该申请项目将主要就以下几个问题展开研究：（a）建立描述细胞内肌动蛋白纤维随机生长过程的数学模型，并得到相关生物物理量（平均生长速度、生长帽子的长度等）的显式表达式；（b）首次建立统一的描述马达蛋白力学化学循环过程的数学模型，并据此对马达蛋白kinesin、dynein、myosin的生物物理性质进行分析；（c）首次建立基于化学主方程与TASEP过程相结合的描述细胞内外离子通过膜上的离子通道进行输运的数学模型。在研究中，模型参数将通过最新的试验数据来确定，并据此预测出更多的有关细胞生命活动的基本生物物理性质。.该项目的研究成果将有助于理解某些细胞生命活动的基本原理，并将会具有一定生物医学意义。该项目研究的基本思路是，首先根据最新的试验现象，并依据有关的生物物理与生物化学原理建立相应的数学模型，再通过具体的试验数据确定模型中的参数，最后再通过理论分析或数值计算的方法得出具有生物意义的预测。

The main projects studied in this proposal are as follows. (a) Mathematical modeling of stochastic growth and shortening of actin filament in cells, and explicit expressions of the mean growth velocity, mean cap length, etc. will be obtained. (b) Presenting a mathematical model to describe the mechanochemical cycles of general processive motor proteins, and then based on this model, the biophysical properties of motor protein kinesin, dynein and myosin will be detailed discussed. (c) The transmembrane transport process of ions will be described by a new model, in which the chemical master equation and the TASEP (totally asymmetry simple exclusion process) are combined. In each model, all the values of model parameters will be obtained by fitting to the updated experimental data, and then corresponding biophysical properties of the related life processes will be analyzed.. The study of above projects will be helpful to understand the basic principles of related processes in living cells, and might be also biomedically meaningful. The basic idea used in this proposal is that, based on the related biophysical and biochemical principles and especially the recent experimental observations, the mathematical models will be firstly designed, and then the corresponding model parameters will be determined by the experimental data. Finally, biologically meaningful predictions will be obtained by theoretical analysis and numerical calculations.