From individual to collective behavior in bacterial chemotaxis
From individual to collective behavior in bacterial chemotaxis
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DOI：
10.1137/s0036139903433232
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发表时间：
2005-01-01
影响因子：
1.9
通讯作者：
Othmer, HG
中科院分区：
文献类型：
--
作者：
Erban, R;Othmer, HG
细菌的趋化性从微观（细胞）和宏观（种群）的角度进行了广泛的研究，在这里，我们通过从单个细胞行为的微观模型推导出经典的宏观描述来连接这些非常不同的描述水平。该分析是基于用于描述个体（例如细菌）的运动的速度跳跃过程，其中每个个体携带根据由依赖于时间和/或空间的外部信号强制的常微分方程系统而演变的内部状态。在这里处理的问题中，个体的转向率是内部状态的函数，而内部状态又取决于外部信号。利用矩封闭技术在一维空间，我们推导和分析了一个宏观系统的双曲型微分方程描述这个速度跳跃过程。使用双曲标度的空间和时间，我们得到一个单一的二阶双曲方程的人口密度，并使用抛物线标度，我们得到经典的趋化性方程，其中的趋化敏感性现在是一个已知的函数的参数的内部动态。数值模拟表明，宏观方程的解与个体运动的蒙特卡罗模拟结果非常一致。
Bacterial chemotaxis is widely studied from both the microscopic ( cell) and macroscopic ( population) points of view, and here we connect these very different levels of description by deriving the classical macroscopic description for chemotaxis from a microscopic model of the behavior of individual cells. The analysis is based on the velocity jump process for describing the motion of individuals such as bacteria, wherein each individual carries an internal state that evolves according to a system of ordinary differential equations forced by a time- and/or space-dependent external signal. In the problem treated here the turning rate of individuals is a functional of the internal state, which in turn depends on the external signal. Using moment closure techniques in one space dimension, we derive and analyze a macroscopic system of hyperbolic differential equations describing this velocity jump process. Using a hyperbolic scaling of space and time, we obtain a single second-order hyperbolic equation for the population density, and using a parabolic scaling, we obtain the classical chemotaxis equation, wherein the chemotactic sensitivity is now a known function of parameters of the internal dynamics. Numerical simulations show that the solutions of the macroscopic equations agree very well with the results of Monte Carlo simulations of individual movement.