生化反应系统的高维矩阵方程

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难题,到目前为止并没有得到解决.这里,通过引进高维矩阵及其运算规则,首先把化学主方程表示为高维矩阵方程,然后给出了其分析解的形式表示,此外还介绍了一种求解高维矩阵方程的高效数值方法.研究表明:高维矩阵方法似乎解决了化学主方程的分析求解和数值求解问题.

The High-Dimensional Matrix Equation for Biochemical Reaction Systems

Chemical master equation gives a framework for mathematical modeling of biochemical reaction systems,but its analysis and simulation has been being difficult in the field of computational systems biology.Here,by introducing a high-dimensional matrix and its operators,first the chemical master equation is transformed into a high-dimensional matrix equation,and then a formal expression for the analytical solution to this matrix equation is given.In addition,a 2-order cyclic iterative algorithm is introduced to numerically solve the high-dimensional matrix equation.In a word,the high-dimensional matrix method seems to solve the questions of analytical and numerical solutions to the chemical master equation.