Biexponential distribution of open times of a toy channel model

The biexponential distributions of open times are observed in various types of ion channels. In this paper, by discussing a simple channel model, we show that there are two different schemes to understand the biexponential distribution of open times. One scheme is mathematically strict based on generator matrix theory, while the other one has a clear physical explanation according to an approximation process with numerical simulation of Markovian channel dynamics. Our comparison results suggest that even for biologically complex channels, in addition to carrying out a stochastic simulation,the strict theoretical analysis should be considered to understand the multiple exponential distributions of open times.     

Dual mechanisms of Bcl-2 regulation in IP3-receptor-mediated Ca2+ release: A computational study

Inositol 1,4,5-trisphosphate receptors (IP₃R)-mediated calcium ion (Ca²⁺) release plays a central role in the regulation of cell survival and death. Bcl-2 limits the Ca²⁺ release function of the IP₃R through a direct or indirect mechanism. However, the two mechanisms are overwhelmingly complex and not completely understood. Here, we convert the mechanisms into a set of ordinary differential equations. We firstly simulate the time evolution of Ca²⁺ concentration under two different levels of Bcl-2 for the direct and indirect mechanism models and compare them with experimental results available in the literature. Secondly, we employ one- and two-parameter bifurcation analysis to demonstrate that Bcl-2 can suppress Ca²⁺ signal from a global point of view both in the direct and indirect mechanism models. We then use mathematical analysis to clarify that the indirect mechanism is more efficient than the direct mechanism in repressing Ca²⁺ signal. Lastly, we predict that the two mechanisms restrict Ca²⁺ signal synergistically. Together, our study provides theoretical insights into Bcl-2 regulation in IP₃R-mediated Ca²⁺ release, which may be instrumental for the successful development of therapies to target Bcl-2 for cancer treatment.     

Bcl-2蛋白抑制钙信号的建模与全局动力学分析

钙离子(Ca~(2+))是生物体内一种"生死攸关"的信号分子,Bcl-2蛋白可以直接或间接调节IP_3R通道释放Ca~(2+)的能力,借此决定细胞命运.本文基于新近的实验成果,针对Bcl-2蛋白间接调控Ca~(2+)的信号通路建立数学模型,得到了与实验数据相符合的结果,从理论上证明了Bcl-2蛋白对钙信号有抑制作用.在对模型进行鲁棒性检验之后,本文对该信号通路中一些关键组分的作用进行了预测.以[IP_3]和[Bcl-2]为双分岔参数分析的结果表明Bcl-2对刺激强度能产生Ca~(2+)振荡的区域有重要影响.以蛋白磷酸酶1[PP1]和蛋白激酶A[PKA]为单分岔参数分析的结果揭示:PP1可以有效地抑制钙信号,而PKA对钙信号的促进作用有一定的局限性.模型结果表明,不同浓度组合的IP_3,Bcl-2和PKA会对钙信号发挥复杂的调控作用.本文不仅对相关生物学实验有一定的指导作用,而且可为治疗因钙信号失调而导致的疾病提供思路.