A population-level model from the microscopic dynamics in Escherichia coli chemotaxis via Langevin approximation

• Published in: Chinese physics B 2012-09, Vol.21 (9), p.583-593, Article 098701
• Main Author: 贺卓然 吴泰霖 欧阳颀 涂豫海
• Format: Article
• Language: English
• Subjects: Approximation; Bacteria; Dynamics; Escherichia coli; Jumping; Mathematical analysis; Mathematical models; Partial differential equations; Simulators; 人口; 偏微分方程; 动力学模型; 大肠杆菌; 微观动力学; 微观控制; 水; 趋化作用
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/21/9/098701

Recent extensive studies of Escherichia coli （E. coli） chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation （PDE） that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel （K-S） equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.