阈下激励与噪声联合作用下肝细胞系统的内钙时空随机共振问题

The spatio-temporal stochastic resonance of calcium in coupled hepatocytes systems affected by subthreshold stimuli and noise

研究阈下周期信号激励对耦合肝细胞系统内钙离子浓度([Ca2+])的时空随机共振性质的影响.当阈下激励的频率等于确定性系统在Hopf分岔点附近的频率时,它就会极大地提高随机耦合系统内发生[Ca2+]喷发的细胞的比例,通过对喷发比的自相关函数计算得知阈下激励增强了系统在高斯白噪声作用下[Ca2+]的时间共振性.通过数值模拟得知,对于不同耦合强度,都存在最优噪声强度使得随机系统内[Ca2+]时间共振达到最佳,并且随着细胞间耦合强度的增加,使得[Ca2+]共振达到最好的噪声强度也在逐渐增加.尽管阈下激励加强了[Ca2+]的时间共振,但通过对系统的空间傅里叶变换函数的分析,得知阈下激励会提高系统对噪声的敏感度,降低系统的空间共振性,从而破坏了中等噪声强度诱发的细胞间规则环形钙波.

The influence of subthreshold periodic stimuli on temporal-spatial resonance of [Ca2＋] in a stochastic coupled hepatocytes system is studied. When the frequency of stimuli is close to that of the determinate coupled system before the Hopf bifurcation, the eruption rate of [Ca2＋] is enhanced greatly in the stochastic system. By computing the autocorrelation function of the eruption rate, it is found that the temporal resonance of [Ca2＋] becomes more ordered by the subthreshold stimuli. Furthermore, for a given coupling strength between cells, there is an optimal noise level to make the [Ca2＋] resonance reach maximum, and the optimal noise level also increases with the coupling strength increasing. Though the action of subthreshold stimuli promotes the temporal resonance of the system, it strengthens the sensibility to noise and then depresses the spatial ordered calcium waves induced by medium-strength noise only, as shown by the analysis by the spatial Fourier transform and its structure function.