Lauffenburger D, Aris R, Keller K
Biophys J. 1982 Dec;40(3):209-19. doi: 10.1016/S0006-3495(82)84476-7.
A mathematical model is developed to elucidate the effects of biophysical transport processes (nutrient diffusion, cell motility, and chemotaxis) along with biochemical reaction processes (cell growth and death, nutrient uptake) upon steady-state bacterial population growth in a finite one-dimensional region. The particular situation considered is that of growth limitation by a nutrient diffusing from an adjacent phase not accessible to the bacteria. It is demonstrated that the cell motility and chemotaxis properties can have great influence on steady-state population size. In fact, motility effects can be as significant as growth kinetic effects, in a manner analogous to diffusion- and reaction-limited regimes in chemically reacting systems. In particular, the following conclusions can be drawn from our analysis for bacterial populations growing at steady-state in a confined, unmixed region: (a) Random motility may lead to decreased population density; (b) chemotaxis can allow increased population density if the chemotactic response is large enough; (c) a species with superior motility properties can outgrow a species with superior growth kinetic properties; (d) motility effects become greater as the size of the confined growth region increases; and (e) motility effects are diminished by significant mass-transfer limitation of the nutrient from the adjacent source phase. The relationships of these results for populations to previous conclusions for individual cells is discussed, and implications for microbial competition are suggested.
建立了一个数学模型，以阐明生物物理传输过程（营养物质扩散、细胞运动性和趋化性）以及生化反应过程（细胞生长和死亡、营养物质摄取）对有限一维区域内稳态细菌种群生长的影响。所考虑的特定情况是，营养物质从细菌无法进入的相邻相扩散，从而限制生长。结果表明，细胞运动性和趋化性特性对稳态种群大小有很大影响。事实上，运动性效应可能与生长动力学效应一样显著，其方式类似于化学反应系统中的扩散和反应受限情况。具体而言，从我们对在有限、未混合区域内稳态生长的细菌种群的分析中可以得出以下结论：（a）随机运动性可能导致种群密度降低；（b）如果趋化反应足够大，趋化性可使种群密度增加；（c）具有优越运动性特性的物种可能会超过具有优越生长动力学特性的物种；（d）随着受限生长区域尺寸的增加，运动性效应变得更大；（e）来自相邻源相的营养物质的显著传质限制会削弱运动性效应。讨论了这些种群结果与先前关于单个细胞结论的关系，并提出了对微生物竞争的影响。
