电压与钙耦合神经元模型的符号动力学

郜志英; 陆启韶

电压与钙耦合神经元模型的符号动力学

北京航空航天大学理学院, 北京 100083

基金项目: 国家自然科学基金资助项目(10432010)

详细信息

作者简介:
郜志英(1979-), 女, 山西榆次人, 博士后, gaozhiying@buaa.edu.cn.

中图分类号: Q 421
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- 被引次数: 0
出版历程
- 收稿日期: 2006-09-26
- 网络出版日期: 2007-08-31

Symbolic dynamics of coupled neuron model of calcium and voltage

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

摘要

摘要: 应用符号动力学研究了跨膜电压与细胞内钙浓度相耦合的R15神经元模型.通过峰峰间期序列(ISIs, Interspike Interval Series)的首归映射构造出描述周期和混沌放电模式的符号序列,并讨论了与切分岔密切联系的阵发混沌与嵌含在混沌区中的周期窗口的产生机理.由符号序列的排序规则,确定具有不同拓扑结构的放电节律与连续变化的参数值的对应关系,从而对实验或模型测得的任意放电模式进行参数识别.研究结果表明符号方法是研究神经放电活动动力学行为的一种有力工具.尤为重要的是,这样一种粗粒化的方法能够推广到神经电生理实验中,从复杂的实验数据中提炼更多有价值的信息.
- 神经元放电节律 /
- 符号动力学 /
- 周期模式 /
- 阵发混沌 /
- 排序规则
Abstract: The R15 neuron model with the intracellular calcium concentrations coupled to the transmembrane voltage was studied by the symbolic dynamics. The symbolic expressions of periodic and chaotic firing patterns were constructed through the first-return maps of ISIs (interspike interval series). And also the intermittent chaos close correlative to the fold bifurcation and the generating mechanism of periodic windows embedded in the chaos region were discussed. The corresponding relation between firing rhythms with different topological structures and continuously varying parameter values was revealed on the basis of ordering rules of symbolic sequences. The corresponding parameter value of some firing pattern measured from the electrophysiological experiment or simulated by the mathematical model could be approximately fixed according to the ordering relation. Results show that symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electrophysiological experiments to extract more valuable information from complicated experiment data.
- neuronal firing rhythm /
- symbolic dynamics /
- periodic pattern /
- intermittency chaos /
- ordering rule

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参考文献(1)

[1] Bootman M D, Berridge M J, Roderick H L. Calcium signaling:more messengers, more channels, more complexity [J]. Current Biology,2002,12:563-565 [2] Hodgkin A L, Huxley A F. A guantitative description of membrane current and application to conduction and excitation in nerve[J]. Journal of Physiology,1952,117:500-544 [3] Chay T R, Fan Y S, Lee Y S. Bursting, spiking, chaos, fractals and universality in biological rhythms[J].International Journal of Bifurcation and Chaos,1995,5(3):595-635 [4] Izhikevich E M. Neural excitability, spiking, and bursting [J]. International Journal of Bifurcation and Chaos,2000,10(6):1171-1266 [5] Morita K, Kotetsu K. Oscillation of Ca²⁺-linked K⁺ conductance in bullfrog sympathetic ganglion cell is sensitive to intercellular anions [J]. Nature,1980,283:204-205 [6] Berridge M J. Neuronal calcium signaling[J]. Neuron,1998,21(1):13-26 [7] Chay T R. Electrical bursting and luminal calcium oscillation in excitable cell models[J]. Biological Cybernetics,1996,75:419-431 [8] Marhl M, Schuster S, Brumen M, et al. Modelling the interrelations between calcium oscillations and ER membrane potential oscillations[J]. Biophysical Chemistry,1997,63:221-239 [9] Friel D D. Mitochondria as regulators of stimulus-evoked calcium signals in neurons[J]. Cell Calcium,2000,28:307-316 [10] Haberichter T, Marhl M, Heeinrich R. Birhythmicity, thirhythmicity and chaos in bursting calcium oscillations[J]. Biophysical Chemistry,2001,90:17-30 [11] 郝柏林.从抛物线谈起:混沌动力学导论[M].上海:上海科技教育出版社,1995:33-103 Hao Bailin. Staring with parabolas:an introduction to chaotic dynamics[M]. Shanghai:Shanghai Scientific and Technological Education Publishing House,1995:33-103(in Chinese) [12] 郑伟谋.实用符号动力学[M].上海:上海科技教育出版社,1994:11-20 Zheng Weimou. Applied symbolic dynamics[M]. Shanghai:Shanghai Scientific and Technological Education Publishing House,1994:11-20(in Chinese) [13] Chay T R. The effect of inactivation of calcium channels by intracellular Ca²⁺ ions in the bursting pancreatic β-cells[J]. Cell Biophysics,1987,11:77-90 [14] Lipscombe D, Madison D V, Poenie M, et al. Spatial distribution of calcium channels and cytosolic calcium transients in growth cones and cell bodies of sympathetic neurons[J]. Proceedings of the National Academy of Sciences,1988,85:2398-2402 [15] Liano L, Dressen J. Intradendritic release of calcium induced by glutamate in cerebellar Purkinje cells[J].Neuron,1991,7:577-583

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