BIASED RANDOM-WALK MODELS FOR CHEMOTAXIS AND RELATED DIFFUSION APPROXIMATIONS
BIASED RANDOM-WALK MODELS FOR CHEMOTAXIS AND RELATED DIFFUSION APPROXIMATIONS
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DOI：
10.1007/bf00275919
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发表时间：
1980-01-01
影响因子：
1.9
通讯作者：
ALT, W
中科院分区：
文献类型：
--
作者：
ALT, W
讨论了有偏随机漫步的随机模型，该模型描述了趋化因子梯度下细菌或白细胞等化学敏感细胞的行为。特别是旋转频率和旋转角度分布是在相关实验观察的背景下根据某些生物学假设推导出来的。在适当的假设条件下，证明了微分积分方程的解近似满足著名的patak - keller - segel扩散方程，其系数可以用微观参数表示。在奇异摄动理论的框架下，通过适当的能量泛函给出了扩散近似的精确误差估计。
Stochastic models of biased random walk are discussed, which describe the behavior of chemosensitive cells like bacteria or leukocytes in the gradient of a chemotactic factor. In particular the turning frequency and turn angle distributions are derived from certain biological hypotheses on the background of related experimental observations. Under suitable assumptions it is shown that solutions of the underlying differential-integral equation approximately satisfy the well-known Patlak-Keller-Segel diffusion equation, whose coefficients can be expressed in terms of the microscopic parameters. By an appropriate energy functional a precise error estimation of the diffusion approximation is given within the framework of singular perturbation theory.