Tyson R, Lubkin S R, Murray J D
Department of Applied Mathematics, University of Washington, Seattle 98195-2420, USA.
J Math Biol. 1999 Apr;38(4):359-75. doi: 10.1007/s002850050153.
A variety of spatial patterns are formed chemotactically by the bacteria Escherichia coli and Salmonella typhimurium. We focus in this paper on patterns formed by E. coli and S. typhimurium in liquid medium experiments. The dynamics of the bacteria, nutrient and chemoattractant are modeled mathematically and give rise to a nonlinear partial differential equation system. We present a simple and intuitively revealing analysis of the patterns generated by our model. Patterns arise from disturbances to a spatially uniform solution state. A linear analysis gives rise to a second order ordinary differential equation for the amplitude of each mode present in the initial disturbance. An exact solution to this equation can be obtained, but a more intuitive understanding of the solutions can be obtained by considering the rate of growth of individual modes over small time intervals.
多种空间模式是由大肠杆菌和鼠伤寒沙门氏菌通过趋化作用形成的。在本文中，我们关注大肠杆菌和鼠伤寒沙门氏菌在液体培养基实验中形成的模式。对细菌、营养物质和化学引诱剂的动力学进行了数学建模，并由此产生了一个非线性偏微分方程组。我们对模型生成的模式进行了简单且直观的分析。模式源于对空间均匀解状态的扰动。线性分析产生了一个二阶常微分方程，用于描述初始扰动中存在的每个模式的振幅。这个方程可以得到精确解，但通过考虑各个模式在小时间间隔内的增长率，可以更直观地理解这些解。
