Moment-flux models for bacterial chemotaxis in large signal gradients

详细信息    查看全文

• 作者：Chuan Xue ; Xige Yang
• 关键词：Chemotaxis ; Large signal gradient ; Derivation of PDE models
• 刊名：Journal of Mathematical Biology
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：73
• 期：4
• 页码：977-1000
• 全文大小：961 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  Applications of Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1416
• 卷排序：73

文摘

Chemotaxis is a fundamental process in the life of many prokaryotic and eukaryotic cells. Chemotaxis of bacterial populations has been modeled by both individual-based stochastic models that take into account the biochemistry of intracellular signaling, and continuum PDE models that track the evolution of the cell density in space and time. Continuum models have been derived from individual-based models that describe intracellular signaling by a system of ODEs. The derivations rely on quasi-steady state approximations of the internal ODE system. While this assumption is valid if cell movement is subject to slowly changing signals, it is often violated if cells are exposed to rapidly changing signals. In the latter case current continuum models break down and do not match the underlying individual-based model quantitatively. In this paper, we derive new PDE models for bacterial chemotaxis in large signal gradients that involve not only the cell density and flux, but also moments of the intracellular signals as a measure of the deviation of cell’s internal state from its steady state. The derivation is based on a new moment closure method without calling the quasi-steady state assumption of intracellular signaling. Numerical simulations suggest that the resulting model matches the population dynamics quantitatively for a much larger range of signals.