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.     

八元数神经网络模型：256色图像的识别

首次把八元数引入到神经网络中，提出了八元数离散神经网络模型，并用信噪比理论初步考察了模型的稳定性和存贮容量。八元数神经网络模型可应用于高精度的２５６级的灰度图像或２５６值的彩色图像的识别中。     

Modelling Moran Process with Network Dynamics for the Evolution of Cooperation

We introduce a simple model based on the Moran process with network dynamics. Using pair approximation, the cooperation frequencies at equilibrium states are deduced for general interactions. Three usual social dilemmas are discussed in the framework of our model. It is found that they all have a phase transition at the same value of cost-to-benefit ratio. For the prisoner＇s dilemma game, notably it is exactly the simple rule reported in the literature [Nature 441 （2006） 502]. In our model, the simple rule results from the parent-offspring link. Thus the basic mechanism for cooperation enhancement in network reciprocity is in line with the Hamilton rule of kin selection. Our simulations verify the analysis obtained from pair approximation.     

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.     

Motile parameters of cell migration in anisotropic environment derived by speed power spectrum fitting with double exponential decay

Cell migration through anisotropic microenvironment is critical to a wide variety of physiological and pathological processes.However,adequate analytical tools to derive motile parameters to characterize the anisotropic migration are lacking.Here,we proposed a method to obtain the four motile parameters of migration cells based on the anisotropic persistent random walk model which is described by two persistence times and two migration speeds at perpendicular directions.The key process is to calculate the velocity power spectra of cell migration along intrinsically perpendicular directions respectively,then to apply maximum likelihood estimation to derive the motile parameters from the power spectra fitting with double exponential decay.The simulation results show that the averaged persistence times and the corrected migration speeds can be good estimations for motile parameters of cell migration.     

Derivation of persistent time for anisotropic migration of cells

Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk(APRW) model, in which two different and independent persistent times are assumed for cell migrations in the x-and y-axis directions. An intrinsic orthogonal coordinates with the primary and non-primary directions can be defined for each migration trajectory based on the singular vector decomposition method. Our simulation results show that the decay time of single exponential distribution of velocity auto-correlation function(VACF) in the primary direction is actually the large persistent time of the APRW model, and the small decay time of double exponential VACF in the non-primary direction equals the small persistent time of the APRW model. Thus, we propose that the two persistent times of anisotropic migration of cells can be properly estimated by discussing the VACFs of trajectory projected to the primary and non-primary directions.