细菌奔跑和翻滚动力学模型的推导:定量和强收敛结果

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED
Alain Blaustein
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引用次数: 0

摘要

在过去的一个世纪里,生物学家和数学家研究了细菌运动的两种机制:细菌沿着直线运动的奔跑阶段和它们改变方向的翻滚阶段。实验表明,当被化学引诱剂包围时,细菌会随着浓度梯度的上升而增加运行时间,从而导致偏向有利区域的随机行走。这一观察结果提出了以下问题,引起了生物学和数学界的强烈兴趣:是什么细胞机制使细菌能够感受到浓度梯度?在这篇文章中,我们研究了一个渐近的制度,被提出来解释这种能力,这要归功于内部机制。更准确地说,我们从一个包含细胞内部机制的更全面的模型中推导出具有浓度梯度依赖的翻滚速率的奔跑-翻滚动力学方程。我们的结果改进了先前的研究,因为我们获得了对梯度依赖的动力学模型的强收敛性,具有定量和正式的最优收敛率。其主要成分在于确定一组细胞内部动力学的坐标,其中浓度梯度明显出现。然后,我们使用相对熵方法来定量测量包含细胞机制的模型与具有浓度梯度依赖的翻滚率的模型之间的距离。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Derivation of the Bacterial Run-and-Tumble Kinetic Model: Quantitative and Strong Convergence Results

During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When surrounded by a chemical attractant, experiments show that bacteria increase their run time as moving up concentration gradients, leading to a biased random walk toward favorable regions. This observation raises the following question, which has drawn intense interest from both biological and mathematical communities: what cellular mechanisms enable bacteria to feel concentration gradients? In this article, we investigate an asymptotic regime that was proposed to explain this ability thanks to internal mechanisms. More precisely, we derive the run-and-tumble kinetic equation with concentration's gradient-dependent tumbling rate from a more comprehensive model, which incorporates internal cellular mechanisms. Our result improves on previous investigations, as we obtain strong convergence toward the gradient-dependent kinetic model with quantitative and formally optimal convergence rates. The main ingredient consists in identifying a set of coordinates for the internal cellular dynamics in which concentration gradients arise explicitly. Then, we use relative entropy methods in order to capture quantitative measurement of the distance between the model incorporating cellular mechanisms and the one with concentration-gradient-dependent tumbling rate.

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来源期刊
Studies in Applied Mathematics
Studies in Applied Mathematics 数学-应用数学
CiteScore
4.30
自引率
3.70%
发文量
66
审稿时长
>12 weeks
期刊介绍: Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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