随机反应扩散格气模型上钙动力学的粗粒化模拟

发展了一种基于随机格气模型的粗粒化方法,该方法能有效模拟内质网表面钙动力学信息. 首先将相邻的微观节点合并成粗粒化节点,再根据局域平均场近似推导出粗粒化反应速率,然后执行粗粒化动力学蒙特卡洛模拟. 发现粗粒化动力学蒙特卡洛模拟结果和微观模拟结果非常吻合. 有趣的是,存在一个最佳的粗粒化比m,使得粗粒化模拟与微观模拟的相变点偏差最小. 固定m,发现临界点随体系尺度增加而单调增加,而且相变点的偏差与体系尺度存在一个标度关系.此外,该粗粒化方法大大地加快了蒙特卡洛模拟速率,并且与微观模拟直接相关. 该方法可以广泛用来研究体系尺度效应,而节省大量计算时间.     

Adaptive co-evolution of strategies and network leading to optimal cooperation level in spatial prisoner’s dilemma game

We study evolutionary prisoner's dilemma game on adaptive networks where a population of players co-evolves with their interaction networks. During the co-evolution process, interacted players with opposite strategies either rewire the link between them with probability $p$ or update their strategies with probability $1-p$ depending on their payoffs. Numerical simulation shows that the final network is either split into some disconnected communities whose players share the same strategy within each community or forms a single connected network in which all nodes are in the same strategy. Interestingly, the density of cooperators in the final state can be maximised in an intermediate range of $p$ via the competition between time scale of the network dynamics and that of the node dynamics. Finally, the mean-field analysis helps to understand the results of numerical simulation. Our results may provide some insight into understanding the emergence of cooperation in the real situation where the individuals' behaviour and their relationship adaptively co-evolve.     

Synchronized Anti-Phase and In-Phase Oscillations of Intracellular Calcium Ions in Two Coupled Hepatocytes System

We study the dynamic behaviour of two intracellufar calcium oscillators that are coupled through gap junctions both to Ca^2＋ and inositol（1,4,5）-trisphosphate （IP3）. It is found that synchronized anti-phase and in-phase oscillations of cytoplasmic cadcium coexist in parameters space. Especially, synchronized anti-phase oscillations only occur near the onset of a Hopf bifurcation point when the velocity of IP3 synthesis is increased. In addition, two kinds of coupling effects, i.e., the diffusions of Ca^2＋ and IP3 among cells on synchronous behaviour, are considered. We fnd that small coupling of Ca^2＋ and large coupling of IP3 facilitate the emergence of synchronized anti-phase oscillations. However, the result is contrary for the synchronized in-phase case. Our findings may provide a qualitative understanding about the mechanism of synchronous behaviour of intercellular calcium signalling.     

延迟基因开关体系的稳定性及转变动力学

对延迟基因开关体系的稳定性及转变动力学进行了系统的研究．通过前向流采样及延迟随机模拟方法,获得了相空间稳态分布、转变路径和速率以及转变态系综的分布等信息．数值结果表明,基因开关体系中的延迟会减小稳态之间的间距,增大体系在转变态的布居．此外,转变速率也会随着延迟时间的增大单调增加,这些现象都说明延迟会削弱双稳基因开关体系的稳定性．转变路径由两种转录因子蛋白质的总的粒子数的差和操纵子位点的状态来描述,对转变路径的数值分析表明转录和翻译过程导致的延迟会显著影响转变动力学．特别是对于转变态系综而言,操纵子结合两种不同二聚体概率的差异随着延迟时间的增加逐渐加大.     

动力学伊辛模型在振荡外场中的成核

研究了二维的动力学伊辛模型在一个具有偏向的振荡外场中的成核过程,主要关注成核时间与外场振荡周期ω的关系．随着ω的变化,成核时间出现最小值,最小的成核时间对应的平均临界核的大小也是最小的,这表明存在一个最佳的振荡频率,相比较于一个确定的外场,它更有利于成核．同时还研究了外场的初始相位的影响．     

细胞丛状化分布对二维耦合体系尺度选择效应的影响

采用随机模拟方法对体系的化学朗之万方程进行了数值模拟，考察了二维耦合细胞体系中，细胞的丛状化分布对于因内噪声作用而产生的尺度选择效应所带来的影响.研究发现，当体系处于Hopf分岔点附近时，由于耦合作用使得处于最佳状态的一定数目的细胞呈现丛状化聚集在一起，而这种丛状化分布的“团队精神”可以极大地提高体系的工作效率，表现为体系对外界刺激信号的响应能力(信噪比)达到极大值.同时还观察到，体系对外界刺激最为敏感时对应的最佳细胞丛尺度大小不随耦合强度的改变而变化，而体系输出信号的信噪比，随着耦合强度的增加有增大趋势.这些现象表明，细胞的丛状化分布将极大地增强细胞中钙离子信号对外界刺激的响应效果.生物体系本身可能具有这种特性，并利用它来改善和提高感受外界信息的能力.     

介观化学反应体系中非平衡相变最可几路径的熵产生

针对一个双稳的介观化学反应体系计算了在非平衡相变时最可几路径的熵产生. 利用概率产生函数和程函近似,将化学主方程转化为经典的哈密顿-雅可比方程并通过相空间的零能轨线找到双稳态之间转变的最可几路径. 通过计算前向和逆向最可几路径的熵产生,发现在共存点系统熵变和介质熵变都为零,而在非共存点系统熵变和介质熵变皆不为零.