Perturbation expansion of Alt's cell balance equations reduces to Segel's one-dimensional equations for shallow chemoattractant gradients
Perturbation expansion of Alt's cell balance equations reduces to Segel's one-dimensional equations for shallow chemoattractant gradients
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DOI：
10.1137/s0036139996301283
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发表时间：
1998-01-01
影响因子：
1.9
通讯作者：
Cummings, PT
中科院分区：
文献类型：
--
作者：
Chen, KC;Ford, RM;Cummings, PT
Alt的细胞平衡方程进行了严格的研究和微扰扩展到类似于西格尔的一维现象学细胞平衡方程的形式，通过考虑简化的情况下，具有对称性的细菌密度在x和y方向上的吸引梯度只存在于z方向。我们证明，对于浅吸引梯度的集总积分涉及翻滚概率频率分布和细菌密度分布在θ方向可以明确表示为三个数量的产品：平均翻滚频率，细菌亚群密度，和逆转概率。我们还推导出Fickian形式的细菌净通量的表达式，其中两个宏观运输参数，随机运动系数和趋化速度，明确涉及到个别细胞的性质和化学梯度。
The cell balance equations of Alt are rigorously studied and perturbatively expanded into forms similar to Segel's one-dimensional phenomenological cell balance equations by considering the simplifying case of bacterial density possessing symmetry in the x and y directions responding to an attractant gradient present only in the z direction. We prove that for shallow attractant gradients the lumped integrals involving the tumbling probability frequency distribution and bacterial density distribution in the theta direction can be explicitly expressed as a product of three quantities: the mean tumbling frequency, the bacterial subpopulation density, and a reversal probability. We also derive expressions for the bacterial net flux in the Fickian form from which two macroscopic transport parameters, the random motility coefficient and the chemotactic velocity, are explicitly related to individual cell properties and chemical gradients.