Chen K C, Ford R M, Cummings P T
Department of Chemical Engineering, University of Virginia, Charlottesville, VA 22903-2442, USA.
J Theor Biol. 1998 Nov 21;195(2):139-55. doi: 10.1006/jtbi.1998.0768.
The angular turning probability density distribution for motile bacteria is usually measured in local coordinates and is therefore inconvenient for global analyses of the chemotactic bacterial migration. In this paper we present analytical derivations that convert the local angular turning probability density distribution into a global one. The explicit expression of a reduced global turning probability density function for motile bacteria was derived and its relevant properties were investigated. Depending on the angle variable being intergrated and the integration range, three types of cosine moments were separately defined and studied. Some statistical indices and parameters such as the directional persistence, persistence number, and one-dimensional reversal probability were found to be embedded in the various moments of the reduced global turning probability density function. Applications of the reduced global turning probability and its integrated moments to a three-dimensional cell balance equation in an axisymmetric system were also discussed.
运动细菌的角转向概率密度分布通常在局部坐标系中测量，因此不利于对趋化性细菌迁移进行全局分析。在本文中，我们给出了将局部角转向概率密度分布转换为全局分布的解析推导。推导了运动细菌简化全局转向概率密度函数的显式表达式，并研究了其相关性质。根据积分的角度变量和积分范围，分别定义并研究了三种类型的余弦矩。发现一些统计指标和参数，如方向持续性、持续性数和一维反转概率，都包含在简化全局转向概率密度函数的各种矩中。还讨论了简化全局转向概率及其积分矩在轴对称系统三维细胞平衡方程中的应用。
