338-49(1994).
[99] A. L. Kindzelskii, and H. R. Petty, Intracellular calcium waves accompany neutrophil polarization, formylmethionylleucylphenylalanine stimulation, and phagocytosis: A highspeed microscopy study, J. Immunol., 170, 64-72(2003).
[100] M. H. Nathanson, P. J. Padfield, A. J. (?)sullivan, A. D. Burgstahler, and J. D.Jamieson, Mechansim of Ca~(2+) wave propagation in pancreatic acinar cells, J. Biol.Chem., 267, 18118-18121(1992).
[101] C. H. Orchard , M. R. Mustafa, and K. White, Oscillations and waves of intracellular [Ca~(2+)] in cardiac muscle cells, Chaos Solitons Fractals, 5, 447-58(1995).
[102] M. H. P. Wussling, and H. Salz, Nonlinear propagation of spherical calcium waves in rat cardiac myocytes, Biophys. J., 70, 1144-53(1996).
[103] P (?)ndrea, and F. Vittur, Spatial and temporal Ca~(2+) signalling in articular chondrocytes, Biochem. Biophys. Res. Commun., 75, 129-35(1995).
[104] 施小民,细胞内钙振荡和钙波的生成,演化及其生理响应,上海大学博士学位论文,2003.
[105] L. F. Jaffe, Classes and mechanisms of calcium waves, Cell Calcium,14,736-745(1993).
[106] G. Dupont, and A. Goldbeter, Properties of intracellular Ca~(2+) waves generated by a model based on Ca~(2+)-induced Ca~(2+) release, Biophys. J., 67, 2191-2204(1994).
[107] J. Sneyd, K. Tsaneva-Atanasova, J. I. E. Bruce, S. Straub, D. V. Giovannucci, and D. I. Yule, A model of calcium waves in pancreatic and parotid acinar cells, Biophys. J., 85, 1392-1405(2003).
[108] B. J. Roth, S. V. Yagodin, L. Holtzclaw, and J. T. Russel, A mathematical model of agonist-induced propagation of calcium waves in astrocytes, Cell Calcium, 17,53-64(1995).
[109] T. R. Rooney D. C. Renard, E. J. Sass, and A. P. Thomas, Oscillatory cytosolic calcium waves independent of stimulated inositol 1,4,5-trisphoasphate formation in hepatocytes, J. Biol. Chem., 266(19), 12272-12282(1991).
[110] G. Dupont, S. Swillens, C. Clair, T. Tordjmann, and L. Combettes, Hierarchical organization of clacium signals in hepatocytes: from experiments to models, Biochim.Biophys. Acta, 1498, 134-152(2000).
[111] A.P.Thomas, G.S. Bird, G.Hajnoczky, L. D.Robb-Gaspers,and J.W. Puthey, Spatial and temporal aspects of cellular calcium signaling, FASEB J., 10,1505-1517(1996).
[112] H. M. Nathanson, A. D. Burgstahler, and M. B. Fallon, Multistep mechanism of polarized Ca~(2+) wave patterns in hepatocytes. Am. J. Physiol., 267, G338-G349(1994).
[113] D. R. Giovannucci, J. L. Bruce, S. V. Straub, J. Arreola, J. Sneyd, T. J. Shuttle-worth, and D. I. Yule, Cytosolic Ca~(2+) and Ca~(2+)-activated Ca~(2+) current dynamics:insights from two functionally distinct mouse exocrine cells, J. Physiol., 540(2),469-484(2002).
[114] J. D. Lechleiter, S. Girard, E. Peralta, and D. Clapham, Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes, Science, 252, 123-126(1991).
[115] J. D. Lechleiter, and E. C. David, Molecular Mechanisms of Intracellular Calcium Excitability in X. laevis Oocytes, Cell, 69, 263-294, (1992).
[116] 陆同兴编,非线性物理学概论,中国科学技术大学出版社,2002.
[117] L.Lam,非线性物理学导论,世界图书出版公司,1999.
[118] 王能超,数值分析简明教程,华中科技大学出版社,2002.
[119] 马文淦编著,计算物理学,科学出版社,2005.
[120] J. P. Keener, and J. J. Tyson, Spiral waves in the Belousov-Zhabotinskii reaction,Physica D, 31, 307(1986).
[121] S. Jakubith, H. H. Rotermund, W. Engel, A. V. Oertzen, and G. Ertl, Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence, Phys. Rev. Lett., 65, 3013(1990).
[122] H. H. Rotermund, S. Jakubith, A. V. Oertzen, and G. Ertl, Solitons in a surface reaction, Phys. Rev. Lett., 66, 3083(1991).
[123] K. Krischer, M. Eiswirth, and G. Ertl, Oscillatory CO oxidation on Pt(llO): Modeling of temporal self-organization, J. Chem. Phys., 96, 9161(1992).
[124] J. M. Davidenko, A. M. Pertsov, K. Salomonsz, W. T. Baxter, and J. Jalife, Stationary and drifting spiral waves of excitation in isolated cardiac muscle, Nature,355, 349(1992).
[125] L. Diambra, and N. Guisoni, Modeling stochastic Ca~(2+) release from a cluster of IP_3-sensitive receptors, Cell Calcium, 37, 321(2005).
[126] W. H. Li, J. Llopis, M. Whitney, G. Zlokarnik, and R. Y. Tsien, Cell-permeant caged InsP_3 ester shows that Ca~(2+) spike frequency can optimize gene expression,Nature, 392, 936(1998).
[127] H. Zhang, J. X. Chen, Y. Q. Li, and J. R. Xu, Control of spiral breakup by an alternating advective field, J. Chem. Phys., 125, 204503(2006).
[128] H. J. Yang, and J. Z. Yang, Spiral waves in linearly coupled reaction-diffusion systems, Phys. Rev. E, 76, 016206(2007).
[129] G. Li, Q. Ouyang, V. Petrov, and H. L. Swinney, Transition from Simple Rotating Chemical Spirals to Meandering and Traveling Spirals, Phys. Rev. Lett., 772105(1996).
[130] V. S. Zykov, and H. Engel, Resonance attractors of spiral waves in excitable media under global feedback, Phys. Rev. E, 66, 016206(2002).
[131] M. Pollmann, M. Bertram, and H. H. Rotermund, Influence of time delayed global feedback on pattern formation in oscillatory CO oxidation on Pt(110),Chem.Phys.Lett.,346, 123(2001).
[132] V. S. Zykov, A. S. Mikhailov, and S. C. M(?)ller, Controlling Spiral Waves in Confined Geometries by Global Feedback, Phys. Rev. Lett., 78, 3398(1997).
[133] S. Alnonso, F. Sagues, and A. S. Mikhailov, Taming Winfree Turbulence of Scroll Waves in Excitable Media, Science, 299, 1722(2003).
[134] J. Ma, Y. L. Li, and J. L. Jiang, et. al., Evolution of spiral waves subjected to parameter modulation under chaotic signal, Phys. A, 369, 387(2006).
[135] P. Y. Wang, and P. Xie, Eliminating spatiotemporal chaos and spiral waves by weak spatial perturbations, Phys. Rev. E, 61, 5120(2000).
[136] H. Zhang, B. B. Hu, and G. Hu, Suppression of spiral waves and spatiotemporal chaos by generating target waves in excitable media, Phys. Rev. E, 68, 026134(2003).
[137] H. Zhang, Z. J. Cao, and N. J. Wu, et. al., Suppress Winfree Turbulence by Local Forcing Excitable Systems, Phys. Rev. Lett., 94, 188301(2005).
[138] J. I. Ramos, Dynamics of spiral waves in excitable media with local time-periodic modulation, Chaos, Solitons Fractals, 13(7), 1383(2002)
[139] J. Ma, C. N. Wang, and Y. L. Li, et. al., Suppression of spiral waves in light-sensitive media using chaotic signal modulated scheme, Chaos, Solitons Fractals, 33(3) 965(2007).
[140] J. Ma, H. P. Ying, and Z. S. Pu, An Anti-Control Scheme for Spiral under Lorenz Chaotic Signals, Chin. Phys. Lett., 22, (1065)2005.
[141] J. Ma, H. P. Ying, and Y. L. Li, Suppression of spiral waves using intermittent local electric shock, Chin. Phys., 16(4), 955(2007).
[142] P. Y. Wang, P. Xie, and H. W. Yin, Control of spiral waves and turbulent states in a cardiac model by travelling-wave perturbations, Chin. Phys., 12, (674)2003.
[143] H. Zhang, B. Hu, G. Hu, and J. Xiao, Drift velocity of rotating spiral w aves in the weak deformation approximation, J. Chem. Phys. 119, (2003)4468.
[144] O. Steinbock, J. Schutze, S. C. Muller, Electric-field-induced drift and deformation of spiral waves in an excitable medium, Phys. Rev. Lett. 68, (1992)248.
[145] J. X. Chen, H. Zhang, Y. Q. Li, Drift of spiral waves controlled by a polarized electric field, J. Chem. Phys. 124, (2006)014505.
[146] A. P. Munuzuri, M. Gomez-Gesteira, V. Perez-Munuzuri, V. I. Krinsky, V. Perez-Villar, Parametric resonance of a vortex in an active medium, Phys. Rev. E, 50,(1994)4258.
[147] A.E.Bugrim,A.M.Zhabotinsky,and I. R. Epstein, Biophys. J.73,2897-2906(1997).
[148] P. Thorn, R. Moreton, and M. Berridge, Multiple, coordinated Ca~(2+)-release events underlie the inositol-trisphosphate-induced local Ca~(2+) spikes in mouse pancreatic acinar cells, EMBO J.,15,999-1003(1996).
[149] R. Kupferman, P. P. Mitra, P. C. Hohenberg, and S. S. Wang, Analytical calculation of intracellular calcium wave characteristics, Biophys. J., 72, 2430-2444(1997).
[150] J. Sneyd, P. D. Dale, and A. Duffy, Traveling waves in buffered systems: Applications to calcium waves, SIAM J. Appl. Math., 58, 1178-1192(1998).
[151] I. Parker, and Y. Yao, Regenerative release of calcium from functionally discrete subcellular stores by inositol trisphosphate, Proc.R. Soc.Lond. B., 246, 269-274(1991)
[152] Y. Yao, J. Choi, and I. Parker, Quantal puffs of intracellular Ca~(2+) evoked by inositol trisphosphate in Xenopus oocytes, J. PhysioL.(Lond.), 482, 533-553(1995);
[153] I. Parker, and Y. Yao, Ca~(2+) transients associated with openings of inositol trisphosphate-gated channels in Xenopus oocytes, J. Physiol.(Lond.), 491,663-668(1996).
[154] J. Marchant, N. Callamaras, and I. Parker, Initiation of IP_3-mediated Ca~(2+) waves in Xenopus oocytes, EMBO J., 18(19), 5285-5299(1999).
[155] M. Bootman, E. Niggli, M. Berridge, and P. Lipp, Imaging the hierarchical Ca~(2+) signalling in HeLa cells, J. Physiol., 499(2), 307-314(1997).
[156] O. H. Petersen, Local calcium spiking in pancreatic acinar cells, In Calcium Waves,Gradients and Oscillations. G. R. Bock and K. Ackrill, editors, Wiley, Chichester,England, 85-103(1995).
[157] S. Yagodin, L. A. Holtzclaw, and J. T. Russell, Mol. Cell. Biochem. 149/150,137-144(1995);
[158] S. Yagodin, L. A. Holtzclaw, C. A. Sheppard, and J. T. Russell, J. Neurobiol. 25,265-280(1994).
[159] J. W. Shuai, and P. Jung, Sub-threshold Ca~(2+) waves, New J. Phys. 5,132.1-132.20(2003).
[160] J. W.Shuai, and P.Jung,Stochastic Properties of Ca~(2+) Release of Inositol 1,4,5-Trisphosphate Receptor Clusters, Biophys. J., 83, 87(2002).
[161] G. Dupont, Theoretical insights into the mechanism of spiral Ca~(2+) wave initiation in Xenopus oocytes, Am. J. Physiol., 275(Cell Physiol. 44), C317-C322(1998).
[2]R.E.Dolmetsch,K.Xu,and R.S.Lewis,Calcium oscillations increase the efficiency and specificity of gene expression,Nature,392,933(1998).
[3]V.A.Golovina,and M.P.Blaustein,Spatially and Functionally Distinct Ca~(2+) Stores in Sarcoplasmic and Endoplasmic Reticulum,Science,275,1643(1997).
[4]A.H.Cornell-Bell,S.M.Finkbeiner,M.S.Cooper,and S.J.Smith,Glutamate induces calcium waves in cultured astrocytes:long-range glial signaling,Science,247,470(1990).
[5]C.A.Swanson,A.P.Arkin,and J.Ross,An endogenous calcium oscillator may control early embryonic division,Proc.Natl.Acad.Sci.,94,1194(1997).
[6]G.Majno,and I.Joris,Apoptosis,oncosis,and necrosis.An overview of cell death,Am.J.Pathol.,146,3(1995).
[7]R.Jacob,J.E.Merritt,T.J.Hallam,and T.R.Rink,Repetitive spikes in cytoplasmic calcium evoked by histamine in human endothelial cells,Nature,335,40-45(1988).
[8]T.Capiod,J.Noel,L.Combettes,and M.Claret,Cyclic AMP-evoked oscillations of intracellular[Ca~(2+)]in guinea-pig hepatocytes,Biochem.J.,275,277—280(1991).
[9]P.Shen,and R.Larter,Chaos in intracellular Ca~(2+) oscillations in a new model for non-excitable cells,Cell calcium,17,225-232(1995).
[10]M.Falcke,Reading the patterns in living cells — the physics of Ca~(2+) signaling,Adv.Phys.53,255(2004).
[11]X.P.Sun,N.Callamaras,J.S.Marchant,and I.Parker,A continuum of Ins P_3-mediated elementary Ca2+ signalling events in Xenopus oocytes,J.Physiol.,509(1),67(1998).
[12]J.W.Shuai,and P.Jung,Optimal Intracellular Calcium Signaling,Phys.Rev.Lett.,88,68102(2002).
[13]N.Callamaras,J.S.Marchant,X.P.Sun,and I.Parker,Activation and co-ordination of InsP_3-mediated elementary Ca~(2+) events during global Ca~(2+) signals in Xenopus oocytes, J. Physiol., 509(1), 81-91(1998).
[14] D. Thomas, P. Lipp, M. J. Berridge, and M. D. Bootman, Hormone-evoked elementary Ca~(2+) signals are not stereotypic, but reflect activation of different size channle clusters and variable recruitment of channels within a cluster, J. Biol. Chem.,273(42), 27130-27136(1998).
[15] D.D.Mak,S.Mcbride,V.Raghuram,Y.Yue,S.K.Joseph,and J. K. Foskett,Single-channel properties in endoplasmic reticulum membrane of recombinant type 3 inositol trisphosphate receptor, J. Gen. Physiol., 115, 241-255(2000).
[16] D. D. Mak, and J. K. Foskett, Effects of divalent cations on single-channel conduction properties of Xenopus IP_3 receptor, Am. J. Physiol., 275(Cell. Physiol. 44),C179-C188(1998).
[17] K. R. Porter, A. Claude, and E. F. Fullam, A Study of Tissue Culture Cells by Electron Microscopy: Methods and Preliminary Observations, J. Exp. Med., 81,233-246(1945).
[18] G. Magnus, and J. Keizer, Minimal model of beta-cell mitochondrial Ca~(2+) handling,Am. J. Physiol., 273, C717-C733(1997).
[19] G. Magnus, and J. Keizer, Model of beta-cell mitochondrial calcium handling and electrical activity, I. Cytoplasmic variables, Am. J. Physiol., 274,C1158-C1173(1998).
[20] G. Magnus, and J. Keizer, Model of beta-cell mitochondrial calcium handling and electrical activity, Ⅱ. Mitochondrial variables, Am. J. Physiol., 274,C1174-C1184(1998).
[21] T. E. Gunter, and D. R. Pfeiffer, Mechanisms by which mitochondria transport calcium, Am. J. Physiol., 258, C755-C786(1990).
[22] T. E. Gunter, L. Buntinas, G. Sparagna, R. Eliseev, and K. Gunter, Mitochondrial calcium transport: mechanisms and functions, Cell Calcium, 28(5/6),285-296(2000).
[23] 詹璇,对胰腺β细胞电活性调控机制的研究及其动力学分析,华中师范大学博士学位论文,2007.
[24] R. Sudbrak, J. Brown, C. Dobson-Stone, Simon Carter, et. al., Hailey-Hailey disease is caused by mutations in ATP2C1 encoding a novel Ca~(2+) pump, Hum. Mol. Genet., 9,1131-1140(2000).
[25] 刘洪国,朱广友,赵子琴,阴茎海绵体平滑肌钙信号通路研究进展,中国男科学杂志,19,63-65(2005).
[26] P. Pinton,T.Pozzan,and R.Rizzuto,The Golgi apparatus is an inositol 1,4,5-trisphosphate-sensitive Ca~(2+) store, with functional properties distinct from those of the endoplasmic reticulum, Embo J., 17, 5298-5308(1998).
[27] L. Santella, and E. Carafoli,Calcium signaling in the cell nucleus, FASEB J., 11,1091-1109(1997).
[28] S. Hatta, J. Sakamoto, and Y. Horio, Ion channels and diseases, Med. Electron Microsc., 35, 117-126(2002).
[29] 张宗明,裘法祖,离子通道与疾病,世界华人消化杂志,1:13(5),585-587(2005March).
[30] 高菁华,汤浩,钙通道的分类和几种主要钙通道的功能,日本医学介绍,26(5),232-235(2005).
[31] T. Quinna, M. Molloya, A. Smytha and A. W. Baird, Capacitative calcium entry in guinea pig gallbladder smooth muscle in vitro, Life Sci.,74(13),1659-1669(2004).
[32] F. V. Abeele, L. Lemonnier, S. Th(?)bault, et. al., Two Types of Store-operated Ca~(2+) Channels with Different Activation Modes and Molecular Origin in LNCaP Human Prostate Cancer Epithelial Cells, J. Biol. Chem., 279, 30326-30337(2004).
[33] M. S. Islam, The ryanodine receptor calcium channel of β cells: molecular regulation and physiological significance, Diabetes 51,1299-1308(2002).
[34] C. Franzini-Armstrong, and F. Protasi, Ryanodine receptors of striated muscles: a complex channel capable of multiple interactions,Physiol. Rev.,77,699-729(1997).
[35] J. Tang, Y. Jia, J. Ma, and M. Yi, Numerical study of IP_3-dependent Ca~(2+) spiral waves in xenopus oocytes, Europhys. Lett. 83, 68001(2008).
[36] J. Tang, J. Ma, M. Yi, and Y. Jia, Numerical study of IP_3-induced Ca~(2+) spiral pattern evolution, Chin. Phys. B 2008 accepted.
[37] J. Tang, Y. Jia, J. Ma, and M. Yi, Theoretical study on the drift of Ca~(2+) spiral waves controlled by electric field, Commun. Theor. Phys., 2008 accepted.
[38] C. W. Taylor, P. C. A. da Fonseca, and E. P. Morris, IP_3 receptors: the search for structure, Trends Biochem. Sci., 29, 210-219(2004).
[39] P. C. A. da Fonseca et al., Domain organisation of the type 1 inositol 1,4,5- trisphosphate receptor as revealed by single-particle analysis, Proc.Natl. Acad.Sci. U. S. A.,100,3936-3941(2003).
[40] I. Bosanac, J.R. Alattia, and T.K. Mal, et. al., Structure of the inositol 1,4,5-trisphosphate receptor binding core in complex with its ligand, Nature 420,696-701(2002).
[41] K. Hamada, A. Terauchi, and K. Mikoshiba,Three-dimensional rearrangements within inositol 1,4,5-trisphosphate receptor by calcium, J. Biol. Chem., 278,52881-52889(2003).
[42] I. I. Serysheva, D.J. Bare, and S. J. Ludtke, et. al., Structure of the type 1 inositol 1,4,5-trisphosphate receptor revealed by cryomicroscopy, J. Biol. Chem., 278,21319-21322(2003).
[43] C. D. Ferris, R. L. Huganir, S. Supattapone, and S. H. Snyder, Purified inositol 1,4,5-trisphosphate receptor mediates calcium flux in reconstituted lipid vesicles,Nature(London), 342, 87-89(1989).
[44] T. Meyer, T. Wensel, and L. Stryer, Kinetics of calcium channel opening by inositol 1, 4, 5-trisphosphate, Biochemistry, 29, 32-37(1990).
[45] J. Watras, I. Bezprozvanny and B.E. Ehrlich, Inositol 1,4,5-trisphosphate-gated channels in cerebellum: presence of multiple conductance states, J. Neurosci., 11,3239-3245(1991).
[46] 刘燕平,沈韫芳,韩凤霞,医学细胞生物学,中南大学出版社(2001)
[47] 寿天德,现代生物学导论,中国科学技术大学出版社(1998)
[48] A. Atri, J. Amundson, D. Clapham, and J. Sneyd, A Single-Pool Model for Intracellular Calcium Oscillations and Waves in the Xenopus laevis Oocyte, Biophys. J.,65, 1727-1739(1993).
[49] B. J. Roth, S. V. Yagodin, L. Holtzclaw, and J. T. Russell, A mathematical model of agonist-induced propagation of calcium waves in astrocytes, Cell Calcium, 17,53-64(1995).
[50] J. Sneyd, J. Keizer, and M. J. Sanderson, Mechanisms of calcium oscillations and waves: a quantitative analysis, FASEB J., 9, 1463-1472(1995).
[51] G. W. De Young, and J. Keizer, A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca~(2+) concentration, Proc. Natl. Acad. Sci. USA, 89, 9895(1992).
[52] Y. X. Li, and J. Rinzel, Equations for InsP_3 receptor-mediated [Ca~(2+)]_i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism, J. Theor.Biol. 166, 461-473(1994).
[53] A. Lebeau, D. I. Yule, G. E. Groblewski, and J. Sneyd, Agonistdependent phos-phorylation of the inositol 1,4,5-trisphosphate receptor-a possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells, J. Gen. Physiol.,113,851-871(1999).
[54] J. Sneyd, A. Lebeau, and D. I. Yule, Traveling waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis, Physica D, 145, 158-179(2000).
[55] J. Sneyd, and J. F. Dufour, A dynamic model of the type-2 inositol trisphosphate receptor, Proc.Nat. Acad. Sci. USA, 99(4), 2398-2403(2002).
[56] A. P. Dawson, E. J. A. Lea, and F. Irvine, Kinetic model of the inositol trisphosphate receptor that shows both steady-state and quantal patterns of Ca~(2+) release from intracellular stores, Biochem.J.,370,621-629(2003).
[57] S. Swillens, L. Combettes, and P. Champeil, Transient inositol 1,4,5-trisphosphate-induced Ca~(2+) release: a model based on regulatory Ca_(2+)-binding sites along the permeation pathway, Proc. Nat. Acad. Sci. USA, 91,10074-10078(1994).
[58] R. Somogyi, and J. W. Stucki, Hormone-induced calcium oscillations in liver cells can be explained by a simple one pool model, J. Biol. Chem., 266,11068-11077(1991).
[59] G. Dupont, and A. Goldbeter, One-pool model for Ca~(2+) oscillations involving Ca~(2+) and inositol 1,4,5-trisphosphate as co-agonists for Ca~(2+) release, Cell Calcium, 14,311-322(1993).
[60] J. Sneyd, An introduction to mathematical modeling in physiology, cell biology and immunology, volume 59 of Proceedings of symposia in applied mathematics, AMS short course lecture notes, Chapter, Calcium excitability; the dynamics of calcium oscillations and waves, American Mathematical Society, (2002).
[61] T. A. Rooney, E. J. Sass, and A. P. Thomas, Characterization of cytosolic calcium oscillations induced by phenylephrine and vasopressin in single fura-2-loaded hep- atocytes,J.Biol.Chem.,264,17131-17141(1989).
[62]M.J.Berridge,and A.Galione,Cytosolic calcium oscillators,FASEB J.,2,3074-3082(1988).
[63]A.Goldbeter(ed.),Cell to Cell Signalling:From Experiments to Theoretical Models,Academic Press,London(1989).
[64]A.Goldbeter,G.Dupont,and M.J.Berridge,Minimal model for signal induced Ca~(2+) oscillations and for their frequency encoding through protein phosphorylation,Proc.Nat.Acad.Sci.USA,87,1461-1465(1990).
[65]G.Dupont,and A.Goldbeter,Theoretical insights into the origin of signal induced Ca~(2+) oscillations,449-459.In Goldbeter,(1989).
[66]Y.Tang,and H.G.Othmer,A model of calcium dynamics in cardiac myocytes based on the kinetics of ryanodine—sensitive calcium channels,Biophys.J.,67,2223-42235(1994).
[67]Y.Tang,and J.Stephenson,Calcium dynamics and homeostasis in a mathematical model of the principal cell of the cortical collecting tubule,J.Gen.Physiol.,107,207-230(1996).
[68]Y.Tang,J.Stephenson,and H.Othmer,Simplification and analysis of models of calcium dynamics based on IP~3—sensitive calcium channel kinetics,Biophys.J.,70,246-263(1996).
[69]M.Falcke,J.L.Hudson,P.Camacho,and J.D.Lechleiter,Impact of Mitochondrial Ca~(2+) Cycling on Pattern Formation and Stability,Biophys.J.,77,37-44(1999).
[70]M.Falcke,Y.Li,J.D.Lechleiter,and P.Camacho,Modeling the dependence of the period of intracellular Ca~(2+) waves on SERCA expression,85,1474-1481(2003).
[71]M.Falcke,Deterministic and stochastic models of intracellular Ca~(2+) waves,New J.Phys.,596.1-96.28(2003).
[72]M Falcke,M.Or—Guil,and M.Bar,Dispersion gap and localized spiral waves in a model for intracellular Ca~(2+) dynamics,Phys.Rev.Lett.,84 4753-6(2000).
[73]G.Dupont,and S.Swillens,Quantal Release,Incremental Detection,and Long—Period Ca2+ Oscillations in a Model Based on Regulatory Ca2+-Binding Sites Along the Permeation Pathway,Biophys.J.,71,1714-1722(1996).
[74]G.DuPont,and C.Erneux,Simulations of the effects of inositol 1,4,5—trisphosphate 3-kinase and 5-phosphatase activities on Ca~(2+) oscillations, Cell Calcium, 22(5),321-331(1997).
[75] G. Dupont, L. Combettes, and L. Leybaert, Calcium Dynamics: Spatio-Temporal Organization from the Subcellular to the Organ Level, Int. Rev. Cytol., 261,193(2007).
[76] K. Hirose, S. Kadowski, M. Tanabe, H. Takeshima, and M. Iino, Spatiotemporal dynamics of inositol 1,4,5-trisphosphate that underlies complex mobilization patterns,Science, 284, 1527-1530(1999).
[77] M. Nash, K. Young, R. Challis, and S. Nahorski, Single-cell imaging of graded Ins (1,4,5)P_3 production following G-protein-coupled-receptor activation, Biochem.J. 356, 137-142(2001).
[78] M. Nash, K. Young, R. Challis, and S. Nahorski, Receptor-specific messenger oscillations, Nature, 413, 381-382(2001).
[79] K. Young, M. Nash, R. Challis, and S. Nahorski, Role of Ca~(2+) feedback on single cell inositol 1,4,5-trisphosphate oscillations mediated by G-protein-coupled receptors,J. Biol.Chem., 278, 20753-20760(2003).
[80] C. Erneux, and K. Takazawa, Intracellular control of inositol phosphates by their metabolizing enzymes, Trends Pharnuzcol. Sci., 12, 174-176(1991).
[81] S. Shears, Metabolism of inositol phosphates. Adv. Second Messenger Phosphoprotein Res., 26, 63-90(1992).
[82] A. Hughes, and J. J. Putney, Inositol phosphate formation and its relationship to calcium signaling, Env. Health Perspect., 84, 141-147(1990).
[83] R. Irvine, Inositol lipids in cell signalling, Curr. Opin. Cell Biol. 4, 212-219(1992).
[84] R. Wilcox, and R. Nahorski, Does Ins( 1,3,4,5)P, play a role in Ca~(2+) signaling? In: Liscovitch M. (Ed.) Signal-activated phospholipases, R. G. Landes Co.,189-212(1994).
[85] G. Bird, and J. J. Putney, Effects of inositol 1,3,4,5-tetrakisphosphate on inositol trisphosphate-activated Ca~(2+) signaling in mouse lacrimal acinar cells, J. Biol.Chem., 271, 6766-6770(1996).
[86] K. Choi, H. Kim, S. Lee, et al., Molecular cloning and expression of a complementary DNA for inositol 1,4,5-trisphosphate 3- kinase, Science, 248, 64-66(1990).
[87] K. Takazawa, J. Vandekerckhove, J. E. Dumont, and C. Emeux, Cloning and expression in Escherichia coli of a rat brain cDNA encoding a Ca~(2+)/calmodulin-sensitive inositol 1,4,5-trisphosphate 3-kinase, Biochem. J., 272, 107-112(1990).
[88] K. Takazawa, J. Perret, J. Dumont, and C. Erneux, Molecular cloning and expression of a human brain inositol 1,4,5-trisphosphate 3-kinase. Biochem. Biophys. Res.Commun., 174, 529-535(1991).
[89] K. Takazawa, J. Perret, J. Dumont, and C. Erneux, Molecular cloning and expression of a new putative inositol 1,4,5-trisphosphate 3-kinase, Biochem. J., 261,483-488(1991).
[90] B. Verjans, F. De Smedt, R. Lecocq, V. Vanweyenberg, C. Moreau, and C. Erneux,Cloning and expression in Escherickia coli of a dog thyroid cDNA encoding a novel inositol 1,4,5-phosphate 5-phosphatase, Biochem. J., 300, 85-90(1994).
[91] C. Emeux, M. Lemos, B. Verjans, P. Vanderhaegen, A. Delvaux, and J. E.Dumont, Soluble and particulate Ins-1,4,5-P,/Ins-1,3,4,5-P, 5-phosphatase in bovine brain, Eur. J. Biochem., 181, 317-322(1989).
[92] B. Verjans, R. Lecocq, C. Moreau, and C. Emeux, Purification of bovine brain inositol 1,4,5-trisphosphate 5-phosphatase, Eur. J. Biochem., 204, 1083-1087(1992).
[93] K. Laxminarayan, M. Matzaris, C. Speed, and C. Mitchell, Purification and characterization of a 43-kDa membrane-associated inositol polyphosphate 5-phosphatase from human placenta, J. Biol. Chem., 268, 4968-4974(1993).
[94] E. B. Ridgway, J. C. Gilkey, and L. F. Jaffe, Free calcium increases explosively in activating medaka eggs, Proc. Natl Acad. Sci. USA, 74 623-7(1977).
[95] R. A. Fontanilla, and R. Nuccitelli, Characterization of the sperm-induced calcium wave in Xenopus eggs using confocal microscopy, Biophys. J., 75, 2079-87(1998).
[96] J. D. Lechleiter, L. M. John, and P. Camacho, Ca~(2+) wave dispersion and spiral wave entrainment in Xenopus laevis oocytes overexpressing Ca~(2+) ATPases, J. Biophys.Chem., 72 123-9(1998).
[97] J. D. Lechleiter, S. Girard, E. Peralta, and D. Clapham, Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes, Science, 252, 123-6(1991).
[98] H. M. Nathanson, A. D. Burgstahler, and M. B. Fallon Multistep mechanism of polarized Ca~(2+) wave patterns in hepatocytes, Am. J. Physiol., 267, G338-49(1994).
[99] A. L. Kindzelskii, and H. R. Petty, Intracellular calcium waves accompany neutrophil polarization, formylmethionylleucylphenylalanine stimulation, and phagocytosis: A highspeed microscopy study, J. Immunol., 170, 64-72(2003).
[100] M. H. Nathanson, P. J. Padfield, A. J. (?)sullivan, A. D. Burgstahler, and J. D.Jamieson, Mechansim of Ca~(2+) wave propagation in pancreatic acinar cells, J. Biol.Chem., 267, 18118-18121(1992).
[101] C. H. Orchard , M. R. Mustafa, and K. White, Oscillations and waves of intracellular [Ca~(2+)] in cardiac muscle cells, Chaos Solitons Fractals, 5, 447-58(1995).
[102] M. H. P. Wussling, and H. Salz, Nonlinear propagation of spherical calcium waves in rat cardiac myocytes, Biophys. J., 70, 1144-53(1996).
[103] P (?)ndrea, and F. Vittur, Spatial and temporal Ca~(2+) signalling in articular chondrocytes, Biochem. Biophys. Res. Commun., 75, 129-35(1995).
[104] 施小民,细胞内钙振荡和钙波的生成,演化及其生理响应,上海大学博士学位论文,2003.
[105] L. F. Jaffe, Classes and mechanisms of calcium waves, Cell Calcium,14,736-745(1993).
[106] G. Dupont, and A. Goldbeter, Properties of intracellular Ca~(2+) waves generated by a model based on Ca~(2+)-induced Ca~(2+) release, Biophys. J., 67, 2191-2204(1994).
[107] J. Sneyd, K. Tsaneva-Atanasova, J. I. E. Bruce, S. Straub, D. V. Giovannucci, and D. I. Yule, A model of calcium waves in pancreatic and parotid acinar cells, Biophys. J., 85, 1392-1405(2003).
[108] B. J. Roth, S. V. Yagodin, L. Holtzclaw, and J. T. Russel, A mathematical model of agonist-induced propagation of calcium waves in astrocytes, Cell Calcium, 17,53-64(1995).
[109] T. R. Rooney D. C. Renard, E. J. Sass, and A. P. Thomas, Oscillatory cytosolic calcium waves independent of stimulated inositol 1,4,5-trisphoasphate formation in hepatocytes, J. Biol. Chem., 266(19), 12272-12282(1991).
[110] G. Dupont, S. Swillens, C. Clair, T. Tordjmann, and L. Combettes, Hierarchical organization of clacium signals in hepatocytes: from experiments to models, Biochim.Biophys. Acta, 1498, 134-152(2000).
[111] A.P.Thomas, G.S. Bird, G.Hajnoczky, L. D.Robb-Gaspers,and J.W. Puthey, Spatial and temporal aspects of cellular calcium signaling, FASEB J., 10,1505-1517(1996).
[112] H. M. Nathanson, A. D. Burgstahler, and M. B. Fallon, Multistep mechanism of polarized Ca~(2+) wave patterns in hepatocytes. Am. J. Physiol., 267, G338-G349(1994).
[113] D. R. Giovannucci, J. L. Bruce, S. V. Straub, J. Arreola, J. Sneyd, T. J. Shuttle-worth, and D. I. Yule, Cytosolic Ca~(2+) and Ca~(2+)-activated Ca~(2+) current dynamics:insights from two functionally distinct mouse exocrine cells, J. Physiol., 540(2),469-484(2002).
[114] J. D. Lechleiter, S. Girard, E. Peralta, and D. Clapham, Spiral calcium wave propagation and annihilation in Xenopus laevis oocytes, Science, 252, 123-126(1991).
[115] J. D. Lechleiter, and E. C. David, Molecular Mechanisms of Intracellular Calcium Excitability in X. laevis Oocytes, Cell, 69, 263-294, (1992).
[116] 陆同兴编,非线性物理学概论,中国科学技术大学出版社,2002.
[117] L.Lam,非线性物理学导论,世界图书出版公司,1999.
[118] 王能超,数值分析简明教程,华中科技大学出版社,2002.
[119] 马文淦编著,计算物理学,科学出版社,2005.
[120] J. P. Keener, and J. J. Tyson, Spiral waves in the Belousov-Zhabotinskii reaction,Physica D, 31, 307(1986).
[121] S. Jakubith, H. H. Rotermund, W. Engel, A. V. Oertzen, and G. Ertl, Spatiotemporal concentration patterns in a surface reaction: Propagating and standing waves, rotating spirals, and turbulence, Phys. Rev. Lett., 65, 3013(1990).
[122] H. H. Rotermund, S. Jakubith, A. V. Oertzen, and G. Ertl, Solitons in a surface reaction, Phys. Rev. Lett., 66, 3083(1991).
[123] K. Krischer, M. Eiswirth, and G. Ertl, Oscillatory CO oxidation on Pt(llO): Modeling of temporal self-organization, J. Chem. Phys., 96, 9161(1992).
[124] J. M. Davidenko, A. M. Pertsov, K. Salomonsz, W. T. Baxter, and J. Jalife, Stationary and drifting spiral waves of excitation in isolated cardiac muscle, Nature,355, 349(1992).
[125] L. Diambra, and N. Guisoni, Modeling stochastic Ca~(2+) release from a cluster of IP_3-sensitive receptors, Cell Calcium, 37, 321(2005).
[126] W. H. Li, J. Llopis, M. Whitney, G. Zlokarnik, and R. Y. Tsien, Cell-permeant caged InsP_3 ester shows that Ca~(2+) spike frequency can optimize gene expression,Nature, 392, 936(1998).
[127] H. Zhang, J. X. Chen, Y. Q. Li, and J. R. Xu, Control of spiral breakup by an alternating advective field, J. Chem. Phys., 125, 204503(2006).
[128] H. J. Yang, and J. Z. Yang, Spiral waves in linearly coupled reaction-diffusion systems, Phys. Rev. E, 76, 016206(2007).
[129] G. Li, Q. Ouyang, V. Petrov, and H. L. Swinney, Transition from Simple Rotating Chemical Spirals to Meandering and Traveling Spirals, Phys. Rev. Lett., 772105(1996).
[130] V. S. Zykov, and H. Engel, Resonance attractors of spiral waves in excitable media under global feedback, Phys. Rev. E, 66, 016206(2002).
[131] M. Pollmann, M. Bertram, and H. H. Rotermund, Influence of time delayed global feedback on pattern formation in oscillatory CO oxidation on Pt(110),Chem.Phys.Lett.,346, 123(2001).
[132] V. S. Zykov, A. S. Mikhailov, and S. C. M(?)ller, Controlling Spiral Waves in Confined Geometries by Global Feedback, Phys. Rev. Lett., 78, 3398(1997).
[133] S. Alnonso, F. Sagues, and A. S. Mikhailov, Taming Winfree Turbulence of Scroll Waves in Excitable Media, Science, 299, 1722(2003).
[134] J. Ma, Y. L. Li, and J. L. Jiang, et. al., Evolution of spiral waves subjected to parameter modulation under chaotic signal, Phys. A, 369, 387(2006).
[135] P. Y. Wang, and P. Xie, Eliminating spatiotemporal chaos and spiral waves by weak spatial perturbations, Phys. Rev. E, 61, 5120(2000).
[136] H. Zhang, B. B. Hu, and G. Hu, Suppression of spiral waves and spatiotemporal chaos by generating target waves in excitable media, Phys. Rev. E, 68, 026134(2003).
[137] H. Zhang, Z. J. Cao, and N. J. Wu, et. al., Suppress Winfree Turbulence by Local Forcing Excitable Systems, Phys. Rev. Lett., 94, 188301(2005).
[138] J. I. Ramos, Dynamics of spiral waves in excitable media with local time-periodic modulation, Chaos, Solitons Fractals, 13(7), 1383(2002)
[139] J. Ma, C. N. Wang, and Y. L. Li, et. al., Suppression of spiral waves in light-sensitive media using chaotic signal modulated scheme, Chaos, Solitons Fractals, 33(3) 965(2007).
[140] J. Ma, H. P. Ying, and Z. S. Pu, An Anti-Control Scheme for Spiral under Lorenz Chaotic Signals, Chin. Phys. Lett., 22, (1065)2005.
[141] J. Ma, H. P. Ying, and Y. L. Li, Suppression of spiral waves using intermittent local electric shock, Chin. Phys., 16(4), 955(2007).
[142] P. Y. Wang, P. Xie, and H. W. Yin, Control of spiral waves and turbulent states in a cardiac model by travelling-wave perturbations, Chin. Phys., 12, (674)2003.
[143] H. Zhang, B. Hu, G. Hu, and J. Xiao, Drift velocity of rotating spiral w aves in the weak deformation approximation, J. Chem. Phys. 119, (2003)4468.
[144] O. Steinbock, J. Schutze, S. C. Muller, Electric-field-induced drift and deformation of spiral waves in an excitable medium, Phys. Rev. Lett. 68, (1992)248.
[145] J. X. Chen, H. Zhang, Y. Q. Li, Drift of spiral waves controlled by a polarized electric field, J. Chem. Phys. 124, (2006)014505.
[146] A. P. Munuzuri, M. Gomez-Gesteira, V. Perez-Munuzuri, V. I. Krinsky, V. Perez-Villar, Parametric resonance of a vortex in an active medium, Phys. Rev. E, 50,(1994)4258.
[147] A.E.Bugrim,A.M.Zhabotinsky,and I. R. Epstein, Biophys. J.73,2897-2906(1997).
[148] P. Thorn, R. Moreton, and M. Berridge, Multiple, coordinated Ca~(2+)-release events underlie the inositol-trisphosphate-induced local Ca~(2+) spikes in mouse pancreatic acinar cells, EMBO J.,15,999-1003(1996).
[149] R. Kupferman, P. P. Mitra, P. C. Hohenberg, and S. S. Wang, Analytical calculation of intracellular calcium wave characteristics, Biophys. J., 72, 2430-2444(1997).
[150] J. Sneyd, P. D. Dale, and A. Duffy, Traveling waves in buffered systems: Applications to calcium waves, SIAM J. Appl. Math., 58, 1178-1192(1998).
[151] I. Parker, and Y. Yao, Regenerative release of calcium from functionally discrete subcellular stores by inositol trisphosphate, Proc.R. Soc.Lond. B., 246, 269-274(1991)
[152] Y. Yao, J. Choi, and I. Parker, Quantal puffs of intracellular Ca~(2+) evoked by inositol trisphosphate in Xenopus oocytes, J. PhysioL.(Lond.), 482, 533-553(1995);
[153] I. Parker, and Y. Yao, Ca~(2+) transients associated with openings of inositol trisphosphate-gated channels in Xenopus oocytes, J. Physiol.(Lond.), 491,663-668(1996).
[154] J. Marchant, N. Callamaras, and I. Parker, Initiation of IP_3-mediated Ca~(2+) waves in Xenopus oocytes, EMBO J., 18(19), 5285-5299(1999).
[155] M. Bootman, E. Niggli, M. Berridge, and P. Lipp, Imaging the hierarchical Ca~(2+) signalling in HeLa cells, J. Physiol., 499(2), 307-314(1997).
[156] O. H. Petersen, Local calcium spiking in pancreatic acinar cells, In Calcium Waves,Gradients and Oscillations. G. R. Bock and K. Ackrill, editors, Wiley, Chichester,England, 85-103(1995).
[157] S. Yagodin, L. A. Holtzclaw, and J. T. Russell, Mol. Cell. Biochem. 149/150,137-144(1995);
[158] S. Yagodin, L. A. Holtzclaw, C. A. Sheppard, and J. T. Russell, J. Neurobiol. 25,265-280(1994).
[159] J. W. Shuai, and P. Jung, Sub-threshold Ca~(2+) waves, New J. Phys. 5,132.1-132.20(2003).
[160] J. W.Shuai, and P.Jung,Stochastic Properties of Ca~(2+) Release of Inositol 1,4,5-Trisphosphate Receptor Clusters, Biophys. J., 83, 87(2002).
[161] G. Dupont, Theoretical insights into the mechanism of spiral Ca~(2+) wave initiation in Xenopus oocytes, Am. J. Physiol., 275(Cell Physiol. 44), C317-C322(1998).