生化反应系统的二项矩和属性因子  

The Binomial Moments and Attribute Factors for Biochemical Reaction Systems

作　　者：周天寿[1] 

机构地区：[1]中山大学数学与计算科学学院,广东广州510275

出　　处：《江西师范大学学报（自然科学版）》2016年第1期1-4,21,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金/重大研究计划/重点支持项目(91230204);科技部973项目子课题(2014CB964703)资助项目

摘　　要：化学主方程对生化反应系统提供了一个建模框架,但它的分析与模拟一直是计算系统生物学的一个挑战.另一方面,矩封闭方法对化学主方程提供了一种逼近,但普通的矩当其阶趋于无穷时并不趋于0,因此具有局限性.这里,对概率密度函数引进二项矩,它具有2个突出的特点:1)当二项矩的阶充分大时二项矩趋于0;2)二项矩能够方便地用来重构相应的概率密度函数.基于二项矩,进一步引进反应物种的属性因子,它比普通的统计指标(如噪声强度、Fano因子)具有某些优势.此外,还给出了用二项矩来表示噪声强度和Fano因子的显式公式,并用简单的生物例子来说明二项矩的优势与3种统计指标的特征.Chemical master equations（ CMEs） provide a framework for modeling of biochemical reaction systems,but its analysis and simulation are a challenge in computational systems biology. On the other hand,moment-closure methods provide approximations for CMEs but ordinary moments have shortcomings,e. g.,they do not tend to zero as their orders go to infinity. Binomial moments for a distribution are introduced,which have two remarkable features： 1） binomial moments tend to zero as their orders go to infinity; 2） they can be conveniently used to reconstruction of the corresponding distribution. Based on binomial moments,it further introduces the attribution factor of a reactive species,which has more advantages than common statistical indices such as noise intensity and Fano factor. In addition,it gives explicit formulae for calculating common statistical indices,and uses simple biological examples to show advantages of binomial moments and characteristics of three statistics.

关 键 词：二项矩 属性因子 噪声强度 Fano因子 反应系统 

分 类 号：O242[理学—计算数学] Q332[理学—数学]