【作者】 唐军；

【导师】 贾亚；

【作者基本信息】 华中师范大学 ， 理论物理， 2009， 博士

【摘要】 钙离子(Ca²⁺)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IP₃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IP₃浓度对细胞内钙离子螺旋波的影响。结果发现: （1）随着IP₃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IP₃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IP₃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。更多还原

【Abstract】 Ca²⁺ is one of the most important messengers. It transmits intracellular signals and takes part in intercellular coordination. The kinetics of the Ca²⁺ concentration involves a transition from locally stochastic release (e.g. Ca²⁺ spark) to intracellular global oscillations and waves, even waves spreading across cells. Ca²⁺ spiral wave is one of the most intriguing Ca²⁺ pattern. In order to explain the dynamics of Ca²⁺ concentration found in experiments, a number of mathematical models are presented.Many important factors in the cell, for example IP₃ concentration, are experimentallycontrollable. Investigating the effect of these controllable factors on Ca²⁺ spiral waves can help us understanding the mechanism of Ca²⁺ exchanging in the cell, and Ca²⁺ signalling. Thus, in this thesis, we have studied the factors effecting the Ca²⁺ spiral waves and the control of Ca²⁺ spiral waves. The main works are as follow:First, based on a spatial extended Tang-Othmer Ca²⁺ model, the dependence of spiral dynamics on IP₃ concentration is studied. we find: （i）The period of Ca²⁺ spiral wave changes un-monotonously with IP₃ concentration, and the increasing of periods corresponds to instability of spiral waves. （ii）Changing IP₃ 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 IP₃-dependent Ca²⁺ spiral dynamics, intuitively, some methods of controlling spirals through the control of IP₃ concentrationare introduced. （iv） Our results are experimentally accessable. Then, Based on previous work in BZ reaction, the electric fields are used to control Ca²⁺ 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= 2ω₀ 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 Ca²⁺ releasing onCa²⁺ 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 Ca²⁺ spiral wave; （iii） when the random distributions are considered, the numerical results accord to experiments.更多还原