从生化途径模型推导细菌的奔跑翻滚动力学方程
Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway
摘要：
到目前为止，动力学传输方程是描述细菌种群通过奔跑和翻滚运动的动力学的标准模型。实验观察表明，当遇到趋化分子的梯度增加时，细菌会增加其运行时间。这导致了第一类模型，其在理论上包括取决于趋化信号的路径方向梯度的翻滚频率。最近，发现了调节鞭毛马达的生化途径。这一知识产生了第二类动力学传输方程，它考虑到细胞内的分子含量，并将翻滚频率与此信息联系起来。事实证明，翻滚频率取决于趋化信号，而不是其梯度。对于这两类模型，Keller-Segel型的宏观方程，已经推导出使用扩散或双曲重标度。我们完成了这个程序，显示如何第一类方程可以从第二类分子内容后，适当的重新缩放。主要的困难是解释为什么趋化信号的路径梯度可以出现在这个渐近过程中。可以包括受体甲基化事件的随机性，并且我们的方法可以用于计算存在这种噪声的翻滚频率。
英文摘要：
Kinetic-transport equations are, by now, standard models to describe the dynamics of populations of bacteria moving by run-and-tumble. Experimental observations show that bacteria increase their run duration when encountering an increasing gradient of chemotactic molecules. This led to a first class of models which heuristically include tumbling frequencies depending on the path-wise gradient of chemotactic signal. More recently, the biochemical pathways regulating the flagellar motors were uncovered. This knowledge gave rise to a second class of kinetic-transport equations, that takes into account an intra-cellular molecular content and which relates the tumbling frequency to this information. It turns out that the tumbling frequency depends on the chemotactic signal, and not on its gradient. For these two classes of models, macroscopic equations of Keller-Segel type, have been derived using diffusion or hyperbolic rescaling. We complete this program by showing how the first class of equations can be derived from the second class with molecular content after appropriate rescaling. The main difficulty is to explain why the path-wise gradient of chemotactic signal can arise in this asymptotic process. Randomness of receptor methylation events can be included, and our approach can be used to compute the tumbling frequency in presence of such a noise.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
